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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZPBSTF( 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: COMPLEX*16 AB( LDAB, * ) 14: * .. 15: * 16: * Purpose 17: * ======= 18: * 19: * ZPBSTF computes a split Cholesky factorization of a complex 20: * Hermitian positive definite band matrix A. 21: * 22: * This routine is designed to be used in conjunction with ZHBGST. 23: * 24: * The factorization has the form A = S**H*S where S is a band matrix 25: * of the same bandwidth as A and the following structure: 26: * 27: * S = ( U ) 28: * ( M L ) 29: * 30: * where U is upper triangular of order m = (n+kd)/2, and L is lower 31: * triangular of order n-m. 32: * 33: * Arguments 34: * ========= 35: * 36: * UPLO (input) CHARACTER*1 37: * = 'U': Upper triangle of A is stored; 38: * = 'L': Lower triangle of A is stored. 39: * 40: * N (input) INTEGER 41: * The order of the 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: * AB (input/output) COMPLEX*16 array, dimension (LDAB,N) 48: * On entry, the upper or lower triangle of the Hermitian band 49: * matrix A, stored in the first kd+1 rows of the array. The 50: * j-th column of A is stored in the j-th column of the array AB 51: * as follows: 52: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; 53: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). 54: * 55: * On exit, if INFO = 0, the factor S from the split Cholesky 56: * factorization A = S**H*S. See Further Details. 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 = -i, the i-th argument had an illegal value 64: * > 0: if INFO = i, the factorization could not be completed, 65: * because the updated element a(i,i) was negative; the 66: * matrix A is not positive definite. 67: * 68: * Further Details 69: * =============== 70: * 71: * The band storage scheme is illustrated by the following example, when 72: * N = 7, KD = 2: 73: * 74: * S = ( s11 s12 s13 ) 75: * ( s22 s23 s24 ) 76: * ( s33 s34 ) 77: * ( s44 ) 78: * ( s53 s54 s55 ) 79: * ( s64 s65 s66 ) 80: * ( s75 s76 s77 ) 81: * 82: * If UPLO = 'U', the array AB holds: 83: * 84: * on entry: on exit: 85: * 86: * * * a13 a24 a35 a46 a57 * * s13 s24 s53' s64' s75' 87: * * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54' s65' s76' 88: * a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 89: * 90: * If UPLO = 'L', the array AB holds: 91: * 92: * on entry: on exit: 93: * 94: * a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 95: * a21 a32 a43 a54 a65 a76 * s12' s23' s34' s54 s65 s76 * 96: * a31 a42 a53 a64 a64 * * s13' s24' s53 s64 s75 * * 97: * 98: * Array elements marked * are not used by the routine; s12' denotes 99: * conjg(s12); the diagonal elements of S are real. 100: * 101: * ===================================================================== 102: * 103: * .. Parameters .. 104: DOUBLE PRECISION ONE, ZERO 105: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 106: * .. 107: * .. Local Scalars .. 108: LOGICAL UPPER 109: INTEGER J, KLD, KM, M 110: DOUBLE PRECISION AJJ 111: * .. 112: * .. External Functions .. 113: LOGICAL LSAME 114: EXTERNAL LSAME 115: * .. 116: * .. External Subroutines .. 117: EXTERNAL XERBLA, ZDSCAL, ZHER, ZLACGV 118: * .. 119: * .. Intrinsic Functions .. 120: INTRINSIC DBLE, MAX, MIN, SQRT 121: * .. 122: * .. Executable Statements .. 123: * 124: * Test the input parameters. 125: * 126: INFO = 0 127: UPPER = LSAME( UPLO, 'U' ) 128: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 129: INFO = -1 130: ELSE IF( N.LT.0 ) THEN 131: INFO = -2 132: ELSE IF( KD.LT.0 ) THEN 133: INFO = -3 134: ELSE IF( LDAB.LT.KD+1 ) THEN 135: INFO = -5 136: END IF 137: IF( INFO.NE.0 ) THEN 138: CALL XERBLA( 'ZPBSTF', -INFO ) 139: RETURN 140: END IF 141: * 142: * Quick return if possible 143: * 144: IF( N.EQ.0 ) 145: $ RETURN 146: * 147: KLD = MAX( 1, LDAB-1 ) 148: * 149: * Set the splitting point m. 150: * 151: M = ( N+KD ) / 2 152: * 153: IF( UPPER ) THEN 154: * 155: * Factorize A(m+1:n,m+1:n) as L**H*L, and update A(1:m,1:m). 156: * 157: DO 10 J = N, M + 1, -1 158: * 159: * Compute s(j,j) and test for non-positive-definiteness. 160: * 161: AJJ = DBLE( AB( KD+1, J ) ) 162: IF( AJJ.LE.ZERO ) THEN 163: AB( KD+1, J ) = AJJ 164: GO TO 50 165: END IF 166: AJJ = SQRT( AJJ ) 167: AB( KD+1, J ) = AJJ 168: KM = MIN( J-1, KD ) 169: * 170: * Compute elements j-km:j-1 of the j-th column and update the 171: * the leading submatrix within the band. 172: * 173: CALL ZDSCAL( KM, ONE / AJJ, AB( KD+1-KM, J ), 1 ) 174: CALL ZHER( 'Upper', KM, -ONE, AB( KD+1-KM, J ), 1, 175: $ AB( KD+1, J-KM ), KLD ) 176: 10 CONTINUE 177: * 178: * Factorize the updated submatrix A(1:m,1:m) as U**H*U. 179: * 180: DO 20 J = 1, M 181: * 182: * Compute s(j,j) and test for non-positive-definiteness. 183: * 184: AJJ = DBLE( AB( KD+1, J ) ) 185: IF( AJJ.LE.ZERO ) THEN 186: AB( KD+1, J ) = AJJ 187: GO TO 50 188: END IF 189: AJJ = SQRT( AJJ ) 190: AB( KD+1, J ) = AJJ 191: KM = MIN( KD, M-J ) 192: * 193: * Compute elements j+1:j+km of the j-th row and update the 194: * trailing submatrix within the band. 195: * 196: IF( KM.GT.0 ) THEN 197: CALL ZDSCAL( KM, ONE / AJJ, AB( KD, J+1 ), KLD ) 198: CALL ZLACGV( KM, AB( KD, J+1 ), KLD ) 199: CALL ZHER( 'Upper', KM, -ONE, AB( KD, J+1 ), KLD, 200: $ AB( KD+1, J+1 ), KLD ) 201: CALL ZLACGV( KM, AB( KD, J+1 ), KLD ) 202: END IF 203: 20 CONTINUE 204: ELSE 205: * 206: * Factorize A(m+1:n,m+1:n) as L**H*L, and update A(1:m,1:m). 207: * 208: DO 30 J = N, M + 1, -1 209: * 210: * Compute s(j,j) and test for non-positive-definiteness. 211: * 212: AJJ = DBLE( AB( 1, J ) ) 213: IF( AJJ.LE.ZERO ) THEN 214: AB( 1, J ) = AJJ 215: GO TO 50 216: END IF 217: AJJ = SQRT( AJJ ) 218: AB( 1, J ) = AJJ 219: KM = MIN( J-1, KD ) 220: * 221: * Compute elements j-km:j-1 of the j-th row and update the 222: * trailing submatrix within the band. 223: * 224: CALL ZDSCAL( KM, ONE / AJJ, AB( KM+1, J-KM ), KLD ) 225: CALL ZLACGV( KM, AB( KM+1, J-KM ), KLD ) 226: CALL ZHER( 'Lower', KM, -ONE, AB( KM+1, J-KM ), KLD, 227: $ AB( 1, J-KM ), KLD ) 228: CALL ZLACGV( KM, AB( KM+1, J-KM ), KLD ) 229: 30 CONTINUE 230: * 231: * Factorize the updated submatrix A(1:m,1:m) as U**H*U. 232: * 233: DO 40 J = 1, M 234: * 235: * Compute s(j,j) and test for non-positive-definiteness. 236: * 237: AJJ = DBLE( AB( 1, J ) ) 238: IF( AJJ.LE.ZERO ) THEN 239: AB( 1, J ) = AJJ 240: GO TO 50 241: END IF 242: AJJ = SQRT( AJJ ) 243: AB( 1, J ) = AJJ 244: KM = MIN( KD, M-J ) 245: * 246: * Compute elements j+1:j+km of the j-th column and update the 247: * trailing submatrix within the band. 248: * 249: IF( KM.GT.0 ) THEN 250: CALL ZDSCAL( KM, ONE / AJJ, AB( 2, J ), 1 ) 251: CALL ZHER( 'Lower', KM, -ONE, AB( 2, J ), 1, 252: $ AB( 1, J+1 ), KLD ) 253: END IF 254: 40 CONTINUE 255: END IF 256: RETURN 257: * 258: 50 CONTINUE 259: INFO = J 260: RETURN 261: * 262: * End of ZPBSTF 263: * 264: END