*> \brief \b DCABS1
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DCABS1(Z)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX Z
* ..
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DCABS1 computes |Re(.)| + |Im(.)| of a double complex number
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] Z
*> \verbatim
*> Z is DOUBLE COMPLEX
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup abs1
*
* =====================================================================
DOUBLE PRECISION FUNCTION DCABS1(Z)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX Z
* ..
* ..
* =====================================================================
*
* .. Intrinsic Functions ..
INTRINSIC ABS,DBLE,DIMAG
*
DCABS1 = ABS(DBLE(Z)) + ABS(DIMAG(Z))
RETURN
*
* End of DCABS1
*
END
*> \brief \b DZASUM
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DZASUM(N,ZX,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,N
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX ZX(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DZASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and
*> returns a double precision result.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in,out] ZX
*> \verbatim
*> ZX is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of ZX
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup asum
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
DOUBLE PRECISION FUNCTION DZASUM(N,ZX,INCX)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,N
* ..
* .. Array Arguments ..
DOUBLE COMPLEX ZX(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
DOUBLE PRECISION STEMP
INTEGER I,NINCX
* ..
* .. External Functions ..
DOUBLE PRECISION DCABS1
EXTERNAL DCABS1
* ..
DZASUM = 0.0d0
STEMP = 0.0d0
IF (N.LE.0 .OR. INCX.LE.0) RETURN
IF (INCX.EQ.1) THEN
*
* code for increment equal to 1
*
DO I = 1,N
STEMP = STEMP + DCABS1(ZX(I))
END DO
ELSE
*
* code for increment not equal to 1
*
NINCX = N*INCX
DO I = 1,NINCX,INCX
STEMP = STEMP + DCABS1(ZX(I))
END DO
END IF
DZASUM = STEMP
RETURN
*
* End of DZASUM
*
END
*> \brief \b IZAMAX
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* INTEGER FUNCTION IZAMAX(N,ZX,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,N
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX ZX(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> IZAMAX finds the index of the first element having maximum |Re(.)| + |Im(.)|
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in] ZX
*> \verbatim
*> ZX is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of ZX
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup iamax
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, 1/15/85.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
INTEGER FUNCTION IZAMAX(N,ZX,INCX)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,N
* ..
* .. Array Arguments ..
DOUBLE COMPLEX ZX(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
DOUBLE PRECISION DMAX
INTEGER I,IX
* ..
* .. External Functions ..
DOUBLE PRECISION DCABS1
EXTERNAL DCABS1
* ..
IZAMAX = 0
IF (N.LT.1 .OR. INCX.LE.0) RETURN
IZAMAX = 1
IF (N.EQ.1) RETURN
IF (INCX.EQ.1) THEN
*
* code for increment equal to 1
*
DMAX = DCABS1(ZX(1))
DO I = 2,N
IF (DCABS1(ZX(I)).GT.DMAX) THEN
IZAMAX = I
DMAX = DCABS1(ZX(I))
END IF
END DO
ELSE
*
* code for increment not equal to 1
*
IX = 1
DMAX = DCABS1(ZX(1))
IX = IX + INCX
DO I = 2,N
IF (DCABS1(ZX(IX)).GT.DMAX) THEN
IZAMAX = I
DMAX = DCABS1(ZX(IX))
END IF
IX = IX + INCX
END DO
END IF
RETURN
*
* End of IZAMAX
*
END
*> \brief \b ZAXPY
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ZA
* INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX ZX(*),ZY(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZAXPY constant times a vector plus a vector.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in] ZA
*> \verbatim
*> ZA is DOUBLE COMPLEX
*> On entry, ZA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] ZX
*> \verbatim
*> ZX is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of ZX
*> \endverbatim
*>
*> \param[in,out] ZY
*> \verbatim
*> ZY is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> storage spacing between elements of ZY
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup axpy
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ZA
INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
DOUBLE COMPLEX ZX(*),ZY(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I,IX,IY
* ..
* .. External Functions ..
DOUBLE PRECISION DCABS1
EXTERNAL DCABS1
* ..
IF (N.LE.0) RETURN
IF (DCABS1(ZA).EQ.0.0d0) RETURN
IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
*
* code for both increments equal to 1
*
DO I = 1,N
ZY(I) = ZY(I) + ZA*ZX(I)
END DO
ELSE
*
* code for unequal increments or equal increments
* not equal to 1
*
IX = 1
IY = 1
IF (INCX.LT.0) IX = (-N+1)*INCX + 1
IF (INCY.LT.0) IY = (-N+1)*INCY + 1
DO I = 1,N
ZY(IY) = ZY(IY) + ZA*ZX(IX)
IX = IX + INCX
IY = IY + INCY
END DO
END IF
*
RETURN
*
* End of ZAXPY
*
END
*> \brief \b ZCOPY
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY)
*
* .. Scalar Arguments ..
* INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX ZX(*),ZY(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZCOPY copies a vector, x, to a vector, y.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in] ZX
*> \verbatim
*> ZX is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of ZX
*> \endverbatim
*>
*> \param[out] ZY
*> \verbatim
*> ZY is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> storage spacing between elements of ZY
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup copy
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, linpack, 4/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
DOUBLE COMPLEX ZX(*),ZY(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I,IX,IY
* ..
IF (N.LE.0) RETURN
IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
*
* code for both increments equal to 1
*
DO I = 1,N
ZY(I) = ZX(I)
END DO
ELSE
*
* code for unequal increments or equal increments
* not equal to 1
*
IX = 1
IY = 1
IF (INCX.LT.0) IX = (-N+1)*INCX + 1
IF (INCY.LT.0) IY = (-N+1)*INCY + 1
DO I = 1,N
ZY(IY) = ZX(IX)
IX = IX + INCX
IY = IY + INCY
END DO
END IF
RETURN
*
* End of ZCOPY
*
END
*> \brief \b ZDOTC
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* DOUBLE COMPLEX FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY)
*
* .. Scalar Arguments ..
* INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX ZX(*),ZY(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZDOTC forms the dot product of two complex vectors
*> ZDOTC = X^H * Y
*>
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in] ZX
*> \verbatim
*> ZX is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of ZX
*> \endverbatim
*>
*> \param[in] ZY
*> \verbatim
*> ZY is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> storage spacing between elements of ZY
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup dot
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
DOUBLE COMPLEX FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
DOUBLE COMPLEX ZX(*),ZY(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
DOUBLE COMPLEX ZTEMP
INTEGER I,IX,IY
* ..
* .. Intrinsic Functions ..
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) THEN
*
* code for both increments equal to 1
*
DO I = 1,N
ZTEMP = ZTEMP + DCONJG(ZX(I))*ZY(I)
END DO
ELSE
*
* code for unequal increments or equal increments
* not equal to 1
*
IX = 1
IY = 1
IF (INCX.LT.0) IX = (-N+1)*INCX + 1
IF (INCY.LT.0) IY = (-N+1)*INCY + 1
DO I = 1,N
ZTEMP = ZTEMP + DCONJG(ZX(IX))*ZY(IY)
IX = IX + INCX
IY = IY + INCY
END DO
END IF
ZDOTC = ZTEMP
RETURN
*
* End of ZDOTC
*
END
*> \brief \b ZDOTU
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* DOUBLE COMPLEX FUNCTION ZDOTU(N,ZX,INCX,ZY,INCY)
*
* .. Scalar Arguments ..
* INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX ZX(*),ZY(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZDOTU forms the dot product of two complex vectors
*> ZDOTU = X^T * Y
*>
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in] ZX
*> \verbatim
*> ZX is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of ZX
*> \endverbatim
*>
*> \param[in] ZY
*> \verbatim
*> ZY is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> storage spacing between elements of ZY
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup dot
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
DOUBLE COMPLEX FUNCTION ZDOTU(N,ZX,INCX,ZY,INCY)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
DOUBLE COMPLEX ZX(*),ZY(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
DOUBLE COMPLEX ZTEMP
INTEGER I,IX,IY
* ..
ZTEMP = (0.0d0,0.0d0)
ZDOTU = (0.0d0,0.0d0)
IF (N.LE.0) RETURN
IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
*
* code for both increments equal to 1
*
DO I = 1,N
ZTEMP = ZTEMP + ZX(I)*ZY(I)
END DO
ELSE
*
* code for unequal increments or equal increments
* not equal to 1
*
IX = 1
IY = 1
IF (INCX.LT.0) IX = (-N+1)*INCX + 1
IF (INCY.LT.0) IY = (-N+1)*INCY + 1
DO I = 1,N
ZTEMP = ZTEMP + ZX(IX)*ZY(IY)
IX = IX + INCX
IY = IY + INCY
END DO
END IF
ZDOTU = ZTEMP
RETURN
*
* End of ZDOTU
*
END
*> \brief \b ZDROT
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZDROT( N, ZX, INCX, ZY, INCY, C, S )
*
* .. Scalar Arguments ..
* INTEGER INCX, INCY, N
* DOUBLE PRECISION C, S
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX ZX( * ), ZY( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> Applies a plane rotation, where the cos and sin (c and s) are real
*> and the vectors cx and cy are complex.
*> jack dongarra, linpack, 3/11/78.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the vectors cx and cy.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in,out] ZX
*> \verbatim
*> ZX is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( N - 1 )*abs( INCX ) ).
*> Before entry, the incremented array ZX must contain the n
*> element vector cx. On exit, ZX is overwritten by the updated
*> vector cx.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> ZX. INCX must not be zero.
*> \endverbatim
*>
*> \param[in,out] ZY
*> \verbatim
*> ZY is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( N - 1 )*abs( INCY ) ).
*> Before entry, the incremented array ZY must contain the n
*> element vector cy. On exit, ZY is overwritten by the updated
*> vector cy.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> ZY. INCY must not be zero.
*> \endverbatim
*>
*> \param[in] C
*> \verbatim
*> C is DOUBLE PRECISION
*> On entry, C specifies the cosine, cos.
*> \endverbatim
*>
*> \param[in] S
*> \verbatim
*> S is DOUBLE PRECISION
*> On entry, S specifies the sine, sin.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup rot
*
* =====================================================================
SUBROUTINE ZDROT( N, ZX, INCX, ZY, INCY, C, S )
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX, INCY, N
DOUBLE PRECISION C, S
* ..
* .. Array Arguments ..
DOUBLE COMPLEX ZX( * ), ZY( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, IX, IY
DOUBLE COMPLEX CTEMP
* ..
* .. Executable Statements ..
*
IF( N.LE.0 )
$ RETURN
IF( INCX.EQ.1 .AND. INCY.EQ.1 ) THEN
*
* code for both increments equal to 1
*
DO I = 1, N
CTEMP = C*ZX( I ) + S*ZY( I )
ZY( I ) = C*ZY( I ) - S*ZX( I )
ZX( I ) = CTEMP
END DO
ELSE
*
* code for unequal increments or equal increments not equal
* to 1
*
IX = 1
IY = 1
IF( INCX.LT.0 )
$ IX = ( -N+1 )*INCX + 1
IF( INCY.LT.0 )
$ IY = ( -N+1 )*INCY + 1
DO I = 1, N
CTEMP = C*ZX( IX ) + S*ZY( IY )
ZY( IY ) = C*ZY( IY ) - S*ZX( IX )
ZX( IX ) = CTEMP
IX = IX + INCX
IY = IY + INCY
END DO
END IF
RETURN
*
* End of ZDROT
*
END
*> \brief \b ZDSCAL
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZDSCAL(N,DA,ZX,INCX)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION DA
* INTEGER INCX,N
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX ZX(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZDSCAL scales a vector by a constant.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in] DA
*> \verbatim
*> DA is DOUBLE PRECISION
*> On entry, DA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in,out] ZX
*> \verbatim
*> ZX is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of ZX
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup scal
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZDSCAL(N,DA,ZX,INCX)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE PRECISION DA
INTEGER INCX,N
* ..
* .. Array Arguments ..
DOUBLE COMPLEX ZX(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I,NINCX
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER (ONE=1.0D+0)
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, DIMAG
* ..
IF (N.LE.0 .OR. INCX.LE.0 .OR. DA.EQ.ONE) RETURN
IF (INCX.EQ.1) THEN
*
* code for increment equal to 1
*
DO I = 1,N
ZX(I) = DCMPLX(DA*DBLE(ZX(I)),DA*DIMAG(ZX(I)))
END DO
ELSE
*
* code for increment not equal to 1
*
NINCX = N*INCX
DO I = 1,NINCX,INCX
ZX(I) = DCMPLX(DA*DBLE(ZX(I)),DA*DIMAG(ZX(I)))
END DO
END IF
RETURN
*
* End of ZDSCAL
*
END
*> \brief \b ZGBMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA,BETA
* INTEGER INCX,INCY,KL,KU,LDA,M,N
* CHARACTER TRANS
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZGBMV performs one of the matrix-vector operations
*>
*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or
*>
*> y := alpha*A**H*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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**T*x + beta*y.
*>
*> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of the matrix A.
*> M must be at least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*> KL is INTEGER
*> On entry, KL specifies the number of sub-diagonals of the
*> matrix A. KL must satisfy 0 .le. KL.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*> KU is INTEGER
*> On entry, KU specifies the number of super-diagonals of the
*> matrix A. KU must satisfy 0 .le. KU.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE COMPLEX
*> On entry, BETA specifies the scalar beta. When BETA is
*> supplied as zero then Y need not be set on input.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*> Y is DOUBLE COMPLEX array, 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.
*> If either m or n is zero, then Y not referenced and the function
*> performs a quick return.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup gbmv
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*> -- 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,
+ BETA,Y,INCY)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER INCX,INCY,KL,KU,LDA,M,N
CHARACTER TRANS
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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
* ..
*
* 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
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
JX = JX + INCX
60 CONTINUE
ELSE
DO 80 J = 1,N
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
JX = JX + INCX
IF (J.GT.KU) KY = KY + INCY
80 CONTINUE
END IF
ELSE
*
* Form y := alpha*A**T*x + y or y := alpha*A**H*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
*> \brief \b ZGEMM
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA,BETA
* INTEGER K,LDA,LDB,LDC,M,N
* CHARACTER TRANSA,TRANSB
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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**T or op( X ) = X**H,
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANSA
*> \verbatim
*> TRANSA is 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**T.
*>
*> TRANSA = 'C' or 'c', op( A ) = A**H.
*> \endverbatim
*>
*> \param[in] TRANSB
*> \verbatim
*> TRANSB is 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**T.
*>
*> TRANSB = 'C' or 'c', op( B ) = B**H.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is 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.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is 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.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is 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 ).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE COMPLEX
*> On entry, BETA specifies the scalar beta. When BETA is
*> supplied as zero then C need not be set on input.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE COMPLEX array, 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 ).
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup gemm
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,
+ BETA,C,LDC)
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER K,LDA,LDB,LDC,M,N
CHARACTER TRANSA,TRANSB
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DCONJG,MAX
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP
INTEGER I,INFO,J,L,NROWA,NROWB
LOGICAL CONJA,CONJB,NOTA,NOTB
* ..
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* 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 and NROWB as the number of rows of A and B respectively.
*
NOTA = LSAME(TRANSA,'N')
NOTB = LSAME(TRANSB,'N')
CONJA = LSAME(TRANSA,'C')
CONJB = LSAME(TRANSB,'C')
IF (NOTA) THEN
NROWA = M
ELSE
NROWA = K
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
TEMP = ALPHA*B(L,J)
DO 70 I = 1,M
C(I,J) = C(I,J) + TEMP*A(I,L)
70 CONTINUE
80 CONTINUE
90 CONTINUE
ELSE IF (CONJA) THEN
*
* Form C := alpha*A**H*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**T*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*B**H + 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
TEMP = ALPHA*DCONJG(B(J,L))
DO 180 I = 1,M
C(I,J) = C(I,J) + TEMP*A(I,L)
180 CONTINUE
190 CONTINUE
200 CONTINUE
ELSE
*
* Form C := alpha*A*B**T + 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
TEMP = ALPHA*B(J,L)
DO 230 I = 1,M
C(I,J) = C(I,J) + TEMP*A(I,L)
230 CONTINUE
240 CONTINUE
250 CONTINUE
END IF
ELSE IF (CONJA) THEN
IF (CONJB) THEN
*
* Form C := alpha*A**H*B**H + 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*A**H*B**T + 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**T*B**H + 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**T*B**T + 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
*> \brief \b ZGEMMTR
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZGEMMTR(UPLO,TRANSA,TRANSB,N,K,ALPHA,A,LDA,B,LDB,BETA,
* C,LDC)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA,BETA
* INTEGER K,LDA,LDB,LDC,N
* CHARACTER TRANSA,TRANSB, UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZGEMMTR 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**T,
*>
*> alpha and beta are scalars, and A, B and C are matrices, with op( A )
*> an n by k matrix, op( B ) a k by n matrix and C an n by n matrix.
*> Thereby, the routine only accesses and updates the upper or lower
*> triangular part of the result matrix C. This behaviour can be used if
*> the resulting matrix C is known to be Hermitian or symmetric.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> On entry, UPLO specifies whether the lower or the upper
*> triangular part of C is access and updated.
*>
*> UPLO = 'L' or 'l', the lower triangular part of C is used.
*>
*> UPLO = 'U' or 'u', the upper triangular part of C is used.
*> \endverbatim
*
*> \param[in] TRANSA
*> \verbatim
*> TRANSA is 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**T.
*>
*> TRANSA = 'C' or 'c', op( A ) = A**H.
*> \endverbatim
*>
*> \param[in] TRANSB
*> \verbatim
*> TRANSB is 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**T.
*>
*> TRANSB = 'C' or 'c', op( B ) = B**H.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of rows and columns of
*> the matrix C, the number of columns of op(B) and the number
*> of rows of op(A). N must be at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is 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.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX.
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, dimension ( LDA, ka ), where ka is
*> k when TRANSA = 'N' or 'n', and is n otherwise.
*> Before entry with TRANSA = 'N' or 'n', the leading n 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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, n ), otherwise LDA must be at
*> least max( 1, k ).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is 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 ).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE COMPLEX.
*> On entry, BETA specifies the scalar beta. When BETA is
*> supplied as zero then C need not be set on input.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE COMPLEX array, dimension ( LDC, N )
*> Before entry, the leading n 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 upper or lower triangular part of the matrix
*> C is overwritten by the n by n matrix
*> ( alpha*op( A )*op( B ) + beta*C ).
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Martin Koehler
*
*> \ingroup gemmtr
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 3 Blas routine.
*>
*> -- Written on 19-July-2023.
*> Martin Koehler, MPI Magdeburg
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZGEMMTR(UPLO,TRANSA,TRANSB,N,K,ALPHA,A,LDA,B,LDB,
+ BETA,C,LDC)
IMPLICIT NONE
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER K,LDA,LDB,LDC,N
CHARACTER TRANSA,TRANSB,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG,MAX
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP
INTEGER I,INFO,J,L,NROWA,NROWB,ISTART, ISTOP
LOGICAL CONJA,CONJB,NOTA,NOTB,UPPER
* ..
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* 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 and NROWB as the number of rows of A and B respectively.
*
NOTA = LSAME(TRANSA,'N')
NOTB = LSAME(TRANSB,'N')
CONJA = LSAME(TRANSA,'C')
CONJB = LSAME(TRANSB,'C')
IF (NOTA) THEN
NROWA = N
ELSE
NROWA = K
END IF
IF (NOTB) THEN
NROWB = K
ELSE
NROWB = N
END IF
UPPER = LSAME(UPLO, 'U')
*
* Test the input parameters.
*
INFO = 0
IF ((.NOT. UPPER) .AND. (.NOT. LSAME(UPLO, 'L'))) THEN
INFO = 1
ELSE IF ((.NOT.NOTA) .AND. (.NOT.CONJA) .AND.
+ (.NOT.LSAME(TRANSA,'T'))) THEN
INFO = 2
ELSE IF ((.NOT.NOTB) .AND. (.NOT.CONJB) .AND.
+ (.NOT.LSAME(TRANSB,'T'))) 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,N)) THEN
INFO = 13
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('ZGEMMTR',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF (N.EQ.0) RETURN
*
* And when alpha.eq.zero.
*
IF (ALPHA.EQ.ZERO) THEN
IF (BETA.EQ.ZERO) THEN
DO 20 J = 1,N
IF (UPPER) THEN
ISTART = 1
ISTOP = J
ELSE
ISTART = J
ISTOP = N
END IF
DO 10 I = ISTART, ISTOP
C(I,J) = ZERO
10 CONTINUE
20 CONTINUE
ELSE
DO 40 J = 1,N
IF (UPPER) THEN
ISTART = 1
ISTOP = J
ELSE
ISTART = J
ISTOP = N
END IF
DO 30 I = ISTART, ISTOP
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 (UPPER) THEN
ISTART = 1
ISTOP = J
ELSE
ISTART = J
ISTOP = N
END IF
IF (BETA.EQ.ZERO) THEN
DO 50 I = ISTART, ISTOP
C(I,J) = ZERO
50 CONTINUE
ELSE IF (BETA.NE.ONE) THEN
DO 60 I = ISTART, ISTOP
C(I,J) = BETA*C(I,J)
60 CONTINUE
END IF
DO 80 L = 1,K
TEMP = ALPHA*B(L,J)
DO 70 I = ISTART, ISTOP
C(I,J) = C(I,J) + TEMP*A(I,L)
70 CONTINUE
80 CONTINUE
90 CONTINUE
ELSE IF (CONJA) THEN
*
* Form C := alpha*A**H*B + beta*C.
*
DO 120 J = 1,N
IF (UPPER) THEN
ISTART = 1
ISTOP = J
ELSE
ISTART = J
ISTOP = N
END IF
DO 110 I = ISTART, ISTOP
TEMP = ZERO
DO 100 L = 1,K
TEMP = TEMP + CONJG(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**T*B + beta*C
*
DO 150 J = 1,N
IF (UPPER) THEN
ISTART = 1
ISTOP = J
ELSE
ISTART = J
ISTOP = N
END IF
DO 140 I = ISTART, ISTOP
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*B**H + beta*C.
*
DO 200 J = 1,N
IF (UPPER) THEN
ISTART = 1
ISTOP = J
ELSE
ISTART = J
ISTOP = N
END IF
IF (BETA.EQ.ZERO) THEN
DO 160 I = ISTART,ISTOP
C(I,J) = ZERO
160 CONTINUE
ELSE IF (BETA.NE.ONE) THEN
DO 170 I = ISTART, ISTOP
C(I,J) = BETA*C(I,J)
170 CONTINUE
END IF
DO 190 L = 1,K
TEMP = ALPHA*CONJG(B(J,L))
DO 180 I = ISTART, ISTOP
C(I,J) = C(I,J) + TEMP*A(I,L)
180 CONTINUE
190 CONTINUE
200 CONTINUE
ELSE
*
* Form C := alpha*A*B**T + beta*C
*
DO 250 J = 1,N
IF (UPPER) THEN
ISTART = 1
ISTOP = J
ELSE
ISTART = J
ISTOP = N
END IF
IF (BETA.EQ.ZERO) THEN
DO 210 I = ISTART, ISTOP
C(I,J) = ZERO
210 CONTINUE
ELSE IF (BETA.NE.ONE) THEN
DO 220 I = ISTART, ISTOP
C(I,J) = BETA*C(I,J)
220 CONTINUE
END IF
DO 240 L = 1,K
TEMP = ALPHA*B(J,L)
DO 230 I = ISTART, ISTOP
C(I,J) = C(I,J) + TEMP*A(I,L)
230 CONTINUE
240 CONTINUE
250 CONTINUE
END IF
ELSE IF (CONJA) THEN
IF (CONJB) THEN
*
* Form C := alpha*A**H*B**H + beta*C.
*
DO 280 J = 1,N
IF (UPPER) THEN
ISTART = 1
ISTOP = J
ELSE
ISTART = J
ISTOP = N
END IF
DO 270 I = ISTART, ISTOP
TEMP = ZERO
DO 260 L = 1,K
TEMP = TEMP + CONJG(A(L,I))*CONJG(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*A**H*B**T + beta*C
*
DO 310 J = 1,N
IF (UPPER) THEN
ISTART = 1
ISTOP = J
ELSE
ISTART = J
ISTOP = N
END IF
DO 300 I = ISTART, ISTOP
TEMP = ZERO
DO 290 L = 1,K
TEMP = TEMP + CONJG(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**T*B**H + beta*C
*
DO 340 J = 1,N
IF (UPPER) THEN
ISTART = 1
ISTOP = J
ELSE
ISTART = J
ISTOP = N
END IF
DO 330 I = ISTART, ISTOP
TEMP = ZERO
DO 320 L = 1,K
TEMP = TEMP + A(L,I)*CONJG(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**T*B**T + beta*C
*
DO 370 J = 1,N
IF (UPPER) THEN
ISTART = 1
ISTOP = J
ELSE
ISTART = J
ISTOP = N
END IF
DO 360 I = ISTART, ISTOP
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 ZGEMMTR
*
END
*> \brief \b ZGEMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA,BETA
* INTEGER INCX,INCY,LDA,M,N
* CHARACTER TRANS
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZGEMV performs one of the matrix-vector operations
*>
*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or
*>
*> y := alpha*A**H*x + beta*y,
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> m by n matrix.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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**T*x + beta*y.
*>
*> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of the matrix A.
*> M must be at least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, dimension ( LDA, N )
*> Before entry, the leading m by n part of the array A must
*> contain the matrix of coefficients.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE COMPLEX
*> On entry, BETA specifies the scalar beta. When BETA is
*> supplied as zero then Y need not be set on input.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*> Y is DOUBLE COMPLEX array, 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.
*> If either m or n is zero, then Y not referenced and the function
*> performs a quick return.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup gemv
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*> -- 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER INCX,INCY,LDA,M,N
CHARACTER TRANS
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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
* ..
*
* 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
TEMP = ALPHA*X(JX)
DO 50 I = 1,M
Y(I) = Y(I) + TEMP*A(I,J)
50 CONTINUE
JX = JX + INCX
60 CONTINUE
ELSE
DO 80 J = 1,N
TEMP = ALPHA*X(JX)
IY = KY
DO 70 I = 1,M
Y(IY) = Y(IY) + TEMP*A(I,J)
IY = IY + INCY
70 CONTINUE
JX = JX + INCX
80 CONTINUE
END IF
ELSE
*
* Form y := alpha*A**T*x + y or y := alpha*A**H*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
*> \brief \b ZGERC
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA
* INTEGER INCX,INCY,LDA,M,N
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZGERC performs the rank 1 operation
*>
*> A := alpha*x*y**H + 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of the matrix A.
*> M must be at least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( m - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the m
*> element vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in] Y
*> \verbatim
*> Y is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCY ) ).
*> Before entry, the incremented array Y must contain the n
*> element vector y.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup ger
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA
INTEGER INCX,INCY,LDA,M,N
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP
INTEGER I,INFO,IX,J,JY,KX
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DCONJG,MAX
* ..
*
* 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
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
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
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
END IF
JY = JY + INCY
40 CONTINUE
END IF
*
RETURN
*
* End of ZGERC
*
END
*> \brief \b ZGERU
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA
* INTEGER INCX,INCY,LDA,M,N
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZGERU performs the rank 1 operation
*>
*> A := alpha*x*y**T + 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of the matrix A.
*> M must be at least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( m - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the m
*> element vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in] Y
*> \verbatim
*> Y is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCY ) ).
*> Before entry, the incremented array Y must contain the n
*> element vector y.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup ger
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA
INTEGER INCX,INCY,LDA,M,N
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP
INTEGER I,INFO,IX,J,JY,KX
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
*
* 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
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
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
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
END IF
JY = JY + INCY
40 CONTINUE
END IF
*
RETURN
*
* End of ZGERU
*
END
*> \brief \b ZHBMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA,BETA
* INTEGER INCX,INCY,K,LDA,N
* CHARACTER UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is INTEGER
*> On entry, K specifies the number of super-diagonals of the
*> matrix A. K must satisfy 0 .le. K.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> On entry, LDA specifies the first dimension of A as declared
*> in the calling (sub) program. LDA must be at least
*> ( k + 1 ).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the
*> vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE COMPLEX
*> On entry, BETA specifies the scalar beta.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*> Y is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hbmv
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*> -- 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER INCX,INCY,K,LDA,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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 DBLE,DCONJG,MAX,MIN
* ..
*
* 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
*> \brief \b ZHEMM
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA,BETA
* INTEGER LDA,LDB,LDC,M,N
* CHARACTER SIDE,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is 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,
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of the matrix C.
*> M must be at least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of the matrix C.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is DOUBLE COMPLEX array, dimension ( LDB, N )
*> Before entry, the leading m by n part of the array B must
*> contain the matrix B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is 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 ).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE COMPLEX
*> On entry, BETA specifies the scalar beta. When BETA is
*> supplied as zero then C need not be set on input.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hemm
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER LDA,LDB,LDC,M,N
CHARACTER SIDE,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE,DCONJG,MAX
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP1,TEMP2
INTEGER I,INFO,J,K,NROWA
LOGICAL UPPER
* ..
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* 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
*> \brief \b ZHEMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA,BETA
* INTEGER INCX,INCY,LDA,N
* CHARACTER UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the n
*> element vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE COMPLEX
*> On entry, BETA specifies the scalar beta. When BETA is
*> supplied as zero then Y need not be set on input.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*> Y is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hemv
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*> -- 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER INCX,INCY,LDA,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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 DBLE,DCONJG,MAX
* ..
*
* 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
*> \brief \b ZHER2
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA
* INTEGER INCX,INCY,LDA,N
* CHARACTER UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZHER2 performs the hermitian rank 2 operation
*>
*> A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
*>
*> where alpha is a scalar, x and y are n element vectors and A is an n
*> by n hermitian matrix.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the n
*> element vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in] Y
*> \verbatim
*> Y is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCY ) ).
*> Before entry, the incremented array Y must contain the n
*> element vector y.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup her2
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA
INTEGER INCX,INCY,LDA,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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 DBLE,DCONJG,MAX
* ..
*
* 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
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)
ELSE
A(J,J) = DBLE(A(J,J))
END IF
20 CONTINUE
ELSE
DO 40 J = 1,N
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)
ELSE
A(J,J) = DBLE(A(J,J))
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
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
ELSE
A(J,J) = DBLE(A(J,J))
END IF
60 CONTINUE
ELSE
DO 80 J = 1,N
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
ELSE
A(J,J) = DBLE(A(J,J))
END IF
JX = JX + INCX
JY = JY + INCY
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of ZHER2
*
END
*> \brief \b ZHER2K
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA
* DOUBLE PRECISION BETA
* INTEGER K,LDA,LDB,LDC,N
* CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZHER2K performs one of the hermitian rank 2k operations
*>
*> C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,
*>
*> or
*>
*> C := alpha*A**H*B + conjg( alpha )*B**H*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> On entry, TRANS specifies the operation to be performed as
*> follows:
*>
*> TRANS = 'N' or 'n' C := alpha*A*B**H +
*> conjg( alpha )*B*A**H +
*> beta*C.
*>
*> TRANS = 'C' or 'c' C := alpha*A**H*B +
*> conjg( alpha )*B**H*A +
*> beta*C.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix C. N must be
*> at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is 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.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX .
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is 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.
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE PRECISION .
*> On entry, BETA specifies the scalar beta.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup her2k
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA
DOUBLE PRECISION BETA
INTEGER K,LDA,LDB,LDC,N
CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE,DCONJG,MAX
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP1,TEMP2
INTEGER I,INFO,J,L,NROWA
LOGICAL UPPER
* ..
