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SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )** -- LAPACK routine (version 3.0) --* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,* Courant Institute, Argonne National Lab, and Rice University* June 30, 1999** .. Scalar Arguments ..CHARACTER VECTINTEGER INFO, K, LDA, LWORK, M, N* ..* .. Array Arguments ..DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )* ..** Purpose* =======** DORGBR generates one of the real orthogonal matrices Q or P**T* determined by DGEBRD when reducing a real matrix A to bidiagonal* form: A = Q * B * P**T. Q and P**T are defined as products of* elementary reflectors H(i) or G(i) respectively.** If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q* is of order M:* if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n* columns of Q, where m >= n >= k;* if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an* M-by-M matrix.** If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T* is of order N:* if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m* rows of P**T, where n >= m >= k;* if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as* an N-by-N matrix.** Arguments* =========** VECT (input) CHARACTER*1* Specifies whether the matrix Q or the matrix P**T is* required, as defined in the transformation applied by DGEBRD:* = 'Q': generate Q;* = 'P': generate P**T.** M (input) INTEGER* The number of rows of the matrix Q or P**T to be returned.* M >= 0.** N (input) INTEGER* The number of columns of the matrix Q or P**T to be returned.* N >= 0.* If VECT = 'Q', M >= N >= min(M,K);* if VECT = 'P', N >= M >= min(N,K).** K (input) INTEGER* If VECT = 'Q', the number of columns in the original M-by-K* matrix reduced by DGEBRD.* If VECT = 'P', the number of rows in the original K-by-N* matrix reduced by DGEBRD.* K >= 0.** A (input/output) DOUBLE PRECISION array, dimension (LDA,N)* On entry, the vectors which define the elementary reflectors,* as returned by DGEBRD.* On exit, the M-by-N matrix Q or P**T.** LDA (input) INTEGER* The leading dimension of the array A. LDA >= max(1,M).** TAU (input) DOUBLE PRECISION array, dimension* (min(M,K)) if VECT = 'Q'* (min(N,K)) if VECT = 'P'* TAU(i) must contain the scalar factor of the elementary* reflector H(i) or G(i), which determines Q or P**T, as* returned by DGEBRD in its array argument TAUQ or TAUP.** WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.** LWORK (input) INTEGER* The dimension of the array WORK. LWORK >= max(1,min(M,N)).* For optimum performance LWORK >= min(M,N)*NB, where NB* is the optimal blocksize.** If LWORK = -1, then a workspace query is assumed; the routine* only calculates the optimal size of the WORK array, returns* this value as the first entry of the WORK array, and no error* message related to LWORK is issued by XERBLA.** INFO (output) INTEGER* = 0: successful exit* < 0: if INFO = -i, the i-th argument had an illegal value** =====================================================================** .. Parameters ..DOUBLE PRECISION ZERO, ONEPARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )* ..* .. Local Scalars ..LOGICAL LQUERY, WANTQINTEGER I, IINFO, J, LWKOPT, MN, NB* ..* .. External Functions ..LOGICAL LSAMEINTEGER ILAENVEXTERNAL LSAME, ILAENV* ..* .. External Subroutines ..EXTERNAL DORGLQ, DORGQR, XERBLA* ..* .. Intrinsic Functions ..INTRINSIC MAX, MIN* ..* .. Executable Statements ..** Test the input arguments*INFO = 0WANTQ = LSAME( VECT, 'Q' )MN = MIN( M, N )LQUERY = ( LWORK.EQ.-1 )IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THENINFO = -1ELSE IF( M.LT.0 ) THENINFO = -2ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,$ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.$ MIN( N, K ) ) ) ) THENINFO = -3ELSE IF( K.LT.0 ) THENINFO = -4ELSE IF( LDA.LT.MAX( 1, M ) ) THENINFO = -6ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THENINFO = -9END IF*IF( INFO.EQ.0 ) THENIF( WANTQ ) THENNB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 )ELSENB = ILAENV( 1, 'DORGLQ', ' ', M, N, K, -1 )END IFLWKOPT = MAX( 1, MN )*NBWORK( 1 ) = LWKOPTEND IF*IF( INFO.NE.0 ) THENCALL XERBLA( 'DORGBR', -INFO )RETURNELSE IF( LQUERY ) THENRETURNEND IF** Quick return if possible*IF( M.EQ.0 .OR. N.EQ.0 ) THENWORK( 1 ) = 1RETURNEND IF*IF( WANTQ ) THEN** Form Q, determined by a call to DGEBRD to reduce an m-by-k* matrix*IF( M.GE.K ) THEN** If m >= k, assume m >= n >= k*CALL DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )*ELSE** If m < k, assume m = n** Shift the vectors which define the elementary reflectors one* column to the right, and set the first row and column of Q* to those of the unit matrix*DO 20 J = M, 2, -1A( 1, J ) = ZERODO 10 I = J + 1, MA( I, J ) = A( I, J-1 )10 CONTINUE20 CONTINUEA( 1, 1 ) = ONEDO 30 I = 2, MA( I, 1 ) = ZERO30 CONTINUEIF( M.GT.1 ) THEN** Form Q(2:m,2:m)*CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,$ LWORK, IINFO )END IFEND IFELSE** Form P', determined by a call to DGEBRD to reduce a k-by-n* matrix*IF( K.LT.N ) THEN** If k < n, assume k <= m <= n*CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )*ELSE** If k >= n, assume m = n** Shift the vectors which define the elementary reflectors one* row downward, and set the first row and column of P' to* those of the unit matrix*A( 1, 1 ) = ONEDO 40 I = 2, NA( I, 1 ) = ZERO40 CONTINUEDO 60 J = 2, NDO 50 I = J - 1, 2, -1A( I, J ) = A( I-1, J )50 CONTINUEA( 1, J ) = ZERO60 CONTINUEIF( N.GT.1 ) THEN** Form P'(2:n,2:n)*CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,$ LWORK, IINFO )END IFEND IFEND IFWORK( 1 ) = LWKOPTRETURN** End of DORGBR*END