ctpmqrt.f man page

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

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.

NB

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

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

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

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

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:

November 2013

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 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 216 of file ctpmqrt.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

ctpmqrt(3) is an alias of ctpmqrt.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK