# dtpqrt.f man page

dtpqrt.f —

## Synopsis

### Functions/Subroutines

subroutinedtpqrt(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)DTPQRT

## Function/Subroutine Documentation

### subroutine dtpqrt (integerM, integerN, integerL, integerNB, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldt, * )T, integerLDT, double precision, dimension( * )WORK, integerINFO)

**DTPQRT**

**Purpose:**

```
DTPQRT computes a blocked QR 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 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2013

**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 189 of file dtpqrt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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