Purpose
  To compute either P or P', with P defined by the matrix formula
     P = op( H )*X*op( E )',
  where H is an upper Hessenberg matrix, X is a symmetric matrix,
  E is an upper triangular matrix, and op( M ) is one of
     op( M ) = M   or   op( M ) = M'.
Specification
      SUBROUTINE MB01OO( UPLO, TRANS, N, H, LDH, X, LDX, E, LDE, P, LDP,
     $                   INFO )
C     .. Scalar Arguments ..
      INTEGER           INFO, LDE, LDH, LDP, LDX, N
      CHARACTER         TRANS, UPLO
C     .. Array Arguments ..
      DOUBLE PRECISION  E(LDE,*), H(LDH,*), P(LDP,*), X(LDX,*)
Arguments
Mode Parameters
  UPLO    CHARACTER*1
          Specifies which triangle of the symmetric matrix X is
          given as follows:
          = 'U':  the upper triangular part is given;
          = 'L':  the lower triangular part is given.
  TRANS   CHARACTER*1
          Specifies the operation to be performed as follows:
          = 'N':         compute P  = H*X*E';
          = 'T' or 'C':  compute P' = E'*X*H.
Input/Output Parameters
  N       (input) INTEGER
          The order of the matrices H, X, E, and P.  N >= 0.
  H       (input) DOUBLE PRECISION array, dimension (LDH,N)
          On entry, the leading N-by-N upper Hessenberg part of this
          array must contain the upper Hessenberg matrix H.
          The remaining part of this array is not referenced.
  LDH     INTEGER
          The leading dimension of the array H.  LDH >= MAX(1,N).
  X       (input) DOUBLE PRECISION array, dimension (LDX,N)
          On entry, if UPLO = 'U', the leading N-by-N upper
          triangular part of this array must contain the upper
          triangular part of the symmetric matrix X and the strictly
          lower triangular part of the array is not referenced.
          On entry, if UPLO = 'L', the leading N-by-N lower
          triangular part of this array must contain the lower
          triangular part of the symmetric matrix X and the strictly
          upper triangular part of the array is not referenced.
  LDX     INTEGER
          The leading dimension of the array X.  LDX >= MAX(1,N).
  E       (input) DOUBLE PRECISION array, dimension (LDE,N)
          On entry, the leading N-by-N upper triangular part of this
          array must contain the upper triangular matrix E.
          The remaining part of this array is not referenced.
  LDE     INTEGER
          The leading dimension of array E.  LDE >= MAX(1,N).
  P       (output) DOUBLE PRECISION array, dimension (LDP,N)
          On exit, the leading N-by-N part of this array contains
          the computed matrix P  = H*X*E', if TRANS = 'N', or
          the computed matrix P' = E'*X*H, if TRANS = 'T'.
  LDP     INTEGER
          The leading dimension of the array P.  LDP >= MAX(1,N).
Error Indicator
  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -k, the k-th argument had an illegal
                value.
Method
The matrix expression is efficiently evaluated taking the structure into account, and using BLAS and SLICOT routines. Let W = H*X, or W = X*H, computed using SLICOT Library routine MB01OS. The result is then obtained calling BLAS 3 routine DTRMM.Numerical Aspects
The algorithm requires approximately N**3 operations.Further Comments
NoneExample
Program Text
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NoneProgram Results
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