Annotation of rpl/lapack/lapack/dlatrz.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DLATRZ( 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: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 13: * ..
! 14: *
! 15: * Purpose
! 16: * =======
! 17: *
! 18: * DLATRZ factors the M-by-(M+L) real 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 orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal
! 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) DOUBLE PRECISION 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: * orthogonal 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) DOUBLE PRECISION array, dimension (M)
! 48: * The scalar factors of the elementary reflectors.
! 49: *
! 50: * WORK (workspace) DOUBLE PRECISION 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: DOUBLE PRECISION ZERO
! 87: PARAMETER ( ZERO = 0.0D+0 )
! 88: * ..
! 89: * .. Local Scalars ..
! 90: INTEGER I
! 91: * ..
! 92: * .. External Subroutines ..
! 93: EXTERNAL DLARFP, DLARZ
! 94: * ..
! 95: * .. Executable Statements ..
! 96: *
! 97: * Test the input arguments
! 98: *
! 99: * Quick return if possible
! 100: *
! 101: IF( M.EQ.0 ) THEN
! 102: RETURN
! 103: ELSE IF( M.EQ.N ) THEN
! 104: DO 10 I = 1, N
! 105: TAU( I ) = ZERO
! 106: 10 CONTINUE
! 107: RETURN
! 108: END IF
! 109: *
! 110: DO 20 I = M, 1, -1
! 111: *
! 112: * Generate elementary reflector H(i) to annihilate
! 113: * [ A(i,i) A(i,n-l+1:n) ]
! 114: *
! 115: CALL DLARFP( L+1, A( I, I ), A( I, N-L+1 ), LDA, TAU( I ) )
! 116: *
! 117: * Apply H(i) to A(1:i-1,i:n) from the right
! 118: *
! 119: CALL DLARZ( 'Right', I-1, N-I+1, L, A( I, N-L+1 ), LDA,
! 120: $ TAU( I ), A( 1, I ), LDA, WORK )
! 121: *
! 122: 20 CONTINUE
! 123: *
! 124: RETURN
! 125: *
! 126: * End of DLATRZ
! 127: *
! 128: END
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