Purpose
To perform one of the special symmetric rank 2k operations R := alpha*R + beta*H*X + beta*X*H', or R := alpha*R + beta*H'*X + beta*X*H, where alpha and beta are scalars, R and X are N-by-N symmetric matrices, and H is an N-by-N upper Hessenberg matrix.Specification
SUBROUTINE MB01OC( UPLO, TRANS, N, ALPHA, BETA, R, LDR, H, LDH, X, $ LDX, INFO ) C .. Scalar Arguments .. CHARACTER TRANS, UPLO INTEGER INFO, LDH, LDR, LDX, N DOUBLE PRECISION ALPHA, BETA C .. Array Arguments .. DOUBLE PRECISION H(LDH,*), R(LDR,*), X(LDX,*)Arguments
Mode Parameters
UPLO CHARACTER*1 Specifies which triangles of the symmetric matrices R and X are 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': R := alpha*R + beta*H*X + beta*X*H'; = 'T' or 'C': R := alpha*R + beta*H'*X + beta*X*H.Input/Output Parameters
N (input) INTEGER The order of the matrices R, H, and X. N >= 0. ALPHA (input) DOUBLE PRECISION The scalar alpha. When alpha is zero then R need not be set before entry, except when R is identified with X in the call. BETA (input) DOUBLE PRECISION The scalar beta. When beta is zero then H and X are not referenced. R (input/output) DOUBLE PRECISION array, dimension (LDR,N) On entry with UPLO = 'U', the leading N-by-N upper triangular part of this array must contain the upper triangular part of the symmetric matrix R. On entry with UPLO = 'L', the leading N-by-N lower triangular part of this array must contain the lower triangular part of the symmetric matrix R. In both cases, the other strictly triangular part is not referenced. On exit, the leading N-by-N upper triangular part (if UPLO = 'U'), or lower triangular part (if UPLO = 'L'), of this array contains the corresponding triangular part of the computed matrix R. LDR INTEGER The leading dimension of the array R. LDR >= MAX(1,N). 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).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 inline code and BLAS1 routines.Numerical Aspects
The algorithm requires approximately N**3/2 operations.Further Comments
This routine acts as a specialization of BLAS Library routine DSYR2K.Example
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