MB04QB

Applying a product of symplectic reflectors and Givens rotations to two general real matrices

Purpose

  To overwrite general real m-by-n matrices C and D, or their
  transposes, with

            [ op(C) ]
      Q  *  [       ]   if TRANQ = 'N', or
            [ op(D) ]

       T    [ op(C) ]
      Q  *  [       ]   if TRANQ = 'T',
            [ op(D) ]

  where Q is defined as the product of symplectic reflectors and
  Givens rotations,

      Q = diag( H(1),H(1) ) G(1) diag( F(1),F(1) )
          diag( H(2),H(2) ) G(2) diag( F(2),F(2) )
                            ....
          diag( H(k),H(k) ) G(k) diag( F(k),F(k) ).

  Blocked version.

      SUBROUTINE MB04QB( TRANC, TRAND, TRANQ, STOREV, STOREW, M, N, K,
     $                   V, LDV, W, LDW, C, LDC, D, LDD, CS, TAU, DWORK,
     $                   LDWORK, INFO )
C     .. Scalar Arguments ..
      CHARACTER         STOREV, STOREW, TRANC, TRAND, TRANQ
      INTEGER           INFO, K, LDC, LDD, LDV, LDW, LDWORK, M, N
C     .. Array Arguments ..
      DOUBLE PRECISION  C(LDC,*), CS(*), D(LDD,*), DWORK(*), TAU(*),
     $                  V(LDV,*), W(LDW,*)

Mode Parameters

  TRANC   CHARACTER*1
          Specifies the form of op( C ) as follows:
          = 'N':  op( C ) = C;
          = 'T':  op( C ) = C';
          = 'C':  op( C ) = C'.

  TRAND   CHARACTER*1
          Specifies the form of op( D ) as follows:
          = 'N':  op( D ) = D;
          = 'T':  op( D ) = D';
          = 'C':  op( D ) = D'.

  TRANQ   CHARACTER*1
          = 'N':  apply Q;
          = 'T':  apply Q'.

  STOREV  CHARACTER*1
          Specifies how the vectors which define the concatenated
          Householder reflectors contained in V are stored:
          = 'C':  columnwise;
          = 'R':  rowwise.

  STOREW  CHARACTER*1
          Specifies how the vectors which define the concatenated
          Householder reflectors contained in W are stored:
          = 'C':  columnwise;
          = 'R':  rowwise.

  M       (input) INTEGER
          The number of rows of the matrices op(C) and op(D).
          M >= 0.

  N       (input) INTEGER
          The number of columns of the matrices op(C) and op(D).
          N >= 0.

  K       (input) INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.  M >= K >= 0.

  V       (input) DOUBLE PRECISION array, dimension
                  (LDV,K) if STOREV = 'C',
                  (LDV,M) if STOREV = 'R'
          On entry with STOREV = 'C', the leading M-by-K part of
          this array must contain in its columns the vectors which
          define the elementary reflectors F(i).
          On entry with STOREV = 'R', the leading K-by-M part of
          this array must contain in its rows the vectors which
          define the elementary reflectors F(i).

  LDV     INTEGER
          The leading dimension of the array V.
          LDV >= MAX(1,M),  if STOREV = 'C';
          LDV >= MAX(1,K),  if STOREV = 'R'.

  W       (input) DOUBLE PRECISION array, dimension
                  (LDW,K) if STOREW = 'C',
                  (LDW,M) if STOREW = 'R'
          On entry with STOREW = 'C', the leading M-by-K part of
          this array must contain in its columns the vectors which
          define the elementary reflectors H(i).
          On entry with STOREW = 'R', the leading K-by-M part of
          this array must contain in its rows the vectors which
          define the elementary reflectors H(i).

  LDW     INTEGER
          The leading dimension of the array W.
          LDW >= MAX(1,M),  if STOREW = 'C';
          LDW >= MAX(1,K),  if STOREW = 'R'.

  C       (input/output) DOUBLE PRECISION array, dimension
                  (LDC,N) if TRANC = 'N',
                  (LDC,M) if TRANC = 'T' or TRANC = 'C'
          On entry with TRANC = 'N', the leading M-by-N part of
          this array must contain the matrix C.
          On entry with TRANC = 'C' or TRANC = 'T', the leading
          N-by-M part of this array must contain the transpose of
          the matrix C.
          On exit with TRANC = 'N', the leading M-by-N part of
          this array contains the updated matrix C.
          On exit with TRANC = 'C' or TRANC = 'T', the leading
          N-by-M part of this array contains the transpose of the
          updated matrix C.

  LDC     INTEGER
          The leading dimension of the array C.
          LDC >= MAX(1,M),  if TRANC = 'N';
          LDC >= MAX(1,N),  if TRANC = 'T' or TRANC = 'C'.

  D       (input/output) DOUBLE PRECISION array, dimension
                  (LDD,N) if TRAND = 'N',
                  (LDD,M) if TRAND = 'T' or TRAND = 'C'
          On entry with TRAND = 'N', the leading M-by-N part of
          this array must contain the matrix D.
          On entry with TRAND = 'C' or TRAND = 'T', the leading
          N-by-M part of this array must contain the transpose of
          the matrix D.
          On exit with TRAND = 'N', the leading M-by-N part of
          this array contains the updated matrix D.
          On exit with TRAND = 'C' or TRAND = 'T', the leading
          N-by-M part of this array contains the transpose of the
          updated matrix D.

  LDD     INTEGER
          The leading dimension of the array D.
          LDD >= MAX(1,M),  if TRAND = 'N';
          LDD >= MAX(1,N),  if TRAND = 'T' or TRAND = 'C'.

  CS      (input) DOUBLE PRECISION array, dimension (2*K)
          On entry, the first 2*K elements of this array must
          contain the cosines and sines of the symplectic Givens
          rotations G(i).

  TAU     (input) DOUBLE PRECISION array, dimension (K)
          On entry, the first K elements of this array must
          contain the scalar factors of the elementary reflectors
          F(i).

  DWORK   DOUBLE PRECISION array, dimension (LDWORK)
          On exit, if INFO = 0,  DWORK(1)  returns the optimal
          value of LDWORK.
          On exit, if  INFO = -20,  DWORK(1)  returns the minimum
          value of LDWORK.

  LDWORK  INTEGER
          The length of the array DWORK.  LDWORK >= MAX(1,N).

          If LDWORK = -1, then a workspace query is assumed;
          the routine only calculates the optimal size of the
          DWORK array, returns this value as the first entry of
          the DWORK array, and no error message related to LDWORK
          is issued by XERBLA.

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value.

  [1] Kressner, D.
      Block algorithms for orthogonal symplectic factorizations.
      BIT, 43 (4), pp. 775-790, 2003.

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