# dtpmqrt.f man page

dtpmqrt.f —

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

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

**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;
= 'C': 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

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 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 216 of file dtpmqrt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK