# sgelqt.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **sgelqt** (M, **N**, MB, A, **LDA**, T, LDT, WORK, INFO)

## Function/Subroutine Documentation

### subroutine sgelqt (integer M, integer N, integer MB, real, dimension( lda, * ) A, integer LDA, real, dimension( ldt, * ) T, integer LDT, real, dimension( * ) WORK, integer INFO)

**Purpose:**

DGELQT computes a blocked LQ 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.

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

*A*A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is lower triangular if M <= N); the elements above the diagonal are the rows 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 >= MB.

*WORK*WORK is REAL array, dimension (MB*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 2017

**Further Details:**

The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is

V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 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/MB), where each block is of order MB except for the last block, which is of order IB = K - (B-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-K matrix T as

T = (T1 T2 ... TB).

Definition at line 124 of file sgelqt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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