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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DPBTF2( UPLO, N, KD, AB, LDAB, 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: * .. Scalar Arguments .. 9: CHARACTER UPLO 10: INTEGER INFO, KD, LDAB, N 11: * .. 12: * .. Array Arguments .. 13: DOUBLE PRECISION AB( LDAB, * ) 14: * .. 15: * 16: * Purpose 17: * ======= 18: * 19: * DPBTF2 computes the Cholesky factorization of a real symmetric 20: * positive definite band matrix A. 21: * 22: * The factorization has the form 23: * A = U' * U , if UPLO = 'U', or 24: * A = L * L', if UPLO = 'L', 25: * where U is an upper triangular matrix, U' is the transpose of U, and 26: * L is lower triangular. 27: * 28: * This is the unblocked version of the algorithm, calling Level 2 BLAS. 29: * 30: * Arguments 31: * ========= 32: * 33: * UPLO (input) CHARACTER*1 34: * Specifies whether the upper or lower triangular part of the 35: * symmetric matrix A is stored: 36: * = 'U': Upper triangular 37: * = 'L': Lower triangular 38: * 39: * N (input) INTEGER 40: * The order of the matrix A. N >= 0. 41: * 42: * KD (input) INTEGER 43: * The number of super-diagonals of the matrix A if UPLO = 'U', 44: * or the number of sub-diagonals if UPLO = 'L'. KD >= 0. 45: * 46: * AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) 47: * On entry, the upper or lower triangle of the symmetric band 48: * matrix A, stored in the first KD+1 rows of the array. The 49: * j-th column of A is stored in the j-th column of the array AB 50: * as follows: 51: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; 52: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). 53: * 54: * On exit, if INFO = 0, the triangular factor U or L from the 55: * Cholesky factorization A = U'*U or A = L*L' of the band 56: * matrix A, in the same storage format as A. 57: * 58: * LDAB (input) INTEGER 59: * The leading dimension of the array AB. LDAB >= KD+1. 60: * 61: * INFO (output) INTEGER 62: * = 0: successful exit 63: * < 0: if INFO = -k, the k-th argument had an illegal value 64: * > 0: if INFO = k, the leading minor of order k is not 65: * positive definite, and the factorization could not be 66: * completed. 67: * 68: * Further Details 69: * =============== 70: * 71: * The band storage scheme is illustrated by the following example, when 72: * N = 6, KD = 2, and UPLO = 'U': 73: * 74: * On entry: On exit: 75: * 76: * * * a13 a24 a35 a46 * * u13 u24 u35 u46 77: * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 78: * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 79: * 80: * Similarly, if UPLO = 'L' the format of A is as follows: 81: * 82: * On entry: On exit: 83: * 84: * a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 85: * a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * 86: * a31 a42 a53 a64 * * l31 l42 l53 l64 * * 87: * 88: * Array elements marked * are not used by the routine. 89: * 90: * ===================================================================== 91: * 92: * .. Parameters .. 93: DOUBLE PRECISION ONE, ZERO 94: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 95: * .. 96: * .. Local Scalars .. 97: LOGICAL UPPER 98: INTEGER J, KLD, KN 99: DOUBLE PRECISION AJJ 100: * .. 101: * .. External Functions .. 102: LOGICAL LSAME 103: EXTERNAL LSAME 104: * .. 105: * .. External Subroutines .. 106: EXTERNAL DSCAL, DSYR, XERBLA 107: * .. 108: * .. Intrinsic Functions .. 109: INTRINSIC MAX, MIN, SQRT 110: * .. 111: * .. Executable Statements .. 112: * 113: * Test the input parameters. 114: * 115: INFO = 0 116: UPPER = LSAME( UPLO, 'U' ) 117: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 118: INFO = -1 119: ELSE IF( N.LT.0 ) THEN 120: INFO = -2 121: ELSE IF( KD.LT.0 ) THEN 122: INFO = -3 123: ELSE IF( LDAB.LT.KD+1 ) THEN 124: INFO = -5 125: END IF 126: IF( INFO.NE.0 ) THEN 127: CALL XERBLA( 'DPBTF2', -INFO ) 128: RETURN 129: END IF 130: * 131: * Quick return if possible 132: * 133: IF( N.EQ.0 ) 134: $ RETURN 135: * 136: KLD = MAX( 1, LDAB-1 ) 137: * 138: IF( UPPER ) THEN 139: * 140: * Compute the Cholesky factorization A = U'*U. 141: * 142: DO 10 J = 1, N 143: * 144: * Compute U(J,J) and test for non-positive-definiteness. 145: * 146: AJJ = AB( KD+1, J ) 147: IF( AJJ.LE.ZERO ) 148: $ GO TO 30 149: AJJ = SQRT( AJJ ) 150: AB( KD+1, J ) = AJJ 151: * 152: * Compute elements J+1:J+KN of row J and update the 153: * trailing submatrix within the band. 154: * 155: KN = MIN( KD, N-J ) 156: IF( KN.GT.0 ) THEN 157: CALL DSCAL( KN, ONE / AJJ, AB( KD, J+1 ), KLD ) 158: CALL DSYR( 'Upper', KN, -ONE, AB( KD, J+1 ), KLD, 159: $ AB( KD+1, J+1 ), KLD ) 160: END IF 161: 10 CONTINUE 162: ELSE 163: * 164: * Compute the Cholesky factorization A = L*L'. 165: * 166: DO 20 J = 1, N 167: * 168: * Compute L(J,J) and test for non-positive-definiteness. 169: * 170: AJJ = AB( 1, J ) 171: IF( AJJ.LE.ZERO ) 172: $ GO TO 30 173: AJJ = SQRT( AJJ ) 174: AB( 1, J ) = AJJ 175: * 176: * Compute elements J+1:J+KN of column J and update the 177: * trailing submatrix within the band. 178: * 179: KN = MIN( KD, N-J ) 180: IF( KN.GT.0 ) THEN 181: CALL DSCAL( KN, ONE / AJJ, AB( 2, J ), 1 ) 182: CALL DSYR( 'Lower', KN, -ONE, AB( 2, J ), 1, 183: $ AB( 1, J+1 ), KLD ) 184: END IF 185: 20 CONTINUE 186: END IF 187: RETURN 188: * 189: 30 CONTINUE 190: INFO = J 191: RETURN 192: * 193: * End of DPBTF2 194: * 195: END