julie
be91086043
Those are just cosmetic changes to update version number and various other minor change.
283 lines
8.6 KiB
FortranFixed
283 lines
8.6 KiB
FortranFixed
SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
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$ LDC, WORK, LWORK, INFO )
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*
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* -- LAPACK routine (version 3.2) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER SIDE, TRANS, VECT
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INTEGER INFO, K, LDA, LDC, LWORK, M, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
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* with
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* SIDE = 'L' SIDE = 'R'
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* TRANS = 'N': Q * C C * Q
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* TRANS = 'T': Q**T * C C * Q**T
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*
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* If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C
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* with
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* SIDE = 'L' SIDE = 'R'
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* TRANS = 'N': P * C C * P
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* TRANS = 'T': P**T * C C * P**T
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*
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* Here Q and P**T are the orthogonal matrices determined by DGEBRD when
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* reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
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* P**T are defined as products of elementary reflectors H(i) and G(i)
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* respectively.
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*
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* Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
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* order of the orthogonal matrix Q or P**T that is applied.
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*
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* If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
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* if nq >= k, Q = H(1) H(2) . . . H(k);
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* if nq < k, Q = H(1) H(2) . . . H(nq-1).
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*
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* If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
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* if k < nq, P = G(1) G(2) . . . G(k);
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* if k >= nq, P = G(1) G(2) . . . G(nq-1).
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*
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* Arguments
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* =========
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*
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* VECT (input) CHARACTER*1
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* = 'Q': apply Q or Q**T;
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* = 'P': apply P or P**T.
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*
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* SIDE (input) CHARACTER*1
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* = 'L': apply Q, Q**T, P or P**T from the Left;
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* = 'R': apply Q, Q**T, P or P**T from the Right.
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*
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* TRANS (input) CHARACTER*1
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* = 'N': No transpose, apply Q or P;
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* = 'T': Transpose, apply Q**T or P**T.
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*
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* M (input) INTEGER
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* The number of rows of the matrix C. M >= 0.
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*
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* N (input) INTEGER
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* The number of columns of the matrix C. N >= 0.
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*
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* K (input) INTEGER
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* If VECT = 'Q', the number of columns in the original
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* matrix reduced by DGEBRD.
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* If VECT = 'P', the number of rows in the original
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* matrix reduced by DGEBRD.
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* K >= 0.
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*
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* A (input) DOUBLE PRECISION array, dimension
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* (LDA,min(nq,K)) if VECT = 'Q'
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* (LDA,nq) if VECT = 'P'
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* The vectors which define the elementary reflectors H(i) and
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* G(i), whose products determine the matrices Q and P, as
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* returned by DGEBRD.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A.
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* If VECT = 'Q', LDA >= max(1,nq);
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* if VECT = 'P', LDA >= max(1,min(nq,K)).
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*
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* TAU (input) DOUBLE PRECISION array, dimension (min(nq,K))
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* TAU(i) must contain the scalar factor of the elementary
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* reflector H(i) or G(i) which determines Q or P, as returned
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* by DGEBRD in the array argument TAUQ or TAUP.
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*
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* C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
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* On entry, the M-by-N matrix C.
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* On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
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* or P*C or P**T*C or C*P or C*P**T.
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*
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* LDC (input) INTEGER
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* The leading dimension of the array C. LDC >= max(1,M).
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*
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* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*
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* LWORK (input) INTEGER
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* The dimension of the array WORK.
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* If SIDE = 'L', LWORK >= max(1,N);
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* if SIDE = 'R', LWORK >= max(1,M).
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* For optimum performance LWORK >= N*NB if SIDE = 'L', and
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* LWORK >= M*NB if SIDE = 'R', where NB is the optimal
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* blocksize.
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*
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* If LWORK = -1, then a workspace query is assumed; the routine
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* only calculates the optimal size of the WORK array, returns
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* this value as the first entry of the WORK array, and no error
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* message related to LWORK is issued by XERBLA.
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN
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CHARACTER TRANST
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INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV
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EXTERNAL LSAME, ILAENV
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* ..
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* .. External Subroutines ..
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EXTERNAL DORMLQ, DORMQR, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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APPLYQ = LSAME( VECT, 'Q' )
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LEFT = LSAME( SIDE, 'L' )
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NOTRAN = LSAME( TRANS, 'N' )
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LQUERY = ( LWORK.EQ.-1 )
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*
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* NQ is the order of Q or P and NW is the minimum dimension of WORK
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*
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IF( LEFT ) THEN
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NQ = M
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NW = N
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ELSE
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NQ = N
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NW = M
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END IF
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IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
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INFO = -2
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ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
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INFO = -3
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ELSE IF( M.LT.0 ) THEN
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INFO = -4
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ELSE IF( N.LT.0 ) THEN
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INFO = -5
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ELSE IF( K.LT.0 ) THEN
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INFO = -6
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ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
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$ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
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$ THEN
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INFO = -8
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ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
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INFO = -11
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ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
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INFO = -13
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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IF( APPLYQ ) THEN
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IF( LEFT ) THEN
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NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1,
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$ -1 )
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ELSE
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NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1,
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$ -1 )
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END IF
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ELSE
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IF( LEFT ) THEN
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NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M-1, N, M-1,
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$ -1 )
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ELSE
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NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N-1, N-1,
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$ -1 )
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END IF
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END IF
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LWKOPT = MAX( 1, NW )*NB
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WORK( 1 ) = LWKOPT
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DORMBR', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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WORK( 1 ) = 1
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IF( M.EQ.0 .OR. N.EQ.0 )
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$ RETURN
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*
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IF( APPLYQ ) THEN
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*
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* Apply Q
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*
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IF( NQ.GE.K ) THEN
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*
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* Q was determined by a call to DGEBRD with nq >= k
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*
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CALL DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
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$ WORK, LWORK, IINFO )
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ELSE IF( NQ.GT.1 ) THEN
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*
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* Q was determined by a call to DGEBRD with nq < k
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*
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IF( LEFT ) THEN
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MI = M - 1
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NI = N
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I1 = 2
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I2 = 1
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ELSE
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MI = M
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NI = N - 1
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I1 = 1
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I2 = 2
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END IF
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CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
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$ C( I1, I2 ), LDC, WORK, LWORK, IINFO )
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END IF
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ELSE
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*
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* Apply P
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*
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IF( NOTRAN ) THEN
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TRANST = 'T'
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ELSE
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TRANST = 'N'
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END IF
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IF( NQ.GT.K ) THEN
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*
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* P was determined by a call to DGEBRD with nq > k
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*
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CALL DORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
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$ WORK, LWORK, IINFO )
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ELSE IF( NQ.GT.1 ) THEN
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*
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* P was determined by a call to DGEBRD with nq <= k
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*
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IF( LEFT ) THEN
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MI = M - 1
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NI = N
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I1 = 2
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I2 = 1
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ELSE
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MI = M
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NI = N - 1
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I1 = 1
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I2 = 2
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END IF
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CALL DORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
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$ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
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END IF
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END IF
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WORK( 1 ) = LWKOPT
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RETURN
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*
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* End of DORMBR
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*
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END
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