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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO ) 2: * 3: * -- LAPACK routine (version 3.2) -- 4: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- 5: * -- Jason Riedy of Univ. of California Berkeley. -- 6: * -- November 2008 -- 7: * 8: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 9: * -- Univ. of California Berkeley and NAG Ltd. -- 10: * 11: IMPLICIT NONE 12: * .. 13: * .. Scalar Arguments .. 14: INTEGER INFO, LDA, N 15: DOUBLE PRECISION AMAX, SCOND 16: * .. 17: * .. Array Arguments .. 18: COMPLEX*16 A( LDA, * ) 19: DOUBLE PRECISION S( * ) 20: * .. 21: * 22: * Purpose 23: * ======= 24: * 25: * ZPOEQUB computes row and column scalings intended to equilibrate a 26: * symmetric positive definite matrix A and reduce its condition number 27: * (with respect to the two-norm). S contains the scale factors, 28: * S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with 29: * elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This 30: * choice of S puts the condition number of B within a factor N of the 31: * smallest possible condition number over all possible diagonal 32: * scalings. 33: * 34: * Arguments 35: * ========= 36: * 37: * N (input) INTEGER 38: * The order of the matrix A. N >= 0. 39: * 40: * A (input) COMPLEX*16 array, dimension (LDA,N) 41: * The N-by-N symmetric positive definite matrix whose scaling 42: * factors are to be computed. Only the diagonal elements of A 43: * are referenced. 44: * 45: * LDA (input) INTEGER 46: * The leading dimension of the array A. LDA >= max(1,N). 47: * 48: * S (output) DOUBLE PRECISION array, dimension (N) 49: * If INFO = 0, S contains the scale factors for A. 50: * 51: * SCOND (output) DOUBLE PRECISION 52: * If INFO = 0, S contains the ratio of the smallest S(i) to 53: * the largest S(i). If SCOND >= 0.1 and AMAX is neither too 54: * large nor too small, it is not worth scaling by S. 55: * 56: * AMAX (output) DOUBLE PRECISION 57: * Absolute value of largest matrix element. If AMAX is very 58: * close to overflow or very close to underflow, the matrix 59: * should be scaled. 60: * 61: * INFO (output) INTEGER 62: * = 0: successful exit 63: * < 0: if INFO = -i, the i-th argument had an illegal value 64: * > 0: if INFO = i, the i-th diagonal element is nonpositive. 65: * 66: * ===================================================================== 67: * 68: * .. Parameters .. 69: DOUBLE PRECISION ZERO, ONE 70: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 71: * .. 72: * .. Local Scalars .. 73: INTEGER I 74: DOUBLE PRECISION SMIN, BASE, TMP 75: COMPLEX*16 ZDUM 76: * .. 77: * .. External Functions .. 78: DOUBLE PRECISION DLAMCH 79: EXTERNAL DLAMCH 80: * .. 81: * .. External Subroutines .. 82: EXTERNAL XERBLA 83: * .. 84: * .. Intrinsic Functions .. 85: INTRINSIC MAX, MIN, SQRT, LOG, INT, REAL, DIMAG 86: * .. 87: * .. Statement Functions .. 88: DOUBLE PRECISION CABS1 89: * .. 90: * .. Statement Function Definitions .. 91: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) 92: * .. 93: * .. Executable Statements .. 94: * 95: * Test the input parameters. 96: * 97: * Positive definite only performs 1 pass of equilibration. 98: * 99: INFO = 0 100: IF( N.LT.0 ) THEN 101: INFO = -1 102: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 103: INFO = -3 104: END IF 105: IF( INFO.NE.0 ) THEN 106: CALL XERBLA( 'ZPOEQUB', -INFO ) 107: RETURN 108: END IF 109: * 110: * Quick return if possible. 111: * 112: IF( N.EQ.0 ) THEN 113: SCOND = ONE 114: AMAX = ZERO 115: RETURN 116: END IF 117: 118: BASE = DLAMCH( 'B' ) 119: TMP = -0.5D+0 / LOG ( BASE ) 120: * 121: * Find the minimum and maximum diagonal elements. 122: * 123: S( 1 ) = A( 1, 1 ) 124: SMIN = S( 1 ) 125: AMAX = S( 1 ) 126: DO 10 I = 2, N 127: S( I ) = A( I, I ) 128: SMIN = MIN( SMIN, S( I ) ) 129: AMAX = MAX( AMAX, S( I ) ) 130: 10 CONTINUE 131: * 132: IF( SMIN.LE.ZERO ) THEN 133: * 134: * Find the first non-positive diagonal element and return. 135: * 136: DO 20 I = 1, N 137: IF( S( I ).LE.ZERO ) THEN 138: INFO = I 139: RETURN 140: END IF 141: 20 CONTINUE 142: ELSE 143: * 144: * Set the scale factors to the reciprocals 145: * of the diagonal elements. 146: * 147: DO 30 I = 1, N 148: S( I ) = BASE ** INT( TMP * LOG( S( I ) ) ) 149: 30 CONTINUE 150: * 151: * Compute SCOND = min(S(I)) / max(S(I)). 152: * 153: SCOND = SQRT( SMIN ) / SQRT( AMAX ) 154: END IF 155: * 156: RETURN 157: * 158: * End of ZPOEQUB 159: * 160: END