MB01KD

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

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.

      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,*)

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.

  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)

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

  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.

  None

Program Text

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