ctpmlqt.f - Man Page
SRC/ctpmlqt.f
Synopsis
Functions/Subroutines
subroutine ctpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
CTPMLQT
Function/Subroutine Documentation
subroutine ctpmlqt (character side, character trans, integer m, integer n, integer k, integer l, integer mb, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer info)
CTPMLQT
Purpose:
CTPMLQT applies a complex unitary matrix Q obtained from a 'triangular-pentagonal' complex block reflector H to a general complex matrix C, which consists of two blocks A and B.
- Parameters
SIDE
SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right.
TRANS
TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**H.
M
M is INTEGER The number of rows of the matrix B. M >= 0.
N
N is INTEGER The number of columns of the matrix B. N >= 0.
K
K is INTEGER The number of elementary reflectors whose product defines the matrix Q.
L
L is INTEGER The order of the trapezoidal part of V. K >= L >= 0. See Further Details.
MB
MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in CTPLQT.
V
V is COMPLEX array, dimension (LDV,K) The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CTPLQT in B. See Further Details.
LDV
LDV is INTEGER The leading dimension of the array V. LDV >= K.
T
T is COMPLEX array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by CTPLQT, stored as a MB-by-K matrix.
LDT
LDT is INTEGER The leading dimension of the array T. LDT >= MB.
A
A is COMPLEX array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R' On entry, the K-by-N or M-by-K matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.
LDA
LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,K); If SIDE = 'R', LDA >= max(1,M).
B
B is COMPLEX array, dimension (LDB,N) On entry, the M-by-N matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.
LDB
LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).
WORK
WORK is COMPLEX array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
INFO
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
- Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
The columns of the pentagonal matrix V contain the elementary reflectors H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a trapezoidal block V2: V = [V1] [V2]. The size of the trapezoidal block V2 is determined by the parameter L, where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L rows of a K-by-K upper triangular matrix. If L=K, V2 is lower triangular; if L=0, there is no trapezoidal block, hence V = V1 is rectangular. If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is K-by-M. [B] If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is K-by-N. The complex unitary matrix Q is formed from V and T. If TRANS='N' and SIDE='L', C is on exit replaced with Q * C. If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C. If TRANS='N' and SIDE='R', C is on exit replaced with C * Q. If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
Definition at line 197 of file ctpmlqt.f.
Author
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Referenced By
The man page ctpmlqt(3) is an alias of ctpmlqt.f(3).
Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK