# ctplqt.f man page

ctplqt.f

## Synopsis

### Functions/Subroutines

subroutine ctplqt (M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK, INFO)

## Function/Subroutine Documentation

### subroutine ctplqt (integer M, integer N, integer L, integer MB, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldt, * ) T, integer LDT, complex, dimension( * ) WORK, integer INFO)

Purpose:

CTPLQT computes a blocked LQ factorization of a complex '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 number of rows of the matrix B, and the order of the
triangular matrix A.
M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix B.
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.```

MB

```          MB is INTEGER
The block size to be used in the blocked QR.  M >= MB >= 1.```

A

```          A is COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LDT,N)
The lower triangular block reflectors stored in compact form
as a sequence of upper triangular blocks.  See Further Details.```

LDT

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

WORK

`          WORK is COMPLEX array, dimension (MB*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.

Date:

June 2017

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 on 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 M-by-M 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, [ V ] = [ 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 number of blocks is B = ceiling(M/MB), where each block is of order MB except for the last block, which is of order IB = M - (M-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-N matrix T as

T = [T1 T2 ... TB].

Definition at line 174 of file ctplqt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK