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Diffstat (limited to 'SRC/dorgbr.f')
| -rw-r--r-- | SRC/dorgbr.f | 244 |
1 files changed, 244 insertions, 0 deletions
diff --git a/SRC/dorgbr.f b/SRC/dorgbr.f new file mode 100644 index 00000000..dc882990 --- /dev/null +++ b/SRC/dorgbr.f @@ -0,0 +1,244 @@ + SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER VECT + INTEGER 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 (MAX(1,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, ONE + PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY, WANTQ + INTEGER I, IINFO, J, LWKOPT, MN, NB +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. External Subroutines .. + EXTERNAL DORGLQ, DORGQR, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. Executable Statements .. +* +* Test the input arguments +* + INFO = 0 + WANTQ = LSAME( VECT, 'Q' ) + MN = MIN( M, N ) + LQUERY = ( LWORK.EQ.-1 ) + IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN + INFO = -1 + ELSE IF( M.LT.0 ) THEN + INFO = -2 + ELSE 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 ) ) ) ) THEN + INFO = -3 + ELSE IF( K.LT.0 ) THEN + INFO = -4 + ELSE IF( LDA.LT.MAX( 1, M ) ) THEN + INFO = -6 + ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN + INFO = -9 + END IF +* + IF( INFO.EQ.0 ) THEN + IF( WANTQ ) THEN + NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 ) + ELSE + NB = ILAENV( 1, 'DORGLQ', ' ', M, N, K, -1 ) + END IF + LWKOPT = MAX( 1, MN )*NB + WORK( 1 ) = LWKOPT + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DORGBR', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( M.EQ.0 .OR. N.EQ.0 ) THEN + WORK( 1 ) = 1 + RETURN + END 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, -1 + A( 1, J ) = ZERO + DO 10 I = J + 1, M + A( I, J ) = A( I, J-1 ) + 10 CONTINUE + 20 CONTINUE + A( 1, 1 ) = ONE + DO 30 I = 2, M + A( I, 1 ) = ZERO + 30 CONTINUE + IF( 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 IF + END IF + ELSE +* +* 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 ) = ONE + DO 40 I = 2, N + A( I, 1 ) = ZERO + 40 CONTINUE + DO 60 J = 2, N + DO 50 I = J - 1, 2, -1 + A( I, J ) = A( I-1, J ) + 50 CONTINUE + A( 1, J ) = ZERO + 60 CONTINUE + IF( 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 IF + END IF + END IF + WORK( 1 ) = LWKOPT + RETURN +* +* End of DORGBR +* + END |