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    1:       SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
    2:      $                   INFO )
    3: *
    4: *  -- LAPACK routine (version 3.2) --
    5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    7: *     November 2006
    8: *
    9: *     .. Scalar Arguments ..
   10:       CHARACTER          SIDE, TRANS, UPLO
   11:       INTEGER            INFO, LDC, M, N
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   AP( * ), C( LDC, * ), TAU( * ), WORK( * )
   15: *     ..
   16: *
   17: *  Purpose
   18: *  =======
   19: *
   20: *  DOPMTR overwrites the general real M-by-N matrix C with
   21: *
   22: *                  SIDE = 'L'     SIDE = 'R'
   23: *  TRANS = 'N':      Q * C          C * Q
   24: *  TRANS = 'T':      Q**T * C       C * Q**T
   25: *
   26: *  where Q is a real orthogonal matrix of order nq, with nq = m if
   27: *  SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
   28: *  nq-1 elementary reflectors, as returned by DSPTRD using packed
   29: *  storage:
   30: *
   31: *  if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
   32: *
   33: *  if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
   34: *
   35: *  Arguments
   36: *  =========
   37: *
   38: *  SIDE    (input) CHARACTER*1
   39: *          = 'L': apply Q or Q**T from the Left;
   40: *          = 'R': apply Q or Q**T from the Right.
   41: *
   42: *  UPLO    (input) CHARACTER*1
   43: *          = 'U': Upper triangular packed storage used in previous
   44: *                 call to DSPTRD;
   45: *          = 'L': Lower triangular packed storage used in previous
   46: *                 call to DSPTRD.
   47: *
   48: *  TRANS   (input) CHARACTER*1
   49: *          = 'N':  No transpose, apply Q;
   50: *          = 'T':  Transpose, apply Q**T.
   51: *
   52: *  M       (input) INTEGER
   53: *          The number of rows of the matrix C. M >= 0.
   54: *
   55: *  N       (input) INTEGER
   56: *          The number of columns of the matrix C. N >= 0.
   57: *
   58: *  AP      (input) DOUBLE PRECISION array, dimension
   59: *                               (M*(M+1)/2) if SIDE = 'L'
   60: *                               (N*(N+1)/2) if SIDE = 'R'
   61: *          The vectors which define the elementary reflectors, as
   62: *          returned by DSPTRD.  AP is modified by the routine but
   63: *          restored on exit.
   64: *
   65: *  TAU     (input) DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L'
   66: *                                     or (N-1) if SIDE = 'R'
   67: *          TAU(i) must contain the scalar factor of the elementary
   68: *          reflector H(i), as returned by DSPTRD.
   69: *
   70: *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
   71: *          On entry, the M-by-N matrix C.
   72: *          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
   73: *
   74: *  LDC     (input) INTEGER
   75: *          The leading dimension of the array C. LDC >= max(1,M).
   76: *
   77: *  WORK    (workspace) DOUBLE PRECISION array, dimension
   78: *                                   (N) if SIDE = 'L'
   79: *                                   (M) if SIDE = 'R'
   80: *
   81: *  INFO    (output) INTEGER
   82: *          = 0:  successful exit
   83: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   84: *
   85: *  =====================================================================
   86: *
   87: *     .. Parameters ..
   88:       DOUBLE PRECISION   ONE
   89:       PARAMETER          ( ONE = 1.0D+0 )
   90: *     ..
   91: *     .. Local Scalars ..
   92:       LOGICAL            FORWRD, LEFT, NOTRAN, UPPER
   93:       INTEGER            I, I1, I2, I3, IC, II, JC, MI, NI, NQ
   94:       DOUBLE PRECISION   AII
   95: *     ..
   96: *     .. External Functions ..
   97:       LOGICAL            LSAME
   98:       EXTERNAL           LSAME
   99: *     ..
  100: *     .. External Subroutines ..
  101:       EXTERNAL           DLARF, XERBLA
  102: *     ..
  103: *     .. Intrinsic Functions ..
  104:       INTRINSIC          MAX
  105: *     ..
  106: *     .. Executable Statements ..
