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ztpmqrt.f -

# SYNOPSIS

## Functions/Subroutines

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

ZTPMQRT

# Function/Subroutine Documentation

## subroutine ztpmqrt (characterSIDE, characterTRANS, integerM, integerN, integerK, integerL, integerNB, complex*16, dimension( ldv, * )V, integerLDV, complex*16, dimension( ldt, * )T, integerLDT, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( * )WORK, integerINFO)

ZTPMQRT
Purpose:
``` ZTPMQRT 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*16 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*16 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*16 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*16 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*16 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
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 ztpmqrt.f.

# Author

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