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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED ) 2: * 3: * -- LAPACK auxiliary routine (version 3.2) -- 4: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 6: * November 2006 7: * 8: * .. Scalar Arguments .. 9: CHARACTER EQUED, UPLO 10: INTEGER KD, LDAB, N 11: DOUBLE PRECISION AMAX, SCOND 12: * .. 13: * .. Array Arguments .. 14: DOUBLE PRECISION S( * ) 15: COMPLEX*16 AB( LDAB, * ) 16: * .. 17: * 18: * Purpose 19: * ======= 20: * 21: * ZLAQSB equilibrates a symmetric band matrix A using the scaling 22: * factors in the vector S. 23: * 24: * Arguments 25: * ========= 26: * 27: * UPLO (input) CHARACTER*1 28: * Specifies whether the upper or lower triangular part of the 29: * symmetric matrix A is stored. 30: * = 'U': Upper triangular 31: * = 'L': Lower triangular 32: * 33: * N (input) INTEGER 34: * The order of the matrix A. N >= 0. 35: * 36: * KD (input) INTEGER 37: * The number of super-diagonals of the matrix A if UPLO = 'U', 38: * or the number of sub-diagonals if UPLO = 'L'. KD >= 0. 39: * 40: * AB (input/output) COMPLEX*16 array, dimension (LDAB,N) 41: * On entry, the upper or lower triangle of the symmetric band 42: * matrix A, stored in the first KD+1 rows of the array. The 43: * j-th column of A is stored in the j-th column of the array AB 44: * as follows: 45: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; 46: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). 47: * 48: * On exit, if INFO = 0, the triangular factor U or L from the 49: * Cholesky factorization A = U'*U or A = L*L' of the band 50: * matrix A, in the same storage format as A. 51: * 52: * LDAB (input) INTEGER 53: * The leading dimension of the array AB. LDAB >= KD+1. 54: * 55: * S (input) DOUBLE PRECISION array, dimension (N) 56: * The scale factors for A. 57: * 58: * SCOND (input) DOUBLE PRECISION 59: * Ratio of the smallest S(i) to the largest S(i). 60: * 61: * AMAX (input) DOUBLE PRECISION 62: * Absolute value of largest matrix entry. 63: * 64: * EQUED (output) CHARACTER*1 65: * Specifies whether or not equilibration was done. 66: * = 'N': No equilibration. 67: * = 'Y': Equilibration was done, i.e., A has been replaced by 68: * diag(S) * A * diag(S). 69: * 70: * Internal Parameters 71: * =================== 72: * 73: * THRESH is a threshold value used to decide if scaling should be done 74: * based on the ratio of the scaling factors. If SCOND < THRESH, 75: * scaling is done. 76: * 77: * LARGE and SMALL are threshold values used to decide if scaling should 78: * be done based on the absolute size of the largest matrix element. 79: * If AMAX > LARGE or AMAX < SMALL, scaling is done. 80: * 81: * ===================================================================== 82: * 83: * .. Parameters .. 84: DOUBLE PRECISION ONE, THRESH 85: PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 ) 86: * .. 87: * .. Local Scalars .. 88: INTEGER I, J 89: DOUBLE PRECISION CJ, LARGE, SMALL 90: * .. 91: * .. External Functions .. 92: LOGICAL LSAME 93: DOUBLE PRECISION DLAMCH 94: EXTERNAL LSAME, DLAMCH 95: * .. 96: * .. Intrinsic Functions .. 97: INTRINSIC MAX, MIN 98: * .. 99: * .. Executable Statements .. 100: * 101: * Quick return if possible 102: * 103: IF( N.LE.0 ) THEN 104: EQUED = 'N' 105: RETURN 106: END IF 107: * 108: * Initialize LARGE and SMALL. 109: * 110: SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' ) 111: LARGE = ONE / SMALL 112: * 113: IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN 114: * 115: * No equilibration 116: * 117: EQUED = 'N' 118: ELSE 119: * 120: * Replace A by diag(S) * A * diag(S). 121: * 122: IF( LSAME( UPLO, 'U' ) ) THEN 123: * 124: * Upper triangle of A is stored in band format. 125: * 126: DO 20 J = 1, N 127: CJ = S( J ) 128: DO 10 I = MAX( 1, J-KD ), J 129: AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J ) 130: 10 CONTINUE 131: 20 CONTINUE 132: ELSE 133: * 134: * Lower triangle of A is stored. 135: * 136: DO 40 J = 1, N 137: CJ = S( J ) 138: DO 30 I = J, MIN( N, J+KD ) 139: AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J ) 140: 30 CONTINUE 141: 40 CONTINUE 142: END IF 143: EQUED = 'Y' 144: END IF 145: * 146: RETURN 147: * 148: * End of ZLAQSB 149: * 150: END