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sopmtr

 NAME
      SOPMTR - overwrite 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 pre-
              vious call to SSPTRD; = 'L': Lower triangular packed
              storage used in previous call to SSPTRD.

      TRANS   (input) CHARACTER*1
              Specifies whether the matrix Q or Q**T is applied to
              C:
              = '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 rou-
              tine 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