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER (ONE=1.0D+0)
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* 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*B**H + conjg( alpha )*B*A**H +
* 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
IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) 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)
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
IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) 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)
END IF
170 CONTINUE
180 CONTINUE
END IF
ELSE
*
* Form C := alpha*A**H*B + conjg( alpha )*B**H*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
*> \brief \b ZHER
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHER(UPLO,N,ALPHA,X,INCX,A,LDA)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION ALPHA
* INTEGER INCX,LDA,N
* CHARACTER UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZHER performs the hermitian rank 1 operation
*>
*> A := alpha*x*x**H + A,
*>
*> where alpha is a real scalar, x is an n element vector and A is an
*> n by n hermitian matrix.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE PRECISION.
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the n
*> element vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup her
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHER(UPLO,N,ALPHA,X,INCX,A,LDA)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER INCX,LDA,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP
INTEGER I,INFO,IX,J,JX,KX
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE,DCONJG,MAX
* ..
*
* 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
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)
ELSE
A(J,J) = DBLE(A(J,J))
END IF
20 CONTINUE
ELSE
JX = KX
DO 40 J = 1,N
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)
ELSE
A(J,J) = DBLE(A(J,J))
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
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
ELSE
A(J,J) = DBLE(A(J,J))
END IF
60 CONTINUE
ELSE
JX = KX
DO 80 J = 1,N
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
ELSE
A(J,J) = DBLE(A(J,J))
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of ZHER
*
END
*> \brief \b ZHERK
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION ALPHA,BETA
* INTEGER K,LDA,LDC,N
* CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),C(LDC,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZHERK performs one of the hermitian rank k operations
*>
*> C := alpha*A*A**H + beta*C,
*>
*> or
*>
*> C := alpha*A**H*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> On entry, TRANS specifies the operation to be performed as
*> follows:
*>
*> TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C.
*>
*> TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix C. N must be
*> at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is 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.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE PRECISION .
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE PRECISION.
*> On entry, BETA specifies the scalar beta.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup herk
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA,BETA
INTEGER K,LDA,LDC,N
CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),C(LDC,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE,DCMPLX,DCONJG,MAX
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP
DOUBLE PRECISION RTEMP
INTEGER I,INFO,J,L,NROWA
LOGICAL UPPER
* ..
* .. Parameters ..
DOUBLE PRECISION ONE,ZERO
PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
* ..
*
* 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*A**H + 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*A**H*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 + DBLE(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 + DBLE(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
*> \brief \b ZHPMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA,BETA
* INTEGER INCX,INCY,N
* CHARACTER UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX AP(*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*> AP is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the n
*> element vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE COMPLEX
*> On entry, BETA specifies the scalar beta. When BETA is
*> supplied as zero then Y need not be set on input.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*> Y is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hpmv
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*> -- 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER INCX,INCY,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX AP(*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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 DBLE,DCONJG
* ..
*
* 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
*> \brief \b ZHPR2
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA
* INTEGER INCX,INCY,N
* CHARACTER UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX AP(*),X(*),Y(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZHPR2 performs the hermitian rank 2 operation
*>
*> A := alpha*x*y**H + conjg( alpha )*y*x**H + 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the n
*> element vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in] Y
*> \verbatim
*> Y is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCY ) ).
*> Before entry, the incremented array Y must contain the n
*> element vector y.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> On entry, INCY specifies the increment for the elements of
*> Y. INCY must not be zero.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*> AP is DOUBLE COMPLEX array, 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hpr2
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA
INTEGER INCX,INCY,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX AP(*),X(*),Y(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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 DBLE,DCONJG
* ..
*
* 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
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)
ELSE
AP(KK+J-1) = DBLE(AP(KK+J-1))
END IF
KK = KK + J
20 CONTINUE
ELSE
DO 40 J = 1,N
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)
ELSE
AP(KK+J-1) = DBLE(AP(KK+J-1))
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
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
ELSE
AP(KK) = DBLE(AP(KK))
END IF
KK = KK + N - J + 1
60 CONTINUE
ELSE
DO 80 J = 1,N
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
ELSE
AP(KK) = DBLE(AP(KK))
END IF
JX = JX + INCX
JY = JY + INCY
KK = KK + N - J + 1
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of ZHPR2
*
END
*> \brief \b ZHPR
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION ALPHA
* INTEGER INCX,N
* CHARACTER UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX AP(*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZHPR performs the hermitian rank 1 operation
*>
*> A := alpha*x*x**H + 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE PRECISION.
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE COMPLEX array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the n
*> element vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*> AP is DOUBLE COMPLEX array, 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hpr
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER INCX,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX AP(*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP
INTEGER I,INFO,IX,J,JX,K,KK,KX
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE,DCONJG
* ..
*
* 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
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)
ELSE
AP(KK+J-1) = DBLE(AP(KK+J-1))
END IF
KK = KK + J
20 CONTINUE
ELSE
JX = KX
DO 40 J = 1,N
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)
ELSE
AP(KK+J-1) = DBLE(AP(KK+J-1))
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
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
ELSE
AP(KK) = DBLE(AP(KK))
END IF
KK = KK + N - J + 1
60 CONTINUE
ELSE
JX = KX
DO 80 J = 1,N
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
ELSE
AP(KK) = DBLE(AP(KK))
END IF
JX = JX + INCX
KK = KK + N - J + 1
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of ZHPR
*
END
*> \brief \b ZSCAL
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZSCAL(N,ZA,ZX,INCX)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ZA
* INTEGER INCX,N
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX ZX(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSCAL scales a vector by a constant.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in] ZA
*> \verbatim
*> ZA is DOUBLE COMPLEX
*> On entry, ZA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in,out] ZX
*> \verbatim
*> ZX is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of ZX
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup scal
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 3/93 to return if incx .le. 0.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZSCAL(N,ZA,ZX,INCX)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ZA
INTEGER INCX,N
* ..
* .. Array Arguments ..
DOUBLE COMPLEX ZX(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I,NINCX
* ..
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
* ..
IF (N.LE.0 .OR. INCX.LE.0 .OR. ZA.EQ.ONE) RETURN
IF (INCX.EQ.1) THEN
*
* code for increment equal to 1
*
DO I = 1,N
ZX(I) = ZA*ZX(I)
END DO
ELSE
*
* code for increment not equal to 1
*
NINCX = N*INCX
DO I = 1,NINCX,INCX
ZX(I) = ZA*ZX(I)
END DO
END IF
RETURN
*
* End of ZSCAL
*
END
*> \brief \b ZSWAP
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY)
*
* .. Scalar Arguments ..
* INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX ZX(*),ZY(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSWAP interchanges two vectors.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> number of elements in input vector(s)
*> \endverbatim
*>
*> \param[in,out] ZX
*> \verbatim
*> ZX is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> storage spacing between elements of ZX
*> \endverbatim
*>
*> \param[in,out] ZY
*> \verbatim
*> ZY is DOUBLE COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*> INCY is INTEGER
*> storage spacing between elements of ZY
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup swap
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> jack dongarra, 3/11/78.
*> modified 12/3/93, array(1) declarations changed to array(*)
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY)
*
* -- Reference BLAS level1 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,INCY,N
* ..
* .. Array Arguments ..
DOUBLE COMPLEX ZX(*),ZY(*)
* ..
*
* =====================================================================
*
* .. Local Scalars ..
DOUBLE COMPLEX ZTEMP
INTEGER I,IX,IY
* ..
IF (N.LE.0) RETURN
IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN
*
* code for both increments equal to 1
DO I = 1,N
ZTEMP = ZX(I)
ZX(I) = ZY(I)
ZY(I) = ZTEMP
END DO
ELSE
*
* code for unequal increments or equal increments not equal
* to 1
*
IX = 1
IY = 1
IF (INCX.LT.0) IX = (-N+1)*INCX + 1
IF (INCY.LT.0) IY = (-N+1)*INCY + 1
DO I = 1,N
ZTEMP = ZX(IX)
ZX(IX) = ZY(IY)
ZY(IY) = ZTEMP
IX = IX + INCX
IY = IY + INCY
END DO
END IF
RETURN
*
* End of ZSWAP
*
END
*> \brief \b ZSYMM
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA,BETA
* INTEGER LDA,LDB,LDC,M,N
* CHARACTER SIDE,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is 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,
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of the matrix C.
*> M must be at least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of the matrix C.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is DOUBLE COMPLEX array, dimension ( LDB, N )
*> Before entry, the leading m by n part of the array B must
*> contain the matrix B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is 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 ).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE COMPLEX
*> On entry, BETA specifies the scalar beta. When BETA is
*> supplied as zero then C need not be set on input.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hemm
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER LDA,LDB,LDC,M,N
CHARACTER SIDE,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP1,TEMP2
INTEGER I,INFO,J,K,NROWA
LOGICAL UPPER
* ..
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* 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
*> \brief \b ZSYR2K
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA,BETA
* INTEGER K,LDA,LDB,LDC,N
* CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSYR2K performs one of the symmetric rank 2k operations
*>
*> C := alpha*A*B**T + alpha*B*A**T + beta*C,
*>
*> or
*>
*> C := alpha*A**T*B + alpha*B**T*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> On entry, TRANS specifies the operation to be performed as
*> follows:
*>
*> TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T +
*> beta*C.
*>
*> TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A +
*> beta*C.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix C. N must be
*> at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is 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.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is 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 ).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE COMPLEX
*> On entry, BETA specifies the scalar beta.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup her2k
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER K,LDA,LDB,LDC,N
CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP1,TEMP2
INTEGER I,INFO,J,L,NROWA
LOGICAL UPPER
* ..
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* 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**T + alpha*B*A**T + 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
IF ((A(J,L).NE.ZERO) .OR. (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
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
IF ((A(J,L).NE.ZERO) .OR. (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
END IF
170 CONTINUE
180 CONTINUE
END IF
ELSE
*
* Form C := alpha*A**T*B + alpha*B**T*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
*> \brief \b ZSYRK
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA,BETA
* INTEGER K,LDA,LDC,N
* CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),C(LDC,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSYRK performs one of the symmetric rank k operations
*>
*> C := alpha*A*A**T + beta*C,
*>
*> or
*>
*> C := alpha*A**T*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> On entry, TRANS specifies the operation to be performed as
*> follows:
*>
*> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C.
*>
*> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix C. N must be
*> at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is 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.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE COMPLEX
*> On entry, BETA specifies the scalar beta.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup herk
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA,BETA
INTEGER K,LDA,LDC,N
CHARACTER TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),C(LDC,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP
INTEGER I,INFO,J,L,NROWA
LOGICAL UPPER
* ..
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* 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**T + 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
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
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
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
END IF
170 CONTINUE
180 CONTINUE
END IF
ELSE
*
* Form C := alpha*A**T*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
*> \brief \b ZTBMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,K,LDA,N
* CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTBMV performs one of the matrix-vector operations
*>
*> x := A*x, or x := A**T*x, or x := A**H*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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**T*x.
*>
*> TRANS = 'C' or 'c' x := A**H*x.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is 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.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> On entry, LDA specifies the first dimension of A as declared
*> in the calling (sub) program. LDA must be at least
*> ( k + 1 ).
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is DOUBLE COMPLEX array, 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
*> transformed vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup tbmv
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*> -- 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,K,LDA,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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
* ..
*
* 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
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)
END IF
20 CONTINUE
ELSE
JX = KX
DO 40 J = 1,N
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)
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
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)
END IF
60 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 80 J = N,1,-1
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)
END IF
JX = JX - INCX
IF ((N-J).GE.K) KX = KX - INCX
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := A**T*x or x := A**H*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
*> \brief \b ZTBSV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,K,LDA,N
* CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTBSV solves one of the systems of equations
*>
*> A*x = b, or A**T*x = b, or A**H*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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**T*x = b.
*>
*> TRANS = 'C' or 'c' A**H*x = b.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is 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.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> On entry, LDA specifies the first dimension of A as declared
*> in the calling (sub) program. LDA must be at least
*> ( k + 1 ).
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup tbsv
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,K,LDA,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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
* ..
*
* 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
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
END IF
20 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 40 J = N,1,-1
KX = KX - INCX
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
END IF
JX = JX - INCX
40 CONTINUE
END IF
ELSE
IF (INCX.EQ.1) THEN
DO 60 J = 1,N
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
END IF
60 CONTINUE
ELSE
JX = KX
DO 80 J = 1,N
KX = KX + INCX
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
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := inv( A**T )*x or x := inv( A**H )*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
*> \brief \b ZTPMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,N
* CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX AP(*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTPMV performs one of the matrix-vector operations
*>
*> x := A*x, or x := A**T*x, or x := A**H*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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**T*x.
*>
*> TRANS = 'C' or 'c' x := A**H*x.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*> AP is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is DOUBLE COMPLEX array, 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
*> transformed vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup tpmv
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*> -- 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX AP(*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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
* ..
