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
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