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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) 2: * 3: * -- LAPACK driver 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 UPLO 10: INTEGER INFO, KD, LDAB, LDB, N, NRHS 11: * .. 12: * .. Array Arguments .. 13: COMPLEX*16 AB( LDAB, * ), B( LDB, * ) 14: * .. 15: * 16: * Purpose 17: * ======= 18: * 19: * ZPBSV computes the solution to a complex system of linear equations 20: * A * X = B, 21: * where A is an N-by-N Hermitian positive definite band matrix and X 22: * and B are N-by-NRHS matrices. 23: * 24: * The Cholesky decomposition is used to factor A as 25: * A = U**H * U, if UPLO = 'U', or 26: * A = L * L**H, if UPLO = 'L', 27: * where U is an upper triangular band matrix, and L is a lower 28: * triangular band matrix, with the same number of superdiagonals or 29: * subdiagonals as A. The factored form of A is then used to solve the 30: * system of equations A * X = B. 31: * 32: * Arguments 33: * ========= 34: * 35: * UPLO (input) CHARACTER*1 36: * = 'U': Upper triangle of A is stored; 37: * = 'L': Lower triangle of A is stored. 38: * 39: * N (input) INTEGER 40: * The number of linear equations, i.e., the order of the 41: * matrix A. N >= 0. 42: * 43: * KD (input) INTEGER 44: * The number of superdiagonals of the matrix A if UPLO = 'U', 45: * or the number of subdiagonals if UPLO = 'L'. KD >= 0. 46: * 47: * NRHS (input) INTEGER 48: * The number of right hand sides, i.e., the number of columns 49: * of the matrix B. NRHS >= 0. 50: * 51: * AB (input/output) COMPLEX*16 array, dimension (LDAB,N) 52: * On entry, the upper or lower triangle of the Hermitian band 53: * matrix A, stored in the first KD+1 rows of the array. The 54: * j-th column of A is stored in the j-th column of the array AB 55: * as follows: 56: * if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; 57: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). 58: * See below for further details. 59: * 60: * On exit, if INFO = 0, the triangular factor U or L from the 61: * Cholesky factorization A = U**H*U or A = L*L**H of the band 62: * matrix A, in the same storage format as A. 63: * 64: * LDAB (input) INTEGER 65: * The leading dimension of the array AB. LDAB >= KD+1. 66: * 67: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) 68: * On entry, the N-by-NRHS right hand side matrix B. 69: * On exit, if INFO = 0, the N-by-NRHS solution matrix X. 70: * 71: * LDB (input) INTEGER 72: * The leading dimension of the array B. LDB >= max(1,N). 73: * 74: * INFO (output) INTEGER 75: * = 0: successful exit 76: * < 0: if INFO = -i, the i-th argument had an illegal value 77: * > 0: if INFO = i, the leading minor of order i of A is not 78: * positive definite, so the factorization could not be 79: * completed, and the solution has not been computed. 80: * 81: * Further Details 82: * =============== 83: * 84: * The band storage scheme is illustrated by the following example, when 85: * N = 6, KD = 2, and UPLO = 'U': 86: * 87: * On entry: On exit: 88: * 89: * * * a13 a24 a35 a46 * * u13 u24 u35 u46 90: * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 91: * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 92: * 93: * Similarly, if UPLO = 'L' the format of A is as follows: 94: * 95: * On entry: On exit: 96: * 97: * a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 98: * a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * 99: * a31 a42 a53 a64 * * l31 l42 l53 l64 * * 100: * 101: * Array elements marked * are not used by the routine. 102: * 103: * ===================================================================== 104: * 105: * .. External Functions .. 106: LOGICAL LSAME 107: EXTERNAL LSAME 108: * .. 109: * .. External Subroutines .. 110: EXTERNAL XERBLA, ZPBTRF, ZPBTRS 111: * .. 112: * .. Intrinsic Functions .. 113: INTRINSIC MAX 114: * .. 115: * .. Executable Statements .. 116: * 117: * Test the input parameters. 118: * 119: INFO = 0 120: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 121: INFO = -1 122: ELSE IF( N.LT.0 ) THEN 123: INFO = -2 124: ELSE IF( KD.LT.0 ) THEN 125: INFO = -3 126: ELSE IF( NRHS.LT.0 ) THEN 127: INFO = -4 128: ELSE IF( LDAB.LT.KD+1 ) THEN 129: INFO = -6 130: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 131: INFO = -8 132: END IF 133: IF( INFO.NE.0 ) THEN 134: CALL XERBLA( 'ZPBSV ', -INFO ) 135: RETURN 136: END IF 137: * 138: * Compute the Cholesky factorization A = U'*U or A = L*L'. 139: * 140: CALL ZPBTRF( UPLO, N, KD, AB, LDAB, INFO ) 141: IF( INFO.EQ.0 ) THEN 142: * 143: * Solve the system A*X = B, overwriting B with X. 144: * 145: CALL ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) 146: * 147: END IF 148: RETURN 149: * 150: * End of ZPBSV 151: * 152: END