*
* 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
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)
END IF
KK = KK + J
20 CONTINUE
ELSE
JX = KX
DO 40 J = 1,N
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)
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
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)
END IF
KK = KK - (N-J+1)
60 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 80 J = N,1,-1
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)
END IF
JX = JX - INCX
KK = KK - (N-J+1)
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := A**T*x or x := A**H*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
*> \brief \b ZTPSV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,N
* CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX AP(*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTPSV solves one of the systems of equations
*>
*> A*x = b, or A**T*x = b, or A**H*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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**T*x = b.
*>
*> TRANS = 'C' or 'c' A**H*x = b.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*> AP is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup tpsv
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX AP(*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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
* ..
*
* 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
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
END IF
KK = KK - J
20 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 40 J = N,1,-1
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
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
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
END IF
KK = KK + (N-J+1)
60 CONTINUE
ELSE
JX = KX
DO 80 J = 1,N
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
END IF
JX = JX + INCX
KK = KK + (N-J+1)
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := inv( A**T )*x or x := inv( A**H )*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
*> \brief \b ZTRMM
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA
* INTEGER LDA,LDB,M,N
* CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),B(LDB,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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**T or op( A ) = A**H.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is 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 ).
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANSA
*> \verbatim
*> TRANSA is 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**T.
*>
*> TRANSA = 'C' or 'c' op( A ) = A**H.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of B. M must be at
*> least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of B. N must be
*> at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha. When alpha is
*> zero then A is not referenced and B need not be set before
*> entry.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup trmm
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA
INTEGER LDA,LDB,M,N
CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),B(LDB,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DCONJG,MAX
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP
INTEGER I,INFO,J,K,NROWA
LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER
* ..
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* 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 (M.EQ.0 .OR. 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
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
END IF
40 CONTINUE
50 CONTINUE
ELSE
DO 80 J = 1,N
DO 70 K = M,1,-1
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
END IF
70 CONTINUE
80 CONTINUE
END IF
ELSE
*
* Form B := alpha*A**T*B or B := alpha*A**H*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
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
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
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
END IF
230 CONTINUE
240 CONTINUE
END IF
ELSE
*
* Form B := alpha*B*A**T or B := alpha*B*A**H.
*
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
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
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
*> \brief \b ZTRMV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,LDA,N
* CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTRMV performs one of the matrix-vector operations
*>
*> x := A*x, or x := A**T*x, or x := A**H*x,
*>
*> where x is an n element vector and A is an n by n unit, or non-unit,
*> upper or lower triangular matrix.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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**T*x.
*>
*> TRANS = 'C' or 'c' x := A**H*x.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is DOUBLE COMPLEX array, 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
*> transformed vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup trmv
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*> The vector and matrix arguments are not referenced when N = 0, or M = 0
*>
*> -- 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,LDA,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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
* ..
*
* 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
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)
END IF
20 CONTINUE
ELSE
JX = KX
DO 40 J = 1,N
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)
END IF
JX = JX + INCX
40 CONTINUE
END IF
ELSE
IF (INCX.EQ.1) THEN
DO 60 J = N,1,-1
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)
END IF
60 CONTINUE
ELSE
KX = KX + (N-1)*INCX
JX = KX
DO 80 J = N,1,-1
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)
END IF
JX = JX - INCX
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := A**T*x or x := A**H*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
*> \brief \b ZTRSM
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* .. Scalar Arguments ..
* DOUBLE COMPLEX ALPHA
* INTEGER LDA,LDB,M,N
* CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),B(LDB,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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**T or op( A ) = A**H.
*>
*> The matrix X is overwritten on B.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is 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.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANSA
*> \verbatim
*> TRANSA is 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**T.
*>
*> TRANSA = 'C' or 'c' op( A ) = A**H.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> On entry, M specifies the number of rows of B. M must be at
*> least zero.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the number of columns of B. N must be
*> at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE COMPLEX
*> On entry, ALPHA specifies the scalar alpha. When alpha is
*> zero then A is not referenced and B need not be set before
*> entry.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, dimension ( LDA, k ),
*> where k is m when SIDE = 'L' or 'l'
*> and k 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is 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 ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup trsm
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
*
* -- Reference BLAS level3 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE COMPLEX ALPHA
INTEGER LDA,LDB,M,N
CHARACTER DIAG,SIDE,TRANSA,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),B(LDB,*)
* ..
*
* =====================================================================
*
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DCONJG,MAX
* ..
* .. Local Scalars ..
DOUBLE COMPLEX TEMP
INTEGER I,INFO,J,K,NROWA
LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER
* ..
* .. Parameters ..
DOUBLE COMPLEX ONE
PARAMETER (ONE= (1.0D+0,0.0D+0))
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
*
* 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 (M.EQ.0 .OR. 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
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
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
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
END IF
90 CONTINUE
100 CONTINUE
END IF
ELSE
*
* Form B := alpha*inv( A**T )*B
* or B := alpha*inv( A**H )*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
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
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
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
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**T )
* or B := alpha*B*inv( A**H ).
*
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
IF (A(J,K).NE.ZERO) THEN
IF (NOCONJ) THEN
TEMP = A(J,K)
ELSE
TEMP = DCONJG(A(J,K))
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
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
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
*> \brief \b ZTRSV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* .. Scalar Arguments ..
* INTEGER INCX,LDA,N
* CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
* DOUBLE COMPLEX A(LDA,*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTRSV solves one of the systems of equations
*>
*> A*x = b, or A**T*x = b, or A**H*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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is 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.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is 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**T*x = b.
*>
*> TRANS = 'C' or 'c' A**H*x = b.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is 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 ).
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is DOUBLE COMPLEX array, 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.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup trsv
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
*
* -- Reference BLAS level2 routine --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INCX,LDA,N
CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
DOUBLE COMPLEX A(LDA,*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE COMPLEX ZERO
PARAMETER (ZERO= (0.0D+0,0.0D+0))
* ..
* .. Local Scalars ..
DOUBLE COMPLEX 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
* ..
*
* 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
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
END IF
20 CONTINUE
ELSE
JX = KX + (N-1)*INCX
DO 40 J = N,1,-1
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
END IF
JX = JX - INCX
40 CONTINUE
END IF
ELSE
IF (INCX.EQ.1) THEN
DO 60 J = 1,N
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
END IF
60 CONTINUE
ELSE
JX = KX
DO 80 J = 1,N
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
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
ELSE
*
* Form x := inv( A**T )*x or x := inv( A**H )*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