# dgeqrt3.f - Man Page

## Synopsis

### Functions/Subroutines

recursive subroutine **dgeqrt3** (M, **N**, A, **LDA**, T, LDT, INFO)**DGEQRT3** recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

## Function/Subroutine Documentation

### recursive subroutine dgeqrt3 (integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldt, * ) T, integer LDT, integer INFO)

**DGEQRT3** recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

**Purpose:**

DGEQRT3 recursively computes a QR factorization of a real M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

**Parameters:***M*M is INTEGER The number of rows of the matrix A. M >= N.

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

*A*A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the real M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details.

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

*T*T is DOUBLE PRECISION array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for 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:**June 2016

**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. The block reflector H is then given by H = I - V * T * V**T where V**T is the transpose of V. For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 134 of file dgeqrt3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dgeqrt3(3) is an alias of dgeqrt3.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK