# sgeqrt.f man page

sgeqrt.f —

## Synopsis

### Functions/Subroutines

subroutinesgeqrt(M, N, NB, A, LDA, T, LDT, WORK, INFO)SGEQRT

## Function/Subroutine Documentation

### subroutine sgeqrt (integerM, integerN, integerNB, real, dimension( lda, * )A, integerLDA, real, dimension( ldt, * )T, integerLDT, real, dimension( * )WORK, integerINFO)

**SGEQRT**

**Purpose:**

```
SGEQRT computes a blocked QR factorization of a real M-by-N matrix A
using the compact WY representation of Q.
```

**Parameters:**

*M*

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

*N*

```
N is INTEGER
The number of columns of the matrix A. N >= 0.
```

*NB*

```
NB is INTEGER
The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1.
```

*A*

```
A is REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if M >= N); the elements below the diagonal
are the columns of V.
```

*LDA*

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

*T*

```
T is REAL array, dimension (LDT,MIN(M,N))
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See below
for further details.
```

*LDT*

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

*WORK*

`WORK is REAL 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 matrix V stores the elementary reflectors H(i) in the i-th column
below the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 )
( v1 1 )
( v1 v2 1 )
( v1 v2 v3 )
( v1 v2 v3 )
where the vi's represent the vectors which define H(i), which are returned
in the matrix A. The 1's along the diagonal of V are not stored in A.
Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each
block is of order NB except for the last block, which is of order
IB = K - (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 142 of file sgeqrt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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