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Annotation of rpl/lapack/lapack/zlatrz.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE ZLATRZ( M, N, L, A, LDA, TAU, 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:       INTEGER            L, LDA, M, N
        !            10: *     ..
        !            11: *     .. Array Arguments ..
        !            12:       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
        !            13: *     ..
        !            14: *
        !            15: *  Purpose
        !            16: *  =======
        !            17: *
        !            18: *  ZLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix
        !            19: *  [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z by means
        !            20: *  of unitary transformations, where  Z is an (M+L)-by-(M+L) unitary
        !            21: *  matrix and, R and A1 are M-by-M upper triangular matrices.
        !            22: *
        !            23: *  Arguments
        !            24: *  =========
        !            25: *
        !            26: *  M       (input) INTEGER
        !            27: *          The number of rows of the matrix A.  M >= 0.
        !            28: *
        !            29: *  N       (input) INTEGER
        !            30: *          The number of columns of the matrix A.  N >= 0.
        !            31: *
        !            32: *  L       (input) INTEGER
        !            33: *          The number of columns of the matrix A containing the
        !            34: *          meaningful part of the Householder vectors. N-M >= L >= 0.
        !            35: *
        !            36: *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
        !            37: *          On entry, the leading M-by-N upper trapezoidal part of the
        !            38: *          array A must contain the matrix to be factorized.
        !            39: *          On exit, the leading M-by-M upper triangular part of A
        !            40: *          contains the upper triangular matrix R, and elements N-L+1 to
        !            41: *          N of the first M rows of A, with the array TAU, represent the
        !            42: *          unitary matrix Z as a product of M elementary reflectors.
        !            43: *
        !            44: *  LDA     (input) INTEGER
        !            45: *          The leading dimension of the array A.  LDA >= max(1,M).
        !            46: *
        !            47: *  TAU     (output) COMPLEX*16 array, dimension (M)
        !            48: *          The scalar factors of the elementary reflectors.
        !            49: *
        !            50: *  WORK    (workspace) COMPLEX*16 array, dimension (M)
        !            51: *
        !            52: *  Further Details
        !            53: *  ===============
        !            54: *
        !            55: *  Based on contributions by
        !            56: *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
        !            57: *
        !            58: *  The factorization is obtained by Householder's method.  The kth
        !            59: *  transformation matrix, Z( k ), which is used to introduce zeros into
        !            60: *  the ( m - k + 1 )th row of A, is given in the form
        !            61: *
        !            62: *     Z( k ) = ( I     0   ),
        !            63: *              ( 0  T( k ) )
        !            64: *
        !            65: *  where
        !            66: *
        !            67: *     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
        !            68: *                                                 (   0    )
        !            69: *                                                 ( z( k ) )
        !            70: *
        !            71: *  tau is a scalar and z( k ) is an l element vector. tau and z( k )
        !            72: *  are chosen to annihilate the elements of the kth row of A2.
        !            73: *
        !            74: *  The scalar tau is returned in the kth element of TAU and the vector
        !            75: *  u( k ) in the kth row of A2, such that the elements of z( k ) are
        !            76: *  in  a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
        !            77: *  the upper triangular part of A1.
        !            78: *
        !            79: *  Z is given by
        !            80: *
        !            81: *     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
        !            82: *
        !            83: *  =====================================================================
        !            84: *
        !            85: *     .. Parameters ..
        !            86:       COMPLEX*16         ZERO
        !            87:       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
        !            88: *     ..
        !            89: *     .. Local Scalars ..
        !            90:       INTEGER            I
        !            91:       COMPLEX*16         ALPHA
        !            92: *     ..
        !            93: *     .. External Subroutines ..
        !            94:       EXTERNAL           ZLACGV, ZLARFP, ZLARZ
        !            95: *     ..
        !            96: *     .. Intrinsic Functions ..
        !            97:       INTRINSIC          DCONJG
        !            98: *     ..
        !            99: *     .. Executable Statements ..
        !           100: *
        !           101: *     Quick return if possible
        !           102: *
        !           103:       IF( M.EQ.0 ) THEN
        !           104:          RETURN
        !           105:       ELSE IF( M.EQ.N ) THEN
        !           106:          DO 10 I = 1, N
        !           107:             TAU( I ) = ZERO
        !           108:    10    CONTINUE
        !           109:          RETURN
        !           110:       END IF
        !           111: *
        !           112:       DO 20 I = M, 1, -1
        !           113: *
        !           114: *        Generate elementary reflector H(i) to annihilate
        !           115: *        [ A(i,i) A(i,n-l+1:n) ]
        !           116: *
        !           117:          CALL ZLACGV( L, A( I, N-L+1 ), LDA )
        !           118:          ALPHA = DCONJG( A( I, I ) )
        !           119:          CALL ZLARFP( L+1, ALPHA, A( I, N-L+1 ), LDA, TAU( I ) )
        !           120:          TAU( I ) = DCONJG( TAU( I ) )
        !           121: *
        !           122: *        Apply H(i) to A(1:i-1,i:n) from the right
        !           123: *
        !           124:          CALL ZLARZ( 'Right', I-1, N-I+1, L, A( I, N-L+1 ), LDA,
        !           125:      $               DCONJG( TAU( I ) ), A( 1, I ), LDA, WORK )
        !           126:          A( I, I ) = DCONJG( ALPHA )
        !           127: *
        !           128:    20 CONTINUE
        !           129: *
        !           130:       RETURN
        !           131: *
        !           132: *     End of ZLATRZ
        !           133: *
        !           134:       END