# dtpmqrt.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dtpmqrt.f

## SYNOPSIS

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine dtpmqrt (character SIDE, character TRANS, integer M, integer N, integer K, integer L, integer NB, double precision, dimension( ldv, * ) V, integer LDV, double precision, dimension( ldt, * ) T, integer LDT, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) WORK, integer INFO)

DTPMQRT

Purpose:

``` DTPMQRT applies a real orthogonal matrix Q obtained from a
"triangular-pentagonal" real block reflector H to a general
real matrix C, which consists of two blocks A and B.
```

Parameters:

SIDE

```          SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
```

TRANS

```          TRANS is CHARACTER*1
= 'N':  No transpose, apply Q;
= 'T':  Transpose, apply Q**T.
```

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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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**T*C or C*Q or C*Q**T.  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 DOUBLE PRECISION 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**T*C or C*Q or C*Q**T.  See Further Details.
```

LDB

```          LDB is INTEGER
The leading dimension of the array B.
LDB >= max(1,M).
```

WORK

```          WORK is DOUBLE PRECISION 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 2017

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 real 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='T' and SIDE='L', C is on exit replaced with Q**T * C.

If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.

If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.
```

Definition at line 218 of file dtpmqrt.f.

## Author

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