ctpmqrt-f(3)

ctpmqrt.f –

Synopsis

Functions/Subroutines

subroutine ctpmqrt (SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
CTPMQRT

Function/Subroutine Documentation

subroutine ctpmqrt (characterSIDE, characterTRANS, integerM, integerN, integerK, integerL, integerNB, complex, dimension( ldv, * )V, integerLDV, complex, dimension( ldt, * )T, integerLDT, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( * )WORK, integerINFO)

CTPMQRT

Purpose:

 CTPMQRT applies a complex orthogonal 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': Transpose, apply Q**H.

 M is INTEGER
 The number of rows of the matrix B. M >= 0.

 N is INTEGER
 The number of columns of the matrix B. N >= 0.

 K is INTEGER
 The number of elementary reflectors whose product defines
 the matrix Q.

 L is INTEGER
 The order of the trapezoidal part of V. 
 K >= L >= 0. See Further Details.

 NB is INTEGER
 The block size used for the storage of T. K >= NB >= 1.
 This must be the same value of NB used to generate T
 in CTPQRT.

 V is COMPLEX array, dimension (LDA,K)
 The i-th column must contain the vector which defines the
 elementary reflector H(i), for i = 1,2,...,k, as returned by
 CTPQRT in B. See Further Details.

LDV

 LDV is INTEGER
 The leading dimension of the array V.
 If SIDE = 'L', LDV >= max(1,M);
 if SIDE = 'R', LDV >= max(1,N).

 T is COMPLEX array, dimension (LDT,K)
 The upper triangular factors of the block reflectors
 as returned by CTPQRT, stored as a NB-by-K matrix.

LDT

 LDT is INTEGER
 The leading dimension of the array T. LDT >= NB.

 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', LDC >= max(1,K);
 If SIDE = 'R', LDC >= max(1,M).

 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*NB if SIDE = 'L', or M*NB 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.

Date:

April 2012

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 upper trapezoidal, consisting of the first L
 rows of a K-by-K upper triangular matrix. If L=K, V2 is upper 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 M-by-K. 
 [B] 
If SIDE = ‘R’: C = [A B] where A is M-by-K, B is M-by-N and V is N-by-K.
The complex orthogonal 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 QH * 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 * QH.

Definition at line 216 of file ctpmqrt.f.

Author

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