MB02CV - SLICOT Library Routine Documentation

## 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, STRUCG, 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          STRUCG, 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.

      STRUCG  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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