MB01VD - SLICOT Library Routine Documentation

## MB01VD

### Kronecker product of two matrices

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

Purpose

      To perform the following matrix operation

         C = alpha*kron( op(A), op(B) ) + beta*C,

      where alpha and beta are real scalars, op(M) is either matrix M or
      its transpose, M', and kron( X, Y ) denotes the Kronecker product
      of the matrices X and Y.

Specification

          SUBROUTINE MB01VD( TRANA, TRANB, MA, NA, MB, NB, ALPHA, BETA,
         $                   A, LDA, B, LDB, C, LDC, MC, NC, INFO )
    C     .. Scalar Arguments ..
          CHARACTER         TRANA, TRANB
          INTEGER           INFO, LDA, LDB, LDC, MA, MB, MC, NA, NB, NC
          DOUBLE PRECISION  ALPHA, BETA
    C     .. Array Arguments ..
          DOUBLE PRECISION  A(LDA,*), B(LDB,*), C(LDC,*)

Arguments

Mode Parameters

      TRANA   CHARACTER*1
              Specifies the form of op(A) to be used as follows:
              = 'N':  op(A) = A;
              = 'T':  op(A) = A';
              = 'C':  op(A) = A'.

      TRANB   CHARACTER*1
              Specifies the form of op(B) to be used as follows:
              = 'N':  op(B) = B;
              = 'T':  op(B) = B';
              = 'C':  op(B) = B'.

Input/Output Parameters

      MA      (input) INTEGER
              The number of rows of the matrix op(A).  MA >= 0.

      NA      (input) INTEGER
              The number of columns of the matrix op(A).  NA >= 0.

      MB      (input) INTEGER
              The number of rows of the matrix op(B).  MB >= 0.

      NB      (input) INTEGER
              The number of columns of the matrix op(B).  NB >= 0.

      ALPHA   (input) DOUBLE PRECISION
              The scalar alpha. When alpha is zero then A and B need not
              be set before entry.

      BETA    (input) DOUBLE PRECISION
              The scalar beta. When beta is zero then C need not be
              set before entry.

      A       (input) DOUBLE PRECISION array, dimension (LDA,ka),
              where ka is NA when TRANA = 'N', and is MA otherwise.
              If TRANA = 'N', the leading MA-by-NA part of this array
              must contain the matrix A; otherwise, the leading NA-by-MA
              part of this array must contain the matrix A.

      LDA     INTEGER
              The leading dimension of the array A.
              LDA >= max(1,MA), if TRANA = 'N';
              LDA >= max(1,NA), if TRANA = 'T' or 'C'.

      B       (input) DOUBLE PRECISION array, dimension (LDB,kb)
              where kb is NB when TRANB = 'N', and is MB otherwise.
              If TRANB = 'N', the leading MB-by-NB part of this array
              must contain the matrix B; otherwise, the leading NB-by-MB
              part of this array must contain the matrix B.

      LDB     INTEGER
              The leading dimension of the array B.
              LDB >= max(1,MB), if TRANB = 'N';
              LDB >= max(1,NB), if TRANB = 'T' or 'C'.

      C       (input/output) DOUBLE PRECISION array, dimension (LDC,NC)
              On entry, if beta is nonzero, the leading MC-by-NC part of
              this array must contain the given matric C, where
              MC = MA*MB and NC = NA*NB.
              On exit, the leading MC-by-NC part of this array contains
              the computed matrix expression
              C = alpha*kron( op(A), op(B) ) + beta*C.

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

      MC      (output) INTEGER
              The number of rows of the matrix C.  MC = MA*MB.

      NC      (output) INTEGER
              The number of columns of the matrix C.  NC = NA*NB.

Error Indicator

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

Method

      The Kronecker product of the matrices op(A) and op(B) is computed
      column by column.

Further Comments

      The multiplications by zero elements in A are avoided, if the
      matrix A is considered to be sparse, i.e., if
      (number of zeros in A)/(MA*NA) >= SPARST = 0.8. The code makes
      NB+1 passes through the matrix A, and MA*NA passes through the
      matrix B. If LDA and/or LDB are very large, and op(A) = A' and/or
      op(B) = B', it could be more efficient to transpose A and/or B
      before calling this routine, and use the 'N' values for TRANA
      and/or TRANB.

Example

Program Text

      None

Program Data

      None

Program Results

      None

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