Chimie Théorique » Opt'n Path

      SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,

     $                   LDC, WORK, LWORK, INFO )

*

*  -- LAPACK routine (version 3.2) --

*  -- LAPACK is a software package provided by Univ. of Tennessee,    --

*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--

*     November 2006

*

*     .. Scalar Arguments ..

      CHARACTER          SIDE, TRANS, VECT

      INTEGER            INFO, K, LDA, LDC, LWORK, M, N

*     ..

*     .. Array Arguments ..

      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

*     ..

*

*  Purpose

*  =======

*

*  If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C

*  with

*                  SIDE = 'L'     SIDE = 'R'

*  TRANS = 'N':      Q * C          C * Q

*  TRANS = 'T':      Q**T * C       C * Q**T

*

*  If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C

*  with

*                  SIDE = 'L'     SIDE = 'R'

*  TRANS = 'N':      P * C          C * P

*  TRANS = 'T':      P**T * C       C * P**T

*

*  Here Q and P**T are the orthogonal matrices 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) and G(i)

*  respectively.

*

*  Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the

*  order of the orthogonal matrix Q or P**T that is applied.

*

*  If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:

*  if nq >= k, Q = H(1) H(2) . . . H(k);

*  if nq < k, Q = H(1) H(2) . . . H(nq-1).

*

*  If VECT = 'P', A is assumed to have been a K-by-NQ matrix:

*  if k < nq, P = G(1) G(2) . . . G(k);

*  if k >= nq, P = G(1) G(2) . . . G(nq-1).

*

*  Arguments

*  =========

*

*  VECT    (input) CHARACTER*1

*          = 'Q': apply Q or Q**T;

*          = 'P': apply P or P**T.

*

*  SIDE    (input) CHARACTER*1

*          = 'L': apply Q, Q**T, P or P**T from the Left;

*          = 'R': apply Q, Q**T, P or P**T from the Right.

*

*  TRANS   (input) CHARACTER*1

*          = 'N':  No transpose, apply Q  or P;

*          = 'T':  Transpose, apply Q**T or P**T.

*

*  M       (input) INTEGER

*          The number of rows of the matrix C. M >= 0.

*

*  N       (input) INTEGER

*          The number of columns of the matrix C. N >= 0.

*

*  K       (input) INTEGER

*          If VECT = 'Q', the number of columns in the original

*          matrix reduced by DGEBRD.

*          If VECT = 'P', the number of rows in the original

*          matrix reduced by DGEBRD.

*          K >= 0.

*

*  A       (input) DOUBLE PRECISION array, dimension

*                                (LDA,min(nq,K)) if VECT = 'Q'

*                                (LDA,nq)        if VECT = 'P'

*          The vectors which define the elementary reflectors H(i) and

*          G(i), whose products determine the matrices Q and P, as

*          returned by DGEBRD.

*

*  LDA     (input) INTEGER

*          The leading dimension of the array A.

*          If VECT = 'Q', LDA >= max(1,nq);

*          if VECT = 'P', LDA >= max(1,min(nq,K)).

*

*  TAU     (input) DOUBLE PRECISION array, dimension (min(nq,K))

*          TAU(i) must contain the scalar factor of the elementary

*          reflector H(i) or G(i) which determines Q or P, as returned

*          by DGEBRD in the array argument TAUQ or TAUP.

*

*  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)

*          On entry, the M-by-N matrix C.

*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q

*          or P*C or P**T*C or C*P or C*P**T.

*

*  LDC     (input) INTEGER

*          The leading dimension of the array C. LDC >= max(1,M).

*

*  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.

*          If SIDE = 'L', LWORK >= max(1,N);

*          if SIDE = 'R', LWORK >= max(1,M).

*          For optimum performance LWORK >= N*NB if SIDE = 'L', and

*          LWORK >= M*NB if SIDE = 'R', 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

*

*  =====================================================================

*

*     .. Local Scalars ..

      LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN

      CHARACTER          TRANST

      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW

*     ..

*     .. External Functions ..

      LOGICAL            LSAME

      INTEGER            ILAENV

      EXTERNAL           LSAME, ILAENV

*     ..

*     .. External Subroutines ..

      EXTERNAL           DORMLQ, DORMQR, XERBLA

*     ..

*     .. Intrinsic Functions ..

      INTRINSIC          MAX, MIN

*     ..

*     .. Executable Statements ..

*

*     Test the input arguments

*

      INFO = 0

      APPLYQ = LSAME( VECT, 'Q' )

      LEFT = LSAME( SIDE, 'L' )

      NOTRAN = LSAME( TRANS, 'N' )

      LQUERY = ( LWORK.EQ.-1 )

*

*     NQ is the order of Q or P and NW is the minimum dimension of WORK

*

      IF( LEFT ) THEN

         NQ = M

         NW = N

      ELSE

         NQ = N

         NW = M

      END IF

      IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN

         INFO = -1

      ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN

         INFO = -2

      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN

         INFO = -3

      ELSE IF( M.LT.0 ) THEN

         INFO = -4

      ELSE IF( N.LT.0 ) THEN

         INFO = -5

      ELSE IF( K.LT.0 ) THEN

         INFO = -6

      ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.

     $         ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )

     $          THEN

         INFO = -8

      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN

         INFO = -11

      ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN

         INFO = -13

      END IF

*

      IF( INFO.EQ.0 ) THEN

         IF( APPLYQ ) THEN

            IF( LEFT ) THEN

               NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1,

     $              -1 )

            ELSE

               NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1,

     $              -1 )

            END IF

         ELSE

            IF( LEFT ) THEN

               NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M-1, N, M-1,

     $              -1 )

            ELSE

               NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N-1, N-1,

     $              -1 )

            END IF

         END IF

         LWKOPT = MAX( 1, NW )*NB

         WORK( 1 ) = LWKOPT

      END IF

*

      IF( INFO.NE.0 ) THEN

         CALL XERBLA( 'DORMBR', -INFO )

         RETURN

      ELSE IF( LQUERY ) THEN

         RETURN

      END IF

*

*     Quick return if possible

*

      WORK( 1 ) = 1

      IF( M.EQ.0 .OR. N.EQ.0 )

     $   RETURN

*

      IF( APPLYQ ) THEN

*

*        Apply Q

*

         IF( NQ.GE.K ) THEN

*

*           Q was determined by a call to DGEBRD with nq >= k

*

            CALL DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,

     $                   WORK, LWORK, IINFO )

         ELSE IF( NQ.GT.1 ) THEN

*

*           Q was determined by a call to DGEBRD with nq < k

*

            IF( LEFT ) THEN

               MI = M - 1

               NI = N

               I1 = 2

               I2 = 1

            ELSE

               MI = M

               NI = N - 1

               I1 = 1

               I2 = 2

            END IF

            CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,

     $                   C( I1, I2 ), LDC, WORK, LWORK, IINFO )

         END IF

      ELSE

*

*        Apply P

*

         IF( NOTRAN ) THEN

            TRANST = 'T'

         ELSE

            TRANST = 'N'

         END IF

         IF( NQ.GT.K ) THEN

*

*           P was determined by a call to DGEBRD with nq > k

*

            CALL DORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,

     $                   WORK, LWORK, IINFO )

         ELSE IF( NQ.GT.1 ) THEN

*

*           P was determined by a call to DGEBRD with nq <= k

*

            IF( LEFT ) THEN

               MI = M - 1

               NI = N

               I1 = 2

               I2 = 1

            ELSE

               MI = M

               NI = N - 1

               I1 = 1

               I2 = 2

            END IF

            CALL DORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,

     $                   TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )

         END IF

      END IF

      WORK( 1 ) = LWKOPT

      RETURN

*

*     End of DORMBR

*

      END