MB02CV

Applying the MB02CU transformations on other columns / rows of the generator

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

  To apply the transformations created by the SLICOT Library routine
  MB02CU on other columns / rows of the generator, contained in the
  arrays F1, F2 and G.

Specification
      SUBROUTINE MB02CV( TYPEG, STRUCT, K, N, P, Q, NB, RNK, A1, LDA1,
     $                   A2, LDA2, B, LDB, F1, LDF1, F2, LDF2, G, LDG,
     $                   CS, DWORK, LDWORK, INFO )
C     .. Scalar Arguments ..
      CHARACTER          STRUCT, TYPEG
      INTEGER            INFO, K, LDA1, LDA2, LDB, LDF1, LDF2, LDG,
     $                   LDWORK, N, NB, P, Q, RNK
C     .. Array Arguments ..
      DOUBLE PRECISION   A1(LDA1,*), A2(LDA2,*), B(LDB,*), CS(*),
     $                   DWORK(*), F1(LDF1,*), F2(LDF2,*), G(LDG,*)

Arguments

Mode Parameters

  TYPEG   CHARACTER*1
          Specifies the type of the generator, as follows:
          = 'D':  generator is column oriented and rank
                  deficient;
          = 'C':  generator is column oriented and not rank
                  deficient;
          = 'R':  generator is row oriented and not rank
                  deficient.
          Note that this parameter must be equivalent with the
          used TYPEG in the call of MB02CU.

  STRUCT  CHARACTER*1
          Information about the structure of the generators,
          as follows:
          = 'T':  the trailing block of the positive generator
                  is upper / lower triangular, and the trailing
                  block of the negative generator is zero;
          = 'N':  no special structure to mention.

Input/Output Parameters
  K       (input)  INTEGER
          The number of rows in A1 to be processed.  K >= 0.

  N       (input)  INTEGER
          If TYPEG = 'D'  or  TYPEG = 'C', the number of rows in F1;
          if TYPEG = 'R', the number of columns in F1.  N >= 0.

  P       (input)  INTEGER
          The number of columns of the positive generator.  P >= K.

  Q       (input)  INTEGER
          The number of columns in B.
          If TYPEG = 'D',        Q >= K;
          If TYPEG = 'C' or 'R', Q >= 0.

  NB      (input)  INTEGER
          On entry, if TYPEG = 'C'  or  TYPEG = 'R', NB specifies
          the block size to be used in the blocked parts of the
          algorithm. NB must be equivalent with the used block size
          in the routine MB02CU.

  RNK     (input)  INTEGER
          If TYPEG = 'D', the number of linearly independent columns
          in the generator as returned by MB02CU.  0 <= RNK <= K.
          If TYPEG = 'C' or 'R', the value of this parameter is
          irrelevant.

  A1      (input)  DOUBLE PRECISION array, dimension
          (LDA1, K)
          On entry, if TYPEG = 'D', the leading K-by-K part of this
          array must contain the matrix A1 as returned by MB02CU.
          If TYPEG = 'C' or 'R', this array is not referenced.

  LDA1    INTEGER
          The leading dimension of the array A1.
          If TYPEG = 'D',                   LDA1 >= MAX(1,K);
          if TYPEG = 'C'  or  TYPEG = 'R',  LDA1 >= 1.

  A2      (input)  DOUBLE PRECISION array,
          if TYPEG = 'D'  or  TYPEG = 'C',  dimension (LDA2, P-K);
          if TYPEG = 'R',                   dimension (LDA2, K).
          On entry, if TYPEG = 'D'  or  TYPEG = 'C', the leading
          K-by-(P-K) part of this array must contain the matrix
          A2 as returned by MB02CU.
          On entry, if TYPEG = 'R', the leading (P-K)-by-K part of
          this array must contain the matrix A2 as returned by
          MB02CU.

  LDA2    INTEGER
          The leading dimension of the array A2.
          If P = K,                  LDA2 >= 1;
          If P > K and (TYPEG = 'D' or TYPEG = 'C'),
                                     LDA2 >= MAX(1,K);
          if P > K and TYPEG = 'R',  LDA2 >= P-K.

  B       (input)  DOUBLE PRECISION array,
          if TYPEG = 'D'  or  TYPEG = 'C',  dimension (LDB, Q);
          if TYPEG = 'R',                   dimension (LDB, K).
          On entry, if TYPEG = 'D'  or  TYPEG = 'C', the leading
          K-by-Q part of this array must contain the matrix B as
          returned by MB02CU.
          On entry, if TYPEG = 'R', the leading Q-by-K part of this
          array must contain the matrix B as returned by MB02CU.

  LDB     INTEGER
          The leading dimension of the array B.
          If Q = 0,                  LDB >= 1;
          If Q > 0 and (TYPEG = 'D' or TYPEG = 'C'),
                                     LDB >= MAX(1,K);
          if Q > 0 and TYPEG = 'R',  LDB >= Q.

  F1      (input/output)  DOUBLE PRECISION array,
          if TYPEG = 'D'  or  TYPEG = 'C',  dimension (LDF1, K);
          if TYPEG = 'R',                   dimension (LDF1, N).
          On entry, if TYPEG = 'D'  or  TYPEG = 'C', the leading
          N-by-K part of this array must contain the first part
          of the positive generator to be processed.
          On entry, if TYPEG = 'R', the leading K-by-N part of this
          array must contain the first part of the positive
          generator to be processed.
          On exit, if TYPEG = 'D'  or  TYPEG = 'C', the leading
          N-by-K part of this array contains the first part of the
          transformed positive generator.
          On exit, if TYPEG = 'R', the leading K-by-N part of this
          array contains the first part of the transformed positive
          generator.

  LDF1    INTEGER
          The leading dimension of the array F1.
          If TYPEG = 'D'  or  TYPEG = 'C',   LDF1 >= MAX(1,N);
          if TYPEG = 'R',                    LDF1 >= MAX(1,K).

  F2      (input/output)  DOUBLE PRECISION array,
          if TYPEG = 'D'  or  TYPEG = 'C',  dimension (LDF2, P-K);
          if TYPEG = 'R',                   dimension (LDF2, N).
          On entry, if TYPEG = 'D'  or  TYPEG = 'C', the leading
          N-by-(P-K) part of this array must contain the second part
          of the positive generator to be processed.
          On entry, if TYPEG = 'R', the leading (P-K)-by-N part of
          this array must contain the second part of the positive
          generator to be processed.
          On exit, if TYPEG = 'D'  or  TYPEG = 'C', the leading
          N-by-(P-K) part of this array contains the second part of
          the transformed positive generator.
          On exit, if TYPEG = 'R', the leading (P-K)-by-N part of
          this array contains the second part of the transformed
          positive generator.

  LDF2    INTEGER
          The leading dimension of the array F2.
          If P = K,                  LDF2 >= 1;
          If P > K and (TYPEG = 'D' or TYPEG = 'C'),
                                     LDF2 >= MAX(1,N);
          if P > K and TYPEG = 'R',  LDF2 >= P-K.

  G       (input/output)  DOUBLE PRECISION array,
          if TYPEG = 'D'  or  TYPEG = 'C',  dimension (LDG, Q);
          if TYPEG = 'R',                   dimension (LDG, N).
          On entry, if TYPEG = 'D'  or  TYPEG = 'C', the leading
          N-by-Q part of this array must contain the negative part
          of the generator to be processed.
          On entry, if TYPEG = 'R', the leading Q-by-N part of this
          array must contain the negative part of the generator to
          be processed.
          On exit, if TYPEG = 'D'  or  TYPEG = 'C', the leading
          N-by-Q part of this array contains the transformed
          negative generator.
          On exit, if TYPEG = 'R', the leading Q-by-N part of this
          array contains the transformed negative generator.

  LDG     INTEGER
          The leading dimension of the array G.
          If Q = 0,                  LDG >= 1;
          If Q > 0 and (TYPEG = 'D' or TYPEG = 'C'),
                                     LDG >= MAX(1,N);
          if Q > 0 and TYPEG = 'R',  LDG >= Q.

  CS      (input)  DOUBLE PRECISION array, dimension (x)
          If TYPEG = 'D' and P = K,                   x = 3*K;
          If TYPEG = 'D' and P > K,                   x = 5*K;
          If (TYPEG = 'C' or TYPEG = 'R') and P = K,  x = 4*K;
          If (TYPEG = 'C' or TYPEG = 'R') and P > K,  x = 6*K.
          On entry, the first x elements of this array must contain
          Givens and modified hyperbolic rotation parameters, and
          scalar factors of the Householder transformations as
          returned by MB02CU.

Workspace
  DWORK   DOUBLE PRECISION array, dimension (LDWORK)
          On exit, if INFO = -23,  DWORK(1) returns the minimum
          value of LDWORK.

  LDWORK  INTEGER
          The length of the array DWORK.
          TYPEG = 'D':               LDWORK >= MAX(1,N);
          (TYPEG = 'C' or TYPEG = 'R')  and  NB <= 0:
                                     LDWORK >= MAX(1,N);
          (TYPEG = 'C' or TYPEG = 'R')  and  NB >= 1:
                                     LDWORK >= MAX(1,( N + K )*NB).

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

Numerical Aspects
  The algorithm requires 0(N*K*( P + Q )) floating point operations.

Method
  The Householder transformations and modified hyperbolic rotations
  computed by SLICOT Library routine MB02CU are applied to the
  corresponding parts of the matrices F1, F2 and G.

Further Comments
  None
Example

Program Text

  None
Program Data
  None
Program Results
  None

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