# stplqt2.f - Man Page

SRC/stplqt2.f

## Synopsis

### Functions/Subroutines

subroutine stplqt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
STPLQT2 computes a LQ factorization of a real or complex 'triangular-pentagonal' matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

## Function/Subroutine Documentation

### subroutine stplqt2 (integer m, integer n, integer l, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldt, * ) t, integer ldt, integer info)

STPLQT2 computes a LQ factorization of a real or complex 'triangular-pentagonal' matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Purpose:

``` STPLQT2 computes a LQ a factorization of a real 'triangular-pentagonal'
matrix C, which is composed of a triangular block A and pentagonal block B,
using the compact WY representation for Q.```
Parameters

M

```          M is INTEGER
The total number of rows of the matrix B.
M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix B, and the order of
the triangular matrix A.
N >= 0.```

L

```          L is INTEGER
The number of rows of the lower trapezoidal part of B.
MIN(M,N) >= L >= 0.  See Further Details.```

A

```          A is REAL array, dimension (LDA,M)
On entry, the lower triangular M-by-M matrix A.
On exit, the elements on and below the diagonal of the array
contain the lower triangular matrix L.```

LDA

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

B

```          B is REAL array, dimension (LDB,N)
On entry, the pentagonal M-by-N matrix B.  The first N-L columns
are rectangular, and the last L columns are lower trapezoidal.
On exit, B contains the pentagonal matrix V.  See Further Details.```

LDB

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

T

```          T is REAL array, dimension (LDT,M)
The N-by-N upper triangular factor T of the block reflector.
See Further Details.```

LDT

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

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 input matrix C is a M-by-(M+N) matrix

C = [ A ][ B ]

where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
matrix consisting of a M-by-(N-L) rectangular matrix B1 left of a M-by-L
upper trapezoidal matrix B2:

B = [ B1 ][ B2 ]
[ B1 ]  <-     M-by-(N-L) rectangular
[ B2 ]  <-     M-by-L lower trapezoidal.

The lower trapezoidal matrix B2 consists of the first L columns of a
N-by-N lower triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
B is rectangular M-by-N; if M=L=N, B is lower triangular.

The matrix W stores the elementary reflectors H(i) in the i-th row
above the diagonal (of A) in the M-by-(M+N) input matrix C

C = [ A ][ B ]
[ A ]  <- lower triangular M-by-M
[ B ]  <- M-by-N pentagonal

so that W can be represented as

W = [ I ][ V ]
[ I ]  <- identity, M-by-M
[ V ]  <- M-by-N, same form as B.

Thus, all of information needed for W is contained on exit in B, which
we call V above.  Note that V has the same form as B; that is,

W = [ V1 ][ V2 ]
[ V1 ] <-     M-by-(N-L) rectangular
[ V2 ] <-     M-by-L lower trapezoidal.

The rows of V represent the vectors which define the H(i)'s.
The (M+N)-by-(M+N) block reflector H is then given by

H = I - W**T * T * W

where W^H is the conjugate transpose of W and T is the upper triangular
factor of the block reflector.```

Definition at line 176 of file stplqt2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page stplqt2(3) is an alias of stplqt2.f(3).

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