The R Project SVN R

      double precision function dcabs1(z)
      double complex z,zz
      double precision t(2)
      equivalence (zz,t(1))
      zz = z
      dcabs1 = dabs(t(1)) + dabs(t(2))
      return
      end
      double precision function dzasum(n,zx,incx)
c
c     takes the sum of the absolute values.
c     jack dongarra, 3/11/78.
c     modified 3/93 to return if incx .le. 0.
c     modified 12/3/93, array(1) declarations changed to array(*)
c
      double complex zx(*)
      double precision stemp,dcabs1
      integer i,incx,ix,n
c
      dzasum = 0.0d0
      stemp = 0.0d0
      if( n.le.0 .or. incx.le.0 )return
      if(incx.eq.1)go to 20
c
c        code for increment not equal to 1
c
      ix = 1
      do 10 i = 1,n
        stemp = stemp + dcabs1(zx(ix))
        ix = ix + incx
   10 continue
      dzasum = stemp
      return
c
c        code for increment equal to 1
c
   20 do 30 i = 1,n
        stemp = stemp + dcabs1(zx(i))
   30 continue
      dzasum = stemp
      return
      end
      DOUBLE PRECISION FUNCTION DZNRM2( N, X, INCX )
*     .. Scalar Arguments ..
      INTEGER                           INCX, N
*     .. Array Arguments ..
      COMPLEX*16                        X( * )
*     ..
*
*  DZNRM2 returns the euclidean norm of a vector via the function
*  name, so that
*
*     DZNRM2 := sqrt( conjg( x' )*x )
*
*
*
*  -- This version written on 25-October-1982.
*     Modified on 14-October-1993 to inline the call to ZLASSQ.
*     Sven Hammarling, Nag Ltd.
*
*
*     .. Parameters ..
      DOUBLE PRECISION      ONE         , ZERO
      PARAMETER           ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     .. Local Scalars ..
      INTEGER               IX
      DOUBLE PRECISION      NORM, SCALE, SSQ, TEMP
*     .. Intrinsic Functions ..
      INTRINSIC             ABS, DIMAG, DBLE, SQRT
*     ..
*     .. Executable Statements ..
      IF( N.LT.1 .OR. INCX.LT.1 )THEN
         NORM  = ZERO
      ELSE
         SCALE = ZERO
         SSQ   = ONE
*        The following loop is equivalent to this call to the LAPACK
*        auxiliary routine:
*        CALL ZLASSQ( N, X, INCX, SCALE, SSQ )
*
         DO 10, IX = 1, 1 + ( N - 1 )*INCX, INCX
            IF( DBLE( X( IX ) ).NE.ZERO )THEN
               TEMP = ABS( DBLE( X( IX ) ) )
               IF( SCALE.LT.TEMP )THEN
                  SSQ   = ONE   + SSQ*( SCALE/TEMP )**2
                  SCALE = TEMP
               ELSE
                  SSQ   = SSQ   +     ( TEMP/SCALE )**2
               END IF
            END IF
            IF( DIMAG( X( IX ) ).NE.ZERO )THEN
               TEMP = ABS( DIMAG( X( IX ) ) )
               IF( SCALE.LT.TEMP )THEN
                  SSQ   = ONE   + SSQ*( SCALE/TEMP )**2
                  SCALE = TEMP
               ELSE
                  SSQ   = SSQ   +     ( TEMP/SCALE )**2
               END IF
            END IF
   10    CONTINUE
         NORM  = SCALE * SQRT( SSQ )
      END IF
*
      DZNRM2 = NORM
      RETURN
*
*     End of DZNRM2.
*
      END
      integer function izamax(n,zx,incx)
c
c     finds the index of element having max. absolute value.
c     jack dongarra, 1/15/85.
c     modified 3/93 to return if incx .le. 0.
c     modified 12/3/93, array(1) declarations changed to array(*)
c
      double complex zx(*)
      double precision smax
      integer i,incx,ix,n
      double precision dcabs1
c
      izamax = 0
      if( n.lt.1 .or. incx.le.0 )return
      izamax = 1
      if(n.eq.1)return
      if(incx.eq.1)go to 20
c
c        code for increment not equal to 1
c
      ix = 1
      smax = dcabs1(zx(1))
      ix = ix + incx
      do 10 i = 2,n
         if(dcabs1(zx(ix)).le.smax) go to 5
         izamax = i
         smax = dcabs1(zx(ix))
    5    ix = ix + incx
   10 continue
      return
c
c        code for increment equal to 1
c
   20 smax = dcabs1(zx(1))
      do 30 i = 2,n
         if(dcabs1(zx(i)).le.smax) go to 30
         izamax = i
         smax = dcabs1(zx(i))
   30 continue
      return
      end
      subroutine zaxpy(n,za,zx,incx,zy,incy)
c
c     constant times a vector plus a vector.
c     jack dongarra, 3/11/78.
c     modified 12/3/93, array(1) declarations changed to array(*)
c
      double complex zx(*),zy(*),za
      integer i,incx,incy,ix,iy,n
      double precision dcabs1
      if(n.le.0)return
      if (dcabs1(za) .eq. 0.0d0) return
      if (incx.eq.1.and.incy.eq.1)go to 20
c
c        code for unequal increments or equal increments
c          not equal to 1
c
      ix = 1
      iy = 1
      if(incx.lt.0)ix = (-n+1)*incx + 1
      if(incy.lt.0)iy = (-n+1)*incy + 1
      do 10 i = 1,n
        zy(iy) = zy(iy) + za*zx(ix)
        ix = ix + incx
        iy = iy + incy
   10 continue
      return
c
c        code for both increments equal to 1
c
   20 do 30 i = 1,n
        zy(i) = zy(i) + za*zx(i)
   30 continue
      return
      end
      subroutine  zcopy(n,zx,incx,zy,incy)
c
c     copies a vector, x, to a vector, y.
c     jack dongarra, linpack, 4/11/78.
c     modified 12/3/93, array(1) declarations changed to array(*)
c
      double complex zx(*),zy(*)
      integer i,incx,incy,ix,iy,n
c
      if(n.le.0)return
      if(incx.eq.1.and.incy.eq.1)go to 20
c
c        code for unequal increments or equal increments
c          not equal to 1
c
      ix = 1
      iy = 1
      if(incx.lt.0)ix = (-n+1)*incx + 1
      if(incy.lt.0)iy = (-n+1)*incy + 1
      do 10 i = 1,n
        zy(iy) = zx(ix)
        ix = ix + incx
        iy = iy + incy
   10 continue
      return
c
c        code for both increments equal to 1
c
   20 do 30 i = 1,n
        zy(i) = zx(i)
   30 continue
      return
      end
      double complex function zdotc(n,zx,incx,zy,incy)
c
c     forms the dot product of a vector.
c     jack dongarra, 3/11/78.
c     modified 12/3/93, array(1) declarations changed to array(*)
c
      double complex zx(*),zy(*),ztemp
      integer i,incx,incy,ix,iy,n
      intrinsic          dconjg
      ztemp = (0.0d0,0.0d0)
      zdotc = (0.0d0,0.0d0)
      if(n.le.0)return
      if(incx.eq.1.and.incy.eq.1)go to 20
c
c        code for unequal increments or equal increments
c          not equal to 1
c
      ix = 1
      iy = 1
      if(incx.lt.0)ix = (-n+1)*incx + 1
      if(incy.lt.0)iy = (-n+1)*incy + 1
      do 10 i = 1,n
        ztemp = ztemp + dconjg(zx(ix))*zy(iy)
        ix = ix + incx
        iy = iy + incy
   10 continue
      zdotc = ztemp
      return
c
c        code for both increments equal to 1
c
   20 do 30 i = 1,n
        ztemp = ztemp + dconjg(zx(i))*zy(i)
   30 continue
      zdotc = ztemp
      return
      end
      double complex function zdotu(n,zx,incx,zy,incy)
c
c     forms the dot product of two vectors.
c     jack dongarra, 3/11/78.
c     modified 12/3/93, array(1) declarations changed to array(*)
c
      double complex zx(*),zy(*),ztemp
      integer i,incx,incy,ix,iy,n
      ztemp = (0.0d0,0.0d0)
      zdotu = (0.0d0,0.0d0)
      if(n.le.0)return
      if(incx.eq.1.and.incy.eq.1)go to 20
c
c        code for unequal increments or equal increments
c          not equal to 1
c
      ix = 1
      iy = 1
      if(incx.lt.0)ix = (-n+1)*incx + 1
      if(incy.lt.0)iy = (-n+1)*incy + 1
      do 10 i = 1,n
        ztemp = ztemp + zx(ix)*zy(iy)
        ix = ix + incx
        iy = iy + incy
   10 continue
      zdotu = ztemp
      return
c
c        code for both increments equal to 1
c
   20 do 30 i = 1,n
        ztemp = ztemp + zx(i)*zy(i)
   30 continue
      zdotu = ztemp
      return
      end
      subroutine  zdscal(n,da,zx,incx)
c
c     scales a vector by a constant.
c     jack dongarra, 3/11/78.
c     modified 3/93 to return if incx .le. 0.
c     modified 12/3/93, array(1) declarations changed to array(*)
c
      intrinsic dcmplx
      double complex zx(*)
      double precision da
      integer i,incx,ix,n
c
      if( n.le.0 .or. incx.le.0 )return
      if(incx.eq.1)go to 20
c
c        code for increment not equal to 1
c
      ix = 1
      do 10 i = 1,n
        zx(ix) = dcmplx(da,0.0d0)*zx(ix)
        ix = ix + incx
   10 continue
      return
c
c        code for increment equal to 1
c
   20 do 30 i = 1,n
        zx(i) = dcmplx(da,0.0d0)*zx(i)
   30 continue
      return
      end
      SUBROUTINE ZGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX,
     $                   BETA, Y, INCY )
*     .. Scalar Arguments ..
      COMPLEX*16         ALPHA, BETA
      INTEGER            INCX, INCY, LDA, M, N
      CHARACTER*1        TRANS
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  ZGEMV  performs one of the matrix-vector operations
*
*     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,   or
*
*     y := alpha*conjg( A' )*x + beta*y,
*
*  where alpha and beta are scalars, x and y are vectors and A is an
*  m by n matrix.
*
*  Parameters
*  ==========
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
*
*              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.
*
*              TRANS = 'C' or 'c'   y := alpha*conjg( A' )*x + beta*y.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of the matrix A.
*           M must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry, the leading m by n part of the array A must
*           contain the matrix of coefficients.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, m ).
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of DIMENSION at least
*           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
*           Before entry, the incremented array X must contain the
*           vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  BETA   - COMPLEX*16      .
*           On entry, BETA specifies the scalar beta. When BETA is
*           supplied as zero then Y need not be set on input.
*           Unchanged on exit.
*
*  Y      - COMPLEX*16       array of DIMENSION at least
*           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
*           Before entry with BETA non-zero, the incremented array Y
*           must contain the vector y. On exit, Y is overwritten by the
*           updated vector y.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY
      LOGICAL            NOCONJ
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( TRANS, 'N' ).AND.
     $         .NOT.LSAME( TRANS, 'T' ).AND.
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
         INFO = 1
      ELSE IF( M.LT.0 )THEN
         INFO = 2
      ELSE IF( N.LT.0 )THEN
         INFO = 3
      ELSE IF( LDA.LT.MAX( 1, M ) )THEN
         INFO = 6
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 8
      ELSE IF( INCY.EQ.0 )THEN
         INFO = 11
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZGEMV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
     $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
      NOCONJ = LSAME( TRANS, 'T' )
*
*     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
*     up the start points in  X  and  Y.
*
      IF( LSAME( TRANS, 'N' ) )THEN
         LENX = N
         LENY = M
      ELSE
         LENX = M
         LENY = N
      END IF
      IF( INCX.GT.0 )THEN
         KX = 1
      ELSE
         KX = 1 - ( LENX - 1 )*INCX
      END IF
      IF( INCY.GT.0 )THEN
         KY = 1
      ELSE
         KY = 1 - ( LENY - 1 )*INCY
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
*     First form  y := beta*y.
*
      IF( BETA.NE.ONE )THEN
         IF( INCY.EQ.1 )THEN
            IF( BETA.EQ.ZERO )THEN
               DO 10, I = 1, LENY
                  Y( I ) = ZERO
   10          CONTINUE
            ELSE
               DO 20, I = 1, LENY
                  Y( I ) = BETA*Y( I )
   20          CONTINUE
            END IF
         ELSE
            IY = KY
            IF( BETA.EQ.ZERO )THEN
               DO 30, I = 1, LENY
                  Y( IY ) = ZERO
                  IY      = IY   + INCY
   30          CONTINUE
            ELSE
               DO 40, I = 1, LENY
                  Y( IY ) = BETA*Y( IY )
                  IY      = IY           + INCY
   40          CONTINUE
            END IF
         END IF
      END IF
      IF( ALPHA.EQ.ZERO )
     $   RETURN
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  y := alpha*A*x + y.
*
         JX = KX
         IF( INCY.EQ.1 )THEN
            DO 60, J = 1, N
c               IF( X( JX ).NE.ZERO )THEN
                  TEMP = ALPHA*X( JX )
                  DO 50, I = 1, M
                     Y( I ) = Y( I ) + TEMP*A( I, J )
   50             CONTINUE
c               END IF
               JX = JX + INCX
   60       CONTINUE
         ELSE
            DO 80, J = 1, N
c               IF( X( JX ).NE.ZERO )THEN
                  TEMP = ALPHA*X( JX )
                  IY   = KY
                  DO 70, I = 1, M
                     Y( IY ) = Y( IY ) + TEMP*A( I, J )
                     IY      = IY      + INCY
   70             CONTINUE
c               END IF
               JX = JX + INCX
   80       CONTINUE
         END IF
      ELSE
*
*        Form  y := alpha*A'*x + y  or  y := alpha*conjg( A' )*x + y.
*
         JY = KY
         IF( INCX.EQ.1 )THEN
            DO 110, J = 1, N
               TEMP = ZERO
               IF( NOCONJ )THEN
                  DO 90, I = 1, M
                     TEMP = TEMP + A( I, J )*X( I )
   90             CONTINUE
               ELSE
                  DO 100, I = 1, M
                     TEMP = TEMP + DCONJG( A( I, J ) )*X( I )
  100             CONTINUE
               END IF
               Y( JY ) = Y( JY ) + ALPHA*TEMP
               JY      = JY      + INCY
  110       CONTINUE
         ELSE
            DO 140, J = 1, N
               TEMP = ZERO
               IX   = KX
               IF( NOCONJ )THEN
                  DO 120, I = 1, M
                     TEMP = TEMP + A( I, J )*X( IX )
                     IX   = IX   + INCX
  120             CONTINUE
               ELSE
                  DO 130, I = 1, M
                     TEMP = TEMP + DCONJG( A( I, J ) )*X( IX )
                     IX   = IX   + INCX
  130             CONTINUE
               END IF
               Y( JY ) = Y( JY ) + ALPHA*TEMP
               JY      = JY      + INCY
  140       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZGEMV .
*
      END
      SUBROUTINE ZGERC ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA )
*     .. Scalar Arguments ..
      COMPLEX*16         ALPHA
      INTEGER            INCX, INCY, LDA, M, N
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  ZGERC  performs the rank 1 operation
*
*     A := alpha*x*conjg( y' ) + A,
*
*  where alpha is a scalar, x is an m element vector, y is an n element
*  vector and A is an m by n matrix.
*
*  Parameters
*  ==========
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of the matrix A.
*           M must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( m - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the m
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  Y      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCY ) ).
*           Before entry, the incremented array Y must contain the n
*           element vector y.
*           Unchanged on exit.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry, the leading m by n part of the array A must
*           contain the matrix of coefficients. On exit, A is
*           overwritten by the updated matrix.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, m ).
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, J, JY, KX
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( M.LT.0 )THEN
         INFO = 1
      ELSE IF( N.LT.0 )THEN
         INFO = 2
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 5
      ELSE IF( INCY.EQ.0 )THEN
         INFO = 7
      ELSE IF( LDA.LT.MAX( 1, M ) )THEN
         INFO = 9
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZGERC ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
     $   RETURN
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
      IF( INCY.GT.0 )THEN
         JY = 1
      ELSE
         JY = 1 - ( N - 1 )*INCY
      END IF
      IF( INCX.EQ.1 )THEN
         DO 20, J = 1, N
c            IF( Y( JY ).NE.ZERO )THEN
               TEMP = ALPHA*DCONJG( Y( JY ) )
               DO 10, I = 1, M
                  A( I, J ) = A( I, J ) + X( I )*TEMP
   10          CONTINUE
c            END IF
            JY = JY + INCY
   20    CONTINUE
      ELSE
         IF( INCX.GT.0 )THEN
            KX = 1
         ELSE
            KX = 1 - ( M - 1 )*INCX
         END IF
         DO 40, J = 1, N
c            IF( Y( JY ).NE.ZERO )THEN
               TEMP = ALPHA*DCONJG( Y( JY ) )
               IX   = KX
               DO 30, I = 1, M
                  A( I, J ) = A( I, J ) + X( IX )*TEMP
                  IX        = IX        + INCX
   30          CONTINUE
c            END IF
            JY = JY + INCY
   40    CONTINUE
      END IF
*
      RETURN
*
*     End of ZGERC .
*
      END
      SUBROUTINE ZHEMV ( UPLO, N, ALPHA, A, LDA, X, INCX,
     $                   BETA, Y, INCY )
*     .. Scalar Arguments ..
      COMPLEX*16         ALPHA, BETA
      INTEGER            INCX, INCY, LDA, N
      CHARACTER*1        UPLO
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  ZHEMV  performs the matrix-vector  operation
*
*     y := alpha*A*x + beta*y,
*
*  where alpha and beta are scalars, x and y are n element vectors and
*  A is an n by n hermitian matrix.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the upper or lower
*           triangular part of the array A is to be referenced as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the upper triangular part of A
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the lower triangular part of A
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry with  UPLO = 'U' or 'u', the leading n by n
*           upper triangular part of the array A must contain the upper
*           triangular part of the hermitian matrix and the strictly
*           lower triangular part of A is not referenced.
*           Before entry with UPLO = 'L' or 'l', the leading n by n
*           lower triangular part of the array A must contain the lower
*           triangular part of the hermitian matrix and the strictly
*           upper triangular part of A is not referenced.
*           Note that the imaginary parts of the diagonal elements need
*           not be set and are assumed to be zero.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, n ).
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  BETA   - COMPLEX*16      .
*           On entry, BETA specifies the scalar beta. When BETA is
*           supplied as zero then Y need not be set on input.
*           Unchanged on exit.
*
*  Y      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCY ) ).
*           Before entry, the incremented array Y must contain the n
*           element vector y. On exit, Y is overwritten by the updated
*           vector y.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP1, TEMP2
      INTEGER            I, INFO, IX, IY, J, JX, JY, KX, KY
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX, DBLE
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
     $         .NOT.LSAME( UPLO, 'L' )      )THEN
         INFO = 1
      ELSE IF( N.LT.0 )THEN
         INFO = 2
      ELSE IF( LDA.LT.MAX( 1, N ) )THEN
         INFO = 5
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 7
      ELSE IF( INCY.EQ.0 )THEN
         INFO = 10
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZHEMV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     Set up the start points in  X  and  Y.
*
      IF( INCX.GT.0 )THEN
         KX = 1
      ELSE
         KX = 1 - ( N - 1 )*INCX
      END IF
      IF( INCY.GT.0 )THEN
         KY = 1
      ELSE
         KY = 1 - ( N - 1 )*INCY
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through the triangular part
*     of A.
*
*     First form  y := beta*y.
*
      IF( BETA.NE.ONE )THEN
         IF( INCY.EQ.1 )THEN
            IF( BETA.EQ.ZERO )THEN
               DO 10, I = 1, N
                  Y( I ) = ZERO
   10          CONTINUE
            ELSE
               DO 20, I = 1, N
                  Y( I ) = BETA*Y( I )
   20          CONTINUE
            END IF
         ELSE
            IY = KY
            IF( BETA.EQ.ZERO )THEN
               DO 30, I = 1, N
                  Y( IY ) = ZERO
                  IY      = IY   + INCY
   30          CONTINUE
            ELSE
               DO 40, I = 1, N
                  Y( IY ) = BETA*Y( IY )
                  IY      = IY           + INCY
   40          CONTINUE
            END IF
         END IF
      END IF
      IF( ALPHA.EQ.ZERO )
     $   RETURN
      IF( LSAME( UPLO, 'U' ) )THEN
*
*        Form  y  when A is stored in upper triangle.
*
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 60, J = 1, N
               TEMP1 = ALPHA*X( J )
               TEMP2 = ZERO
               DO 50, I = 1, J - 1
                  Y( I ) = Y( I ) + TEMP1*A( I, J )
                  TEMP2  = TEMP2  + DCONJG( A( I, J ) )*X( I )
   50          CONTINUE
               Y( J ) = Y( J ) + TEMP1*DBLE( A( J, J ) ) + ALPHA*TEMP2
   60       CONTINUE
         ELSE
            JX = KX
            JY = KY
            DO 80, J = 1, N
               TEMP1 = ALPHA*X( JX )
               TEMP2 = ZERO
               IX    = KX
               IY    = KY
               DO 70, I = 1, J - 1
                  Y( IY ) = Y( IY ) + TEMP1*A( I, J )
                  TEMP2   = TEMP2   + DCONJG( A( I, J ) )*X( IX )
                  IX      = IX      + INCX
                  IY      = IY      + INCY
   70          CONTINUE
               Y( JY ) = Y( JY ) + TEMP1*DBLE( A( J, J ) ) + ALPHA*TEMP2
               JX      = JX      + INCX
               JY      = JY      + INCY
   80       CONTINUE
         END IF
      ELSE
*
*        Form  y  when A is stored in lower triangle.
*
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 100, J = 1, N
               TEMP1  = ALPHA*X( J )
               TEMP2  = ZERO
               Y( J ) = Y( J ) + TEMP1*DBLE( A( J, J ) )
               DO 90, I = J + 1, N
                  Y( I ) = Y( I ) + TEMP1*A( I, J )
                  TEMP2  = TEMP2  + DCONJG( A( I, J ) )*X( I )
   90          CONTINUE
               Y( J ) = Y( J ) + ALPHA*TEMP2
  100       CONTINUE
         ELSE
            JX = KX
            JY = KY
            DO 120, J = 1, N
               TEMP1   = ALPHA*X( JX )
               TEMP2   = ZERO
               Y( JY ) = Y( JY ) + TEMP1*DBLE( A( J, J ) )
               IX      = JX
               IY      = JY
               DO 110, I = J + 1, N
                  IX      = IX      + INCX
                  IY      = IY      + INCY
                  Y( IY ) = Y( IY ) + TEMP1*A( I, J )
                  TEMP2   = TEMP2   + DCONJG( A( I, J ) )*X( IX )
  110          CONTINUE
               Y( JY ) = Y( JY ) + ALPHA*TEMP2
               JX      = JX      + INCX
               JY      = JY      + INCY
  120       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZHEMV .
*
      END
      SUBROUTINE ZHER2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )
*     .. Scalar Arguments ..
      COMPLEX*16         ALPHA
      INTEGER            INCX, INCY, LDA, N
      CHARACTER*1        UPLO
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  ZHER2  performs the hermitian rank 2 operation
*
*     A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
*
*  where alpha is a scalar, x and y are n element vectors and A is an n
*  by n hermitian matrix.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the upper or lower
*           triangular part of the array A is to be referenced as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the upper triangular part of A
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the lower triangular part of A
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  Y      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCY ) ).
*           Before entry, the incremented array Y must contain the n
*           element vector y.
*           Unchanged on exit.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry with  UPLO = 'U' or 'u', the leading n by n
*           upper triangular part of the array A must contain the upper
*           triangular part of the hermitian matrix and the strictly
*           lower triangular part of A is not referenced. On exit, the
*           upper triangular part of the array A is overwritten by the
*           upper triangular part of the updated matrix.
*           Before entry with UPLO = 'L' or 'l', the leading n by n
*           lower triangular part of the array A must contain the lower
*           triangular part of the hermitian matrix and the strictly
*           upper triangular part of A is not referenced. On exit, the
*           lower triangular part of the array A is overwritten by the
*           lower triangular part of the updated matrix.
*           Note that the imaginary parts of the diagonal elements need
*           not be set, they are assumed to be zero, and on exit they
*           are set to zero.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, n ).
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP1, TEMP2
      INTEGER            I, INFO, IX, IY, J, JX, JY, KX, KY
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX, DBLE
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
     $         .NOT.LSAME( UPLO, 'L' )      )THEN
         INFO = 1
      ELSE IF( N.LT.0 )THEN
         INFO = 2
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 5
      ELSE IF( INCY.EQ.0 )THEN
         INFO = 7
      ELSE IF( LDA.LT.MAX( 1, N ) )THEN
         INFO = 9
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZHER2 ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
     $   RETURN
*
*     Set up the start points in X and Y if the increments are not both
*     unity.
*
      IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN
         IF( INCX.GT.0 )THEN
            KX = 1
         ELSE
            KX = 1 - ( N - 1 )*INCX
         END IF
         IF( INCY.GT.0 )THEN
            KY = 1
         ELSE
            KY = 1 - ( N - 1 )*INCY
         END IF
         JX = KX
         JY = KY
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through the triangular part
*     of A.
*
      IF( LSAME( UPLO, 'U' ) )THEN
*
*        Form  A  when A is stored in the upper triangle.
*
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 20, J = 1, N
c               IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN
                  TEMP1 = ALPHA*DCONJG( Y( J ) )
                  TEMP2 = DCONJG( ALPHA*X( J ) )
                  DO 10, I = 1, J - 1
                     A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2
   10             CONTINUE
                  A( J, J ) = DBLE( A( J, J ) ) +
     $                        DBLE( X( J )*TEMP1 + Y( J )*TEMP2 )
c               ELSE
c                  A( J, J ) = DBLE( A( J, J ) )
c               END IF
   20       CONTINUE
         ELSE
            DO 40, J = 1, N
c               IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN
                  TEMP1 = ALPHA*DCONJG( Y( JY ) )
                  TEMP2 = DCONJG( ALPHA*X( JX ) )
                  IX    = KX
                  IY    = KY
                  DO 30, I = 1, J - 1
                     A( I, J ) = A( I, J ) + X( IX )*TEMP1
     $                                     + Y( IY )*TEMP2
                     IX        = IX        + INCX
                     IY        = IY        + INCY
   30             CONTINUE
                  A( J, J ) = DBLE( A( J, J ) ) +
     $                        DBLE( X( JX )*TEMP1 + Y( JY )*TEMP2 )
c               ELSE
c                  A( J, J ) = DBLE( A( J, J ) )
c               END IF
               JX = JX + INCX
               JY = JY + INCY
   40       CONTINUE
         END IF
      ELSE
*
*        Form  A  when A is stored in the lower triangle.
*
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 60, J = 1, N
c               IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN
                  TEMP1     = ALPHA*DCONJG( Y( J ) )
                  TEMP2     = DCONJG( ALPHA*X( J ) )
                  A( J, J ) = DBLE( A( J, J ) ) +
     $                        DBLE( X( J )*TEMP1 + Y( J )*TEMP2 )
                  DO 50, I = J + 1, N
                     A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2
   50             CONTINUE
c               ELSE
c                  A( J, J ) = DBLE( A( J, J ) )
c               END IF
   60       CONTINUE
         ELSE
            DO 80, J = 1, N
c               IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN
                  TEMP1     = ALPHA*DCONJG( Y( JY ) )
                  TEMP2     = DCONJG( ALPHA*X( JX ) )
                  A( J, J ) = DBLE( A( J, J ) ) +
     $                        DBLE( X( JX )*TEMP1 + Y( JY )*TEMP2 )
                  IX        = JX
                  IY        = JY
                  DO 70, I = J + 1, N
                     IX        = IX        + INCX
                     IY        = IY        + INCY
                     A( I, J ) = A( I, J ) + X( IX )*TEMP1
     $                                     + Y( IY )*TEMP2
   70             CONTINUE
c               ELSE
c                  A( J, J ) = DBLE( A( J, J ) )
c               END IF
               JX = JX + INCX
               JY = JY + INCY
   80       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZHER2 .
*
      END
      SUBROUTINE ZHER2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA,
     $                   C, LDC )
*     .. Scalar Arguments ..
      CHARACTER          TRANS, UPLO
      INTEGER            K, LDA, LDB, LDC, N
      DOUBLE PRECISION   BETA
      COMPLEX*16         ALPHA
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), B( LDB, * ), C( LDC, * )
*     ..
*
*  Purpose
*  =======
*
*  ZHER2K  performs one of the hermitian rank 2k operations
*
*     C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,
*
*  or
*
*     C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C,
*
*  where  alpha and beta  are scalars with  beta  real,  C is an  n by n
*  hermitian matrix and  A and B  are  n by k matrices in the first case
*  and  k by n  matrices in the second case.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On  entry,   UPLO  specifies  whether  the  upper  or  lower
*           triangular  part  of the  array  C  is to be  referenced  as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry,  TRANS  specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'    C := alpha*A*conjg( B' )          +
*                                         conjg( alpha )*B*conjg( A' ) +
*                                         beta*C.
*
*              TRANS = 'C' or 'c'    C := alpha*conjg( A' )*B          +
*                                         conjg( alpha )*conjg( B' )*A +
*                                         beta*C.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry,  N specifies the order of the matrix C.  N must be
*           at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
*           of  columns  of the  matrices  A and B,  and on  entry  with
*           TRANS = 'C' or 'c',  K  specifies  the number of rows of the
*           matrices  A and B.  K must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16         .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is
*           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
*           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
*           part of the array  A  must contain the matrix  A,  otherwise
*           the leading  k by n  part of the array  A  must contain  the
*           matrix A.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
*           then  LDA must be at least  max( 1, n ), otherwise  LDA must
*           be at least  max( 1, k ).
*           Unchanged on exit.
*
*  B      - COMPLEX*16       array of DIMENSION ( LDB, kb ), where kb is
*           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
*           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
*           part of the array  B  must contain the matrix  B,  otherwise
*           the leading  k by n  part of the array  B  must contain  the
*           matrix B.
*           Unchanged on exit.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
*           then  LDB must be at least  max( 1, n ), otherwise  LDB must
*           be at least  max( 1, k ).
*           Unchanged on exit.
*
*  BETA   - DOUBLE PRECISION            .
*           On entry, BETA specifies the scalar beta.
*           Unchanged on exit.
*
*  C      - COMPLEX*16          array of DIMENSION ( LDC, n ).
*           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
*           upper triangular part of the array C must contain the upper
*           triangular part  of the  hermitian matrix  and the strictly
*           lower triangular part of C is not referenced.  On exit, the
*           upper triangular part of the array  C is overwritten by the
*           upper triangular part of the updated matrix.
*           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
*           lower triangular part of the array C must contain the lower
*           triangular part  of the  hermitian matrix  and the strictly
*           upper triangular part of C is not referenced.  On exit, the
*           lower triangular part of the array  C is overwritten by the
*           lower triangular part of the updated matrix.
*           Note that the imaginary parts of the diagonal elements need
*           not be set,  they are assumed to be zero,  and on exit they
*           are set to zero.
*
*  LDC    - INTEGER.
*           On entry, LDC specifies the first dimension of C as declared
*           in  the  calling  (sub)  program.   LDC  must  be  at  least
*           max( 1, n ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*  -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
*     Ed Anderson, Cray Research Inc.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          DBLE, DCONJG, MAX
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, INFO, J, L, NROWA
      COMPLEX*16         TEMP1, TEMP2
*     ..
*     .. Parameters ..
      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
      COMPLEX*16         ZERO
      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      IF( LSAME( TRANS, 'N' ) ) THEN
         NROWA = N
      ELSE
         NROWA = K
      END IF
      UPPER = LSAME( UPLO, 'U' )
*
      INFO = 0
      IF( ( .NOT.UPPER ) .AND. ( .NOT.LSAME( UPLO, 'L' ) ) ) THEN
         INFO = 1
      ELSE IF( ( .NOT.LSAME( TRANS, 'N' ) ) .AND.
     $         ( .NOT.LSAME( TRANS, 'C' ) ) ) THEN
         INFO = 2
      ELSE IF( N.LT.0 ) THEN
         INFO = 3
      ELSE IF( K.LT.0 ) THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, NROWA ) ) THEN
         INFO = 7
      ELSE IF( LDB.LT.MAX( 1, NROWA ) ) THEN
         INFO = 9
      ELSE IF( LDC.LT.MAX( 1, N ) ) THEN
         INFO = 12
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'ZHER2K', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ) .OR. ( ( ( ALPHA.EQ.ZERO ) .OR. ( K.EQ.0 ) ) .AND.
     $    ( BETA.EQ.ONE ) ) )RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO ) THEN
         IF( UPPER ) THEN
            IF( BETA.EQ.DBLE( ZERO ) ) THEN
               DO 20 J = 1, N
                  DO 10 I = 1, J
                     C( I, J ) = ZERO
   10             CONTINUE
   20          CONTINUE
            ELSE
               DO 40 J = 1, N
                  DO 30 I = 1, J - 1
                     C( I, J ) = BETA*C( I, J )
   30             CONTINUE
                  C( J, J ) = BETA*DBLE( C( J, J ) )
   40          CONTINUE
            END IF
         ELSE
            IF( BETA.EQ.DBLE( ZERO ) ) THEN
               DO 60 J = 1, N
                  DO 50 I = J, N
                     C( I, J ) = ZERO
   50             CONTINUE
   60          CONTINUE
            ELSE
               DO 80 J = 1, N
                  C( J, J ) = BETA*DBLE( C( J, J ) )
                  DO 70 I = J + 1, N
                     C( I, J ) = BETA*C( I, J )
   70             CONTINUE
   80          CONTINUE
            END IF
         END IF
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSAME( TRANS, 'N' ) ) THEN
*
*        Form  C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) +
*                   C.
*
         IF( UPPER ) THEN
            DO 130 J = 1, N
               IF( BETA.EQ.DBLE( ZERO ) ) THEN
                  DO 90 I = 1, J
                     C( I, J ) = ZERO
   90             CONTINUE
               ELSE IF( BETA.NE.ONE ) THEN
                  DO 100 I = 1, J - 1
                     C( I, J ) = BETA*C( I, J )
  100             CONTINUE
                  C( J, J ) = BETA*DBLE( C( J, J ) )
               ELSE
                  C( J, J ) = DBLE( C( J, J ) )
               END IF
               DO 120 L = 1, K
c                  IF( ( A( J, L ).NE.ZERO ) .OR. ( B( J, L ).NE.ZERO ) )
c     $                 THEN
                     TEMP1 = ALPHA*DCONJG( B( J, L ) )
                     TEMP2 = DCONJG( ALPHA*A( J, L ) )
                     DO 110 I = 1, J - 1
                        C( I, J ) = C( I, J ) + A( I, L )*TEMP1 +
     $                              B( I, L )*TEMP2
  110                CONTINUE
                     C( J, J ) = DBLE( C( J, J ) ) +
     $                           DBLE( A( J, L )*TEMP1+B( J, L )*TEMP2 )
c                  END IF
  120          CONTINUE
  130       CONTINUE
         ELSE
            DO 180 J = 1, N
               IF( BETA.EQ.DBLE( ZERO ) ) THEN
                  DO 140 I = J, N
                     C( I, J ) = ZERO
  140             CONTINUE
               ELSE IF( BETA.NE.ONE ) THEN
                  DO 150 I = J + 1, N
                     C( I, J ) = BETA*C( I, J )
  150             CONTINUE
                  C( J, J ) = BETA*DBLE( C( J, J ) )
               ELSE
                  C( J, J ) = DBLE( C( J, J ) )
               END IF
               DO 170 L = 1, K
c                  IF( ( A( J, L ).NE.ZERO ) .OR. ( B( J, L ).NE.ZERO ) )
c     $                 THEN
                     TEMP1 = ALPHA*DCONJG( B( J, L ) )
                     TEMP2 = DCONJG( ALPHA*A( J, L ) )
                     DO 160 I = J + 1, N
                        C( I, J ) = C( I, J ) + A( I, L )*TEMP1 +
     $                              B( I, L )*TEMP2
  160                CONTINUE
                     C( J, J ) = DBLE( C( J, J ) ) +
     $                           DBLE( A( J, L )*TEMP1+B( J, L )*TEMP2 )
c                  END IF
  170          CONTINUE
  180       CONTINUE
         END IF
      ELSE
*
*        Form  C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A +
*                   C.
*
         IF( UPPER ) THEN
            DO 210 J = 1, N
               DO 200 I = 1, J
                  TEMP1 = ZERO
                  TEMP2 = ZERO
                  DO 190 L = 1, K
                     TEMP1 = TEMP1 + DCONJG( A( L, I ) )*B( L, J )
                     TEMP2 = TEMP2 + DCONJG( B( L, I ) )*A( L, J )
  190             CONTINUE
                  IF( I.EQ.J ) THEN
                     IF( BETA.EQ.DBLE( ZERO ) ) THEN
                        C( J, J ) = DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*
     $                              TEMP2 )
                     ELSE
                        C( J, J ) = BETA*DBLE( C( J, J ) ) +
     $                              DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*
     $                              TEMP2 )
                     END IF
                  ELSE
                     IF( BETA.EQ.DBLE( ZERO ) ) THEN
                        C( I, J ) = ALPHA*TEMP1 + DCONJG( ALPHA )*TEMP2
                     ELSE
                        C( I, J ) = BETA*C( I, J ) + ALPHA*TEMP1 +
     $                              DCONJG( ALPHA )*TEMP2
                     END IF
                  END IF
  200          CONTINUE
  210       CONTINUE
         ELSE
            DO 240 J = 1, N
               DO 230 I = J, N
                  TEMP1 = ZERO
                  TEMP2 = ZERO
                  DO 220 L = 1, K
                     TEMP1 = TEMP1 + DCONJG( A( L, I ) )*B( L, J )
                     TEMP2 = TEMP2 + DCONJG( B( L, I ) )*A( L, J )
  220             CONTINUE
                  IF( I.EQ.J ) THEN
                     IF( BETA.EQ.DBLE( ZERO ) ) THEN
                        C( J, J ) = DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*
     $                              TEMP2 )
                     ELSE
                        C( J, J ) = BETA*DBLE( C( J, J ) ) +
     $                              DBLE( ALPHA*TEMP1+DCONJG( ALPHA )*
     $                              TEMP2 )
                     END IF
                  ELSE
                     IF( BETA.EQ.DBLE( ZERO ) ) THEN
                        C( I, J ) = ALPHA*TEMP1 + DCONJG( ALPHA )*TEMP2
                     ELSE
                        C( I, J ) = BETA*C( I, J ) + ALPHA*TEMP1 +
     $                              DCONJG( ALPHA )*TEMP2
                     END IF
                  END IF
  230          CONTINUE
  240       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZHER2K.
*
      END
      subroutine  zscal(n,za,zx,incx)
c
c     scales a vector by a constant.
c     jack dongarra, 3/11/78.
c     modified 3/93 to return if incx .le. 0.
c     modified 12/3/93, array(1) declarations changed to array(*)
c
      double complex za,zx(*)
      integer i,incx,ix,n
c
      if( n.le.0 .or. incx.le.0 )return
      if(incx.eq.1)go to 20
c
c        code for increment not equal to 1
c
      ix = 1
      do 10 i = 1,n
        zx(ix) = za*zx(ix)
        ix = ix + incx
   10 continue
      return
c
c        code for increment equal to 1
c
   20 do 30 i = 1,n
        zx(i) = za*zx(i)
   30 continue
      return
      end
      subroutine  zswap (n,zx,incx,zy,incy)
c
c     interchanges two vectors.
c     jack dongarra, 3/11/78.
c     modified 12/3/93, array(1) declarations changed to array(*)
c
      double complex zx(*),zy(*),ztemp
      integer i,incx,incy,ix,iy,n
c
      if(n.le.0)return
      if(incx.eq.1.and.incy.eq.1)go to 20
c
c       code for unequal increments or equal increments not equal
c         to 1
c
      ix = 1
      iy = 1
      if(incx.lt.0)ix = (-n+1)*incx + 1
      if(incy.lt.0)iy = (-n+1)*incy + 1
      do 10 i = 1,n
        ztemp = zx(ix)
        zx(ix) = zy(iy)
        zy(iy) = ztemp
        ix = ix + incx
        iy = iy + incy
   10 continue
      return
c
c       code for both increments equal to 1
   20 do 30 i = 1,n
        ztemp = zx(i)
        zx(i) = zy(i)
        zy(i) = ztemp
   30 continue
      return
      end
      SUBROUTINE ZTRMM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA,
     $                   B, LDB )
*     .. Scalar Arguments ..
      CHARACTER*1        SIDE, UPLO, TRANSA, DIAG
      INTEGER            M, N, LDA, LDB
      COMPLEX*16         ALPHA
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), B( LDB, * )
*     ..
*
*  Purpose
*  =======
*
*  ZTRMM  performs one of the matrix-matrix operations
*
*     B := alpha*op( A )*B,   or   B := alpha*B*op( A )
*
*  where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
*  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
*
*     op( A ) = A   or   op( A ) = A'   or   op( A ) = conjg( A' ).
*
*  Parameters
*  ==========
*
*  SIDE   - CHARACTER*1.
*           On entry,  SIDE specifies whether  op( A ) multiplies B from
*           the left or right as follows:
*
*              SIDE = 'L' or 'l'   B := alpha*op( A )*B.
*
*              SIDE = 'R' or 'r'   B := alpha*B*op( A ).
*
*           Unchanged on exit.
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix A is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANSA - CHARACTER*1.
*           On entry, TRANSA specifies the form of op( A ) to be used in
*           the matrix multiplication as follows:
*
*              TRANSA = 'N' or 'n'   op( A ) = A.
*
*              TRANSA = 'T' or 't'   op( A ) = A'.
*
*              TRANSA = 'C' or 'c'   op( A ) = conjg( A' ).
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit triangular
*           as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of B. M must be at
*           least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of B.  N must be
*           at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
*           zero then  A is not referenced and  B need not be set before
*           entry.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, k ), where k is m
*           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
*           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
*           upper triangular part of the array  A must contain the upper
*           triangular matrix  and the strictly lower triangular part of
*           A is not referenced.
*           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
*           lower triangular part of the array  A must contain the lower
*           triangular matrix  and the strictly upper triangular part of
*           A is not referenced.
*           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
*           A  are not referenced either,  but are assumed to be  unity.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
*           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
*           then LDA must be at least max( 1, n ).
*           Unchanged on exit.
*
*  B      - COMPLEX*16       array of DIMENSION ( LDB, n ).
*           Before entry,  the leading  m by n part of the array  B must
*           contain the matrix  B,  and  on exit  is overwritten  by the
*           transformed matrix.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in  the  calling  (sub)  program.   LDB  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX
*     .. Local Scalars ..
      LOGICAL            LSIDE, NOCONJ, NOUNIT, UPPER
      INTEGER            I, INFO, J, K, NROWA
      COMPLEX*16         TEMP
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      LSIDE  = LSAME( SIDE  , 'L' )
      IF( LSIDE )THEN
         NROWA = M
      ELSE
         NROWA = N
      END IF
      NOCONJ = LSAME( TRANSA, 'T' )
      NOUNIT = LSAME( DIAG  , 'N' )
      UPPER  = LSAME( UPLO  , 'U' )
*
      INFO   = 0
      IF(      ( .NOT.LSIDE                ).AND.
     $         ( .NOT.LSAME( SIDE  , 'R' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.UPPER                ).AND.
     $         ( .NOT.LSAME( UPLO  , 'L' ) )      )THEN
         INFO = 2
      ELSE IF( ( .NOT.LSAME( TRANSA, 'N' ) ).AND.
     $         ( .NOT.LSAME( TRANSA, 'T' ) ).AND.
     $         ( .NOT.LSAME( TRANSA, 'C' ) )      )THEN
         INFO = 3
      ELSE IF( ( .NOT.LSAME( DIAG  , 'U' ) ).AND.
     $         ( .NOT.LSAME( DIAG  , 'N' ) )      )THEN
         INFO = 4
      ELSE IF( M  .LT.0               )THEN
         INFO = 5
      ELSE IF( N  .LT.0               )THEN
         INFO = 6
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 9
      ELSE IF( LDB.LT.MAX( 1, M     ) )THEN
         INFO = 11
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZTRMM ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         DO 20, J = 1, N
            DO 10, I = 1, M
               B( I, J ) = ZERO
   10       CONTINUE
   20    CONTINUE
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSIDE )THEN
         IF( LSAME( TRANSA, 'N' ) )THEN
*
*           Form  B := alpha*A*B.
*
            IF( UPPER )THEN
               DO 50, J = 1, N
                  DO 40, K = 1, M
c                     IF( B( K, J ).NE.ZERO )THEN
                        TEMP = ALPHA*B( K, J )
                        DO 30, I = 1, K - 1
                           B( I, J ) = B( I, J ) + TEMP*A( I, K )
   30                   CONTINUE
                        IF( NOUNIT )
     $                     TEMP = TEMP*A( K, K )
                        B( K, J ) = TEMP
c                     END IF
   40             CONTINUE
   50          CONTINUE
            ELSE
               DO 80, J = 1, N
                  DO 70 K = M, 1, -1
c                     IF( B( K, J ).NE.ZERO )THEN
                        TEMP      = ALPHA*B( K, J )
                        B( K, J ) = TEMP
                        IF( NOUNIT )
     $                     B( K, J ) = B( K, J )*A( K, K )
                        DO 60, I = K + 1, M
                           B( I, J ) = B( I, J ) + TEMP*A( I, K )
   60                   CONTINUE
c                     END IF
   70             CONTINUE
   80          CONTINUE
            END IF
         ELSE
*
*           Form  B := alpha*A'*B   or   B := alpha*conjg( A' )*B.
*
            IF( UPPER )THEN
               DO 120, J = 1, N
                  DO 110, I = M, 1, -1
                     TEMP = B( I, J )
                     IF( NOCONJ )THEN
                        IF( NOUNIT )
     $                     TEMP = TEMP*A( I, I )
                        DO 90, K = 1, I - 1
                           TEMP = TEMP + A( K, I )*B( K, J )
   90                   CONTINUE
                     ELSE
                        IF( NOUNIT )
     $                     TEMP = TEMP*DCONJG( A( I, I ) )
                        DO 100, K = 1, I - 1
                           TEMP = TEMP + DCONJG( A( K, I ) )*B( K, J )
  100                   CONTINUE
                     END IF
                     B( I, J ) = ALPHA*TEMP
  110             CONTINUE
  120          CONTINUE
            ELSE
               DO 160, J = 1, N
                  DO 150, I = 1, M
                     TEMP = B( I, J )
                     IF( NOCONJ )THEN
                        IF( NOUNIT )
     $                     TEMP = TEMP*A( I, I )
                        DO 130, K = I + 1, M
                           TEMP = TEMP + A( K, I )*B( K, J )
  130                   CONTINUE
                     ELSE
                        IF( NOUNIT )
     $                     TEMP = TEMP*DCONJG( A( I, I ) )
                        DO 140, K = I + 1, M
                           TEMP = TEMP + DCONJG( A( K, I ) )*B( K, J )
  140                   CONTINUE
                     END IF
                     B( I, J ) = ALPHA*TEMP
  150             CONTINUE
  160          CONTINUE
            END IF
         END IF
      ELSE
         IF( LSAME( TRANSA, 'N' ) )THEN
*
*           Form  B := alpha*B*A.
*
            IF( UPPER )THEN
               DO 200, J = N, 1, -1
                  TEMP = ALPHA
                  IF( NOUNIT )
     $               TEMP = TEMP*A( J, J )
                  DO 170, I = 1, M
                     B( I, J ) = TEMP*B( I, J )
  170             CONTINUE
                  DO 190, K = 1, J - 1
c                     IF( A( K, J ).NE.ZERO )THEN
                        TEMP = ALPHA*A( K, J )
                        DO 180, I = 1, M
                           B( I, J ) = B( I, J ) + TEMP*B( I, K )
  180                   CONTINUE
c                     END IF
  190             CONTINUE
  200          CONTINUE
            ELSE
               DO 240, J = 1, N
                  TEMP = ALPHA
                  IF( NOUNIT )
     $               TEMP = TEMP*A( J, J )
                  DO 210, I = 1, M
                     B( I, J ) = TEMP*B( I, J )
  210             CONTINUE
                  DO 230, K = J + 1, N
c                     IF( A( K, J ).NE.ZERO )THEN
                        TEMP = ALPHA*A( K, J )
                        DO 220, I = 1, M
                           B( I, J ) = B( I, J ) + TEMP*B( I, K )
  220                   CONTINUE
c                     END IF
  230             CONTINUE
  240          CONTINUE
            END IF
         ELSE
*
*           Form  B := alpha*B*A'   or   B := alpha*B*conjg( A' ).
*
            IF( UPPER )THEN
               DO 280, K = 1, N
                  DO 260, J = 1, K - 1
                     IF( A( J, K ).NE.ZERO )THEN
                        IF( NOCONJ )THEN
                           TEMP = ALPHA*A( J, K )
                        ELSE
                           TEMP = ALPHA*DCONJG( A( J, K ) )
                        END IF
                        DO 250, I = 1, M
                           B( I, J ) = B( I, J ) + TEMP*B( I, K )
  250                   CONTINUE
                     END IF
  260             CONTINUE
                  TEMP = ALPHA
                  IF( NOUNIT )THEN
                     IF( NOCONJ )THEN
                        TEMP = TEMP*A( K, K )
                     ELSE
                        TEMP = TEMP*DCONJG( A( K, K ) )
                     END IF
                  END IF
                  IF( TEMP.NE.ONE )THEN
                     DO 270, I = 1, M
                        B( I, K ) = TEMP*B( I, K )
  270                CONTINUE
                  END IF
  280          CONTINUE
            ELSE
               DO 320, K = N, 1, -1
                  DO 300, J = K + 1, N
c                     IF( A( J, K ).NE.ZERO )THEN
                        IF( NOCONJ )THEN
                           TEMP = ALPHA*A( J, K )
                        ELSE
                           TEMP = ALPHA*DCONJG( A( J, K ) )
                        END IF
                        DO 290, I = 1, M
                           B( I, J ) = B( I, J ) + TEMP*B( I, K )
  290                   CONTINUE
c                     END IF
  300             CONTINUE
                  TEMP = ALPHA
                  IF( NOUNIT )THEN
                     IF( NOCONJ )THEN
                        TEMP = TEMP*A( K, K )
                     ELSE
                        TEMP = TEMP*DCONJG( A( K, K ) )
                     END IF
                  END IF
                  IF( TEMP.NE.ONE )THEN
                     DO 310, I = 1, M
                        B( I, K ) = TEMP*B( I, K )
  310                CONTINUE
                  END IF
  320          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of ZTRMM .
*
      END
      SUBROUTINE ZTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
*     .. Scalar Arguments ..
      INTEGER            INCX, LDA, N
      CHARACTER*1        DIAG, TRANS, UPLO
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZTRMV  performs one of the matrix-vector operations
*
*     x := A*x,   or   x := A'*x,   or   x := conjg( A' )*x,
*
*  where x is an n element vector and  A is an n by n unit, or non-unit,
*  upper or lower triangular matrix.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   x := A*x.
*
*              TRANS = 'T' or 't'   x := A'*x.
*
*              TRANS = 'C' or 'c'   x := conjg( A' )*x.
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit
*           triangular as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry with  UPLO = 'U' or 'u', the leading n by n
*           upper triangular part of the array A must contain the upper
*           triangular matrix and the strictly lower triangular part of
*           A is not referenced.
*           Before entry with UPLO = 'L' or 'l', the leading n by n
*           lower triangular part of the array A must contain the lower
*           triangular matrix and the strictly upper triangular part of
*           A is not referenced.
*           Note that when  DIAG = 'U' or 'u', the diagonal elements of
*           A are not referenced either, but are assumed to be unity.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, n ).
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x. On exit, X is overwritten with the
*           tranformed vector x.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, J, JX, KX
      LOGICAL            NOCONJ, NOUNIT
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO , 'U' ).AND.
     $         .NOT.LSAME( UPLO , 'L' )      )THEN
         INFO = 1
      ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
     $         .NOT.LSAME( TRANS, 'T' ).AND.
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
         INFO = 2
      ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
     $         .NOT.LSAME( DIAG , 'N' )      )THEN
         INFO = 3
      ELSE IF( N.LT.0 )THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, N ) )THEN
         INFO = 6
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 8
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZTRMV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
*
      NOCONJ = LSAME( TRANS, 'T' )
      NOUNIT = LSAME( DIAG , 'N' )
*
*     Set up the start point in X if the increment is not unity. This
*     will be  ( N - 1 )*INCX  too small for descending loops.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  x := A*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            IF( INCX.EQ.1 )THEN
               DO 20, J = 1, N
c                  IF( X( J ).NE.ZERO )THEN
                     TEMP = X( J )
                     DO 10, I = 1, J - 1
                        X( I ) = X( I ) + TEMP*A( I, J )
   10                CONTINUE
                     IF( NOUNIT )
     $                  X( J ) = X( J )*A( J, J )
c                  END IF
   20          CONTINUE
            ELSE
               JX = KX
               DO 40, J = 1, N
c                  IF( X( JX ).NE.ZERO )THEN
                     TEMP = X( JX )
                     IX   = KX
                     DO 30, I = 1, J - 1
                        X( IX ) = X( IX ) + TEMP*A( I, J )
                        IX      = IX      + INCX
   30                CONTINUE
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )*A( J, J )
c                  END IF
                  JX = JX + INCX
   40          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 60, J = N, 1, -1
c                  IF( X( J ).NE.ZERO )THEN
                     TEMP = X( J )
                     DO 50, I = N, J + 1, -1
                        X( I ) = X( I ) + TEMP*A( I, J )
   50                CONTINUE
                     IF( NOUNIT )
     $                  X( J ) = X( J )*A( J, J )
c                  END IF
   60          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 80, J = N, 1, -1
c                  IF( X( JX ).NE.ZERO )THEN
                     TEMP = X( JX )
                     IX   = KX
                     DO 70, I = N, J + 1, -1
                        X( IX ) = X( IX ) + TEMP*A( I, J )
                        IX      = IX      - INCX
   70                CONTINUE
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )*A( J, J )
c                  END IF
                  JX = JX - INCX
   80          CONTINUE
            END IF
         END IF
      ELSE
*
*        Form  x := A'*x  or  x := conjg( A' )*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            IF( INCX.EQ.1 )THEN
               DO 110, J = N, 1, -1
                  TEMP = X( J )
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( J, J )
                     DO 90, I = J - 1, 1, -1
                        TEMP = TEMP + A( I, J )*X( I )
   90                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( A( J, J ) )
                     DO 100, I = J - 1, 1, -1
                        TEMP = TEMP + DCONJG( A( I, J ) )*X( I )
  100                CONTINUE
                  END IF
                  X( J ) = TEMP
  110          CONTINUE
            ELSE
               JX = KX + ( N - 1 )*INCX
               DO 140, J = N, 1, -1
                  TEMP = X( JX )
                  IX   = JX
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( J, J )
                     DO 120, I = J - 1, 1, -1
                        IX   = IX   - INCX
                        TEMP = TEMP + A( I, J )*X( IX )
  120                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( A( J, J ) )
                     DO 130, I = J - 1, 1, -1
                        IX   = IX   - INCX
                        TEMP = TEMP + DCONJG( A( I, J ) )*X( IX )
  130                CONTINUE
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   - INCX
  140          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 170, J = 1, N
                  TEMP = X( J )
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( J, J )
                     DO 150, I = J + 1, N
                        TEMP = TEMP + A( I, J )*X( I )
  150                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( A( J, J ) )
                     DO 160, I = J + 1, N
                        TEMP = TEMP + DCONJG( A( I, J ) )*X( I )
  160                CONTINUE
                  END IF
                  X( J ) = TEMP
  170          CONTINUE
            ELSE
               JX = KX
               DO 200, J = 1, N
                  TEMP = X( JX )
                  IX   = JX
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( J, J )
                     DO 180, I = J + 1, N
                        IX   = IX   + INCX
                        TEMP = TEMP + A( I, J )*X( IX )
  180                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( A( J, J ) )
                     DO 190, I = J + 1, N
                        IX   = IX   + INCX
                        TEMP = TEMP + DCONJG( A( I, J ) )*X( IX )
  190                CONTINUE
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   + INCX
  200          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of ZTRMV .
*
      END
      SUBROUTINE ZTRSM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA,
     $                   B, LDB )
*     .. Scalar Arguments ..
      CHARACTER*1        SIDE, UPLO, TRANSA, DIAG
      INTEGER            M, N, LDA, LDB
      COMPLEX*16         ALPHA
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), B( LDB, * )
*     ..
*
*  Purpose
*  =======
*
*  ZTRSM  solves one of the matrix equations
*
*     op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,
*
*  where alpha is a scalar, X and B are m by n matrices, A is a unit, or
*  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
*
*     op( A ) = A   or   op( A ) = A'   or   op( A ) = conjg( A' ).
*
*  The matrix X is overwritten on B.
*
*  Parameters
*  ==========
*
*  SIDE   - CHARACTER*1.
*           On entry, SIDE specifies whether op( A ) appears on the left
*           or right of X as follows:
*
*              SIDE = 'L' or 'l'   op( A )*X = alpha*B.
*
*              SIDE = 'R' or 'r'   X*op( A ) = alpha*B.
*
*           Unchanged on exit.
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix A is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANSA - CHARACTER*1.
*           On entry, TRANSA specifies the form of op( A ) to be used in
*           the matrix multiplication as follows:
*
*              TRANSA = 'N' or 'n'   op( A ) = A.
*
*              TRANSA = 'T' or 't'   op( A ) = A'.
*
*              TRANSA = 'C' or 'c'   op( A ) = conjg( A' ).
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit triangular
*           as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of B. M must be at
*           least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of B.  N must be
*           at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
*           zero then  A is not referenced and  B need not be set before
*           entry.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, k ), where k is m
*           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
*           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
*           upper triangular part of the array  A must contain the upper
*           triangular matrix  and the strictly lower triangular part of
*           A is not referenced.
*           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
*           lower triangular part of the array  A must contain the lower
*           triangular matrix  and the strictly upper triangular part of
*           A is not referenced.
*           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
*           A  are not referenced either,  but are assumed to be  unity.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
*           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
*           then LDA must be at least max( 1, n ).
*           Unchanged on exit.
*
*  B      - COMPLEX*16       array of DIMENSION ( LDB, n ).
*           Before entry,  the leading  m by n part of the array  B must
*           contain  the  right-hand  side  matrix  B,  and  on exit  is
*           overwritten by the solution matrix  X.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in  the  calling  (sub)  program.   LDB  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX
*     .. Local Scalars ..
      LOGICAL            LSIDE, NOCONJ, NOUNIT, UPPER
      INTEGER            I, INFO, J, K, NROWA
      COMPLEX*16         TEMP
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      LSIDE  = LSAME( SIDE  , 'L' )
      IF( LSIDE )THEN
         NROWA = M
      ELSE
         NROWA = N
      END IF
      NOCONJ = LSAME( TRANSA, 'T' )
      NOUNIT = LSAME( DIAG  , 'N' )
      UPPER  = LSAME( UPLO  , 'U' )
*
      INFO   = 0
      IF(      ( .NOT.LSIDE                ).AND.
     $         ( .NOT.LSAME( SIDE  , 'R' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.UPPER                ).AND.
     $         ( .NOT.LSAME( UPLO  , 'L' ) )      )THEN
         INFO = 2
      ELSE IF( ( .NOT.LSAME( TRANSA, 'N' ) ).AND.
     $         ( .NOT.LSAME( TRANSA, 'T' ) ).AND.
     $         ( .NOT.LSAME( TRANSA, 'C' ) )      )THEN
         INFO = 3
      ELSE IF( ( .NOT.LSAME( DIAG  , 'U' ) ).AND.
     $         ( .NOT.LSAME( DIAG  , 'N' ) )      )THEN
         INFO = 4
      ELSE IF( M  .LT.0               )THEN
         INFO = 5
      ELSE IF( N  .LT.0               )THEN
         INFO = 6
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 9
      ELSE IF( LDB.LT.MAX( 1, M     ) )THEN
         INFO = 11
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZTRSM ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         DO 20, J = 1, N
            DO 10, I = 1, M
               B( I, J ) = ZERO
   10       CONTINUE
   20    CONTINUE
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSIDE )THEN
         IF( LSAME( TRANSA, 'N' ) )THEN
*
*           Form  B := alpha*inv( A )*B.
*
            IF( UPPER )THEN
               DO 60, J = 1, N
                  IF( ALPHA.NE.ONE )THEN
                     DO 30, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
   30                CONTINUE
                  END IF
                  DO 50, K = M, 1, -1
c                     IF( B( K, J ).NE.ZERO )THEN
                        IF( NOUNIT )
     $                     B( K, J ) = B( K, J )/A( K, K )
                        DO 40, I = 1, K - 1
                           B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
   40                   CONTINUE
c                     END IF
   50             CONTINUE
   60          CONTINUE
            ELSE
               DO 100, J = 1, N
                  IF( ALPHA.NE.ONE )THEN
                     DO 70, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
   70                CONTINUE
                  END IF
                  DO 90 K = 1, M
c                     IF( B( K, J ).NE.ZERO )THEN
                        IF( NOUNIT )
     $                     B( K, J ) = B( K, J )/A( K, K )
                        DO 80, I = K + 1, M
                           B( I, J ) = B( I, J ) - B( K, J )*A( I, K )
   80                   CONTINUE
c                     END IF
   90             CONTINUE
  100          CONTINUE
            END IF
         ELSE
*
*           Form  B := alpha*inv( A' )*B
*           or    B := alpha*inv( conjg( A' ) )*B.
*
            IF( UPPER )THEN
               DO 140, J = 1, N
                  DO 130, I = 1, M
                     TEMP = ALPHA*B( I, J )
                     IF( NOCONJ )THEN
                        DO 110, K = 1, I - 1
                           TEMP = TEMP - A( K, I )*B( K, J )
  110                   CONTINUE
                        IF( NOUNIT )
     $                     TEMP = TEMP/A( I, I )
                     ELSE
                        DO 120, K = 1, I - 1
                           TEMP = TEMP - DCONJG( A( K, I ) )*B( K, J )
  120                   CONTINUE
                        IF( NOUNIT )
     $                     TEMP = TEMP/DCONJG( A( I, I ) )
                     END IF
                     B( I, J ) = TEMP
  130             CONTINUE
  140          CONTINUE
            ELSE
               DO 180, J = 1, N
                  DO 170, I = M, 1, -1
                     TEMP = ALPHA*B( I, J )
                     IF( NOCONJ )THEN
                        DO 150, K = I + 1, M
                           TEMP = TEMP - A( K, I )*B( K, J )
  150                   CONTINUE
                        IF( NOUNIT )
     $                     TEMP = TEMP/A( I, I )
                     ELSE
                        DO 160, K = I + 1, M
                           TEMP = TEMP - DCONJG( A( K, I ) )*B( K, J )
  160                   CONTINUE
                        IF( NOUNIT )
     $                     TEMP = TEMP/DCONJG( A( I, I ) )
                     END IF
                     B( I, J ) = TEMP
  170             CONTINUE
  180          CONTINUE
            END IF
         END IF
      ELSE
         IF( LSAME( TRANSA, 'N' ) )THEN
*
*           Form  B := alpha*B*inv( A ).
*
            IF( UPPER )THEN
               DO 230, J = 1, N
                  IF( ALPHA.NE.ONE )THEN
                     DO 190, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
  190                CONTINUE
                  END IF
                  DO 210, K = 1, J - 1
c                     IF( A( K, J ).NE.ZERO )THEN
                        DO 200, I = 1, M
                           B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
  200                   CONTINUE
c                     END IF
  210             CONTINUE
                  IF( NOUNIT )THEN
                     TEMP = ONE/A( J, J )
                     DO 220, I = 1, M
                        B( I, J ) = TEMP*B( I, J )
  220                CONTINUE
                  END IF
  230          CONTINUE
            ELSE
               DO 280, J = N, 1, -1
                  IF( ALPHA.NE.ONE )THEN
                     DO 240, I = 1, M
                        B( I, J ) = ALPHA*B( I, J )
  240                CONTINUE
                  END IF
                  DO 260, K = J + 1, N
c                     IF( A( K, J ).NE.ZERO )THEN
                        DO 250, I = 1, M
                           B( I, J ) = B( I, J ) - A( K, J )*B( I, K )
  250                   CONTINUE
c                     END IF
  260             CONTINUE
                  IF( NOUNIT )THEN
                     TEMP = ONE/A( J, J )
                     DO 270, I = 1, M
                       B( I, J ) = TEMP*B( I, J )
  270                CONTINUE
                  END IF
  280          CONTINUE
            END IF
         ELSE
*
*           Form  B := alpha*B*inv( A' )
*           or    B := alpha*B*inv( conjg( A' ) ).
*
            IF( UPPER )THEN
               DO 330, K = N, 1, -1
                  IF( NOUNIT )THEN
                     IF( NOCONJ )THEN
                        TEMP = ONE/A( K, K )
                     ELSE
                        TEMP = ONE/DCONJG( A( K, K ) )
                     END IF
                     DO 290, I = 1, M
                        B( I, K ) = TEMP*B( I, K )
  290                CONTINUE
                  END IF
                  DO 310, J = 1, K - 1
c                     IF( A( J, K ).NE.ZERO )THEN
                        IF( NOCONJ )THEN
                           TEMP = A( J, K )
                        ELSE
                           TEMP = DCONJG( A( J, K ) )
c                        END IF
                        DO 300, I = 1, M
                           B( I, J ) = B( I, J ) - TEMP*B( I, K )
  300                   CONTINUE
                     END IF
  310             CONTINUE
                  IF( ALPHA.NE.ONE )THEN
                     DO 320, I = 1, M
                        B( I, K ) = ALPHA*B( I, K )
  320                CONTINUE
                  END IF
  330          CONTINUE
            ELSE
               DO 380, K = 1, N
                  IF( NOUNIT )THEN
                     IF( NOCONJ )THEN
                        TEMP = ONE/A( K, K )
                     ELSE
                        TEMP = ONE/DCONJG( A( K, K ) )
                     END IF
                     DO 340, I = 1, M
                        B( I, K ) = TEMP*B( I, K )
  340                CONTINUE
                  END IF
                  DO 360, J = K + 1, N
c                     IF( A( J, K ).NE.ZERO )THEN
                        IF( NOCONJ )THEN
                           TEMP = A( J, K )
                        ELSE
                           TEMP = DCONJG( A( J, K ) )
                        END IF
                        DO 350, I = 1, M
                           B( I, J ) = B( I, J ) - TEMP*B( I, K )
  350                   CONTINUE
c                     END IF
  360             CONTINUE
                  IF( ALPHA.NE.ONE )THEN
                     DO 370, I = 1, M
                        B( I, K ) = ALPHA*B( I, K )
  370                CONTINUE
                  END IF
  380          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of ZTRSM .
*
      END
      SUBROUTINE ZTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
*     .. Scalar Arguments ..
      INTEGER            INCX, LDA, N
      CHARACTER*1        DIAG, TRANS, UPLO
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZTRSV  solves one of the systems of equations
*
*     A*x = b,   or   A'*x = b,   or   conjg( A' )*x = b,
*
*  where b and x are n element vectors and A is an n by n unit, or
*  non-unit, upper or lower triangular matrix.
*
*  No test for singularity or near-singularity is included in this
*  routine. Such tests must be performed before calling this routine.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the equations to be solved as
*           follows:
*
*              TRANS = 'N' or 'n'   A*x = b.
*
*              TRANS = 'T' or 't'   A'*x = b.
*
*              TRANS = 'C' or 'c'   conjg( A' )*x = b.
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit
*           triangular as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry with  UPLO = 'U' or 'u', the leading n by n
*           upper triangular part of the array A must contain the upper
*           triangular matrix and the strictly lower triangular part of
*           A is not referenced.
*           Before entry with UPLO = 'L' or 'l', the leading n by n
*           lower triangular part of the array A must contain the lower
*           triangular matrix and the strictly upper triangular part of
*           A is not referenced.
*           Note that when  DIAG = 'U' or 'u', the diagonal elements of
*           A are not referenced either, but are assumed to be unity.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, n ).
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element right-hand side vector b. On exit, X is overwritten
*           with the solution vector x.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, J, JX, KX
      LOGICAL            NOCONJ, NOUNIT
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO , 'U' ).AND.
     $         .NOT.LSAME( UPLO , 'L' )      )THEN
         INFO = 1
      ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
     $         .NOT.LSAME( TRANS, 'T' ).AND.
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
         INFO = 2
      ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
     $         .NOT.LSAME( DIAG , 'N' )      )THEN
         INFO = 3
      ELSE IF( N.LT.0 )THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, N ) )THEN
         INFO = 6
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 8
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZTRSV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
*
      NOCONJ = LSAME( TRANS, 'T' )
      NOUNIT = LSAME( DIAG , 'N' )
*
*     Set up the start point in X if the increment is not unity. This
*     will be  ( N - 1 )*INCX  too small for descending loops.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  x := inv( A )*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            IF( INCX.EQ.1 )THEN
               DO 20, J = N, 1, -1
c                  IF( X( J ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( J ) = X( J )/A( J, J )
                     TEMP = X( J )
                     DO 10, I = J - 1, 1, -1
                        X( I ) = X( I ) - TEMP*A( I, J )
   10                CONTINUE
c                  END IF
   20          CONTINUE
            ELSE
               JX = KX + ( N - 1 )*INCX
               DO 40, J = N, 1, -1
c                  IF( X( JX ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )/A( J, J )
                     TEMP = X( JX )
                     IX   = JX
                     DO 30, I = J - 1, 1, -1
                        IX      = IX      - INCX
                        X( IX ) = X( IX ) - TEMP*A( I, J )
   30                CONTINUE
c                  END IF
                  JX = JX - INCX
   40          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 60, J = 1, N
c                  IF( X( J ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( J ) = X( J )/A( J, J )
                     TEMP = X( J )
                     DO 50, I = J + 1, N
                        X( I ) = X( I ) - TEMP*A( I, J )
   50                CONTINUE
c                  END IF
   60          CONTINUE
            ELSE
               JX = KX
               DO 80, J = 1, N
c                  IF( X( JX ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )/A( J, J )
                     TEMP = X( JX )
                     IX   = JX
                     DO 70, I = J + 1, N
                        IX      = IX      + INCX
                        X( IX ) = X( IX ) - TEMP*A( I, J )
   70                CONTINUE
c                  END IF
                  JX = JX + INCX
   80          CONTINUE
            END IF
         END IF
      ELSE
*
*        Form  x := inv( A' )*x  or  x := inv( conjg( A' ) )*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            IF( INCX.EQ.1 )THEN
               DO 110, J = 1, N
                  TEMP = X( J )
                  IF( NOCONJ )THEN
                     DO 90, I = 1, J - 1
                        TEMP = TEMP - A( I, J )*X( I )
   90                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/A( J, J )
                  ELSE
                     DO 100, I = 1, J - 1
                        TEMP = TEMP - DCONJG( A( I, J ) )*X( I )
  100                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( A( J, J ) )
                  END IF
                  X( J ) = TEMP
  110          CONTINUE
            ELSE
               JX = KX
               DO 140, J = 1, N
                  IX   = KX
                  TEMP = X( JX )
                  IF( NOCONJ )THEN
                     DO 120, I = 1, J - 1
                        TEMP = TEMP - A( I, J )*X( IX )
                        IX   = IX   + INCX
  120                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/A( J, J )
                  ELSE
                     DO 130, I = 1, J - 1
                        TEMP = TEMP - DCONJG( A( I, J ) )*X( IX )
                        IX   = IX   + INCX
  130                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( A( J, J ) )
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   + INCX
  140          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 170, J = N, 1, -1
                  TEMP = X( J )
                  IF( NOCONJ )THEN
                     DO 150, I = N, J + 1, -1
                        TEMP = TEMP - A( I, J )*X( I )
  150                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/A( J, J )
                  ELSE
                     DO 160, I = N, J + 1, -1
                        TEMP = TEMP - DCONJG( A( I, J ) )*X( I )
  160                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( A( J, J ) )
                  END IF
                  X( J ) = TEMP
  170          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 200, J = N, 1, -1
                  IX   = KX
                  TEMP = X( JX )
                  IF( NOCONJ )THEN
                     DO 180, I = N, J + 1, -1
                        TEMP = TEMP - A( I, J )*X( IX )
                        IX   = IX   - INCX
  180                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/A( J, J )
                  ELSE
                     DO 190, I = N, J + 1, -1
                        TEMP = TEMP - DCONJG( A( I, J ) )*X( IX )
                        IX   = IX   - INCX
  190                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( A( J, J ) )
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   - INCX
  200          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of ZTRSV .
*
      END
      subroutine  zdrot (n,zx,incx,zy,incy,c,s)
c
c     applies a plane rotation, where the cos and sin (c and s) are
c     double precision and the vectors zx and zy are double complex.
c     jack dongarra, linpack, 3/11/78.
c
      double complex zx(1),zy(1),ztemp
      double precision c,s
      integer i,incx,incy,ix,iy,n
c
      if(n.le.0)return
      if(incx.eq.1.and.incy.eq.1)go to 20
c
c       code for unequal increments or equal increments not equal
c         to 1
c
      ix = 1
      iy = 1
      if(incx.lt.0)ix = (-n+1)*incx + 1
      if(incy.lt.0)iy = (-n+1)*incy + 1
      do 10 i = 1,n
        ztemp = c*zx(ix) + s*zy(iy)
        zy(iy) = c*zy(iy) - s*zx(ix)
        zx(ix) = ztemp
        ix = ix + incx
        iy = iy + incy
   10 continue
      return
c
c       code for both increments equal to 1
c
   20 do 30 i = 1,n
        ztemp = c*zx(i) + s*zy(i)
        zy(i) = c*zy(i) - s*zx(i)
        zx(i) = ztemp
   30 continue
      return
      end
      SUBROUTINE ZGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX,
     $                   BETA, Y, INCY )
*     .. Scalar Arguments ..
      COMPLEX*16         ALPHA, BETA
      INTEGER            INCX, INCY, KL, KU, LDA, M, N
      CHARACTER*1        TRANS
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  ZGBMV  performs one of the matrix-vector operations
*
*     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,   or
*
*     y := alpha*conjg( A' )*x + beta*y,
*
*  where alpha and beta are scalars, x and y are vectors and A is an
*  m by n band matrix, with kl sub-diagonals and ku super-diagonals.
*
*  Parameters
*  ==========
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
*
*              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.
*
*              TRANS = 'C' or 'c'   y := alpha*conjg( A' )*x + beta*y.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of the matrix A.
*           M must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  KL     - INTEGER.
*           On entry, KL specifies the number of sub-diagonals of the
*           matrix A. KL must satisfy  0 .le. KL.
*           Unchanged on exit.
*
*  KU     - INTEGER.
*           On entry, KU specifies the number of super-diagonals of the
*           matrix A. KU must satisfy  0 .le. KU.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry, the leading ( kl + ku + 1 ) by n part of the
*           array A must contain the matrix of coefficients, supplied
*           column by column, with the leading diagonal of the matrix in
*           row ( ku + 1 ) of the array, the first super-diagonal
*           starting at position 2 in row ku, the first sub-diagonal
*           starting at position 1 in row ( ku + 2 ), and so on.
*           Elements in the array A that do not correspond to elements
*           in the band matrix (such as the top left ku by ku triangle)
*           are not referenced.
*           The following program segment will transfer a band matrix
*           from conventional full matrix storage to band storage:
*
*                 DO 20, J = 1, N
*                    K = KU + 1 - J
*                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
*                       A( K + I, J ) = matrix( I, J )
*              10    CONTINUE
*              20 CONTINUE
*
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           ( kl + ku + 1 ).
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of DIMENSION at least
*           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
*           Before entry, the incremented array X must contain the
*           vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  BETA   - COMPLEX*16      .
*           On entry, BETA specifies the scalar beta. When BETA is
*           supplied as zero then Y need not be set on input.
*           Unchanged on exit.
*
*  Y      - COMPLEX*16       array of DIMENSION at least
*           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
*           Before entry, the incremented array Y must contain the
*           vector y. On exit, Y is overwritten by the updated vector y.
*
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, IY, J, JX, JY, K, KUP1, KX, KY,
     $                   LENX, LENY
      LOGICAL            NOCONJ
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX, MIN
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( TRANS, 'N' ).AND.
     $         .NOT.LSAME( TRANS, 'T' ).AND.
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
         INFO = 1
      ELSE IF( M.LT.0 )THEN
         INFO = 2
      ELSE IF( N.LT.0 )THEN
         INFO = 3
      ELSE IF( KL.LT.0 )THEN
         INFO = 4
      ELSE IF( KU.LT.0 )THEN
         INFO = 5
      ELSE IF( LDA.LT.( KL + KU + 1 ) )THEN
         INFO = 8
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 10
      ELSE IF( INCY.EQ.0 )THEN
         INFO = 13
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZGBMV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
     $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
      NOCONJ = LSAME( TRANS, 'T' )
*
*     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
*     up the start points in  X  and  Y.
*
      IF( LSAME( TRANS, 'N' ) )THEN
         LENX = N
         LENY = M
      ELSE
         LENX = M
         LENY = N
      END IF
      IF( INCX.GT.0 )THEN
         KX = 1
      ELSE
         KX = 1 - ( LENX - 1 )*INCX
      END IF
      IF( INCY.GT.0 )THEN
         KY = 1
      ELSE
         KY = 1 - ( LENY - 1 )*INCY
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through the band part of A.
*
*     First form  y := beta*y.
*
      IF( BETA.NE.ONE )THEN
         IF( INCY.EQ.1 )THEN
            IF( BETA.EQ.ZERO )THEN
               DO 10, I = 1, LENY
                  Y( I ) = ZERO
   10          CONTINUE
            ELSE
               DO 20, I = 1, LENY
                  Y( I ) = BETA*Y( I )
   20          CONTINUE
            END IF
         ELSE
            IY = KY
            IF( BETA.EQ.ZERO )THEN
               DO 30, I = 1, LENY
                  Y( IY ) = ZERO
                  IY      = IY   + INCY
   30          CONTINUE
            ELSE
               DO 40, I = 1, LENY
                  Y( IY ) = BETA*Y( IY )
                  IY      = IY           + INCY
   40          CONTINUE
            END IF
         END IF
      END IF
      IF( ALPHA.EQ.ZERO )
     $   RETURN
      KUP1 = KU + 1
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  y := alpha*A*x + y.
*
         JX = KX
         IF( INCY.EQ.1 )THEN
            DO 60, J = 1, N
c               IF( X( JX ).NE.ZERO )THEN
                  TEMP = ALPHA*X( JX )
                  K    = KUP1 - J
                  DO 50, I = MAX( 1, J - KU ), MIN( M, J + KL )
                     Y( I ) = Y( I ) + TEMP*A( K + I, J )
   50             CONTINUE
c               END IF
               JX = JX + INCX
   60       CONTINUE
         ELSE
            DO 80, J = 1, N
c               IF( X( JX ).NE.ZERO )THEN
                  TEMP = ALPHA*X( JX )
                  IY   = KY
                  K    = KUP1 - J
                  DO 70, I = MAX( 1, J - KU ), MIN( M, J + KL )
                     Y( IY ) = Y( IY ) + TEMP*A( K + I, J )
                     IY      = IY      + INCY
   70             CONTINUE
c               END IF
               JX = JX + INCX
               IF( J.GT.KU )
     $            KY = KY + INCY
   80       CONTINUE
         END IF
      ELSE
*
*        Form  y := alpha*A'*x + y  or  y := alpha*conjg( A' )*x + y.
*
         JY = KY
         IF( INCX.EQ.1 )THEN
            DO 110, J = 1, N
               TEMP = ZERO
               K    = KUP1 - J
               IF( NOCONJ )THEN
                  DO 90, I = MAX( 1, J - KU ), MIN( M, J + KL )
                     TEMP = TEMP + A( K + I, J )*X( I )
   90             CONTINUE
               ELSE
                  DO 100, I = MAX( 1, J - KU ), MIN( M, J + KL )
                     TEMP = TEMP + DCONJG( A( K + I, J ) )*X( I )
  100             CONTINUE
               END IF
               Y( JY ) = Y( JY ) + ALPHA*TEMP
               JY      = JY      + INCY
  110       CONTINUE
         ELSE
            DO 140, J = 1, N
               TEMP = ZERO
               IX   = KX
               K    = KUP1 - J
               IF( NOCONJ )THEN
                  DO 120, I = MAX( 1, J - KU ), MIN( M, J + KL )
                     TEMP = TEMP + A( K + I, J )*X( IX )
                     IX   = IX   + INCX
  120             CONTINUE
               ELSE
                  DO 130, I = MAX( 1, J - KU ), MIN( M, J + KL )
                     TEMP = TEMP + DCONJG( A( K + I, J ) )*X( IX )
                     IX   = IX   + INCX
  130             CONTINUE
               END IF
               Y( JY ) = Y( JY ) + ALPHA*TEMP
               JY      = JY      + INCY
               IF( J.GT.KU )
     $            KX = KX + INCX
  140       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZGBMV .
*
      END
      SUBROUTINE ZGERU ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA )
*     .. Scalar Arguments ..
      COMPLEX*16         ALPHA
      INTEGER            INCX, INCY, LDA, M, N
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  ZGERU  performs the rank 1 operation
*
*     A := alpha*x*y' + A,
*
*  where alpha is a scalar, x is an m element vector, y is an n element
*  vector and A is an m by n matrix.
*
*  Parameters
*  ==========
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of the matrix A.
*           M must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( m - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the m
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  Y      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCY ) ).
*           Before entry, the incremented array Y must contain the n
*           element vector y.
*           Unchanged on exit.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry, the leading m by n part of the array A must
*           contain the matrix of coefficients. On exit, A is
*           overwritten by the updated matrix.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, m ).
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, J, JY, KX
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( M.LT.0 )THEN
         INFO = 1
      ELSE IF( N.LT.0 )THEN
         INFO = 2
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 5
      ELSE IF( INCY.EQ.0 )THEN
         INFO = 7
      ELSE IF( LDA.LT.MAX( 1, M ) )THEN
         INFO = 9
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZGERU ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
     $   RETURN
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
      IF( INCY.GT.0 )THEN
         JY = 1
      ELSE
         JY = 1 - ( N - 1 )*INCY
      END IF
      IF( INCX.EQ.1 )THEN
         DO 20, J = 1, N
c            IF( Y( JY ).NE.ZERO )THEN
               TEMP = ALPHA*Y( JY )
               DO 10, I = 1, M
                  A( I, J ) = A( I, J ) + X( I )*TEMP
   10          CONTINUE
c            END IF
            JY = JY + INCY
   20    CONTINUE
      ELSE
         IF( INCX.GT.0 )THEN
            KX = 1
         ELSE
            KX = 1 - ( M - 1 )*INCX
         END IF
         DO 40, J = 1, N
c            IF( Y( JY ).NE.ZERO )THEN
               TEMP = ALPHA*Y( JY )
               IX   = KX
               DO 30, I = 1, M
                  A( I, J ) = A( I, J ) + X( IX )*TEMP
                  IX        = IX        + INCX
   30          CONTINUE
c            END IF
            JY = JY + INCY
   40    CONTINUE
      END IF
*
      RETURN
*
*     End of ZGERU .
*
      END
      SUBROUTINE ZHBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX,
     $                   BETA, Y, INCY )
*     .. Scalar Arguments ..
      COMPLEX*16         ALPHA, BETA
      INTEGER            INCX, INCY, K, LDA, N
      CHARACTER*1        UPLO
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  ZHBMV  performs the matrix-vector  operation
*
*     y := alpha*A*x + beta*y,
*
*  where alpha and beta are scalars, x and y are n element vectors and
*  A is an n by n hermitian band matrix, with k super-diagonals.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the upper or lower
*           triangular part of the band matrix A is being supplied as
*           follows:
*
*              UPLO = 'U' or 'u'   The upper triangular part of A is
*                                  being supplied.
*
*              UPLO = 'L' or 'l'   The lower triangular part of A is
*                                  being supplied.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry, K specifies the number of super-diagonals of the
*           matrix A. K must satisfy  0 .le. K.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
*           by n part of the array A must contain the upper triangular
*           band part of the hermitian matrix, supplied column by
*           column, with the leading diagonal of the matrix in row
*           ( k + 1 ) of the array, the first super-diagonal starting at
*           position 2 in row k, and so on. The top left k by k triangle
*           of the array A is not referenced.
*           The following program segment will transfer the upper
*           triangular part of a hermitian band matrix from conventional
*           full matrix storage to band storage:
*
*                 DO 20, J = 1, N
*                    M = K + 1 - J
*                    DO 10, I = MAX( 1, J - K ), J
*                       A( M + I, J ) = matrix( I, J )
*              10    CONTINUE
*              20 CONTINUE
*
*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
*           by n part of the array A must contain the lower triangular
*           band part of the hermitian matrix, supplied column by
*           column, with the leading diagonal of the matrix in row 1 of
*           the array, the first sub-diagonal starting at position 1 in
*           row 2, and so on. The bottom right k by k triangle of the
*           array A is not referenced.
*           The following program segment will transfer the lower
*           triangular part of a hermitian band matrix from conventional
*           full matrix storage to band storage:
*
*                 DO 20, J = 1, N
*                    M = 1 - J
*                    DO 10, I = J, MIN( N, J + K )
*                       A( M + I, J ) = matrix( I, J )
*              10    CONTINUE
*              20 CONTINUE
*
*           Note that the imaginary parts of the diagonal elements need
*           not be set and are assumed to be zero.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           ( k + 1 ).
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of DIMENSION at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the
*           vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  BETA   - COMPLEX*16      .
*           On entry, BETA specifies the scalar beta.
*           Unchanged on exit.
*
*  Y      - COMPLEX*16       array of DIMENSION at least
*           ( 1 + ( n - 1 )*abs( INCY ) ).
*           Before entry, the incremented array Y must contain the
*           vector y. On exit, Y is overwritten by the updated vector y.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP1, TEMP2
      INTEGER            I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX, MIN, DBLE
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
     $         .NOT.LSAME( UPLO, 'L' )      )THEN
         INFO = 1
      ELSE IF( N.LT.0 )THEN
         INFO = 2
      ELSE IF( K.LT.0 )THEN
         INFO = 3
      ELSE IF( LDA.LT.( K + 1 ) )THEN
         INFO = 6
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 8
      ELSE IF( INCY.EQ.0 )THEN
         INFO = 11
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZHBMV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     Set up the start points in  X  and  Y.
*
      IF( INCX.GT.0 )THEN
         KX = 1
      ELSE
         KX = 1 - ( N - 1 )*INCX
      END IF
      IF( INCY.GT.0 )THEN
         KY = 1
      ELSE
         KY = 1 - ( N - 1 )*INCY
      END IF
*
*     Start the operations. In this version the elements of the array A
*     are accessed sequentially with one pass through A.
*
*     First form  y := beta*y.
*
      IF( BETA.NE.ONE )THEN
         IF( INCY.EQ.1 )THEN
            IF( BETA.EQ.ZERO )THEN
               DO 10, I = 1, N
                  Y( I ) = ZERO
   10          CONTINUE
            ELSE
               DO 20, I = 1, N
                  Y( I ) = BETA*Y( I )
   20          CONTINUE
            END IF
         ELSE
            IY = KY
            IF( BETA.EQ.ZERO )THEN
               DO 30, I = 1, N
                  Y( IY ) = ZERO
                  IY      = IY   + INCY
   30          CONTINUE
            ELSE
               DO 40, I = 1, N
                  Y( IY ) = BETA*Y( IY )
                  IY      = IY           + INCY
   40          CONTINUE
            END IF
         END IF
      END IF
      IF( ALPHA.EQ.ZERO )
     $   RETURN
      IF( LSAME( UPLO, 'U' ) )THEN
*
*        Form  y  when upper triangle of A is stored.
*
         KPLUS1 = K + 1
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 60, J = 1, N
               TEMP1 = ALPHA*X( J )
               TEMP2 = ZERO
               L     = KPLUS1 - J
               DO 50, I = MAX( 1, J - K ), J - 1
                  Y( I ) = Y( I ) + TEMP1*A( L + I, J )
                  TEMP2  = TEMP2  + DCONJG( A( L + I, J ) )*X( I )
   50          CONTINUE
               Y( J ) = Y( J ) + TEMP1*DBLE( A( KPLUS1, J ) )
     $                         + ALPHA*TEMP2
   60       CONTINUE
         ELSE
            JX = KX
            JY = KY
            DO 80, J = 1, N
               TEMP1 = ALPHA*X( JX )
               TEMP2 = ZERO
               IX    = KX
               IY    = KY
               L     = KPLUS1 - J
               DO 70, I = MAX( 1, J - K ), J - 1
                  Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
                  TEMP2   = TEMP2   + DCONJG( A( L + I, J ) )*X( IX )
                  IX      = IX      + INCX
                  IY      = IY      + INCY
   70          CONTINUE
               Y( JY ) = Y( JY ) + TEMP1*DBLE( A( KPLUS1, J ) )
     $                           + ALPHA*TEMP2
               JX      = JX      + INCX
               JY      = JY      + INCY
               IF( J.GT.K )THEN
                  KX = KX + INCX
                  KY = KY + INCY
               END IF
   80       CONTINUE
         END IF
      ELSE
*
*        Form  y  when lower triangle of A is stored.
*
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 100, J = 1, N
               TEMP1  = ALPHA*X( J )
               TEMP2  = ZERO
               Y( J ) = Y( J ) + TEMP1*DBLE( A( 1, J ) )
               L      = 1      - J
               DO 90, I = J + 1, MIN( N, J + K )
                  Y( I ) = Y( I ) + TEMP1*A( L + I, J )
                  TEMP2  = TEMP2  + DCONJG( A( L + I, J ) )*X( I )
   90          CONTINUE
               Y( J ) = Y( J ) + ALPHA*TEMP2
  100       CONTINUE
         ELSE
            JX = KX
            JY = KY
            DO 120, J = 1, N
               TEMP1   = ALPHA*X( JX )
               TEMP2   = ZERO
               Y( JY ) = Y( JY ) + TEMP1*DBLE( A( 1, J ) )
               L       = 1       - J
               IX      = JX
               IY      = JY
               DO 110, I = J + 1, MIN( N, J + K )
                  IX      = IX      + INCX
                  IY      = IY      + INCY
                  Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
                  TEMP2   = TEMP2   + DCONJG( A( L + I, J ) )*X( IX )
  110          CONTINUE
               Y( JY ) = Y( JY ) + ALPHA*TEMP2
               JX      = JX      + INCX
               JY      = JY      + INCY
  120       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZHBMV .
*
      END
      SUBROUTINE ZHEMM ( SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB,
     $                   BETA, C, LDC )
*     .. Scalar Arguments ..
      CHARACTER*1        SIDE, UPLO
      INTEGER            M, N, LDA, LDB, LDC
      COMPLEX*16         ALPHA, BETA
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), B( LDB, * ), C( LDC, * )
*     ..
*
*  Purpose
*  =======
*
*  ZHEMM  performs one of the matrix-matrix operations
*
*     C := alpha*A*B + beta*C,
*
*  or
*
*     C := alpha*B*A + beta*C,
*
*  where alpha and beta are scalars, A is an hermitian matrix and  B and
*  C are m by n matrices.
*
*  Parameters
*  ==========
*
*  SIDE   - CHARACTER*1.
*           On entry,  SIDE  specifies whether  the  hermitian matrix  A
*           appears on the  left or right  in the  operation as follows:
*
*              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
*
*              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
*
*           Unchanged on exit.
*
*  UPLO   - CHARACTER*1.
*           On  entry,   UPLO  specifies  whether  the  upper  or  lower
*           triangular  part  of  the  hermitian  matrix   A  is  to  be
*           referenced as follows:
*
*              UPLO = 'U' or 'u'   Only the upper triangular part of the
*                                  hermitian matrix is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the lower triangular part of the
*                                  hermitian matrix is to be referenced.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry,  M  specifies the number of rows of the matrix  C.
*           M  must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix C.
*           N  must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is
*           m  when  SIDE = 'L' or 'l'  and is n  otherwise.
*           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
*           the array  A  must contain the  hermitian matrix,  such that
*           when  UPLO = 'U' or 'u', the leading m by m upper triangular
*           part of the array  A  must contain the upper triangular part
*           of the  hermitian matrix and the  strictly  lower triangular
*           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
*           the leading  m by m  lower triangular part  of the  array  A
*           must  contain  the  lower triangular part  of the  hermitian
*           matrix and the  strictly upper triangular part of  A  is not
*           referenced.
*           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
*           the array  A  must contain the  hermitian matrix,  such that
*           when  UPLO = 'U' or 'u', the leading n by n upper triangular
*           part of the array  A  must contain the upper triangular part
*           of the  hermitian matrix and the  strictly  lower triangular
*           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
*           the leading  n by n  lower triangular part  of the  array  A
*           must  contain  the  lower triangular part  of the  hermitian
*           matrix and the  strictly upper triangular part of  A  is not
*           referenced.
*           Note that the imaginary parts  of the diagonal elements need
*           not be set, they are assumed to be zero.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the  calling (sub) program. When  SIDE = 'L' or 'l'  then
*           LDA must be at least  max( 1, m ), otherwise  LDA must be at
*           least max( 1, n ).
*           Unchanged on exit.
*
*  B      - COMPLEX*16       array of DIMENSION ( LDB, n ).
*           Before entry, the leading  m by n part of the array  B  must
*           contain the matrix B.
*           Unchanged on exit.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in  the  calling  (sub)  program.   LDB  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*  BETA   - COMPLEX*16      .
*           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
*           supplied as zero then C need not be set on input.
*           Unchanged on exit.
*
*  C      - COMPLEX*16       array of DIMENSION ( LDC, n ).
*           Before entry, the leading  m by n  part of the array  C must
*           contain the matrix  C,  except when  beta  is zero, in which
*           case C need not be set on entry.
*           On exit, the array  C  is overwritten by the  m by n updated
*           matrix.
*
*  LDC    - INTEGER.
*           On entry, LDC specifies the first dimension of C as declared
*           in  the  calling  (sub)  program.   LDC  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX, DBLE
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, INFO, J, K, NROWA
      COMPLEX*16         TEMP1, TEMP2
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Executable Statements ..
*
*     Set NROWA as the number of rows of A.
*
      IF( LSAME( SIDE, 'L' ) )THEN
         NROWA = M
      ELSE
         NROWA = N
      END IF
      UPPER = LSAME( UPLO, 'U' )
*
*     Test the input parameters.
*
      INFO = 0
      IF(      ( .NOT.LSAME( SIDE, 'L' ) ).AND.
     $         ( .NOT.LSAME( SIDE, 'R' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.UPPER              ).AND.
     $         ( .NOT.LSAME( UPLO, 'L' ) )      )THEN
         INFO = 2
      ELSE IF( M  .LT.0               )THEN
         INFO = 3
      ELSE IF( N  .LT.0               )THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 7
      ELSE IF( LDB.LT.MAX( 1, M     ) )THEN
         INFO = 9
      ELSE IF( LDC.LT.MAX( 1, M     ) )THEN
         INFO = 12
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZHEMM ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
     $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         IF( BETA.EQ.ZERO )THEN
            DO 20, J = 1, N
               DO 10, I = 1, M
                  C( I, J ) = ZERO
   10          CONTINUE
   20       CONTINUE
         ELSE
            DO 40, J = 1, N
               DO 30, I = 1, M
                  C( I, J ) = BETA*C( I, J )
   30          CONTINUE
   40       CONTINUE
         END IF
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSAME( SIDE, 'L' ) )THEN
*
*        Form  C := alpha*A*B + beta*C.
*
         IF( UPPER )THEN
            DO 70, J = 1, N
               DO 60, I = 1, M
                  TEMP1 = ALPHA*B( I, J )
                  TEMP2 = ZERO
                  DO 50, K = 1, I - 1
                     C( K, J ) = C( K, J ) + TEMP1*A( K, I )
                     TEMP2     = TEMP2     +
     $                           B( K, J )*DCONJG( A( K, I ) )
   50             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = TEMP1*DBLE( A( I, I ) ) +
     $                           ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J )         +
     $                           TEMP1*DBLE( A( I, I ) ) +
     $                           ALPHA*TEMP2
                  END IF
   60          CONTINUE
   70       CONTINUE
         ELSE
            DO 100, J = 1, N
               DO 90, I = M, 1, -1
                  TEMP1 = ALPHA*B( I, J )
                  TEMP2 = ZERO
                  DO 80, K = I + 1, M
                     C( K, J ) = C( K, J ) + TEMP1*A( K, I )
                     TEMP2     = TEMP2     +
     $                           B( K, J )*DCONJG( A( K, I ) )
   80             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = TEMP1*DBLE( A( I, I ) ) +
     $                           ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J )         +
     $                           TEMP1*DBLE( A( I, I ) ) +
     $                           ALPHA*TEMP2
                  END IF
   90          CONTINUE
  100       CONTINUE
         END IF
      ELSE
*
*        Form  C := alpha*B*A + beta*C.
*
         DO 170, J = 1, N
            TEMP1 = ALPHA*DBLE( A( J, J ) )
            IF( BETA.EQ.ZERO )THEN
               DO 110, I = 1, M
                  C( I, J ) = TEMP1*B( I, J )
  110          CONTINUE
            ELSE
               DO 120, I = 1, M
                  C( I, J ) = BETA*C( I, J ) + TEMP1*B( I, J )
  120          CONTINUE
            END IF
            DO 140, K = 1, J - 1
               IF( UPPER )THEN
                  TEMP1 = ALPHA*A( K, J )
               ELSE
                  TEMP1 = ALPHA*DCONJG( A( J, K ) )
               END IF
               DO 130, I = 1, M
                  C( I, J ) = C( I, J ) + TEMP1*B( I, K )
  130          CONTINUE
  140       CONTINUE
            DO 160, K = J + 1, N
               IF( UPPER )THEN
                  TEMP1 = ALPHA*DCONJG( A( J, K ) )
               ELSE
                  TEMP1 = ALPHA*A( K, J )
               END IF
               DO 150, I = 1, M
                  C( I, J ) = C( I, J ) + TEMP1*B( I, K )
  150          CONTINUE
  160       CONTINUE
  170    CONTINUE
      END IF
*
      RETURN
*
*     End of ZHEMM .
*
      END
      SUBROUTINE ZHER  ( UPLO, N, ALPHA, X, INCX, A, LDA )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA
      INTEGER            INCX, LDA, N
      CHARACTER*1        UPLO
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZHER   performs the hermitian rank 1 operation
*
*     A := alpha*x*conjg( x' ) + A,
*
*  where alpha is a real scalar, x is an n element vector and A is an
*  n by n hermitian matrix.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the upper or lower
*           triangular part of the array A is to be referenced as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the upper triangular part of A
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the lower triangular part of A
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry with  UPLO = 'U' or 'u', the leading n by n
*           upper triangular part of the array A must contain the upper
*           triangular part of the hermitian matrix and the strictly
*           lower triangular part of A is not referenced. On exit, the
*           upper triangular part of the array A is overwritten by the
*           upper triangular part of the updated matrix.
*           Before entry with UPLO = 'L' or 'l', the leading n by n
*           lower triangular part of the array A must contain the lower
*           triangular part of the hermitian matrix and the strictly
*           upper triangular part of A is not referenced. On exit, the
*           lower triangular part of the array A is overwritten by the
*           lower triangular part of the updated matrix.
*           Note that the imaginary parts of the diagonal elements need
*           not be set, they are assumed to be zero, and on exit they
*           are set to zero.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, n ).
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, J, JX, KX
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX, DBLE
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
     $         .NOT.LSAME( UPLO, 'L' )      )THEN
         INFO = 1
      ELSE IF( N.LT.0 )THEN
         INFO = 2
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 5
      ELSE IF( LDA.LT.MAX( 1, N ) )THEN
         INFO = 7
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZHER  ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.( ALPHA.EQ.DBLE( ZERO ) ) )
     $   RETURN
*
*     Set the start point in X if the increment is not unity.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through the triangular part
*     of A.
*
      IF( LSAME( UPLO, 'U' ) )THEN
*
*        Form  A  when A is stored in upper triangle.
*
         IF( INCX.EQ.1 )THEN
            DO 20, J = 1, N
c               IF( X( J ).NE.ZERO )THEN
                  TEMP = ALPHA*DCONJG( X( J ) )
                  DO 10, I = 1, J - 1
                     A( I, J ) = A( I, J ) + X( I )*TEMP
   10             CONTINUE
                  A( J, J ) = DBLE( A( J, J ) ) + DBLE( X( J )*TEMP )
c               ELSE
c                  A( J, J ) = DBLE( A( J, J ) )
c               END IF
   20       CONTINUE
         ELSE
            JX = KX
            DO 40, J = 1, N
c               IF( X( JX ).NE.ZERO )THEN
                  TEMP = ALPHA*DCONJG( X( JX ) )
                  IX   = KX
                  DO 30, I = 1, J - 1
                     A( I, J ) = A( I, J ) + X( IX )*TEMP
                     IX        = IX        + INCX
   30             CONTINUE
                  A( J, J ) = DBLE( A( J, J ) ) + DBLE( X( JX )*TEMP )
c               ELSE
c                  A( J, J ) = DBLE( A( J, J ) )
c               END IF
               JX = JX + INCX
   40       CONTINUE
         END IF
      ELSE
*
*        Form  A  when A is stored in lower triangle.
*
         IF( INCX.EQ.1 )THEN
            DO 60, J = 1, N
c               IF( X( J ).NE.ZERO )THEN
                  TEMP      = ALPHA*DCONJG( X( J ) )
                  A( J, J ) = DBLE( A( J, J ) ) + DBLE( TEMP*X( J ) )
                  DO 50, I = J + 1, N
                     A( I, J ) = A( I, J ) + X( I )*TEMP
   50             CONTINUE
c               ELSE
c                  A( J, J ) = DBLE( A( J, J ) )
c               END IF
   60       CONTINUE
         ELSE
            JX = KX
            DO 80, J = 1, N
c               IF( X( JX ).NE.ZERO )THEN
                  TEMP      = ALPHA*DCONJG( X( JX ) )
                  A( J, J ) = DBLE( A( J, J ) ) + DBLE( TEMP*X( JX ) )
                  IX        = JX
                  DO 70, I = J + 1, N
                     IX        = IX        + INCX
                     A( I, J ) = A( I, J ) + X( IX )*TEMP
   70             CONTINUE
c               ELSE
c                  A( J, J ) = DBLE( A( J, J ) )
c               END IF
               JX = JX + INCX
   80       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZHER  .
*
      END
      SUBROUTINE ZHERK( UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC )
*     .. Scalar Arguments ..
      CHARACTER          TRANS, UPLO
      INTEGER            K, LDA, LDC, N
      DOUBLE PRECISION   ALPHA, BETA
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), C( LDC, * )
*     ..
*
*  Purpose
*  =======
*
*  ZHERK  performs one of the hermitian rank k operations
*
*     C := alpha*A*conjg( A' ) + beta*C,
*
*  or
*
*     C := alpha*conjg( A' )*A + beta*C,
*
*  where  alpha and beta  are  real scalars,  C is an  n by n  hermitian
*  matrix and  A  is an  n by k  matrix in the  first case and a  k by n
*  matrix in the second case.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On  entry,   UPLO  specifies  whether  the  upper  or  lower
*           triangular  part  of the  array  C  is to be  referenced  as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry,  TRANS  specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   C := alpha*A*conjg( A' ) + beta*C.
*
*              TRANS = 'C' or 'c'   C := alpha*conjg( A' )*A + beta*C.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry,  N specifies the order of the matrix C.  N must be
*           at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
*           of  columns   of  the   matrix   A,   and  on   entry   with
*           TRANS = 'C' or 'c',  K  specifies  the number of rows of the
*           matrix A.  K must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION            .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is
*           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
*           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
*           part of the array  A  must contain the matrix  A,  otherwise
*           the leading  k by n  part of the array  A  must contain  the
*           matrix A.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
*           then  LDA must be at least  max( 1, n ), otherwise  LDA must
*           be at least  max( 1, k ).
*           Unchanged on exit.
*
*  BETA   - DOUBLE PRECISION.
*           On entry, BETA specifies the scalar beta.
*           Unchanged on exit.
*
*  C      - COMPLEX*16          array of DIMENSION ( LDC, n ).
*           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
*           upper triangular part of the array C must contain the upper
*           triangular part  of the  hermitian matrix  and the strictly
*           lower triangular part of C is not referenced.  On exit, the
*           upper triangular part of the array  C is overwritten by the
*           upper triangular part of the updated matrix.
*           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
*           lower triangular part of the array C must contain the lower
*           triangular part  of the  hermitian matrix  and the strictly
*           upper triangular part of C is not referenced.  On exit, the
*           lower triangular part of the array  C is overwritten by the
*           lower triangular part of the updated matrix.
*           Note that the imaginary parts of the diagonal elements need
*           not be set,  they are assumed to be zero,  and on exit they
*           are set to zero.
*
*  LDC    - INTEGER.
*           On entry, LDC specifies the first dimension of C as declared
*           in  the  calling  (sub)  program.   LDC  must  be  at  least
*           max( 1, n ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*  -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
*     Ed Anderson, Cray Research Inc.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          DBLE, DCMPLX, DCONJG, MAX
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, INFO, J, L, NROWA
      DOUBLE PRECISION   RTEMP
      COMPLEX*16         TEMP
*     ..
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      IF( LSAME( TRANS, 'N' ) ) THEN
         NROWA = N
      ELSE
         NROWA = K
      END IF
      UPPER = LSAME( UPLO, 'U' )
*
      INFO = 0
      IF( ( .NOT.UPPER ) .AND. ( .NOT.LSAME( UPLO, 'L' ) ) ) THEN
         INFO = 1
      ELSE IF( ( .NOT.LSAME( TRANS, 'N' ) ) .AND.
     $         ( .NOT.LSAME( TRANS, 'C' ) ) ) THEN
         INFO = 2
      ELSE IF( N.LT.0 ) THEN
         INFO = 3
      ELSE IF( K.LT.0 ) THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, NROWA ) ) THEN
         INFO = 7
      ELSE IF( LDC.LT.MAX( 1, N ) ) THEN
         INFO = 10
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'ZHERK ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ) .OR. ( ( ( ALPHA.EQ.ZERO ) .OR. ( K.EQ.0 ) ) .AND.
     $    ( BETA.EQ.ONE ) ) )RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO ) THEN
         IF( UPPER ) THEN
            IF( BETA.EQ.ZERO ) THEN
               DO 20 J = 1, N
                  DO 10 I = 1, J
                     C( I, J ) = ZERO
   10             CONTINUE
   20          CONTINUE
            ELSE
               DO 40 J = 1, N
                  DO 30 I = 1, J - 1
                     C( I, J ) = BETA*C( I, J )
   30             CONTINUE
                  C( J, J ) = BETA*DBLE( C( J, J ) )
   40          CONTINUE
            END IF
         ELSE
            IF( BETA.EQ.ZERO ) THEN
               DO 60 J = 1, N
                  DO 50 I = J, N
                     C( I, J ) = ZERO
   50             CONTINUE
   60          CONTINUE
            ELSE
               DO 80 J = 1, N
                  C( J, J ) = BETA*DBLE( C( J, J ) )
                  DO 70 I = J + 1, N
                     C( I, J ) = BETA*C( I, J )
   70             CONTINUE
   80          CONTINUE
            END IF
         END IF
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSAME( TRANS, 'N' ) ) THEN
*
*        Form  C := alpha*A*conjg( A' ) + beta*C.
*
         IF( UPPER ) THEN
            DO 130 J = 1, N
               IF( BETA.EQ.ZERO ) THEN
                  DO 90 I = 1, J
                     C( I, J ) = ZERO
   90             CONTINUE
               ELSE IF( BETA.NE.ONE ) THEN
                  DO 100 I = 1, J - 1
                     C( I, J ) = BETA*C( I, J )
  100             CONTINUE
                  C( J, J ) = BETA*DBLE( C( J, J ) )
               ELSE
                  C( J, J ) = DBLE( C( J, J ) )
               END IF
               DO 120 L = 1, K
                  IF( A( J, L ).NE.DCMPLX( ZERO ) ) THEN
                     TEMP = ALPHA*DCONJG( A( J, L ) )
                     DO 110 I = 1, J - 1
                        C( I, J ) = C( I, J ) + TEMP*A( I, L )
  110                CONTINUE
                     C( J, J ) = DBLE( C( J, J ) ) +
     $                           DBLE( TEMP*A( I, L ) )
                  END IF
  120          CONTINUE
  130       CONTINUE
         ELSE
            DO 180 J = 1, N
               IF( BETA.EQ.ZERO ) THEN
                  DO 140 I = J, N
                     C( I, J ) = ZERO
  140             CONTINUE
               ELSE IF( BETA.NE.ONE ) THEN
                  C( J, J ) = BETA*DBLE( C( J, J ) )
                  DO 150 I = J + 1, N
                     C( I, J ) = BETA*C( I, J )
  150             CONTINUE
               ELSE
                  C( J, J ) = DBLE( C( J, J ) )
               END IF
               DO 170 L = 1, K
                  IF( A( J, L ).NE.DCMPLX( ZERO ) ) THEN
                     TEMP = ALPHA*DCONJG( A( J, L ) )
                     C( J, J ) = DBLE( C( J, J ) ) +
     $                           DBLE( TEMP*A( J, L ) )
                     DO 160 I = J + 1, N
                        C( I, J ) = C( I, J ) + TEMP*A( I, L )
  160                CONTINUE
                  END IF
  170          CONTINUE
  180       CONTINUE
         END IF
      ELSE
*
*        Form  C := alpha*conjg( A' )*A + beta*C.
*
         IF( UPPER ) THEN
            DO 220 J = 1, N
               DO 200 I = 1, J - 1
                  TEMP = ZERO
                  DO 190 L = 1, K
                     TEMP = TEMP + DCONJG( A( L, I ) )*A( L, J )
  190             CONTINUE
                  IF( BETA.EQ.ZERO ) THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  200          CONTINUE
               RTEMP = ZERO
               DO 210 L = 1, K
                  RTEMP = RTEMP + DCONJG( A( L, J ) )*A( L, J )
  210          CONTINUE
               IF( BETA.EQ.ZERO ) THEN
                  C( J, J ) = ALPHA*RTEMP
               ELSE
                  C( J, J ) = ALPHA*RTEMP + BETA*DBLE( C( J, J ) )
               END IF
  220       CONTINUE
         ELSE
            DO 260 J = 1, N
               RTEMP = ZERO
               DO 230 L = 1, K
                  RTEMP = RTEMP + DCONJG( A( L, J ) )*A( L, J )
  230          CONTINUE
               IF( BETA.EQ.ZERO ) THEN
                  C( J, J ) = ALPHA*RTEMP
               ELSE
                  C( J, J ) = ALPHA*RTEMP + BETA*DBLE( C( J, J ) )
               END IF
               DO 250 I = J + 1, N
                  TEMP = ZERO
                  DO 240 L = 1, K
                     TEMP = TEMP + DCONJG( A( L, I ) )*A( L, J )
  240             CONTINUE
                  IF( BETA.EQ.ZERO ) THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  250          CONTINUE
  260       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZHERK .
*
      END
      SUBROUTINE ZHPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
*     .. Scalar Arguments ..
      COMPLEX*16         ALPHA, BETA
      INTEGER            INCX, INCY, N
      CHARACTER*1        UPLO
*     .. Array Arguments ..
      COMPLEX*16         AP( * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  ZHPMV  performs the matrix-vector operation
*
*     y := alpha*A*x + beta*y,
*
*  where alpha and beta are scalars, x and y are n element vectors and
*  A is an n by n hermitian matrix, supplied in packed form.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the upper or lower
*           triangular part of the matrix A is supplied in the packed
*           array AP as follows:
*
*              UPLO = 'U' or 'u'   The upper triangular part of A is
*                                  supplied in AP.
*
*              UPLO = 'L' or 'l'   The lower triangular part of A is
*                                  supplied in AP.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  AP     - COMPLEX*16       array of DIMENSION at least
*           ( ( n*( n + 1 ) )/2 ).
*           Before entry with UPLO = 'U' or 'u', the array AP must
*           contain the upper triangular part of the hermitian matrix
*           packed sequentially, column by column, so that AP( 1 )
*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
*           and a( 2, 2 ) respectively, and so on.
*           Before entry with UPLO = 'L' or 'l', the array AP must
*           contain the lower triangular part of the hermitian matrix
*           packed sequentially, column by column, so that AP( 1 )
*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
*           and a( 3, 1 ) respectively, and so on.
*           Note that the imaginary parts of the diagonal elements need
*           not be set and are assumed to be zero.
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  BETA   - COMPLEX*16      .
*           On entry, BETA specifies the scalar beta. When BETA is
*           supplied as zero then Y need not be set on input.
*           Unchanged on exit.
*
*  Y      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCY ) ).
*           Before entry, the incremented array Y must contain the n
*           element vector y. On exit, Y is overwritten by the updated
*           vector y.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP1, TEMP2
      INTEGER            I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, DBLE
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
     $         .NOT.LSAME( UPLO, 'L' )      )THEN
         INFO = 1
      ELSE IF( N.LT.0 )THEN
         INFO = 2
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 6
      ELSE IF( INCY.EQ.0 )THEN
         INFO = 9
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZHPMV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     Set up the start points in  X  and  Y.
*
      IF( INCX.GT.0 )THEN
         KX = 1
      ELSE
         KX = 1 - ( N - 1 )*INCX
      END IF
      IF( INCY.GT.0 )THEN
         KY = 1
      ELSE
         KY = 1 - ( N - 1 )*INCY
      END IF
*
*     Start the operations. In this version the elements of the array AP
*     are accessed sequentially with one pass through AP.
*
*     First form  y := beta*y.
*
      IF( BETA.NE.ONE )THEN
         IF( INCY.EQ.1 )THEN
            IF( BETA.EQ.ZERO )THEN
               DO 10, I = 1, N
                  Y( I ) = ZERO
   10          CONTINUE
            ELSE
               DO 20, I = 1, N
                  Y( I ) = BETA*Y( I )
   20          CONTINUE
            END IF
         ELSE
            IY = KY
            IF( BETA.EQ.ZERO )THEN
               DO 30, I = 1, N
                  Y( IY ) = ZERO
                  IY      = IY   + INCY
   30          CONTINUE
            ELSE
               DO 40, I = 1, N
                  Y( IY ) = BETA*Y( IY )
                  IY      = IY           + INCY
   40          CONTINUE
            END IF
         END IF
      END IF
      IF( ALPHA.EQ.ZERO )
     $   RETURN
      KK = 1
      IF( LSAME( UPLO, 'U' ) )THEN
*
*        Form  y  when AP contains the upper triangle.
*
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 60, J = 1, N
               TEMP1 = ALPHA*X( J )
               TEMP2 = ZERO
               K     = KK
               DO 50, I = 1, J - 1
                  Y( I ) = Y( I ) + TEMP1*AP( K )
                  TEMP2  = TEMP2  + DCONJG( AP( K ) )*X( I )
                  K      = K      + 1
   50          CONTINUE
               Y( J ) = Y( J ) + TEMP1*DBLE( AP( KK + J - 1 ) )
     $                         + ALPHA*TEMP2
               KK     = KK     + J
   60       CONTINUE
         ELSE
            JX = KX
            JY = KY
            DO 80, J = 1, N
               TEMP1 = ALPHA*X( JX )
               TEMP2 = ZERO
               IX    = KX
               IY    = KY
               DO 70, K = KK, KK + J - 2
                  Y( IY ) = Y( IY ) + TEMP1*AP( K )
                  TEMP2   = TEMP2   + DCONJG( AP( K ) )*X( IX )
                  IX      = IX      + INCX
                  IY      = IY      + INCY
   70          CONTINUE
               Y( JY ) = Y( JY ) + TEMP1*DBLE( AP( KK + J - 1 ) )
     $                           + ALPHA*TEMP2
               JX      = JX      + INCX
               JY      = JY      + INCY
               KK      = KK      + J
   80       CONTINUE
         END IF
      ELSE
*
*        Form  y  when AP contains the lower triangle.
*
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 100, J = 1, N
               TEMP1  = ALPHA*X( J )
               TEMP2  = ZERO
               Y( J ) = Y( J ) + TEMP1*DBLE( AP( KK ) )
               K      = KK     + 1
               DO 90, I = J + 1, N
                  Y( I ) = Y( I ) + TEMP1*AP( K )
                  TEMP2  = TEMP2  + DCONJG( AP( K ) )*X( I )
                  K      = K      + 1
   90          CONTINUE
               Y( J ) = Y( J ) + ALPHA*TEMP2
               KK     = KK     + ( N - J + 1 )
  100       CONTINUE
         ELSE
            JX = KX
            JY = KY
            DO 120, J = 1, N
               TEMP1   = ALPHA*X( JX )
               TEMP2   = ZERO
               Y( JY ) = Y( JY ) + TEMP1*DBLE( AP( KK ) )
               IX      = JX
               IY      = JY
               DO 110, K = KK + 1, KK + N - J
                  IX      = IX      + INCX
                  IY      = IY      + INCY
                  Y( IY ) = Y( IY ) + TEMP1*AP( K )
                  TEMP2   = TEMP2   + DCONJG( AP( K ) )*X( IX )
  110          CONTINUE
               Y( JY ) = Y( JY ) + ALPHA*TEMP2
               JX      = JX      + INCX
               JY      = JY      + INCY
               KK      = KK      + ( N - J + 1 )
  120       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZHPMV .
*
      END
      SUBROUTINE ZHPR  ( UPLO, N, ALPHA, X, INCX, AP )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA
      INTEGER            INCX, N
      CHARACTER*1        UPLO
*     .. Array Arguments ..
      COMPLEX*16         AP( * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZHPR    performs the hermitian rank 1 operation
*
*     A := alpha*x*conjg( x' ) + A,
*
*  where alpha is a real scalar, x is an n element vector and A is an
*  n by n hermitian matrix, supplied in packed form.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the upper or lower
*           triangular part of the matrix A is supplied in the packed
*           array AP as follows:
*
*              UPLO = 'U' or 'u'   The upper triangular part of A is
*                                  supplied in AP.
*
*              UPLO = 'L' or 'l'   The lower triangular part of A is
*                                  supplied in AP.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  AP     - COMPLEX*16       array of DIMENSION at least
*           ( ( n*( n + 1 ) )/2 ).
*           Before entry with  UPLO = 'U' or 'u', the array AP must
*           contain the upper triangular part of the hermitian matrix
*           packed sequentially, column by column, so that AP( 1 )
*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
*           and a( 2, 2 ) respectively, and so on. On exit, the array
*           AP is overwritten by the upper triangular part of the
*           updated matrix.
*           Before entry with UPLO = 'L' or 'l', the array AP must
*           contain the lower triangular part of the hermitian matrix
*           packed sequentially, column by column, so that AP( 1 )
*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
*           and a( 3, 1 ) respectively, and so on. On exit, the array
*           AP is overwritten by the lower triangular part of the
*           updated matrix.
*           Note that the imaginary parts of the diagonal elements need
*           not be set, they are assumed to be zero, and on exit they
*           are set to zero.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, J, JX, K, KK, KX
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, DBLE
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
     $         .NOT.LSAME( UPLO, 'L' )      )THEN
         INFO = 1
      ELSE IF( N.LT.0 )THEN
         INFO = 2
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 5
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZHPR  ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.( ALPHA.EQ.DBLE( ZERO ) ) )
     $   RETURN
*
*     Set the start point in X if the increment is not unity.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of the array AP
*     are accessed sequentially with one pass through AP.
*
      KK = 1
      IF( LSAME( UPLO, 'U' ) )THEN
*
*        Form  A  when upper triangle is stored in AP.
*
         IF( INCX.EQ.1 )THEN
            DO 20, J = 1, N
c               IF( X( J ).NE.ZERO )THEN
                  TEMP = ALPHA*DCONJG( X( J ) )
                  K    = KK
                  DO 10, I = 1, J - 1
                     AP( K ) = AP( K ) + X( I )*TEMP
                     K       = K       + 1
   10             CONTINUE
                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) )
     $                               + DBLE( X( J )*TEMP )
c               ELSE
c                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) )
c               END IF
               KK = KK + J
   20       CONTINUE
         ELSE
            JX = KX
            DO 40, J = 1, N
c               IF( X( JX ).NE.ZERO )THEN
                  TEMP = ALPHA*DCONJG( X( JX ) )
                  IX   = KX
                  DO 30, K = KK, KK + J - 2
                     AP( K ) = AP( K ) + X( IX )*TEMP
                     IX      = IX      + INCX
   30             CONTINUE
                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) )
     $                               + DBLE( X( JX )*TEMP )
c               ELSE
c                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) )
c               END IF
               JX = JX + INCX
               KK = KK + J
   40       CONTINUE
         END IF
      ELSE
*
*        Form  A  when lower triangle is stored in AP.
*
         IF( INCX.EQ.1 )THEN
            DO 60, J = 1, N
c               IF( X( J ).NE.ZERO )THEN
                  TEMP     = ALPHA*DCONJG( X( J ) )
                  AP( KK ) = DBLE( AP( KK ) ) + DBLE( TEMP*X( J ) )
                  K        = KK               + 1
                  DO 50, I = J + 1, N
                     AP( K ) = AP( K ) + X( I )*TEMP
                     K       = K       + 1
   50             CONTINUE
c               ELSE
c                  AP( KK ) = DBLE( AP( KK ) )
c               END IF
               KK = KK + N - J + 1
   60       CONTINUE
         ELSE
            JX = KX
            DO 80, J = 1, N
c               IF( X( JX ).NE.ZERO )THEN
                  TEMP    = ALPHA*DCONJG( X( JX ) )
                  AP( KK ) = DBLE( AP( KK ) ) + DBLE( TEMP*X( JX ) )
                  IX      = JX
                  DO 70, K = KK + 1, KK + N - J
                     IX      = IX      + INCX
                     AP( K ) = AP( K ) + X( IX )*TEMP
   70             CONTINUE
c               ELSE
c                  AP( KK ) = DBLE( AP( KK ) )
c               END IF
               JX = JX + INCX
               KK = KK + N - J + 1
   80       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZHPR  .
*
      END
      SUBROUTINE ZHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP )
*     .. Scalar Arguments ..
      COMPLEX*16         ALPHA
      INTEGER            INCX, INCY, N
      CHARACTER*1        UPLO
*     .. Array Arguments ..
      COMPLEX*16         AP( * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  ZHPR2  performs the hermitian rank 2 operation
*
*     A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
*
*  where alpha is a scalar, x and y are n element vectors and A is an
*  n by n hermitian matrix, supplied in packed form.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the upper or lower
*           triangular part of the matrix A is supplied in the packed
*           array AP as follows:
*
*              UPLO = 'U' or 'u'   The upper triangular part of A is
*                                  supplied in AP.
*
*              UPLO = 'L' or 'l'   The lower triangular part of A is
*                                  supplied in AP.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  Y      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCY ) ).
*           Before entry, the incremented array Y must contain the n
*           element vector y.
*           Unchanged on exit.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*  AP     - COMPLEX*16       array of DIMENSION at least
*           ( ( n*( n + 1 ) )/2 ).
*           Before entry with  UPLO = 'U' or 'u', the array AP must
*           contain the upper triangular part of the hermitian matrix
*           packed sequentially, column by column, so that AP( 1 )
*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
*           and a( 2, 2 ) respectively, and so on. On exit, the array
*           AP is overwritten by the upper triangular part of the
*           updated matrix.
*           Before entry with UPLO = 'L' or 'l', the array AP must
*           contain the lower triangular part of the hermitian matrix
*           packed sequentially, column by column, so that AP( 1 )
*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
*           and a( 3, 1 ) respectively, and so on. On exit, the array
*           AP is overwritten by the lower triangular part of the
*           updated matrix.
*           Note that the imaginary parts of the diagonal elements need
*           not be set, they are assumed to be zero, and on exit they
*           are set to zero.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP1, TEMP2
      INTEGER            I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, DBLE
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
     $         .NOT.LSAME( UPLO, 'L' )      )THEN
         INFO = 1
      ELSE IF( N.LT.0 )THEN
         INFO = 2
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 5
      ELSE IF( INCY.EQ.0 )THEN
         INFO = 7
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZHPR2 ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
     $   RETURN
*
*     Set up the start points in X and Y if the increments are not both
*     unity.
*
      IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN
         IF( INCX.GT.0 )THEN
            KX = 1
         ELSE
            KX = 1 - ( N - 1 )*INCX
         END IF
         IF( INCY.GT.0 )THEN
            KY = 1
         ELSE
            KY = 1 - ( N - 1 )*INCY
         END IF
         JX = KX
         JY = KY
      END IF
*
*     Start the operations. In this version the elements of the array AP
*     are accessed sequentially with one pass through AP.
*
      KK = 1
      IF( LSAME( UPLO, 'U' ) )THEN
*
*        Form  A  when upper triangle is stored in AP.
*
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 20, J = 1, N
c               IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN
                  TEMP1 = ALPHA*DCONJG( Y( J ) )
                  TEMP2 = DCONJG( ALPHA*X( J ) )
                  K     = KK
                  DO 10, I = 1, J - 1
                     AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2
                     K       = K       + 1
   10             CONTINUE
                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) +
     $                               DBLE( X( J )*TEMP1 + Y( J )*TEMP2 )
c               ELSE
c                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) )
c               END IF
               KK = KK + J
   20       CONTINUE
         ELSE
            DO 40, J = 1, N
c               IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN
                  TEMP1 = ALPHA*DCONJG( Y( JY ) )
                  TEMP2 = DCONJG( ALPHA*X( JX ) )
                  IX    = KX
                  IY    = KY
                  DO 30, K = KK, KK + J - 2
                     AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2
                     IX      = IX      + INCX
                     IY      = IY      + INCY
   30             CONTINUE
                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) +
     $                               DBLE( X( JX )*TEMP1 +
     $                                     Y( JY )*TEMP2 )
c               ELSE
c                  AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) )
c               END IF
               JX = JX + INCX
               JY = JY + INCY
               KK = KK + J
   40       CONTINUE
         END IF
      ELSE
*
*        Form  A  when lower triangle is stored in AP.
*
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 60, J = 1, N
c               IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN
                  TEMP1   = ALPHA*DCONJG( Y( J ) )
                  TEMP2   = DCONJG( ALPHA*X( J ) )
                  AP( KK ) = DBLE( AP( KK ) ) +
     $                       DBLE( X( J )*TEMP1 + Y( J )*TEMP2 )
                  K        = KK               + 1
                  DO 50, I = J + 1, N
                     AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2
                     K       = K       + 1
   50             CONTINUE
c               ELSE
c                  AP( KK ) = DBLE( AP( KK ) )
c               END IF
               KK = KK + N - J + 1
   60       CONTINUE
         ELSE
            DO 80, J = 1, N
c               IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN
                  TEMP1    = ALPHA*DCONJG( Y( JY ) )
                  TEMP2    = DCONJG( ALPHA*X( JX ) )
                  AP( KK ) = DBLE( AP( KK ) ) +
     $                       DBLE( X( JX )*TEMP1 + Y( JY )*TEMP2 )
                  IX       = JX
                  IY       = JY
                  DO 70, K = KK + 1, KK + N - J
                     IX      = IX      + INCX
                     IY      = IY      + INCY
                     AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2
   70             CONTINUE
c               ELSE
c                  AP( KK ) = DBLE( AP( KK ) )
c               END IF
               JX = JX + INCX
               JY = JY + INCY
               KK = KK + N - J + 1
   80       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZHPR2 .
*
      END
      subroutine zrotg(ca,cb,c,s)
      double complex ca,cb,s
      double precision c
      double precision norm,scale
      double complex alpha
      intrinsic dconjg, dcmplx
      if (cdabs(ca) .ne. 0.0d0) go to 10
         c = 0.0d0
         s = (1.0d0,0.0d0)
         ca = cb
         go to 20
   10 continue
         scale = cdabs(ca) + cdabs(cb)
         norm = scale*dsqrt((cdabs(ca/dcmplx(scale,0.0d0)))**2 +
     *                      (cdabs(cb/dcmplx(scale,0.0d0)))**2)
         alpha = ca /cdabs(ca)
         c = cdabs(ca) / norm
         s = alpha * dconjg(cb) / norm
         ca = alpha * norm
   20 continue
      return
      end
      SUBROUTINE ZSYMM ( SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB,
     $                   BETA, C, LDC )
*     .. Scalar Arguments ..
      CHARACTER*1        SIDE, UPLO
      INTEGER            M, N, LDA, LDB, LDC
      COMPLEX*16         ALPHA, BETA
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), B( LDB, * ), C( LDC, * )
*     ..
*
*  Purpose
*  =======
*
*  ZSYMM  performs one of the matrix-matrix operations
*
*     C := alpha*A*B + beta*C,
*
*  or
*
*     C := alpha*B*A + beta*C,
*
*  where  alpha and beta are scalars, A is a symmetric matrix and  B and
*  C are m by n matrices.
*
*  Parameters
*  ==========
*
*  SIDE   - CHARACTER*1.
*           On entry,  SIDE  specifies whether  the  symmetric matrix  A
*           appears on the  left or right  in the  operation as follows:
*
*              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
*
*              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
*
*           Unchanged on exit.
*
*  UPLO   - CHARACTER*1.
*           On  entry,   UPLO  specifies  whether  the  upper  or  lower
*           triangular  part  of  the  symmetric  matrix   A  is  to  be
*           referenced as follows:
*
*              UPLO = 'U' or 'u'   Only the upper triangular part of the
*                                  symmetric matrix is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the lower triangular part of the
*                                  symmetric matrix is to be referenced.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry,  M  specifies the number of rows of the matrix  C.
*           M  must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix C.
*           N  must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is
*           m  when  SIDE = 'L' or 'l'  and is n  otherwise.
*           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
*           the array  A  must contain the  symmetric matrix,  such that
*           when  UPLO = 'U' or 'u', the leading m by m upper triangular
*           part of the array  A  must contain the upper triangular part
*           of the  symmetric matrix and the  strictly  lower triangular
*           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
*           the leading  m by m  lower triangular part  of the  array  A
*           must  contain  the  lower triangular part  of the  symmetric
*           matrix and the  strictly upper triangular part of  A  is not
*           referenced.
*           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
*           the array  A  must contain the  symmetric matrix,  such that
*           when  UPLO = 'U' or 'u', the leading n by n upper triangular
*           part of the array  A  must contain the upper triangular part
*           of the  symmetric matrix and the  strictly  lower triangular
*           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
*           the leading  n by n  lower triangular part  of the  array  A
*           must  contain  the  lower triangular part  of the  symmetric
*           matrix and the  strictly upper triangular part of  A  is not
*           referenced.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the  calling (sub) program. When  SIDE = 'L' or 'l'  then
*           LDA must be at least  max( 1, m ), otherwise  LDA must be at
*           least max( 1, n ).
*           Unchanged on exit.
*
*  B      - COMPLEX*16       array of DIMENSION ( LDB, n ).
*           Before entry, the leading  m by n part of the array  B  must
*           contain the matrix B.
*           Unchanged on exit.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in  the  calling  (sub)  program.   LDB  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*  BETA   - COMPLEX*16      .
*           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
*           supplied as zero then C need not be set on input.
*           Unchanged on exit.
*
*  C      - COMPLEX*16       array of DIMENSION ( LDC, n ).
*           Before entry, the leading  m by n  part of the array  C must
*           contain the matrix  C,  except when  beta  is zero, in which
*           case C need not be set on entry.
*           On exit, the array  C  is overwritten by the  m by n updated
*           matrix.
*
*  LDC    - INTEGER.
*           On entry, LDC specifies the first dimension of C as declared
*           in  the  calling  (sub)  program.   LDC  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, INFO, J, K, NROWA
      COMPLEX*16         TEMP1, TEMP2
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Executable Statements ..
*
*     Set NROWA as the number of rows of A.
*
      IF( LSAME( SIDE, 'L' ) )THEN
         NROWA = M
      ELSE
         NROWA = N
      END IF
      UPPER = LSAME( UPLO, 'U' )
*
*     Test the input parameters.
*
      INFO = 0
      IF(      ( .NOT.LSAME( SIDE, 'L' ) ).AND.
     $         ( .NOT.LSAME( SIDE, 'R' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.UPPER              ).AND.
     $         ( .NOT.LSAME( UPLO, 'L' ) )      )THEN
         INFO = 2
      ELSE IF( M  .LT.0               )THEN
         INFO = 3
      ELSE IF( N  .LT.0               )THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 7
      ELSE IF( LDB.LT.MAX( 1, M     ) )THEN
         INFO = 9
      ELSE IF( LDC.LT.MAX( 1, M     ) )THEN
         INFO = 12
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZSYMM ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
     $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         IF( BETA.EQ.ZERO )THEN
            DO 20, J = 1, N
               DO 10, I = 1, M
                  C( I, J ) = ZERO
   10          CONTINUE
   20       CONTINUE
         ELSE
            DO 40, J = 1, N
               DO 30, I = 1, M
                  C( I, J ) = BETA*C( I, J )
   30          CONTINUE
   40       CONTINUE
         END IF
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSAME( SIDE, 'L' ) )THEN
*
*        Form  C := alpha*A*B + beta*C.
*
         IF( UPPER )THEN
            DO 70, J = 1, N
               DO 60, I = 1, M
                  TEMP1 = ALPHA*B( I, J )
                  TEMP2 = ZERO
                  DO 50, K = 1, I - 1
                     C( K, J ) = C( K, J ) + TEMP1    *A( K, I )
                     TEMP2     = TEMP2     + B( K, J )*A( K, I )
   50             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J ) +
     $                           TEMP1*A( I, I ) + ALPHA*TEMP2
                  END IF
   60          CONTINUE
   70       CONTINUE
         ELSE
            DO 100, J = 1, N
               DO 90, I = M, 1, -1
                  TEMP1 = ALPHA*B( I, J )
                  TEMP2 = ZERO
                  DO 80, K = I + 1, M
                     C( K, J ) = C( K, J ) + TEMP1    *A( K, I )
                     TEMP2     = TEMP2     + B( K, J )*A( K, I )
   80             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J ) +
     $                           TEMP1*A( I, I ) + ALPHA*TEMP2
                  END IF
   90          CONTINUE
  100       CONTINUE
         END IF
      ELSE
*
*        Form  C := alpha*B*A + beta*C.
*
         DO 170, J = 1, N
            TEMP1 = ALPHA*A( J, J )
            IF( BETA.EQ.ZERO )THEN
               DO 110, I = 1, M
                  C( I, J ) = TEMP1*B( I, J )
  110          CONTINUE
            ELSE
               DO 120, I = 1, M
                  C( I, J ) = BETA*C( I, J ) + TEMP1*B( I, J )
  120          CONTINUE
            END IF
            DO 140, K = 1, J - 1
               IF( UPPER )THEN
                  TEMP1 = ALPHA*A( K, J )
               ELSE
                  TEMP1 = ALPHA*A( J, K )
               END IF
               DO 130, I = 1, M
                  C( I, J ) = C( I, J ) + TEMP1*B( I, K )
  130          CONTINUE
  140       CONTINUE
            DO 160, K = J + 1, N
               IF( UPPER )THEN
                  TEMP1 = ALPHA*A( J, K )
               ELSE
                  TEMP1 = ALPHA*A( K, J )
               END IF
               DO 150, I = 1, M
                  C( I, J ) = C( I, J ) + TEMP1*B( I, K )
  150          CONTINUE
  160       CONTINUE
  170    CONTINUE
      END IF
*
      RETURN
*
*     End of ZSYMM .
*
      END
      SUBROUTINE ZSYR2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB,
     $                   BETA, C, LDC )
*     .. Scalar Arguments ..
      CHARACTER*1        UPLO, TRANS
      INTEGER            N, K, LDA, LDB, LDC
      COMPLEX*16         ALPHA, BETA
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), B( LDB, * ), C( LDC, * )
*     ..
*
*  Purpose
*  =======
*
*  ZSYR2K  performs one of the symmetric rank 2k operations
*
*     C := alpha*A*B' + alpha*B*A' + beta*C,
*
*  or
*
*     C := alpha*A'*B + alpha*B'*A + beta*C,
*
*  where  alpha and beta  are scalars,  C is an  n by n symmetric matrix
*  and  A and B  are  n by k  matrices  in the  first  case  and  k by n
*  matrices in the second case.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On  entry,   UPLO  specifies  whether  the  upper  or  lower
*           triangular  part  of the  array  C  is to be  referenced  as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry,  TRANS  specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'    C := alpha*A*B' + alpha*B*A' +
*                                         beta*C.
*
*              TRANS = 'T' or 't'    C := alpha*A'*B + alpha*B'*A +
*                                         beta*C.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry,  N specifies the order of the matrix C.  N must be
*           at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
*           of  columns  of the  matrices  A and B,  and on  entry  with
*           TRANS = 'T' or 't',  K  specifies  the number of rows of the
*           matrices  A and B.  K must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is
*           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
*           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
*           part of the array  A  must contain the matrix  A,  otherwise
*           the leading  k by n  part of the array  A  must contain  the
*           matrix A.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
*           then  LDA must be at least  max( 1, n ), otherwise  LDA must
*           be at least  max( 1, k ).
*           Unchanged on exit.
*
*  B      - COMPLEX*16       array of DIMENSION ( LDB, kb ), where kb is
*           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
*           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
*           part of the array  B  must contain the matrix  B,  otherwise
*           the leading  k by n  part of the array  B  must contain  the
*           matrix B.
*           Unchanged on exit.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
*           then  LDB must be at least  max( 1, n ), otherwise  LDB must
*           be at least  max( 1, k ).
*           Unchanged on exit.
*
*  BETA   - COMPLEX*16      .
*           On entry, BETA specifies the scalar beta.
*           Unchanged on exit.
*
*  C      - COMPLEX*16       array of DIMENSION ( LDC, n ).
*           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
*           upper triangular part of the array C must contain the upper
*           triangular part  of the  symmetric matrix  and the strictly
*           lower triangular part of C is not referenced.  On exit, the
*           upper triangular part of the array  C is overwritten by the
*           upper triangular part of the updated matrix.
*           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
*           lower triangular part of the array C must contain the lower
*           triangular part  of the  symmetric matrix  and the strictly
*           upper triangular part of C is not referenced.  On exit, the
*           lower triangular part of the array  C is overwritten by the
*           lower triangular part of the updated matrix.
*
*  LDC    - INTEGER.
*           On entry, LDC specifies the first dimension of C as declared
*           in  the  calling  (sub)  program.   LDC  must  be  at  least
*           max( 1, n ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, INFO, J, L, NROWA
      COMPLEX*16         TEMP1, TEMP2
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      IF( LSAME( TRANS, 'N' ) )THEN
         NROWA = N
      ELSE
         NROWA = K
      END IF
      UPPER = LSAME( UPLO, 'U' )
*
      INFO = 0
      IF(      ( .NOT.UPPER               ).AND.
     $         ( .NOT.LSAME( UPLO , 'L' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.LSAME( TRANS, 'N' ) ).AND.
     $         ( .NOT.LSAME( TRANS, 'T' ) )      )THEN
         INFO = 2
      ELSE IF( N  .LT.0               )THEN
         INFO = 3
      ELSE IF( K  .LT.0               )THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 7
      ELSE IF( LDB.LT.MAX( 1, NROWA ) )THEN
         INFO = 9
      ELSE IF( LDC.LT.MAX( 1, N     ) )THEN
         INFO = 12
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZSYR2K', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.
     $    ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         IF( UPPER )THEN
            IF( BETA.EQ.ZERO )THEN
               DO 20, J = 1, N
                  DO 10, I = 1, J
                     C( I, J ) = ZERO
   10             CONTINUE
   20          CONTINUE
            ELSE
               DO 40, J = 1, N
                  DO 30, I = 1, J
                     C( I, J ) = BETA*C( I, J )
   30             CONTINUE
   40          CONTINUE
            END IF
         ELSE
            IF( BETA.EQ.ZERO )THEN
               DO 60, J = 1, N
                  DO 50, I = J, N
                     C( I, J ) = ZERO
   50             CONTINUE
   60          CONTINUE
            ELSE
               DO 80, J = 1, N
                  DO 70, I = J, N
                     C( I, J ) = BETA*C( I, J )
   70             CONTINUE
   80          CONTINUE
            END IF
         END IF
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  C := alpha*A*B' + alpha*B*A' + C.
*
         IF( UPPER )THEN
            DO 130, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 90, I = 1, J
                     C( I, J ) = ZERO
   90             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 100, I = 1, J
                     C( I, J ) = BETA*C( I, J )
  100             CONTINUE
               END IF
               DO 120, L = 1, K
c                  IF( ( A( J, L ).NE.ZERO ).OR.
c     $                ( B( J, L ).NE.ZERO )     )THEN
                     TEMP1 = ALPHA*B( J, L )
                     TEMP2 = ALPHA*A( J, L )
                     DO 110, I = 1, J
                        C( I, J ) = C( I, J ) + A( I, L )*TEMP1 +
     $                                          B( I, L )*TEMP2
  110                CONTINUE
c                  END IF
  120          CONTINUE
  130       CONTINUE
         ELSE
            DO 180, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 140, I = J, N
                     C( I, J ) = ZERO
  140             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 150, I = J, N
                     C( I, J ) = BETA*C( I, J )
  150             CONTINUE
               END IF
               DO 170, L = 1, K
c                  IF( ( A( J, L ).NE.ZERO ).OR.
c     $                ( B( J, L ).NE.ZERO )     )THEN
                     TEMP1 = ALPHA*B( J, L )
                     TEMP2 = ALPHA*A( J, L )
                     DO 160, I = J, N
                        C( I, J ) = C( I, J ) + A( I, L )*TEMP1 +
     $                                          B( I, L )*TEMP2
  160                CONTINUE
c                  END IF
  170          CONTINUE
  180       CONTINUE
         END IF
      ELSE
*
*        Form  C := alpha*A'*B + alpha*B'*A + C.
*
         IF( UPPER )THEN
            DO 210, J = 1, N
               DO 200, I = 1, J
                  TEMP1 = ZERO
                  TEMP2 = ZERO
                  DO 190, L = 1, K
                     TEMP1 = TEMP1 + A( L, I )*B( L, J )
                     TEMP2 = TEMP2 + B( L, I )*A( L, J )
  190             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP1 + ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J ) +
     $                           ALPHA*TEMP1 + ALPHA*TEMP2
                  END IF
  200          CONTINUE
  210       CONTINUE
         ELSE
            DO 240, J = 1, N
               DO 230, I = J, N
                  TEMP1 = ZERO
                  TEMP2 = ZERO
                  DO 220, L = 1, K
                     TEMP1 = TEMP1 + A( L, I )*B( L, J )
                     TEMP2 = TEMP2 + B( L, I )*A( L, J )
  220             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP1 + ALPHA*TEMP2
                  ELSE
                     C( I, J ) = BETA *C( I, J ) +
     $                           ALPHA*TEMP1 + ALPHA*TEMP2
                  END IF
  230          CONTINUE
  240       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZSYR2K.
*
      END
      SUBROUTINE ZSYRK ( UPLO, TRANS, N, K, ALPHA, A, LDA,
     $                   BETA, C, LDC )
*     .. Scalar Arguments ..
      CHARACTER*1        UPLO, TRANS
      INTEGER            N, K, LDA, LDC
      COMPLEX*16         ALPHA, BETA
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), C( LDC, * )
*     ..
*
*  Purpose
*  =======
*
*  ZSYRK  performs one of the symmetric rank k operations
*
*     C := alpha*A*A' + beta*C,
*
*  or
*
*     C := alpha*A'*A + beta*C,
*
*  where  alpha and beta  are scalars,  C is an  n by n symmetric matrix
*  and  A  is an  n by k  matrix in the first case and a  k by n  matrix
*  in the second case.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On  entry,   UPLO  specifies  whether  the  upper  or  lower
*           triangular  part  of the  array  C  is to be  referenced  as
*           follows:
*
*              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
*                                  is to be referenced.
*
*              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
*                                  is to be referenced.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry,  TRANS  specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   C := alpha*A*A' + beta*C.
*
*              TRANS = 'T' or 't'   C := alpha*A'*A + beta*C.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry,  N specifies the order of the matrix C.  N must be
*           at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
*           of  columns   of  the   matrix   A,   and  on   entry   with
*           TRANS = 'T' or 't',  K  specifies  the number of rows of the
*           matrix A.  K must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is
*           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
*           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
*           part of the array  A  must contain the matrix  A,  otherwise
*           the leading  k by n  part of the array  A  must contain  the
*           matrix A.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
*           then  LDA must be at least  max( 1, n ), otherwise  LDA must
*           be at least  max( 1, k ).
*           Unchanged on exit.
*
*  BETA   - COMPLEX*16      .
*           On entry, BETA specifies the scalar beta.
*           Unchanged on exit.
*
*  C      - COMPLEX*16       array of DIMENSION ( LDC, n ).
*           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
*           upper triangular part of the array C must contain the upper
*           triangular part  of the  symmetric matrix  and the strictly
*           lower triangular part of C is not referenced.  On exit, the
*           upper triangular part of the array  C is overwritten by the
*           upper triangular part of the updated matrix.
*           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
*           lower triangular part of the array C must contain the lower
*           triangular part  of the  symmetric matrix  and the strictly
*           upper triangular part of C is not referenced.  On exit, the
*           lower triangular part of the array  C is overwritten by the
*           lower triangular part of the updated matrix.
*
*  LDC    - INTEGER.
*           On entry, LDC specifies the first dimension of C as declared
*           in  the  calling  (sub)  program.   LDC  must  be  at  least
*           max( 1, n ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            I, INFO, J, L, NROWA
      COMPLEX*16         TEMP
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      IF( LSAME( TRANS, 'N' ) )THEN
         NROWA = N
      ELSE
         NROWA = K
      END IF
      UPPER = LSAME( UPLO, 'U' )
*
      INFO = 0
      IF(      ( .NOT.UPPER               ).AND.
     $         ( .NOT.LSAME( UPLO , 'L' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.LSAME( TRANS, 'N' ) ).AND.
     $         ( .NOT.LSAME( TRANS, 'T' ) )      )THEN
         INFO = 2
      ELSE IF( N  .LT.0               )THEN
         INFO = 3
      ELSE IF( K  .LT.0               )THEN
         INFO = 4
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 7
      ELSE IF( LDC.LT.MAX( 1, N     ) )THEN
         INFO = 10
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZSYRK ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.
     $    ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         IF( UPPER )THEN
            IF( BETA.EQ.ZERO )THEN
               DO 20, J = 1, N
                  DO 10, I = 1, J
                     C( I, J ) = ZERO
   10             CONTINUE
   20          CONTINUE
            ELSE
               DO 40, J = 1, N
                  DO 30, I = 1, J
                     C( I, J ) = BETA*C( I, J )
   30             CONTINUE
   40          CONTINUE
            END IF
         ELSE
            IF( BETA.EQ.ZERO )THEN
               DO 60, J = 1, N
                  DO 50, I = J, N
                     C( I, J ) = ZERO
   50             CONTINUE
   60          CONTINUE
            ELSE
               DO 80, J = 1, N
                  DO 70, I = J, N
                     C( I, J ) = BETA*C( I, J )
   70             CONTINUE
   80          CONTINUE
            END IF
         END IF
         RETURN
      END IF
*
*     Start the operations.
*
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  C := alpha*A*A' + beta*C.
*
         IF( UPPER )THEN
            DO 130, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 90, I = 1, J
                     C( I, J ) = ZERO
   90             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 100, I = 1, J
                     C( I, J ) = BETA*C( I, J )
  100             CONTINUE
               END IF
               DO 120, L = 1, K
c                  IF( A( J, L ).NE.ZERO )THEN
                     TEMP = ALPHA*A( J, L )
                     DO 110, I = 1, J
                        C( I, J ) = C( I, J ) + TEMP*A( I, L )
  110                CONTINUE
c                  END IF
  120          CONTINUE
  130       CONTINUE
         ELSE
            DO 180, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 140, I = J, N
                     C( I, J ) = ZERO
  140             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 150, I = J, N
                     C( I, J ) = BETA*C( I, J )
  150             CONTINUE
               END IF
               DO 170, L = 1, K
c                  IF( A( J, L ).NE.ZERO )THEN
                     TEMP      = ALPHA*A( J, L )
                     DO 160, I = J, N
                        C( I, J ) = C( I, J ) + TEMP*A( I, L )
  160                CONTINUE
c                  END IF
  170          CONTINUE
  180       CONTINUE
         END IF
      ELSE
*
*        Form  C := alpha*A'*A + beta*C.
*
         IF( UPPER )THEN
            DO 210, J = 1, N
               DO 200, I = 1, J
                  TEMP = ZERO
                  DO 190, L = 1, K
                     TEMP = TEMP + A( L, I )*A( L, J )
  190             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  200          CONTINUE
  210       CONTINUE
         ELSE
            DO 240, J = 1, N
               DO 230, I = J, N
                  TEMP = ZERO
                  DO 220, L = 1, K
                     TEMP = TEMP + A( L, I )*A( L, J )
  220             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  230          CONTINUE
  240       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZSYRK .
*
      END
      SUBROUTINE ZTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
*     .. Scalar Arguments ..
      INTEGER            INCX, K, LDA, N
      CHARACTER*1        DIAG, TRANS, UPLO
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZTBMV  performs one of the matrix-vector operations
*
*     x := A*x,   or   x := A'*x,   or   x := conjg( A' )*x,
*
*  where x is an n element vector and  A is an n by n unit, or non-unit,
*  upper or lower triangular band matrix, with ( k + 1 ) diagonals.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   x := A*x.
*
*              TRANS = 'T' or 't'   x := A'*x.
*
*              TRANS = 'C' or 'c'   x := conjg( A' )*x.
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit
*           triangular as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry with UPLO = 'U' or 'u', K specifies the number of
*           super-diagonals of the matrix A.
*           On entry with UPLO = 'L' or 'l', K specifies the number of
*           sub-diagonals of the matrix A.
*           K must satisfy  0 .le. K.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
*           by n part of the array A must contain the upper triangular
*           band part of the matrix of coefficients, supplied column by
*           column, with the leading diagonal of the matrix in row
*           ( k + 1 ) of the array, the first super-diagonal starting at
*           position 2 in row k, and so on. The top left k by k triangle
*           of the array A is not referenced.
*           The following program segment will transfer an upper
*           triangular band matrix from conventional full matrix storage
*           to band storage:
*
*                 DO 20, J = 1, N
*                    M = K + 1 - J
*                    DO 10, I = MAX( 1, J - K ), J
*                       A( M + I, J ) = matrix( I, J )
*              10    CONTINUE
*              20 CONTINUE
*
*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
*           by n part of the array A must contain the lower triangular
*           band part of the matrix of coefficients, supplied column by
*           column, with the leading diagonal of the matrix in row 1 of
*           the array, the first sub-diagonal starting at position 1 in
*           row 2, and so on. The bottom right k by k triangle of the
*           array A is not referenced.
*           The following program segment will transfer a lower
*           triangular band matrix from conventional full matrix storage
*           to band storage:
*
*                 DO 20, J = 1, N
*                    M = 1 - J
*                    DO 10, I = J, MIN( N, J + K )
*                       A( M + I, J ) = matrix( I, J )
*              10    CONTINUE
*              20 CONTINUE
*
*           Note that when DIAG = 'U' or 'u' the elements of the array A
*           corresponding to the diagonal elements of the matrix are not
*           referenced, but are assumed to be unity.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           ( k + 1 ).
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x. On exit, X is overwritten with the
*           tranformed vector x.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, J, JX, KPLUS1, KX, L
      LOGICAL            NOCONJ, NOUNIT
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX, MIN
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO , 'U' ).AND.
     $         .NOT.LSAME( UPLO , 'L' )      )THEN
         INFO = 1
      ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
     $         .NOT.LSAME( TRANS, 'T' ).AND.
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
         INFO = 2
      ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
     $         .NOT.LSAME( DIAG , 'N' )      )THEN
         INFO = 3
      ELSE IF( N.LT.0 )THEN
         INFO = 4
      ELSE IF( K.LT.0 )THEN
         INFO = 5
      ELSE IF( LDA.LT.( K + 1 ) )THEN
         INFO = 7
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 9
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZTBMV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
*
      NOCONJ = LSAME( TRANS, 'T' )
      NOUNIT = LSAME( DIAG , 'N' )
*
*     Set up the start point in X if the increment is not unity. This
*     will be  ( N - 1 )*INCX   too small for descending loops.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
      IF( LSAME( TRANS, 'N' ) )THEN
*
*         Form  x := A*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            KPLUS1 = K + 1
            IF( INCX.EQ.1 )THEN
               DO 20, J = 1, N
c                  IF( X( J ).NE.ZERO )THEN
                     TEMP = X( J )
                     L    = KPLUS1 - J
                     DO 10, I = MAX( 1, J - K ), J - 1
                        X( I ) = X( I ) + TEMP*A( L + I, J )
   10                CONTINUE
                     IF( NOUNIT )
     $                  X( J ) = X( J )*A( KPLUS1, J )
c                  END IF
   20          CONTINUE
            ELSE
               JX = KX
               DO 40, J = 1, N
c                  IF( X( JX ).NE.ZERO )THEN
                     TEMP = X( JX )
                     IX   = KX
                     L    = KPLUS1  - J
                     DO 30, I = MAX( 1, J - K ), J - 1
                        X( IX ) = X( IX ) + TEMP*A( L + I, J )
                        IX      = IX      + INCX
   30                CONTINUE
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )*A( KPLUS1, J )
c                  END IF
                  JX = JX + INCX
                  IF( J.GT.K )
     $               KX = KX + INCX
   40          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 60, J = N, 1, -1
c                  IF( X( J ).NE.ZERO )THEN
                     TEMP = X( J )
                     L    = 1      - J
                     DO 50, I = MIN( N, J + K ), J + 1, -1
                        X( I ) = X( I ) + TEMP*A( L + I, J )
   50                CONTINUE
                     IF( NOUNIT )
     $                  X( J ) = X( J )*A( 1, J )
c                  END IF
   60          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 80, J = N, 1, -1
c                  IF( X( JX ).NE.ZERO )THEN
                     TEMP = X( JX )
                     IX   = KX
                     L    = 1       - J
                     DO 70, I = MIN( N, J + K ), J + 1, -1
                        X( IX ) = X( IX ) + TEMP*A( L + I, J )
                        IX      = IX      - INCX
   70                CONTINUE
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )*A( 1, J )
c                  END IF
                  JX = JX - INCX
                  IF( ( N - J ).GE.K )
     $               KX = KX - INCX
   80          CONTINUE
            END IF
         END IF
      ELSE
*
*        Form  x := A'*x  or  x := conjg( A' )*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            KPLUS1 = K + 1
            IF( INCX.EQ.1 )THEN
               DO 110, J = N, 1, -1
                  TEMP = X( J )
                  L    = KPLUS1 - J
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( KPLUS1, J )
                     DO 90, I = J - 1, MAX( 1, J - K ), -1
                        TEMP = TEMP + A( L + I, J )*X( I )
   90                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( A( KPLUS1, J ) )
                     DO 100, I = J - 1, MAX( 1, J - K ), -1
                        TEMP = TEMP + DCONJG( A( L + I, J ) )*X( I )
  100                CONTINUE
                  END IF
                  X( J ) = TEMP
  110          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 140, J = N, 1, -1
                  TEMP = X( JX )
                  KX   = KX      - INCX
                  IX   = KX
                  L    = KPLUS1  - J
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( KPLUS1, J )
                     DO 120, I = J - 1, MAX( 1, J - K ), -1
                        TEMP = TEMP + A( L + I, J )*X( IX )
                        IX   = IX   - INCX
  120                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( A( KPLUS1, J ) )
                     DO 130, I = J - 1, MAX( 1, J - K ), -1
                        TEMP = TEMP + DCONJG( A( L + I, J ) )*X( IX )
                        IX   = IX   - INCX
  130                CONTINUE
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   - INCX
  140          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 170, J = 1, N
                  TEMP = X( J )
                  L    = 1      - J
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( 1, J )
                     DO 150, I = J + 1, MIN( N, J + K )
                        TEMP = TEMP + A( L + I, J )*X( I )
  150                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( A( 1, J ) )
                     DO 160, I = J + 1, MIN( N, J + K )
                        TEMP = TEMP + DCONJG( A( L + I, J ) )*X( I )
  160                CONTINUE
                  END IF
                  X( J ) = TEMP
  170          CONTINUE
            ELSE
               JX = KX
               DO 200, J = 1, N
                  TEMP = X( JX )
                  KX   = KX      + INCX
                  IX   = KX
                  L    = 1       - J
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*A( 1, J )
                     DO 180, I = J + 1, MIN( N, J + K )
                        TEMP = TEMP + A( L + I, J )*X( IX )
                        IX   = IX   + INCX
  180                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( A( 1, J ) )
                     DO 190, I = J + 1, MIN( N, J + K )
                        TEMP = TEMP + DCONJG( A( L + I, J ) )*X( IX )
                        IX   = IX   + INCX
  190                CONTINUE
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   + INCX
  200          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of ZTBMV .
*
      END
      SUBROUTINE ZTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
*     .. Scalar Arguments ..
      INTEGER            INCX, K, LDA, N
      CHARACTER*1        DIAG, TRANS, UPLO
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZTBSV  solves one of the systems of equations
*
*     A*x = b,   or   A'*x = b,   or   conjg( A' )*x = b,
*
*  where b and x are n element vectors and A is an n by n unit, or
*  non-unit, upper or lower triangular band matrix, with ( k + 1 )
*  diagonals.
*
*  No test for singularity or near-singularity is included in this
*  routine. Such tests must be performed before calling this routine.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the equations to be solved as
*           follows:
*
*              TRANS = 'N' or 'n'   A*x = b.
*
*              TRANS = 'T' or 't'   A'*x = b.
*
*              TRANS = 'C' or 'c'   conjg( A' )*x = b.
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit
*           triangular as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry with UPLO = 'U' or 'u', K specifies the number of
*           super-diagonals of the matrix A.
*           On entry with UPLO = 'L' or 'l', K specifies the number of
*           sub-diagonals of the matrix A.
*           K must satisfy  0 .le. K.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
*           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
*           by n part of the array A must contain the upper triangular
*           band part of the matrix of coefficients, supplied column by
*           column, with the leading diagonal of the matrix in row
*           ( k + 1 ) of the array, the first super-diagonal starting at
*           position 2 in row k, and so on. The top left k by k triangle
*           of the array A is not referenced.
*           The following program segment will transfer an upper
*           triangular band matrix from conventional full matrix storage
*           to band storage:
*
*                 DO 20, J = 1, N
*                    M = K + 1 - J
*                    DO 10, I = MAX( 1, J - K ), J
*                       A( M + I, J ) = matrix( I, J )
*              10    CONTINUE
*              20 CONTINUE
*
*           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
*           by n part of the array A must contain the lower triangular
*           band part of the matrix of coefficients, supplied column by
*           column, with the leading diagonal of the matrix in row 1 of
*           the array, the first sub-diagonal starting at position 1 in
*           row 2, and so on. The bottom right k by k triangle of the
*           array A is not referenced.
*           The following program segment will transfer a lower
*           triangular band matrix from conventional full matrix storage
*           to band storage:
*
*                 DO 20, J = 1, N
*                    M = 1 - J
*                    DO 10, I = J, MIN( N, J + K )
*                       A( M + I, J ) = matrix( I, J )
*              10    CONTINUE
*              20 CONTINUE
*
*           Note that when DIAG = 'U' or 'u' the elements of the array A
*           corresponding to the diagonal elements of the matrix are not
*           referenced, but are assumed to be unity.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           ( k + 1 ).
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element right-hand side vector b. On exit, X is overwritten
*           with the solution vector x.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, J, JX, KPLUS1, KX, L
      LOGICAL            NOCONJ, NOUNIT
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX, MIN
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO , 'U' ).AND.
     $         .NOT.LSAME( UPLO , 'L' )      )THEN
         INFO = 1
      ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
     $         .NOT.LSAME( TRANS, 'T' ).AND.
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
         INFO = 2
      ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
     $         .NOT.LSAME( DIAG , 'N' )      )THEN
         INFO = 3
      ELSE IF( N.LT.0 )THEN
         INFO = 4
      ELSE IF( K.LT.0 )THEN
         INFO = 5
      ELSE IF( LDA.LT.( K + 1 ) )THEN
         INFO = 7
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 9
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZTBSV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
*
      NOCONJ = LSAME( TRANS, 'T' )
      NOUNIT = LSAME( DIAG , 'N' )
*
*     Set up the start point in X if the increment is not unity. This
*     will be  ( N - 1 )*INCX  too small for descending loops.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed by sequentially with one pass through A.
*
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  x := inv( A )*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            KPLUS1 = K + 1
            IF( INCX.EQ.1 )THEN
               DO 20, J = N, 1, -1
c                  IF( X( J ).NE.ZERO )THEN
                     L = KPLUS1 - J
                     IF( NOUNIT )
     $                  X( J ) = X( J )/A( KPLUS1, J )
                     TEMP = X( J )
                     DO 10, I = J - 1, MAX( 1, J - K ), -1
                        X( I ) = X( I ) - TEMP*A( L + I, J )
   10                CONTINUE
c                  END IF
   20          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 40, J = N, 1, -1
                  KX = KX - INCX
c                  IF( X( JX ).NE.ZERO )THEN
                     IX = KX
                     L  = KPLUS1 - J
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )/A( KPLUS1, J )
                     TEMP = X( JX )
                     DO 30, I = J - 1, MAX( 1, J - K ), -1
                        X( IX ) = X( IX ) - TEMP*A( L + I, J )
                        IX      = IX      - INCX
   30                CONTINUE
c                  END IF
                  JX = JX - INCX
   40          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 60, J = 1, N
c                  IF( X( J ).NE.ZERO )THEN
                     L = 1 - J
                     IF( NOUNIT )
     $                  X( J ) = X( J )/A( 1, J )
                     TEMP = X( J )
                     DO 50, I = J + 1, MIN( N, J + K )
                        X( I ) = X( I ) - TEMP*A( L + I, J )
   50                CONTINUE
c                  END IF
   60          CONTINUE
            ELSE
               JX = KX
               DO 80, J = 1, N
                  KX = KX + INCX
c                  IF( X( JX ).NE.ZERO )THEN
                     IX = KX
                     L  = 1  - J
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )/A( 1, J )
                     TEMP = X( JX )
                     DO 70, I = J + 1, MIN( N, J + K )
                        X( IX ) = X( IX ) - TEMP*A( L + I, J )
                        IX      = IX      + INCX
   70                CONTINUE
c                  END IF
                  JX = JX + INCX
   80          CONTINUE
            END IF
         END IF
      ELSE
*
*        Form  x := inv( A' )*x  or  x := inv( conjg( A') )*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            KPLUS1 = K + 1
            IF( INCX.EQ.1 )THEN
               DO 110, J = 1, N
                  TEMP = X( J )
                  L    = KPLUS1 - J
                  IF( NOCONJ )THEN
                     DO 90, I = MAX( 1, J - K ), J - 1
                        TEMP = TEMP - A( L + I, J )*X( I )
   90                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/A( KPLUS1, J )
                  ELSE
                     DO 100, I = MAX( 1, J - K ), J - 1
                        TEMP = TEMP - DCONJG( A( L + I, J ) )*X( I )
  100                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( A( KPLUS1, J ) )
                  END IF
                  X( J ) = TEMP
  110          CONTINUE
            ELSE
               JX = KX
               DO 140, J = 1, N
                  TEMP = X( JX )
                  IX   = KX
                  L    = KPLUS1  - J
                  IF( NOCONJ )THEN
                     DO 120, I = MAX( 1, J - K ), J - 1
                        TEMP = TEMP - A( L + I, J )*X( IX )
                        IX   = IX   + INCX
  120                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/A( KPLUS1, J )
                  ELSE
                     DO 130, I = MAX( 1, J - K ), J - 1
                        TEMP = TEMP - DCONJG( A( L + I, J ) )*X( IX )
                        IX   = IX   + INCX
  130                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( A( KPLUS1, J ) )
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   + INCX
                  IF( J.GT.K )
     $               KX = KX + INCX
  140          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 170, J = N, 1, -1
                  TEMP = X( J )
                  L    = 1      - J
                  IF( NOCONJ )THEN
                     DO 150, I = MIN( N, J + K ), J + 1, -1
                        TEMP = TEMP - A( L + I, J )*X( I )
  150                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/A( 1, J )
                  ELSE
                     DO 160, I = MIN( N, J + K ), J + 1, -1
                        TEMP = TEMP - DCONJG( A( L + I, J ) )*X( I )
  160                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( A( 1, J ) )
                  END IF
                  X( J ) = TEMP
  170          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 200, J = N, 1, -1
                  TEMP = X( JX )
                  IX   = KX
                  L    = 1       - J
                  IF( NOCONJ )THEN
                     DO 180, I = MIN( N, J + K ), J + 1, -1
                        TEMP = TEMP - A( L + I, J )*X( IX )
                        IX   = IX   - INCX
  180                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/A( 1, J )
                  ELSE
                     DO 190, I = MIN( N, J + K ), J + 1, -1
                        TEMP = TEMP - DCONJG( A( L + I, J ) )*X( IX )
                        IX   = IX   - INCX
  190                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( A( 1, J ) )
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   - INCX
                  IF( ( N - J ).GE.K )
     $               KX = KX - INCX
  200          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of ZTBSV .
*
      END
      SUBROUTINE ZTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      CHARACTER*1        DIAG, TRANS, UPLO
*     .. Array Arguments ..
      COMPLEX*16         AP( * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZTPMV  performs one of the matrix-vector operations
*
*     x := A*x,   or   x := A'*x,   or   x := conjg( A' )*x,
*
*  where x is an n element vector and  A is an n by n unit, or non-unit,
*  upper or lower triangular matrix, supplied in packed form.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   x := A*x.
*
*              TRANS = 'T' or 't'   x := A'*x.
*
*              TRANS = 'C' or 'c'   x := conjg( A' )*x.
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit
*           triangular as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  AP     - COMPLEX*16       array of DIMENSION at least
*           ( ( n*( n + 1 ) )/2 ).
*           Before entry with  UPLO = 'U' or 'u', the array AP must
*           contain the upper triangular matrix packed sequentially,
*           column by column, so that AP( 1 ) contains a( 1, 1 ),
*           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
*           respectively, and so on.
*           Before entry with UPLO = 'L' or 'l', the array AP must
*           contain the lower triangular matrix packed sequentially,
*           column by column, so that AP( 1 ) contains a( 1, 1 ),
*           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
*           respectively, and so on.
*           Note that when  DIAG = 'U' or 'u', the diagonal elements of
*           A are not referenced, but are assumed to be unity.
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x. On exit, X is overwritten with the
*           tranformed vector x.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, J, JX, K, KK, KX
      LOGICAL            NOCONJ, NOUNIT
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO , 'U' ).AND.
     $         .NOT.LSAME( UPLO , 'L' )      )THEN
         INFO = 1
      ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
     $         .NOT.LSAME( TRANS, 'T' ).AND.
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
         INFO = 2
      ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
     $         .NOT.LSAME( DIAG , 'N' )      )THEN
         INFO = 3
      ELSE IF( N.LT.0 )THEN
         INFO = 4
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 7
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZTPMV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
*
      NOCONJ = LSAME( TRANS, 'T' )
      NOUNIT = LSAME( DIAG , 'N' )
*
*     Set up the start point in X if the increment is not unity. This
*     will be  ( N - 1 )*INCX  too small for descending loops.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of AP are
*     accessed sequentially with one pass through AP.
*
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  x:= A*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            KK = 1
            IF( INCX.EQ.1 )THEN
               DO 20, J = 1, N
c                  IF( X( J ).NE.ZERO )THEN
                     TEMP = X( J )
                     K    = KK
                     DO 10, I = 1, J - 1
                        X( I ) = X( I ) + TEMP*AP( K )
                        K      = K      + 1
   10                CONTINUE
                     IF( NOUNIT )
     $                  X( J ) = X( J )*AP( KK + J - 1 )
c                  END IF
                  KK = KK + J
   20          CONTINUE
            ELSE
               JX = KX
               DO 40, J = 1, N
c                  IF( X( JX ).NE.ZERO )THEN
                     TEMP = X( JX )
                     IX   = KX
                     DO 30, K = KK, KK + J - 2
                        X( IX ) = X( IX ) + TEMP*AP( K )
                        IX      = IX      + INCX
   30                CONTINUE
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )*AP( KK + J - 1 )
c                  END IF
                  JX = JX + INCX
                  KK = KK + J
   40          CONTINUE
            END IF
         ELSE
            KK = ( N*( N + 1 ) )/2
            IF( INCX.EQ.1 )THEN
               DO 60, J = N, 1, -1
c                  IF( X( J ).NE.ZERO )THEN
                     TEMP = X( J )
                     K    = KK
                     DO 50, I = N, J + 1, -1
                        X( I ) = X( I ) + TEMP*AP( K )
                        K      = K      - 1
   50                CONTINUE
                     IF( NOUNIT )
     $                  X( J ) = X( J )*AP( KK - N + J )
c                  END IF
                  KK = KK - ( N - J + 1 )
   60          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 80, J = N, 1, -1
c                  IF( X( JX ).NE.ZERO )THEN
                     TEMP = X( JX )
                     IX   = KX
                     DO 70, K = KK, KK - ( N - ( J + 1 ) ), -1
                        X( IX ) = X( IX ) + TEMP*AP( K )
                        IX      = IX      - INCX
   70                CONTINUE
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )*AP( KK - N + J )
c                  END IF
                  JX = JX - INCX
                  KK = KK - ( N - J + 1 )
   80          CONTINUE
            END IF
         END IF
      ELSE
*
*        Form  x := A'*x  or  x := conjg( A' )*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            KK = ( N*( N + 1 ) )/2
            IF( INCX.EQ.1 )THEN
               DO 110, J = N, 1, -1
                  TEMP = X( J )
                  K    = KK     - 1
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*AP( KK )
                     DO 90, I = J - 1, 1, -1
                        TEMP = TEMP + AP( K )*X( I )
                        K    = K    - 1
   90                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( AP( KK ) )
                     DO 100, I = J - 1, 1, -1
                        TEMP = TEMP + DCONJG( AP( K ) )*X( I )
                        K    = K    - 1
  100                CONTINUE
                  END IF
                  X( J ) = TEMP
                  KK     = KK   - J
  110          CONTINUE
            ELSE
               JX = KX + ( N - 1 )*INCX
               DO 140, J = N, 1, -1
                  TEMP = X( JX )
                  IX   = JX
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*AP( KK )
                     DO 120, K = KK - 1, KK - J + 1, -1
                        IX   = IX   - INCX
                        TEMP = TEMP + AP( K )*X( IX )
  120                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( AP( KK ) )
                     DO 130, K = KK - 1, KK - J + 1, -1
                        IX   = IX   - INCX
                        TEMP = TEMP + DCONJG( AP( K ) )*X( IX )
  130                CONTINUE
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   - INCX
                  KK      = KK   - J
  140          CONTINUE
            END IF
         ELSE
            KK = 1
            IF( INCX.EQ.1 )THEN
               DO 170, J = 1, N
                  TEMP = X( J )
                  K    = KK     + 1
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*AP( KK )
                     DO 150, I = J + 1, N
                        TEMP = TEMP + AP( K )*X( I )
                        K    = K    + 1
  150                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( AP( KK ) )
                     DO 160, I = J + 1, N
                        TEMP = TEMP + DCONJG( AP( K ) )*X( I )
                        K    = K    + 1
  160                CONTINUE
                  END IF
                  X( J ) = TEMP
                  KK     = KK   + ( N - J + 1 )
  170          CONTINUE
            ELSE
               JX = KX
               DO 200, J = 1, N
                  TEMP = X( JX )
                  IX   = JX
                  IF( NOCONJ )THEN
                     IF( NOUNIT )
     $                  TEMP = TEMP*AP( KK )
                     DO 180, K = KK + 1, KK + N - J
                        IX   = IX   + INCX
                        TEMP = TEMP + AP( K )*X( IX )
  180                CONTINUE
                  ELSE
                     IF( NOUNIT )
     $                  TEMP = TEMP*DCONJG( AP( KK ) )
                     DO 190, K = KK + 1, KK + N - J
                        IX   = IX   + INCX
                        TEMP = TEMP + DCONJG( AP( K ) )*X( IX )
  190                CONTINUE
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   + INCX
                  KK      = KK   + ( N - J + 1 )
  200          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of ZTPMV .
*
      END
      SUBROUTINE ZTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      CHARACTER*1        DIAG, TRANS, UPLO
*     .. Array Arguments ..
      COMPLEX*16         AP( * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZTPSV  solves one of the systems of equations
*
*     A*x = b,   or   A'*x = b,   or   conjg( A' )*x = b,
*
*  where b and x are n element vectors and A is an n by n unit, or
*  non-unit, upper or lower triangular matrix, supplied in packed form.
*
*  No test for singularity or near-singularity is included in this
*  routine. Such tests must be performed before calling this routine.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the equations to be solved as
*           follows:
*
*              TRANS = 'N' or 'n'   A*x = b.
*
*              TRANS = 'T' or 't'   A'*x = b.
*
*              TRANS = 'C' or 'c'   conjg( A' )*x = b.
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit
*           triangular as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  AP     - COMPLEX*16       array of DIMENSION at least
*           ( ( n*( n + 1 ) )/2 ).
*           Before entry with  UPLO = 'U' or 'u', the array AP must
*           contain the upper triangular matrix packed sequentially,
*           column by column, so that AP( 1 ) contains a( 1, 1 ),
*           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
*           respectively, and so on.
*           Before entry with UPLO = 'L' or 'l', the array AP must
*           contain the lower triangular matrix packed sequentially,
*           column by column, so that AP( 1 ) contains a( 1, 1 ),
*           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
*           respectively, and so on.
*           Note that when  DIAG = 'U' or 'u', the diagonal elements of
*           A are not referenced, but are assumed to be unity.
*           Unchanged on exit.
*
*  X      - COMPLEX*16       array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element right-hand side vector b. On exit, X is overwritten
*           with the solution vector x.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     .. Local Scalars ..
      COMPLEX*16         TEMP
      INTEGER            I, INFO, IX, J, JX, K, KK, KX
      LOGICAL            NOCONJ, NOUNIT
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( UPLO , 'U' ).AND.
     $         .NOT.LSAME( UPLO , 'L' )      )THEN
         INFO = 1
      ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
     $         .NOT.LSAME( TRANS, 'T' ).AND.
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
         INFO = 2
      ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
     $         .NOT.LSAME( DIAG , 'N' )      )THEN
         INFO = 3
      ELSE IF( N.LT.0 )THEN
         INFO = 4
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 7
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZTPSV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
*
      NOCONJ = LSAME( TRANS, 'T' )
      NOUNIT = LSAME( DIAG , 'N' )
*
*     Set up the start point in X if the increment is not unity. This
*     will be  ( N - 1 )*INCX  too small for descending loops.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of AP are
*     accessed sequentially with one pass through AP.
*
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  x := inv( A )*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            KK = ( N*( N + 1 ) )/2
            IF( INCX.EQ.1 )THEN
               DO 20, J = N, 1, -1
c                  IF( X( J ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( J ) = X( J )/AP( KK )
                     TEMP = X( J )
                     K    = KK     - 1
                     DO 10, I = J - 1, 1, -1
                        X( I ) = X( I ) - TEMP*AP( K )
                        K      = K      - 1
   10                CONTINUE
c                  END IF
                  KK = KK - J
   20          CONTINUE
            ELSE
               JX = KX + ( N - 1 )*INCX
               DO 40, J = N, 1, -1
c                  IF( X( JX ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )/AP( KK )
                     TEMP = X( JX )
                     IX   = JX
                     DO 30, K = KK - 1, KK - J + 1, -1
                        IX      = IX      - INCX
                        X( IX ) = X( IX ) - TEMP*AP( K )
   30                CONTINUE
c                  END IF
                  JX = JX - INCX
                  KK = KK - J
   40          CONTINUE
            END IF
         ELSE
            KK = 1
            IF( INCX.EQ.1 )THEN
               DO 60, J = 1, N
c                  IF( X( J ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( J ) = X( J )/AP( KK )
                     TEMP = X( J )
                     K    = KK     + 1
                     DO 50, I = J + 1, N
                        X( I ) = X( I ) - TEMP*AP( K )
                        K      = K      + 1
   50                CONTINUE
c                  END IF
                  KK = KK + ( N - J + 1 )
   60          CONTINUE
            ELSE
               JX = KX
               DO 80, J = 1, N
c                  IF( X( JX ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )/AP( KK )
                     TEMP = X( JX )
                     IX   = JX
                     DO 70, K = KK + 1, KK + N - J
                        IX      = IX      + INCX
                        X( IX ) = X( IX ) - TEMP*AP( K )
   70                CONTINUE
c                  END IF
                  JX = JX + INCX
                  KK = KK + ( N - J + 1 )
   80          CONTINUE
            END IF
         END IF
      ELSE
*
*        Form  x := inv( A' )*x  or  x := inv( conjg( A' ) )*x.
*
         IF( LSAME( UPLO, 'U' ) )THEN
            KK = 1
            IF( INCX.EQ.1 )THEN
               DO 110, J = 1, N
                  TEMP = X( J )
                  K    = KK
                  IF( NOCONJ )THEN
                     DO 90, I = 1, J - 1
                        TEMP = TEMP - AP( K )*X( I )
                        K    = K    + 1
   90                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/AP( KK + J - 1 )
                  ELSE
                     DO 100, I = 1, J - 1
                        TEMP = TEMP - DCONJG( AP( K ) )*X( I )
                        K    = K    + 1
  100                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( AP( KK + J - 1 ) )
                  END IF
                  X( J ) = TEMP
                  KK     = KK   + J
  110          CONTINUE
            ELSE
               JX = KX
               DO 140, J = 1, N
                  TEMP = X( JX )
                  IX   = KX
                  IF( NOCONJ )THEN
                     DO 120, K = KK, KK + J - 2
                        TEMP = TEMP - AP( K )*X( IX )
                        IX   = IX   + INCX
  120                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/AP( KK + J - 1 )
                  ELSE
                     DO 130, K = KK, KK + J - 2
                        TEMP = TEMP - DCONJG( AP( K ) )*X( IX )
                        IX   = IX   + INCX
  130                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( AP( KK + J - 1 ) )
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   + INCX
                  KK      = KK   + J
  140          CONTINUE
            END IF
         ELSE
            KK = ( N*( N + 1 ) )/2
            IF( INCX.EQ.1 )THEN
               DO 170, J = N, 1, -1
                  TEMP = X( J )
                  K    = KK
                  IF( NOCONJ )THEN
                     DO 150, I = N, J + 1, -1
                        TEMP = TEMP - AP( K )*X( I )
                        K    = K    - 1
  150                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/AP( KK - N + J )
                  ELSE
                     DO 160, I = N, J + 1, -1
                        TEMP = TEMP - DCONJG( AP( K ) )*X( I )
                        K    = K    - 1
  160                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( AP( KK - N + J ) )
                  END IF
                  X( J ) = TEMP
                  KK     = KK   - ( N - J + 1 )
  170          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 200, J = N, 1, -1
                  TEMP = X( JX )
                  IX   = KX
                  IF( NOCONJ )THEN
                     DO 180, K = KK, KK - ( N - ( J + 1 ) ), -1
                        TEMP = TEMP - AP( K )*X( IX )
                        IX   = IX   - INCX
  180                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/AP( KK - N + J )
                  ELSE
                     DO 190, K = KK, KK - ( N - ( J + 1 ) ), -1
                        TEMP = TEMP - DCONJG( AP( K ) )*X( IX )
                        IX   = IX   - INCX
  190                CONTINUE
                     IF( NOUNIT )
     $                  TEMP = TEMP/DCONJG( AP( KK - N + J ) )
                  END IF
                  X( JX ) = TEMP
                  JX      = JX   - INCX
                  KK      = KK   - ( N - J + 1 )
  200          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of ZTPSV .
*
      END
      SUBROUTINE ZGEMM ( TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB,
     $                   BETA, C, LDC )
*     .. Scalar Arguments ..
      CHARACTER*1        TRANSA, TRANSB
      INTEGER            M, N, K, LDA, LDB, LDC
      COMPLEX*16         ALPHA, BETA
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), B( LDB, * ), C( LDC, * )
*     ..
*
*  Purpose
*  =======
*
*  ZGEMM  performs one of the matrix-matrix operations
*
*     C := alpha*op( A )*op( B ) + beta*C,
*
*  where  op( X ) is one of
*
*     op( X ) = X   or   op( X ) = X'   or   op( X ) = conjg( X' ),
*
*  alpha and beta are scalars, and A, B and C are matrices, with op( A )
*  an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
*
*  Parameters
*  ==========
*
*  TRANSA - CHARACTER*1.
*           On entry, TRANSA specifies the form of op( A ) to be used in
*           the matrix multiplication as follows:
*
*              TRANSA = 'N' or 'n',  op( A ) = A.
*
*              TRANSA = 'T' or 't',  op( A ) = A'.
*
*              TRANSA = 'C' or 'c',  op( A ) = conjg( A' ).
*
*           Unchanged on exit.
*
*  TRANSB - CHARACTER*1.
*           On entry, TRANSB specifies the form of op( B ) to be used in
*           the matrix multiplication as follows:
*
*              TRANSB = 'N' or 'n',  op( B ) = B.
*
*              TRANSB = 'T' or 't',  op( B ) = B'.
*
*              TRANSB = 'C' or 'c',  op( B ) = conjg( B' ).
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry,  M  specifies  the number  of rows  of the  matrix
*           op( A )  and of the  matrix  C.  M  must  be at least  zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry,  N  specifies the number  of columns of the matrix
*           op( B ) and the number of columns of the matrix C. N must be
*           at least zero.
*           Unchanged on exit.
*
*  K      - INTEGER.
*           On entry,  K  specifies  the number of columns of the matrix
*           op( A ) and the number of rows of the matrix op( B ). K must
*           be at least  zero.
*           Unchanged on exit.
*
*  ALPHA  - COMPLEX*16      .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is
*           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
*           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
*           part of the array  A  must contain the matrix  A,  otherwise
*           the leading  k by m  part of the array  A  must contain  the
*           matrix A.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
*           LDA must be at least  max( 1, m ), otherwise  LDA must be at
*           least  max( 1, k ).
*           Unchanged on exit.
*
*  B      - COMPLEX*16       array of DIMENSION ( LDB, kb ), where kb is
*           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
*           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
*           part of the array  B  must contain the matrix  B,  otherwise
*           the leading  n by k  part of the array  B  must contain  the
*           matrix B.
*           Unchanged on exit.
*
*  LDB    - INTEGER.
*           On entry, LDB specifies the first dimension of B as declared
*           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
*           LDB must be at least  max( 1, k ), otherwise  LDB must be at
*           least  max( 1, n ).
*           Unchanged on exit.
*
*  BETA   - COMPLEX*16      .
*           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
*           supplied as zero then C need not be set on input.
*           Unchanged on exit.
*
*  C      - COMPLEX*16       array of DIMENSION ( LDC, n ).
*           Before entry, the leading  m by n  part of the array  C must
*           contain the matrix  C,  except when  beta  is zero, in which
*           case C need not be set on entry.
*           On exit, the array  C  is overwritten by the  m by n  matrix
*           ( alpha*op( A )*op( B ) + beta*C ).
*
*  LDC    - INTEGER.
*           On entry, LDC specifies the first dimension of C as declared
*           in  the  calling  (sub)  program.   LDC  must  be  at  least
*           max( 1, m ).
*           Unchanged on exit.
*
*
*  Level 3 Blas routine.
*
*  -- Written on 8-February-1989.
*     Jack Dongarra, Argonne National Laboratory.
*     Iain Duff, AERE Harwell.
*     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*     Sven Hammarling, Numerical Algorithms Group Ltd.
*
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX
*     .. Local Scalars ..
      LOGICAL            CONJA, CONJB, NOTA, NOTB
      INTEGER            I, INFO, J, L, NCOLA, NROWA, NROWB
      COMPLEX*16         TEMP
*     .. Parameters ..
      COMPLEX*16         ONE
      PARAMETER        ( ONE  = ( 1.0D+0, 0.0D+0 ) )
      COMPLEX*16         ZERO
      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Executable Statements ..
*
*     Set  NOTA  and  NOTB  as  true if  A  and  B  respectively are not
*     conjugated or transposed, set  CONJA and CONJB  as true if  A  and
*     B  respectively are to be  transposed but  not conjugated  and set
*     NROWA, NCOLA and  NROWB  as the number of rows and  columns  of  A
*     and the number of rows of  B  respectively.
*
      NOTA  = LSAME( TRANSA, 'N' )
      NOTB  = LSAME( TRANSB, 'N' )
      CONJA = LSAME( TRANSA, 'C' )
      CONJB = LSAME( TRANSB, 'C' )
      IF( NOTA )THEN
         NROWA = M
         NCOLA = K
      ELSE
         NROWA = K
         NCOLA = M
      END IF
      IF( NOTB )THEN
         NROWB = K
      ELSE
         NROWB = N
      END IF
*
*     Test the input parameters.
*
      INFO = 0
      IF(      ( .NOT.NOTA                 ).AND.
     $         ( .NOT.CONJA                ).AND.
     $         ( .NOT.LSAME( TRANSA, 'T' ) )      )THEN
         INFO = 1
      ELSE IF( ( .NOT.NOTB                 ).AND.
     $         ( .NOT.CONJB                ).AND.
     $         ( .NOT.LSAME( TRANSB, 'T' ) )      )THEN
         INFO = 2
      ELSE IF( M  .LT.0               )THEN
         INFO = 3
      ELSE IF( N  .LT.0               )THEN
         INFO = 4
      ELSE IF( K  .LT.0               )THEN
         INFO = 5
      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
         INFO = 8
      ELSE IF( LDB.LT.MAX( 1, NROWB ) )THEN
         INFO = 10
      ELSE IF( LDC.LT.MAX( 1, M     ) )THEN
         INFO = 13
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'ZGEMM ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
     $    ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     And when  alpha.eq.zero.
*
      IF( ALPHA.EQ.ZERO )THEN
         IF( BETA.EQ.ZERO )THEN
            DO 20, J = 1, N
               DO 10, I = 1, M
                  C( I, J ) = ZERO
   10          CONTINUE
   20       CONTINUE
         ELSE
            DO 40, J = 1, N
               DO 30, I = 1, M
                  C( I, J ) = BETA*C( I, J )
   30          CONTINUE
   40       CONTINUE
         END IF
         RETURN
      END IF
*
*     Start the operations.
*
      IF( NOTB )THEN
         IF( NOTA )THEN
*
*           Form  C := alpha*A*B + beta*C.
*
            DO 90, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 50, I = 1, M
                     C( I, J ) = ZERO
   50             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 60, I = 1, M
                     C( I, J ) = BETA*C( I, J )
   60             CONTINUE
               END IF
               DO 80, L = 1, K
c                  IF( B( L, J ).NE.ZERO )THEN
                     TEMP = ALPHA*B( L, J )
                     DO 70, I = 1, M
                        C( I, J ) = C( I, J ) + TEMP*A( I, L )
   70                CONTINUE
c                  END IF
   80          CONTINUE
   90       CONTINUE
         ELSE IF( CONJA )THEN
*
*           Form  C := alpha*conjg( A' )*B + beta*C.
*
            DO 120, J = 1, N
               DO 110, I = 1, M
                  TEMP = ZERO
                  DO 100, L = 1, K
                     TEMP = TEMP + DCONJG( A( L, I ) )*B( L, J )
  100             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  110          CONTINUE
  120       CONTINUE
         ELSE
*
*           Form  C := alpha*A'*B + beta*C
*
            DO 150, J = 1, N
               DO 140, I = 1, M
                  TEMP = ZERO
                  DO 130, L = 1, K
                     TEMP = TEMP + A( L, I )*B( L, J )
  130             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  140          CONTINUE
  150       CONTINUE
         END IF
      ELSE IF( NOTA )THEN
         IF( CONJB )THEN
*
*           Form  C := alpha*A*conjg( B' ) + beta*C.
*
            DO 200, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 160, I = 1, M
                     C( I, J ) = ZERO
  160             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 170, I = 1, M
                     C( I, J ) = BETA*C( I, J )
  170             CONTINUE
               END IF
               DO 190, L = 1, K
c                  IF( B( J, L ).NE.ZERO )THEN
                     TEMP = ALPHA*DCONJG( B( J, L ) )
                     DO 180, I = 1, M
                        C( I, J ) = C( I, J ) + TEMP*A( I, L )
  180                CONTINUE
c                  END IF
  190          CONTINUE
  200       CONTINUE
         ELSE
*
*           Form  C := alpha*A*B'          + beta*C
*
            DO 250, J = 1, N
               IF( BETA.EQ.ZERO )THEN
                  DO 210, I = 1, M
                     C( I, J ) = ZERO
  210             CONTINUE
               ELSE IF( BETA.NE.ONE )THEN
                  DO 220, I = 1, M
                     C( I, J ) = BETA*C( I, J )
  220             CONTINUE
               END IF
               DO 240, L = 1, K
c                  IF( B( J, L ).NE.ZERO )THEN
                     TEMP = ALPHA*B( J, L )
                     DO 230, I = 1, M
                        C( I, J ) = C( I, J ) + TEMP*A( I, L )
  230                CONTINUE
c                  END IF
  240          CONTINUE
  250       CONTINUE
         END IF
      ELSE IF( CONJA )THEN
         IF( CONJB )THEN
*
*           Form  C := alpha*conjg( A' )*conjg( B' ) + beta*C.
*
            DO 280, J = 1, N
               DO 270, I = 1, M
                  TEMP = ZERO
                  DO 260, L = 1, K
                     TEMP = TEMP +
     $                      DCONJG( A( L, I ) )*DCONJG( B( J, L ) )
  260             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  270          CONTINUE
  280       CONTINUE
         ELSE
*
*           Form  C := alpha*conjg( A' )*B' + beta*C
*
            DO 310, J = 1, N
               DO 300, I = 1, M
                  TEMP = ZERO
                  DO 290, L = 1, K
                     TEMP = TEMP + DCONJG( A( L, I ) )*B( J, L )
  290             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  300          CONTINUE
  310       CONTINUE
         END IF
      ELSE
         IF( CONJB )THEN
*
*           Form  C := alpha*A'*conjg( B' ) + beta*C
*
            DO 340, J = 1, N
               DO 330, I = 1, M
                  TEMP = ZERO
                  DO 320, L = 1, K
                     TEMP = TEMP + A( L, I )*DCONJG( B( J, L ) )
  320             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  330          CONTINUE
  340       CONTINUE
         ELSE
*
*           Form  C := alpha*A'*B' + beta*C
*
            DO 370, J = 1, N
               DO 360, I = 1, M
                  TEMP = ZERO
                  DO 350, L = 1, K
                     TEMP = TEMP + A( L, I )*B( J, L )
  350             CONTINUE
                  IF( BETA.EQ.ZERO )THEN
                     C( I, J ) = ALPHA*TEMP
                  ELSE
                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
                  END IF
  360          CONTINUE
  370       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of ZGEMM .
*
      END