# ctpqrt2.f man page

ctpqrt2.f —

## Synopsis

### Functions/Subroutines

subroutinectpqrt2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)CTPQRT2computes a QR 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 ctpqrt2 (integerM, integerN, integerL, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldt, * )T, integerLDT, integerINFO)

**CTPQRT2** computes a QR 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:**

```
CTPQRT2 computes a 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 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 upper trapezoidal part of B.
MIN(M,N) >= L >= 0. See Further Details.
```

*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 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,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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**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 (M+N)-by-(M+N) block reflector H is then given by
H = I - W * T * W**H
where W**H is the conjugate transpose of W and T is the upper triangular
factor of the block reflector.
```

Definition at line 174 of file ctpqrt2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

ctpqrt2(3) is an alias of ctpqrt2.f(3).