# stpmlqt.f - Man Page

SRC/stpmlqt.f

## Synopsis

### Functions/Subroutines

subroutine stpmlqt (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
STPMLQT

## Function/Subroutine Documentation

### subroutine stpmlqt (character side, character trans, integer m, integer n, integer k, integer l, integer mb, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer info)

STPMLQT

Purpose:

``` STPMLQT 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.```

MB

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

V

```          V is REAL array, dimension (LDV,K)
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
STPLQT in B.  See Further Details.```

LDV

```          LDV is INTEGER
The leading dimension of the array V. LDV >= K.```

T

```          T is REAL array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by STPLQT, stored as a MB-by-K matrix.```

LDT

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

A

```          A is REAL 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', LDA >= max(1,K);
If SIDE = 'R', LDA >= max(1,M).```

B

```          B is REAL 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 REAL array. The dimension of WORK is
N*MB if SIDE = 'L', or  M*MB 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.

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 lower trapezoidal, consisting of the first L
rows of a K-by-K upper triangular matrix.  If L=K, V2 is lower 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 K-by-M.
[B]

If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.

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 212 of file stpmlqt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page stpmlqt(3) is an alias of stpmlqt.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK