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