sormrz (l) - Linux Manuals
sormrz: overwrites the general real M-by-N matrix C with SIDE = aqLaq SIDE = aqRaq TRANS = aqNaq
NAME
SORMRZ - overwrites the general real M-by-N matrix C with SIDE = aqLaq SIDE = aqRaq TRANS = aqNaqSYNOPSIS
- SUBROUTINE SORMRZ(
- SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )
- CHARACTER SIDE, TRANS
- INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
- REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
PURPOSE
SORMRZ overwrites the general real M-by-N matrix C with TRANS = aqTaq: Q**T * C C * Q**Twhere Q is a real orthogonal matrix defined as the product of k elementary reflectors
Q
as returned by STZRZF. Q is of order M if SIDE = aqLaq and of order N if SIDE = aqRaq.
ARGUMENTS
- SIDE (input) CHARACTER*1
-
= aqLaq: apply Q or Q**T from the Left;
= aqRaq: apply Q or Q**T from the Right. - TRANS (input) CHARACTER*1
-
= aqNaq: No transpose, apply Q;
= aqTaq: Transpose, apply Q**T. - M (input) INTEGER
- The number of rows of the matrix C. M >= 0.
- N (input) INTEGER
- The number of columns of the matrix C. N >= 0.
- K (input) INTEGER
- The number of elementary reflectors whose product defines the matrix Q. If SIDE = aqLaq, M >= K >= 0; if SIDE = aqRaq, N >= K >= 0.
- L (input) INTEGER
- The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = aqLaq, M >= L >= 0, if SIDE = aqRaq, N >= L >= 0.
- A (input) REAL array, dimension
- (LDA,M) if SIDE = aqLaq, (LDA,N) if SIDE = aqRaq The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by STZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.
- LDA (input) INTEGER
- The leading dimension of the array A. LDA >= max(1,K).
- TAU (input) REAL array, dimension (K)
- TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by STZRZF.
- C (input/output) REAL array, dimension (LDC,N)
- On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
- LDC (input) INTEGER
- The leading dimension of the array C. LDC >= max(1,M).
- WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
- On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
- LWORK (input) INTEGER
- The dimension of the array WORK. If SIDE = aqLaq, LWORK >= max(1,N); if SIDE = aqRaq, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = aqLaq, and LWORK >= M*NB if SIDE = aqRaq, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
- INFO (output) INTEGER
-
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
FURTHER DETAILS
Based on contributions by