root / src / lapack / double / dlatrz.f @ 1
Historique | Voir | Annoter | Télécharger (3,83 ko)
| 1 | 1 | equemene | SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK ) |
|---|---|---|---|
| 2 | 1 | equemene | * |
| 3 | 1 | equemene | * -- LAPACK routine (version 3.2.2) -- |
| 4 | 1 | equemene | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 5 | 1 | equemene | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 6 | 1 | equemene | * June 2010 |
| 7 | 1 | equemene | * |
| 8 | 1 | equemene | * .. Scalar Arguments .. |
| 9 | 1 | equemene | INTEGER L, LDA, M, N |
| 10 | 1 | equemene | * .. |
| 11 | 1 | equemene | * .. Array Arguments .. |
| 12 | 1 | equemene | DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) |
| 13 | 1 | equemene | * .. |
| 14 | 1 | equemene | * |
| 15 | 1 | equemene | * Purpose |
| 16 | 1 | equemene | * ======= |
| 17 | 1 | equemene | * |
| 18 | 1 | equemene | * DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix |
| 19 | 1 | equemene | * [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means |
| 20 | 1 | equemene | * of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal |
| 21 | 1 | equemene | * matrix and, R and A1 are M-by-M upper triangular matrices. |
| 22 | 1 | equemene | * |
| 23 | 1 | equemene | * Arguments |
| 24 | 1 | equemene | * ========= |
| 25 | 1 | equemene | * |
| 26 | 1 | equemene | * M (input) INTEGER |
| 27 | 1 | equemene | * The number of rows of the matrix A. M >= 0. |
| 28 | 1 | equemene | * |
| 29 | 1 | equemene | * N (input) INTEGER |
| 30 | 1 | equemene | * The number of columns of the matrix A. N >= 0. |
| 31 | 1 | equemene | * |
| 32 | 1 | equemene | * L (input) INTEGER |
| 33 | 1 | equemene | * The number of columns of the matrix A containing the |
| 34 | 1 | equemene | * meaningful part of the Householder vectors. N-M >= L >= 0. |
| 35 | 1 | equemene | * |
| 36 | 1 | equemene | * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
| 37 | 1 | equemene | * On entry, the leading M-by-N upper trapezoidal part of the |
| 38 | 1 | equemene | * array A must contain the matrix to be factorized. |
| 39 | 1 | equemene | * On exit, the leading M-by-M upper triangular part of A |
| 40 | 1 | equemene | * contains the upper triangular matrix R, and elements N-L+1 to |
| 41 | 1 | equemene | * N of the first M rows of A, with the array TAU, represent the |
| 42 | 1 | equemene | * orthogonal matrix Z as a product of M elementary reflectors. |
| 43 | 1 | equemene | * |
| 44 | 1 | equemene | * LDA (input) INTEGER |
| 45 | 1 | equemene | * The leading dimension of the array A. LDA >= max(1,M). |
| 46 | 1 | equemene | * |
| 47 | 1 | equemene | * TAU (output) DOUBLE PRECISION array, dimension (M) |
| 48 | 1 | equemene | * The scalar factors of the elementary reflectors. |
| 49 | 1 | equemene | * |
| 50 | 1 | equemene | * WORK (workspace) DOUBLE PRECISION array, dimension (M) |
| 51 | 1 | equemene | * |
| 52 | 1 | equemene | * Further Details |
| 53 | 1 | equemene | * =============== |
| 54 | 1 | equemene | * |
| 55 | 1 | equemene | * Based on contributions by |
| 56 | 1 | equemene | * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
| 57 | 1 | equemene | * |
| 58 | 1 | equemene | * The factorization is obtained by Householder's method. The kth |
| 59 | 1 | equemene | * transformation matrix, Z( k ), which is used to introduce zeros into |
| 60 | 1 | equemene | * the ( m - k + 1 )th row of A, is given in the form |
| 61 | 1 | equemene | * |
| 62 | 1 | equemene | * Z( k ) = ( I 0 ), |
| 63 | 1 | equemene | * ( 0 T( k ) ) |
| 64 | 1 | equemene | * |
| 65 | 1 | equemene | * where |
| 66 | 1 | equemene | * |
| 67 | 1 | equemene | * T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ), |
| 68 | 1 | equemene | * ( 0 ) |
| 69 | 1 | equemene | * ( z( k ) ) |
| 70 | 1 | equemene | * |
| 71 | 1 | equemene | * tau is a scalar and z( k ) is an l element vector. tau and z( k ) |
| 72 | 1 | equemene | * are chosen to annihilate the elements of the kth row of A2. |
| 73 | 1 | equemene | * |
| 74 | 1 | equemene | * The scalar tau is returned in the kth element of TAU and the vector |
| 75 | 1 | equemene | * u( k ) in the kth row of A2, such that the elements of z( k ) are |
| 76 | 1 | equemene | * in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in |
| 77 | 1 | equemene | * the upper triangular part of A1. |
| 78 | 1 | equemene | * |
| 79 | 1 | equemene | * Z is given by |
| 80 | 1 | equemene | * |
| 81 | 1 | equemene | * Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). |
| 82 | 1 | equemene | * |
| 83 | 1 | equemene | * ===================================================================== |
| 84 | 1 | equemene | * |
| 85 | 1 | equemene | * .. Parameters .. |
| 86 | 1 | equemene | DOUBLE PRECISION ZERO |
| 87 | 1 | equemene | PARAMETER ( ZERO = 0.0D+0 ) |
| 88 | 1 | equemene | * .. |
| 89 | 1 | equemene | * .. Local Scalars .. |
| 90 | 1 | equemene | INTEGER I |
| 91 | 1 | equemene | * .. |
| 92 | 1 | equemene | * .. External Subroutines .. |
| 93 | 1 | equemene | EXTERNAL DLARFG, DLARZ |
| 94 | 1 | equemene | * .. |
| 95 | 1 | equemene | * .. Executable Statements .. |
| 96 | 1 | equemene | * |
| 97 | 1 | equemene | * Test the input arguments |
| 98 | 1 | equemene | * |
| 99 | 1 | equemene | * Quick return if possible |
| 100 | 1 | equemene | * |
| 101 | 1 | equemene | IF( M.EQ.0 ) THEN |
| 102 | 1 | equemene | RETURN |
| 103 | 1 | equemene | ELSE IF( M.EQ.N ) THEN |
| 104 | 1 | equemene | DO 10 I = 1, N |
| 105 | 1 | equemene | TAU( I ) = ZERO |
| 106 | 1 | equemene | 10 CONTINUE |
| 107 | 1 | equemene | RETURN |
| 108 | 1 | equemene | END IF |
| 109 | 1 | equemene | * |
| 110 | 1 | equemene | DO 20 I = M, 1, -1 |
| 111 | 1 | equemene | * |
| 112 | 1 | equemene | * Generate elementary reflector H(i) to annihilate |
| 113 | 1 | equemene | * [ A(i,i) A(i,n-l+1:n) ] |
| 114 | 1 | equemene | * |
| 115 | 1 | equemene | CALL DLARFG( L+1, A( I, I ), A( I, N-L+1 ), LDA, TAU( I ) ) |
| 116 | 1 | equemene | * |
| 117 | 1 | equemene | * Apply H(i) to A(1:i-1,i:n) from the right |
| 118 | 1 | equemene | * |
| 119 | 1 | equemene | CALL DLARZ( 'Right', I-1, N-I+1, L, A( I, N-L+1 ), LDA, |
| 120 | 1 | equemene | $ TAU( I ), A( 1, I ), LDA, WORK ) |
| 121 | 1 | equemene | * |
| 122 | 1 | equemene | 20 CONTINUE |
| 123 | 1 | equemene | * |
| 124 | 1 | equemene | RETURN |
| 125 | 1 | equemene | * |
| 126 | 1 | equemene | * End of DLATRZ |
| 127 | 1 | equemene | * |
| 128 | 1 | equemene | END |