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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, 2: $ INFO ) 3: * 4: * -- LAPACK routine (version 3.2) -- 5: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 7: * November 2006 8: * 9: * Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. 10: * 11: * .. Scalar Arguments .. 12: CHARACTER UPLO 13: INTEGER INFO, LDA, N 14: DOUBLE PRECISION ANORM, RCOND 15: * .. 16: * .. Array Arguments .. 17: INTEGER IPIV( * ) 18: COMPLEX*16 A( LDA, * ), WORK( * ) 19: * .. 20: * 21: * Purpose 22: * ======= 23: * 24: * ZHECON estimates the reciprocal of the condition number of a complex 25: * Hermitian matrix A using the factorization A = U*D*U**H or 26: * A = L*D*L**H computed by ZHETRF. 27: * 28: * An estimate is obtained for norm(inv(A)), and the reciprocal of the 29: * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). 30: * 31: * Arguments 32: * ========= 33: * 34: * UPLO (input) CHARACTER*1 35: * Specifies whether the details of the factorization are stored 36: * as an upper or lower triangular matrix. 37: * = 'U': Upper triangular, form is A = U*D*U**H; 38: * = 'L': Lower triangular, form is A = L*D*L**H. 39: * 40: * N (input) INTEGER 41: * The order of the matrix A. N >= 0. 42: * 43: * A (input) COMPLEX*16 array, dimension (LDA,N) 44: * The block diagonal matrix D and the multipliers used to 45: * obtain the factor U or L as computed by ZHETRF. 46: * 47: * LDA (input) INTEGER 48: * The leading dimension of the array A. LDA >= max(1,N). 49: * 50: * IPIV (input) INTEGER array, dimension (N) 51: * Details of the interchanges and the block structure of D 52: * as determined by ZHETRF. 53: * 54: * ANORM (input) DOUBLE PRECISION 55: * The 1-norm of the original matrix A. 56: * 57: * RCOND (output) DOUBLE PRECISION 58: * The reciprocal of the condition number of the matrix A, 59: * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an 60: * estimate of the 1-norm of inv(A) computed in this routine. 61: * 62: * WORK (workspace) COMPLEX*16 array, dimension (2*N) 63: * 64: * INFO (output) INTEGER 65: * = 0: successful exit 66: * < 0: if INFO = -i, the i-th argument had an illegal value 67: * 68: * ===================================================================== 69: * 70: * .. Parameters .. 71: DOUBLE PRECISION ONE, ZERO 72: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 73: * .. 74: * .. Local Scalars .. 75: LOGICAL UPPER 76: INTEGER I, KASE 77: DOUBLE PRECISION AINVNM 78: * .. 79: * .. Local Arrays .. 80: INTEGER ISAVE( 3 ) 81: * .. 82: * .. External Functions .. 83: LOGICAL LSAME 84: EXTERNAL LSAME 85: * .. 86: * .. External Subroutines .. 87: EXTERNAL XERBLA, ZHETRS, ZLACN2 88: * .. 89: * .. Intrinsic Functions .. 90: INTRINSIC MAX 91: * .. 92: * .. Executable Statements .. 93: * 94: * Test the input parameters. 95: * 96: INFO = 0 97: UPPER = LSAME( UPLO, 'U' ) 98: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 99: INFO = -1 100: ELSE IF( N.LT.0 ) THEN 101: INFO = -2 102: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 103: INFO = -4 104: ELSE IF( ANORM.LT.ZERO ) THEN 105: INFO = -6 106: END IF 107: IF( INFO.NE.0 ) THEN 108: CALL XERBLA( 'ZHECON', -INFO ) 109: RETURN 110: END IF 111: * 112: * Quick return if possible 113: * 114: RCOND = ZERO 115: IF( N.EQ.0 ) THEN 116: RCOND = ONE 117: RETURN 118: ELSE IF( ANORM.LE.ZERO ) THEN 119: RETURN 120: END IF 121: * 122: * Check that the diagonal matrix D is nonsingular. 123: * 124: IF( UPPER ) THEN 125: * 126: * Upper triangular storage: examine D from bottom to top 127: * 128: DO 10 I = N, 1, -1 129: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO ) 130: $ RETURN 131: 10 CONTINUE 132: ELSE 133: * 134: * Lower triangular storage: examine D from top to bottom. 135: * 136: DO 20 I = 1, N 137: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO ) 138: $ RETURN 139: 20 CONTINUE 140: END IF 141: * 142: * Estimate the 1-norm of the inverse. 143: * 144: KASE = 0 145: 30 CONTINUE 146: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) 147: IF( KASE.NE.0 ) THEN 148: * 149: * Multiply by inv(L*D*L') or inv(U*D*U'). 150: * 151: CALL ZHETRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO ) 152: GO TO 30 153: END IF 154: * 155: * Compute the estimate of the reciprocal condition number. 156: * 157: IF( AINVNM.NE.ZERO ) 158: $ RCOND = ( ONE / AINVNM ) / ANORM 159: * 160: RETURN 161: * 162: * End of ZHECON 163: * 164: END