  107: *
  108: *     Test the input arguments
  109: *
  110:       INFO = 0
  111:       LEFT = LSAME( SIDE, 'L' )
  112:       NOTRAN = LSAME( TRANS, 'N' )
  113:       UPPER = LSAME( UPLO, 'U' )
  114: *
  115: *     NQ is the order of Q
  116: *
  117:       IF( LEFT ) THEN
  118:          NQ = M
  119:       ELSE
  120:          NQ = N
  121:       END IF
  122:       IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
  123:          INFO = -1
  124:       ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  125:          INFO = -2
  126:       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
  127:          INFO = -3
  128:       ELSE IF( M.LT.0 ) THEN
  129:          INFO = -4
  130:       ELSE IF( N.LT.0 ) THEN
  131:          INFO = -5
  132:       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
  133:          INFO = -9
  134:       END IF
  135:       IF( INFO.NE.0 ) THEN
  136:          CALL XERBLA( 'DOPMTR', -INFO )
  137:          RETURN
  138:       END IF
  139: *
  140: *     Quick return if possible
  141: *
  142:       IF( M.EQ.0 .OR. N.EQ.0 )
  143:      $   RETURN
  144: *
  145:       IF( UPPER ) THEN
  146: *
  147: *        Q was determined by a call to DSPTRD with UPLO = 'U'
  148: *
  149:          FORWRD = ( LEFT .AND. NOTRAN ) .OR.
  150:      $            ( .NOT.LEFT .AND. .NOT.NOTRAN )
  151: *
  152:          IF( FORWRD ) THEN
  153:             I1 = 1
  154:             I2 = NQ - 1
  155:             I3 = 1
  156:             II = 2
  157:          ELSE
  158:             I1 = NQ - 1
  159:             I2 = 1
  160:             I3 = -1
  161:             II = NQ*( NQ+1 ) / 2 - 1
  162:          END IF
  163: *
  164:          IF( LEFT ) THEN
  165:             NI = N
  166:          ELSE
  167:             MI = M
  168:          END IF
  169: *
  170:          DO 10 I = I1, I2, I3
  171:             IF( LEFT ) THEN
  172: *
  173: *              H(i) is applied to C(1:i,1:n)
  174: *
  175:                MI = I
  176:             ELSE
  177: *
  178: *              H(i) is applied to C(1:m,1:i)
  179: *
  180:                NI = I
  181:             END IF
  182: *
  183: *           Apply H(i)
  184: *
  185:             AII = AP( II )
  186:             AP( II ) = ONE
  187:             CALL DLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAU( I ), C, LDC,
  188:      $                  WORK )
  189:             AP( II ) = AII
  190: *
  191:             IF( FORWRD ) THEN
  192:                II = II + I + 2
  193:             ELSE
  194:                II = II - I - 1
  195:             END IF
  196:    10    CONTINUE
  197:       ELSE
  198: *
  199: *        Q was determined by a call to DSPTRD with UPLO = 'L'.
  200: *
  201:          FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR.
  202:      $            ( .NOT.LEFT .AND. NOTRAN )
  203: *
  204:          IF( FORWRD ) THEN
  205:             I1 = 1
  206:             I2 = NQ - 1
  207:             I3 = 1
  208:             II = 2
  209:          ELSE
  210:             I1 = NQ - 1
  211:             I2 = 1
  212:             I3 = -1
  213:             II = NQ*( NQ+1 ) / 2 - 1
  214:          END IF
  215: *
  216:          IF( LEFT ) THEN
  217:             NI = N
  218:             JC = 1
  219:          ELSE
  220:             MI = M
  221:             IC = 1
  222:          END IF
  223: *
  224:          DO 20 I = I1, I2, I3
  225:             AII = AP( II )
  226:             AP( II ) = ONE
  227:             IF( LEFT ) THEN
  228: *
  229: *              H(i) is applied to C(i+1:m,1:n)
  230: *
  231:                MI = M - I
  232:                IC = I + 1
  233:             ELSE
  234: *
  235: *              H(i) is applied to C(1:m,i+1:n)
  236: *
  237:                NI = N - I
  238:                JC = I + 1
  239:             END IF
  240: *
  241: *           Apply H(i)
  242: *
  243:             CALL DLARF( SIDE, MI, NI, AP( II ), 1, TAU( I ),
  244:      $                  C( IC, JC ), LDC, WORK )
  245:             AP( II ) = AII
  246: *
  247:             IF( FORWRD ) THEN
  248:                II = II + NQ - I + 1
  249:             ELSE
  250:                II = II - NQ + I - 2
  251:             END IF
  252:    20    CONTINUE
  253:       END IF
  254:       RETURN
  255: *
  256: *     End of DOPMTR
  257: *
  258:       END