SOPMTR(3) overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

## SYNOPSIS

SUBROUTINE SOPMTR(
SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, INFO )

CHARACTER SIDE, TRANS, UPLO

INTEGER INFO, LDC, M, N

REAL AP( * ), C( LDC, * ), TAU( * ), WORK( * )

## PURPOSE

SOPMTR overwrites the general real M-by-N matrix C with 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 SSPTRD using packed storage:
if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

## ARGUMENTS

SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
UPLO (input) CHARACTER*1

= 'U': Upper triangular packed storage used in previous call to SSPTRD; = 'L': Lower triangular packed storage used in previous call to SSPTRD.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
AP (input) REAL array, dimension
(M*(M+1)/2) if SIDE = 'L' (N*(N+1)/2) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by SSPTRD. AP is modified by the routine but restored on exit.
TAU (input) REAL array, dimension (M-1) if SIDE = 'L'
or (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSPTRD.
C (input/output) 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 (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace) REAL array, dimension
(N) if SIDE = 'L' (M) if SIDE = 'R'
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
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