SORMR3 (3) Linux Manual Page

sormr3.f –

Synopsis

Functions/Subroutines

subroutine sormr3 (SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO)
SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Function/Subroutine Documentation

subroutine sormr3 (characterSIDE, characterTRANS, integerM, integerN, integerK, integerL, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( ldc, * )C, integerLDC, real, dimension( * )WORK, integerINFO)

SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Purpose:

 SORMR3 overwrites the general real m by n matrix C with

 Q * C if SIDE = ‘L’ and TRANS = ‘N’, or

 Q**T* C if SIDE = ‘L’ and TRANS = ‘C’, or

 C * Q if SIDE = ‘R’ and TRANS = ‘N’, or

 C * Q**T if SIDE = ‘R’ and TRANS = ‘C’,

 where Q is a real orthogonal matrix defined as the product of k

 elementary reflectors

 Q = H(1) H(2) . . . H(k)

 as returned by STZRZF. 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’: apply Q (No transpose)

 = ‘T’: apply Q**T (Transpose)

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.

L

 L is INTEGER

 The number of columns of the matrix A containing

 the meaningful part of the Householder reflectors.

 If SIDE = ‘L’, M >= L >= 0, if SIDE = ‘R’, N >= L >= 0.

A

 A is REAL array, dimension

 (LDA,M) if SIDE = ‘L’,

 (LDA,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

 STZRZF in the last k rows of its array argument A.

 A is modified by the routine but restored on exit.

LDA

 LDA is INTEGER

 The leading dimension of the array A. LDA >= max(1,K).

TAU

 TAU is REAL array, dimension (K)

 TAU(i) must contain the scalar factor of the elementary

 reflector H(i), as returned by STZRZF.

C

 C is REAL 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 REAL array, dimension

 (N) if SIDE = ‘L’,

 (M) 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:

September 2012

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

 

Definition at line 178 of file sormr3.f.

Author

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