MB04QS

Multiplication with a product of symplectic reflectors and Givens rotations

Purpose

  Overwrites general real m-by-n/n-by-m matrices C and D with

            [ op(C) ]
      U  *  [       ]   if TRANU = 'N', or
            [ op(D) ]

       T    [ op(C) ]
      U  *  [       ]   if TRANU = 'T',
            [ op(D) ]

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

      U = 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) ),

  with k = m-1, as returned by the SLICOT Library routines MB04PU
  or MB04RU.

      SUBROUTINE MB04QS( TRANC, TRAND, TRANU, M, N, ILO, V, LDV, W, LDW,
     $                   C, LDC, D, LDD, CS, TAU, DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
      CHARACTER         TRANC, TRAND, TRANU
      INTEGER           ILO, INFO, 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'.

  TRANU   CHARACTER*1
          Specifies whether U or U' is applied as follows:
          = 'N':  apply U;
          = 'T':  apply U'.

  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.

  ILO     (input) INTEGER
          ILO must have the same value as in the previous call of
          MB04PU or MB04RU. U is equal to the unit matrix except in
          the submatrix
          U([ilo+1:m m+ilo+1:2*m], [ilo+1:m m+ilo+1:2*m]).
          1 <= ILO <= M+1.

  V       (input) DOUBLE PRECISION array, dimension (LDV,M)
          On entry, the leading M-by-M part of this array must
          contain in its columns the vectors which define the
          elementary reflectors H(i).

  LDV     INTEGER
          The leading dimension of the array V.  LDV >= MAX(1,M).

  W       (input) DOUBLE PRECISION array, dimension (LDW,M)
          On entry, the leading M-by-M part of this array must
          contain in its columns the vectors which define the
          elementary reflectors F(i).

  LDW     INTEGER
          The leading dimension of the array W.  LDW >= MAX(1,M).

  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 = 'T' or TRANC = 'C', 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 = 'T' or TRANC = 'C', 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 = 'T' or TRAND = 'C', 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 = 'T' or TRAND = 'C', 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*N-2)
          On entry, the first 2*N-2 elements of this array must
          contain the cosines and sines of the symplectic Givens
          rotations G(i), as returned by MB04PU or MB04RU.

  TAU     (input) DOUBLE PRECISION array, dimension (N-1)
          On entry, the first N-1 elements of this array must
          contain the scalar factors of the elementary reflectors
          F(i), as returned by MB04PU or MB04RU.

  DWORK   DOUBLE PRECISION array, dimension (LDWORK)
          On exit, if INFO = 0,  DWORK(1)  returns the optimal value
          of LDWORK.
          On exit, if  INFO = -18,  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.

  None

Program Text

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