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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZTZRQF( 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: COMPLEX*16 A( LDA, * ), TAU( * ) 13: * .. 14: * 15: * Purpose 16: * ======= 17: * 18: * This routine is deprecated and has been replaced by routine ZTZRZF. 19: * 20: * ZTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A 21: * to upper triangular form by means of unitary 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 unitary 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) COMPLEX*16 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: * unitary 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) COMPLEX*16 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 ), whose conjugate transpose is used to 62: * introduce zeros into 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: COMPLEX*16 CONE, CZERO 90: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ), 91: $ CZERO = ( 0.0D+0, 0.0D+0 ) ) 92: * .. 93: * .. Local Scalars .. 94: INTEGER I, K, M1 95: COMPLEX*16 ALPHA 96: * .. 97: * .. Intrinsic Functions .. 98: INTRINSIC DCONJG, MAX, MIN 99: * .. 100: * .. External Subroutines .. 101: EXTERNAL XERBLA, ZAXPY, ZCOPY, ZGEMV, ZGERC, ZLACGV, 102: $ ZLARFG 103: * .. 104: * .. Executable Statements .. 105: * 106: * Test the input parameters. 107: * 108: INFO = 0 109: IF( M.LT.0 ) THEN 110: INFO = -1 111: ELSE IF( N.LT.M ) THEN 112: INFO = -2 113: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 114: INFO = -4 115: END IF 116: IF( INFO.NE.0 ) THEN 117: CALL XERBLA( 'ZTZRQF', -INFO ) 118: RETURN 119: END IF 120: * 121: * Perform the factorization. 122: * 123: IF( M.EQ.0 ) 124: $ RETURN 125: IF( M.EQ.N ) THEN 126: DO 10 I = 1, N 127: TAU( I ) = CZERO 128: 10 CONTINUE 129: ELSE 130: M1 = MIN( M+1, N ) 131: DO 20 K = M, 1, -1 132: * 133: * Use a Householder reflection to zero the kth row of A. 134: * First set up the reflection. 135: * 136: A( K, K ) = DCONJG( A( K, K ) ) 137: CALL ZLACGV( N-M, A( K, M1 ), LDA ) 138: ALPHA = A( K, K ) 139: CALL ZLARFG( N-M+1, ALPHA, A( K, M1 ), LDA, TAU( K ) ) 140: A( K, K ) = ALPHA 141: TAU( K ) = DCONJG( TAU( K ) ) 142: * 143: IF( TAU( K ).NE.CZERO .AND. K.GT.1 ) THEN 144: * 145: * We now perform the operation A := A*P( k )'. 146: * 147: * Use the first ( k - 1 ) elements of TAU to store a( k ), 148: * where a( k ) consists of the first ( k - 1 ) elements of 149: * the kth column of A. Also let B denote the first 150: * ( k - 1 ) rows of the last ( n - m ) columns of A. 151: * 152: CALL ZCOPY( K-1, A( 1, K ), 1, TAU, 1 ) 153: * 154: * Form w = a( k ) + B*z( k ) in TAU. 155: * 156: CALL ZGEMV( 'No transpose', K-1, N-M, CONE, A( 1, M1 ), 157: $ LDA, A( K, M1 ), LDA, CONE, TAU, 1 ) 158: * 159: * Now form a( k ) := a( k ) - conjg(tau)*w 160: * and B := B - conjg(tau)*w*z( k )'. 161: * 162: CALL ZAXPY( K-1, -DCONJG( TAU( K ) ), TAU, 1, A( 1, K ), 163: $ 1 ) 164: CALL ZGERC( K-1, N-M, -DCONJG( TAU( K ) ), TAU, 1, 165: $ A( K, M1 ), LDA, A( 1, M1 ), LDA ) 166: END IF 167: 20 CONTINUE 168: END IF 169: * 170: RETURN 171: * 172: * End of ZTZRQF 173: * 174: END