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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DTZRQF( M, N, A, LDA, TAU, INFO ) 2: * 3: * -- LAPACK routine (version 3.2.2) -- 4: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 6: * June 2010 7: * 8: * .. Scalar Arguments .. 9: INTEGER INFO, LDA, M, N 10: * .. 11: * .. Array Arguments .. 12: DOUBLE PRECISION A( LDA, * ), TAU( * ) 13: * .. 14: * 15: * Purpose 16: * ======= 17: * 18: * This routine is deprecated and has been replaced by routine DTZRZF. 19: * 20: * DTZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A 21: * to upper triangular form by means of orthogonal transformations. 22: * 23: * The upper trapezoidal matrix A is factored as 24: * 25: * A = ( R 0 ) * Z, 26: * 27: * where Z is an N-by-N orthogonal matrix and R is an M-by-M upper 28: * triangular matrix. 29: * 30: * Arguments 31: * ========= 32: * 33: * M (input) INTEGER 34: * The number of rows of the matrix A. M >= 0. 35: * 36: * N (input) INTEGER 37: * The number of columns of the matrix A. N >= M. 38: * 39: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) 40: * On entry, the leading M-by-N upper trapezoidal part of the 41: * array A must contain the matrix to be factorized. 42: * On exit, the leading M-by-M upper triangular part of A 43: * contains the upper triangular matrix R, and elements M+1 to 44: * N of the first M rows of A, with the array TAU, represent the 45: * orthogonal matrix Z as a product of M elementary reflectors. 46: * 47: * LDA (input) INTEGER 48: * The leading dimension of the array A. LDA >= max(1,M). 49: * 50: * TAU (output) DOUBLE PRECISION array, dimension (M) 51: * The scalar factors of the elementary reflectors. 52: * 53: * INFO (output) INTEGER 54: * = 0: successful exit 55: * < 0: if INFO = -i, the i-th argument had an illegal value 56: * 57: * Further Details 58: * =============== 59: * 60: * The factorization is obtained by Householder's method. The kth 61: * transformation matrix, Z( k ), which is used to introduce zeros into 62: * the ( m - k + 1 )th row of A, is given in the form 63: * 64: * Z( k ) = ( I 0 ), 65: * ( 0 T( k ) ) 66: * 67: * where 68: * 69: * T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ), 70: * ( 0 ) 71: * ( z( k ) ) 72: * 73: * tau is a scalar and z( k ) is an ( n - m ) element vector. 74: * tau and z( k ) are chosen to annihilate the elements of the kth row 75: * of X. 76: * 77: * The scalar tau is returned in the kth element of TAU and the vector 78: * u( k ) in the kth row of A, such that the elements of z( k ) are 79: * in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in 80: * the upper triangular part of A. 81: * 82: * Z is given by 83: * 84: * Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). 85: * 86: * ===================================================================== 87: * 88: * .. Parameters .. 89: DOUBLE PRECISION ONE, ZERO 90: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 91: * .. 92: * .. Local Scalars .. 93: INTEGER I, K, M1 94: * .. 95: * .. Intrinsic Functions .. 96: INTRINSIC MAX, MIN 97: * .. 98: * .. External Subroutines .. 99: EXTERNAL DAXPY, DCOPY, DGEMV, DGER, DLARFG, XERBLA 100: * .. 101: * .. Executable Statements .. 102: * 103: * Test the input parameters. 104: * 105: INFO = 0 106: IF( M.LT.0 ) THEN 107: INFO = -1 108: ELSE IF( N.LT.M ) THEN 109: INFO = -2 110: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 111: INFO = -4 112: END IF 113: IF( INFO.NE.0 ) THEN 114: CALL XERBLA( 'DTZRQF', -INFO ) 115: RETURN 116: END IF 117: * 118: * Perform the factorization. 119: * 120: IF( M.EQ.0 ) 121: $ RETURN 122: IF( M.EQ.N ) THEN 123: DO 10 I = 1, N 124: TAU( I ) = ZERO 125: 10 CONTINUE 126: ELSE 127: M1 = MIN( M+1, N ) 128: DO 20 K = M, 1, -1 129: * 130: * Use a Householder reflection to zero the kth row of A. 131: * First set up the reflection. 132: * 133: CALL DLARFG( N-M+1, A( K, K ), A( K, M1 ), LDA, TAU( K ) ) 134: * 135: IF( ( TAU( K ).NE.ZERO ) .AND. ( K.GT.1 ) ) THEN 136: * 137: * We now perform the operation A := A*P( k ). 138: * 139: * Use the first ( k - 1 ) elements of TAU to store a( k ), 140: * where a( k ) consists of the first ( k - 1 ) elements of 141: * the kth column of A. Also let B denote the first 142: * ( k - 1 ) rows of the last ( n - m ) columns of A. 143: * 144: CALL DCOPY( K-1, A( 1, K ), 1, TAU, 1 ) 145: * 146: * Form w = a( k ) + B*z( k ) in TAU. 147: * 148: CALL DGEMV( 'No transpose', K-1, N-M, ONE, A( 1, M1 ), 149: $ LDA, A( K, M1 ), LDA, ONE, TAU, 1 ) 150: * 151: * Now form a( k ) := a( k ) - tau*w 152: * and B := B - tau*w*z( k )'. 153: * 154: CALL DAXPY( K-1, -TAU( K ), TAU, 1, A( 1, K ), 1 ) 155: CALL DGER( K-1, N-M, -TAU( K ), TAU, 1, A( K, M1 ), LDA, 156: $ A( 1, M1 ), LDA ) 157: END IF 158: 20 CONTINUE 159: END IF 160: * 161: RETURN 162: * 163: * End of DTZRQF 164: * 165: END