Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-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 LAPACK routine (version 3.2) April 2011 SOPMTR(3lapack)