# dormtr.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **dormtr** (SIDE, UPLO, TRANS, M, **N**, A, **LDA**, TAU, C, LDC, WORK, LWORK, INFO)**DORMTR**

## Function/Subroutine Documentation

### subroutine dormtr (character SIDE, character UPLO, character TRANS, integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) WORK, integer LWORK, integer INFO)

**DORMTR**

**Purpose:**

DORMTR 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 of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by DSYTRD: if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

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

*UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from DSYTRD; = 'L': Lower triangle of A contains elementary reflectors from DSYTRD.

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

*A*A is DOUBLE PRECISION array, dimension (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by DSYTRD.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.

*TAU*TAU is DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DSYTRD.

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

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

*WORK*WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

*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:**December 2016

Definition at line 173 of file dormtr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK