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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZGEQL2( M, N, A, LDA, TAU, WORK, 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( * ), WORK( * ) 13: * .. 14: * 15: * Purpose 16: * ======= 17: * 18: * ZGEQL2 computes a QL factorization of a complex m by n matrix A: 19: * A = Q * L. 20: * 21: * Arguments 22: * ========= 23: * 24: * M (input) INTEGER 25: * The number of rows of the matrix A. M >= 0. 26: * 27: * N (input) INTEGER 28: * The number of columns of the matrix A. N >= 0. 29: * 30: * A (input/output) COMPLEX*16 array, dimension (LDA,N) 31: * On entry, the m by n matrix A. 32: * On exit, if m >= n, the lower triangle of the subarray 33: * A(m-n+1:m,1:n) contains the n by n lower triangular matrix L; 34: * if m <= n, the elements on and below the (n-m)-th 35: * superdiagonal contain the m by n lower trapezoidal matrix L; 36: * the remaining elements, with the array TAU, represent the 37: * unitary matrix Q as a product of elementary reflectors 38: * (see Further Details). 39: * 40: * LDA (input) INTEGER 41: * The leading dimension of the array A. LDA >= max(1,M). 42: * 43: * TAU (output) COMPLEX*16 array, dimension (min(M,N)) 44: * The scalar factors of the elementary reflectors (see Further 45: * Details). 46: * 47: * WORK (workspace) COMPLEX*16 array, dimension (N) 48: * 49: * INFO (output) INTEGER 50: * = 0: successful exit 51: * < 0: if INFO = -i, the i-th argument had an illegal value 52: * 53: * Further Details 54: * =============== 55: * 56: * The matrix Q is represented as a product of elementary reflectors 57: * 58: * Q = H(k) . . . H(2) H(1), where k = min(m,n). 59: * 60: * Each H(i) has the form 61: * 62: * H(i) = I - tau * v * v' 63: * 64: * where tau is a complex scalar, and v is a complex vector with 65: * v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in 66: * A(1:m-k+i-1,n-k+i), and tau in TAU(i). 67: * 68: * ===================================================================== 69: * 70: * .. Parameters .. 71: COMPLEX*16 ONE 72: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) 73: * .. 74: * .. Local Scalars .. 75: INTEGER I, K 76: COMPLEX*16 ALPHA 77: * .. 78: * .. External Subroutines .. 79: EXTERNAL XERBLA, ZLARF, ZLARFG 80: * .. 81: * .. Intrinsic Functions .. 82: INTRINSIC DCONJG, MAX, MIN 83: * .. 84: * .. Executable Statements .. 85: * 86: * Test the input arguments 87: * 88: INFO = 0 89: IF( M.LT.0 ) THEN 90: INFO = -1 91: ELSE IF( N.LT.0 ) THEN 92: INFO = -2 93: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 94: INFO = -4 95: END IF 96: IF( INFO.NE.0 ) THEN 97: CALL XERBLA( 'ZGEQL2', -INFO ) 98: RETURN 99: END IF 100: * 101: K = MIN( M, N ) 102: * 103: DO 10 I = K, 1, -1 104: * 105: * Generate elementary reflector H(i) to annihilate 106: * A(1:m-k+i-1,n-k+i) 107: * 108: ALPHA = A( M-K+I, N-K+I ) 109: CALL ZLARFG( M-K+I, ALPHA, A( 1, N-K+I ), 1, TAU( I ) ) 110: * 111: * Apply H(i)' to A(1:m-k+i,1:n-k+i-1) from the left 112: * 113: A( M-K+I, N-K+I ) = ONE 114: CALL ZLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1, 115: $ DCONJG( TAU( I ) ), A, LDA, WORK ) 116: A( M-K+I, N-K+I ) = ALPHA 117: 10 CONTINUE 118: RETURN 119: * 120: * End of ZGEQL2 121: * 122: END