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Annotation of rpl/lapack/lapack/zlarz.f, revision 1.7

1.1       bertrand    1:       SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
                      2: *
                      3: *  -- LAPACK routine (version 3.2) --
                      4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                      5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                      6: *     November 2006
                      7: *
                      8: *     .. Scalar Arguments ..
                      9:       CHARACTER          SIDE
                     10:       INTEGER            INCV, L, LDC, M, N
                     11:       COMPLEX*16         TAU
                     12: *     ..
                     13: *     .. Array Arguments ..
                     14:       COMPLEX*16         C( LDC, * ), V( * ), WORK( * )
                     15: *     ..
                     16: *
                     17: *  Purpose
                     18: *  =======
                     19: *
                     20: *  ZLARZ applies a complex elementary reflector H to a complex
                     21: *  M-by-N matrix C, from either the left or the right. H is represented
                     22: *  in the form
                     23: *
                     24: *        H = I - tau * v * v'
                     25: *
                     26: *  where tau is a complex scalar and v is a complex vector.
                     27: *
                     28: *  If tau = 0, then H is taken to be the unit matrix.
                     29: *
                     30: *  To apply H' (the conjugate transpose of H), supply conjg(tau) instead
                     31: *  tau.
                     32: *
                     33: *  H is a product of k elementary reflectors as returned by ZTZRZF.
                     34: *
                     35: *  Arguments
                     36: *  =========
                     37: *
                     38: *  SIDE    (input) CHARACTER*1
                     39: *          = 'L': form  H * C
                     40: *          = 'R': form  C * H
                     41: *
                     42: *  M       (input) INTEGER
                     43: *          The number of rows of the matrix C.
                     44: *
                     45: *  N       (input) INTEGER
                     46: *          The number of columns of the matrix C.
                     47: *
                     48: *  L       (input) INTEGER
                     49: *          The number of entries of the vector V containing
                     50: *          the meaningful part of the Householder vectors.
                     51: *          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
                     52: *
                     53: *  V       (input) COMPLEX*16 array, dimension (1+(L-1)*abs(INCV))
                     54: *          The vector v in the representation of H as returned by
                     55: *          ZTZRZF. V is not used if TAU = 0.
                     56: *
                     57: *  INCV    (input) INTEGER
                     58: *          The increment between elements of v. INCV <> 0.
                     59: *
                     60: *  TAU     (input) COMPLEX*16
                     61: *          The value tau in the representation of H.
                     62: *
                     63: *  C       (input/output) COMPLEX*16 array, dimension (LDC,N)
                     64: *          On entry, the M-by-N matrix C.
                     65: *          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
                     66: *          or C * H if SIDE = 'R'.
                     67: *
                     68: *  LDC     (input) INTEGER
                     69: *          The leading dimension of the array C. LDC >= max(1,M).
                     70: *
                     71: *  WORK    (workspace) COMPLEX*16 array, dimension
                     72: *                         (N) if SIDE = 'L'
                     73: *                      or (M) if SIDE = 'R'
                     74: *
                     75: *  Further Details
                     76: *  ===============
                     77: *
                     78: *  Based on contributions by
                     79: *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
                     80: *
                     81: *  =====================================================================
                     82: *
                     83: *     .. Parameters ..
                     84:       COMPLEX*16         ONE, ZERO
                     85:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
                     86:      $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
                     87: *     ..
                     88: *     .. External Subroutines ..
                     89:       EXTERNAL           ZAXPY, ZCOPY, ZGEMV, ZGERC, ZGERU, ZLACGV
                     90: *     ..
                     91: *     .. External Functions ..
                     92:       LOGICAL            LSAME
                     93:       EXTERNAL           LSAME
                     94: *     ..
                     95: *     .. Executable Statements ..
                     96: *
                     97:       IF( LSAME( SIDE, 'L' ) ) THEN
                     98: *
                     99: *        Form  H * C
                    100: *
                    101:          IF( TAU.NE.ZERO ) THEN
                    102: *
                    103: *           w( 1:n ) = conjg( C( 1, 1:n ) )
                    104: *
                    105:             CALL ZCOPY( N, C, LDC, WORK, 1 )
                    106:             CALL ZLACGV( N, WORK, 1 )
                    107: *
                    108: *           w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l ) )
                    109: *
                    110:             CALL ZGEMV( 'Conjugate transpose', L, N, ONE, C( M-L+1, 1 ),
                    111:      $                  LDC, V, INCV, ONE, WORK, 1 )
                    112:             CALL ZLACGV( N, WORK, 1 )
                    113: *
                    114: *           C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
                    115: *
                    116:             CALL ZAXPY( N, -TAU, WORK, 1, C, LDC )
                    117: *
                    118: *           C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
                    119: *                               tau * v( 1:l ) * conjg( w( 1:n )' )
                    120: *
                    121:             CALL ZGERU( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
                    122:      $                  LDC )
                    123:          END IF
                    124: *
                    125:       ELSE
                    126: *
                    127: *        Form  C * H
                    128: *
                    129:          IF( TAU.NE.ZERO ) THEN
                    130: *
                    131: *           w( 1:m ) = C( 1:m, 1 )
                    132: *
                    133:             CALL ZCOPY( M, C, 1, WORK, 1 )
                    134: *
                    135: *           w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
                    136: *
                    137:             CALL ZGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
                    138:      $                  V, INCV, ONE, WORK, 1 )
                    139: *
                    140: *           C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
                    141: *
                    142:             CALL ZAXPY( M, -TAU, WORK, 1, C, 1 )
                    143: *
                    144: *           C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
                    145: *                               tau * w( 1:m ) * v( 1:l )'
                    146: *
                    147:             CALL ZGERC( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
                    148:      $                  LDC )
                    149: *
                    150:          END IF
                    151: *
                    152:       END IF
                    153: *
                    154:       RETURN
                    155: *
                    156: *     End of ZLARZ
                    157: *
                    158:       END