# ctpqrt.f man page

ctpqrt.f

## Synopsis

### Functions/Subroutines

subroutine ctpqrt (M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
CTPQRT

## Function/Subroutine Documentation

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

CTPQRT

Purpose:

``` CTPQRT computes a blocked QR 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.
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 upper trapezoidal part of B.
MIN(M,N) >= L >= 0.  See Further Details.```

NB

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

A

```          A is COMPLEX array, dimension (LDA,N)
On entry, the upper triangular N-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the upper triangular matrix R.```

LDA

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

B

```          B is COMPLEX array, dimension (LDB,N)
On entry, the pentagonal M-by-N matrix B.  The first M-L rows
are rectangular, and the last L rows are upper 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 upper 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 >= NB.```

WORK

`          WORK is COMPLEX array, dimension (NB*N)`

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:

December 2016

Further Details:

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

C = [ A ]
[ B ]

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

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

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

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

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

so that W can be represented as

W = [ I ]  <- identity, N-by-N
[ 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 ] <- (M-L)-by-N rectangular
[ V2 ] <-     L-by-N upper trapezoidal.

The columns of V represent the vectors which define the H(i)'s.

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

T = [T1 T2 ... TB].```

Definition at line 191 of file ctpqrt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK