MB01KD - SLICOT Library Routine Documentation

## MB01KD

### Rank 2k operation alpha*A*trans(B) - alpha*B*trans(A) + beta*C, with A and C skew-symmetric matrices

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

Purpose

      To perform one of the skew-symmetric rank 2k operations

          C := alpha*A*B' - alpha*B*A' + beta*C,

      or

          C := alpha*A'*B - alpha*B'*A + beta*C,

      where alpha and beta are scalars, C is a real N-by-N skew-
      symmetric matrix and A, B are N-by-K matrices in the first case
      and K-by-N matrices in the second case.

      This is a modified version of the vanilla implemented BLAS
      routine DSYR2K written by Jack Dongarra, Iain Duff,
      Jeremy Du Croz and Sven Hammarling.

Specification

          SUBROUTINE MB01KD( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA,
         $                   C, LDC, INFO )
    C     .. Scalar Arguments ..
          CHARACTER         UPLO, TRANS
          INTEGER           INFO, K, LDA, LDB, LDC, N
          DOUBLE PRECISION  ALPHA, BETA
    C     .. Array Arguments ..
          DOUBLE PRECISION  A(LDA,*), B(LDB,*), C(LDC,*)

Arguments

Mode Parameters

      UPLO    CHARACTER*1
              Specifies whether the upper or lower triangular part of
              the array C is to be referenced, as follows:
              = 'U':  only the strictly upper triangular part of C is to
                      be referenced;
              = 'L':  only the striclty lower triangular part of C is to
                      be referenced.

      TRANS   CHARACTER*1
              Specifies the operation to be performed, as follows:
              = 'N':         C := alpha*A*B' - alpha*B*A' + beta*C;
              = 'T' or 'C':  C := alpha*A'*B - alpha*B'*A + beta*C.

Input/Output Parameters

      N       (input) INTEGER
              The order of the matrix C.  N >= 0.

      K       (input) INTEGER
              If TRANS = 'N' the number of columns of A and B; and if
              TRANS = 'T' or TRANS = 'C' the number of rows of A and B.
              K >= 0.

      ALPHA   (input) DOUBLE PRECISION
              The scalar alpha. If alpha is zero, or N <= 1, or K = 0,
              A and B are not referenced.

      A       (input)  DOUBLE PRECISION array, dimension (LDA,KA),
              where KA is K when TRANS = 'N', and is N otherwise.
              On entry with TRANS = 'N', the leading N-by-K part of
              of this array must contain the matrix A.
              On entry with TRANS = 'T' or TRANS = 'C', the leading
              K-by-N part of this array must contain the matrix A.

      LDA     INTEGER
              The leading dimension of the array A.
              LDA >= MAX(1,N),  if TRANS = 'N';
              LDA >= MAX(1,K),  if TRANS = 'T' or TRANS = 'C'.

      B       (input)  DOUBLE PRECISION array, dimension (LDB,KB),
              where KB is K when TRANS = 'N', and is N otherwise.
              On entry with TRANS = 'N', the leading N-by-K part of
              of this array must contain the matrix B.
              On entry with TRANS = 'T' or TRANS = 'C', the leading
              K-by-N part of this array must contain the matrix B.

      LDB     INTEGER
              The leading dimension of the array B.
              LDB >= MAX(1,N),  if TRANS = 'N';
              LDB >= MAX(1,K),  if TRANS = 'T' or TRANS = 'C'.

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

      C       (input/output)  DOUBLE PRECISION array, dimension (LDC,N)
              On entry with UPLO = 'U', the leading N-by-N part of this
              array must contain the strictly upper triangular part of
              the matrix C. The lower triangular part of this array is
              not referenced.
              On entry with UPLO = 'L', the leading N-by-N part of this
              array must contain the strictly lower triangular part of
              the matrix C. The upper triangular part of this array is
              not referenced.
              On exit with UPLO = 'U', the leading N-by-N part of this
              array contains the strictly upper triangular part of the
              updated matrix C.
              On exit with UPLO = 'L', the leading N-by-N part of this
              array contains the strictly lower triangular part of the
              updated matrix C.

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

Error Indicator

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

Numerical Aspects

      Though being almost identical with the vanilla implementation
      of the BLAS routine DSYR2K the performance of this routine could
      be significantly lower in the case of vendor supplied, highly
      optimized BLAS.

Further Comments

      None

Example

Program Text

      None

Program Data

      None

Program Results

      None

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