# sgemlqt.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **sgemlqt** (SIDE, TRANS, M, **N**, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)

## Function/Subroutine Documentation

### subroutine sgemlqt (character SIDE, character TRANS, integer M, integer N, integer K, integer MB, real, dimension( ldv, * ) V, integer LDV, real, dimension( ldt, * ) T, integer LDT, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer INFO)

**Purpose:**

DGEMLQT overwrites the general real M-by-N matrix C with

SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'T': Q**T C C Q**T

where Q is a real orthogonal matrix defined as the product of K elementary reflectors:

Q = H(1) H(2) . . . H(K) = I - V T V**T

generated using the compact WY representation as returned by DGELQT.

Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

**Parameters:***SIDE*SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.

*TRANS*TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Transpose, apply Q**T.

*M*M is INTEGER The number of rows of the matrix C. M >= 0.

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

*K*K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.

*MB*MB is INTEGER The block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in DGELQT.

*V*V is REAL array, dimension (LDV,M) if SIDE = 'L', (LDV,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGELQT in the first K rows of its array argument A.

*LDV*LDV is INTEGER The leading dimension of the array V. LDV >= max(1,K).

*T*T is REAL array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by DGELQT, stored as a MB-by-K matrix.

*LDT*LDT is INTEGER The leading dimension of the array T. LDT >= MB.

*C*C is REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.

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

*WORK*WORK is REAL array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.

*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

Definition at line 153 of file sgemlqt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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