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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZHPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU, 2: $ IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, 3: $ IWORK, IFAIL, INFO ) 4: * 5: * -- LAPACK driver routine (version 3.2) -- 6: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 7: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 8: * November 2006 9: * 10: * .. Scalar Arguments .. 11: CHARACTER JOBZ, RANGE, UPLO 12: INTEGER IL, INFO, ITYPE, IU, LDZ, M, N 13: DOUBLE PRECISION ABSTOL, VL, VU 14: * .. 15: * .. Array Arguments .. 16: INTEGER IFAIL( * ), IWORK( * ) 17: DOUBLE PRECISION RWORK( * ), W( * ) 18: COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) 19: * .. 20: * 21: * Purpose 22: * ======= 23: * 24: * ZHPGVX computes selected eigenvalues and, optionally, eigenvectors 25: * of a complex generalized Hermitian-definite eigenproblem, of the form 26: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and 27: * B are assumed to be Hermitian, stored in packed format, and B is also 28: * positive definite. Eigenvalues and eigenvectors can be selected by 29: * specifying either a range of values or a range of indices for the 30: * desired eigenvalues. 31: * 32: * Arguments 33: * ========= 34: * 35: * ITYPE (input) INTEGER 36: * Specifies the problem type to be solved: 37: * = 1: A*x = (lambda)*B*x 38: * = 2: A*B*x = (lambda)*x 39: * = 3: B*A*x = (lambda)*x 40: * 41: * JOBZ (input) CHARACTER*1 42: * = 'N': Compute eigenvalues only; 43: * = 'V': Compute eigenvalues and eigenvectors. 44: * 45: * RANGE (input) CHARACTER*1 46: * = 'A': all eigenvalues will be found; 47: * = 'V': all eigenvalues in the half-open interval (VL,VU] 48: * will be found; 49: * = 'I': the IL-th through IU-th eigenvalues will be found. 50: * 51: * UPLO (input) CHARACTER*1 52: * = 'U': Upper triangles of A and B are stored; 53: * = 'L': Lower triangles of A and B are stored. 54: * 55: * N (input) INTEGER 56: * The order of the matrices A and B. N >= 0. 57: * 58: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) 59: * On entry, the upper or lower triangle of the Hermitian matrix 60: * A, packed columnwise in a linear array. The j-th column of A 61: * is stored in the array AP as follows: 62: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 63: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. 64: * 65: * On exit, the contents of AP are destroyed. 66: * 67: * BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) 68: * On entry, the upper or lower triangle of the Hermitian matrix 69: * B, packed columnwise in a linear array. The j-th column of B 70: * is stored in the array BP as follows: 71: * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; 72: * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. 73: * 74: * On exit, the triangular factor U or L from the Cholesky 75: * factorization B = U**H*U or B = L*L**H, in the same storage 76: * format as B. 77: * 78: * VL (input) DOUBLE PRECISION 79: * VU (input) DOUBLE PRECISION 80: * If RANGE='V', the lower and upper bounds of the interval to 81: * be searched for eigenvalues. VL < VU. 82: * Not referenced if RANGE = 'A' or 'I'. 83: * 84: * IL (input) INTEGER 85: * IU (input) INTEGER 86: * If RANGE='I', the indices (in ascending order) of the 87: * smallest and largest eigenvalues to be returned. 88: * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. 89: * Not referenced if RANGE = 'A' or 'V'. 90: * 91: * ABSTOL (input) DOUBLE PRECISION 92: * The absolute error tolerance for the eigenvalues. 93: * An approximate eigenvalue is accepted as converged 94: * when it is determined to lie in an interval [a,b] 95: * of width less than or equal to 96: * 97: * ABSTOL + EPS * max( |a|,|b| ) , 98: * 99: * where EPS is the machine precision. If ABSTOL is less than 100: * or equal to zero, then EPS*|T| will be used in its place, 101: * where |T| is the 1-norm of the tridiagonal matrix obtained 102: * by reducing AP to tridiagonal form. 103: * 104: * Eigenvalues will be computed most accurately when ABSTOL is 105: * set to twice the underflow threshold 2*DLAMCH('S'), not zero. 106: * If this routine returns with INFO>0, indicating that some 107: * eigenvectors did not converge, try setting ABSTOL to 108: * 2*DLAMCH('S'). 109: * 110: * M (output) INTEGER 111: * The total number of eigenvalues found. 0 <= M <= N. 112: * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. 113: * 114: * W (output) DOUBLE PRECISION array, dimension (N) 115: * On normal exit, the first M elements contain the selected 116: * eigenvalues in ascending order. 117: * 118: * Z (output) COMPLEX*16 array, dimension (LDZ, N) 119: * If JOBZ = 'N', then Z is not referenced. 120: * If JOBZ = 'V', then if INFO = 0, the first M columns of Z 121: * contain the orthonormal eigenvectors of the matrix A 122: * corresponding to the selected eigenvalues, with the i-th 123: * column of Z holding the eigenvector associated with W(i). 124: * The eigenvectors are normalized as follows: 125: * if ITYPE = 1 or 2, Z**H*B*Z = I; 126: * if ITYPE = 3, Z**H*inv(B)*Z = I. 127: * 128: * If an eigenvector fails to converge, then that column of Z 129: * contains the latest approximation to the eigenvector, and the 130: * index of the eigenvector is returned in IFAIL. 131: * Note: the user must ensure that at least max(1,M) columns are 132: * supplied in the array Z; if RANGE = 'V', the exact value of M 133: * is not known in advance and an upper bound must be used. 134: * 135: * LDZ (input) INTEGER 136: * The leading dimension of the array Z. LDZ >= 1, and if 137: * JOBZ = 'V', LDZ >= max(1,N). 138: * 139: * WORK (workspace) COMPLEX*16 array, dimension (2*N) 140: * 141: * RWORK (workspace) DOUBLE PRECISION array, dimension (7*N) 142: * 143: * IWORK (workspace) INTEGER array, dimension (5*N) 144: * 145: * IFAIL (output) INTEGER array, dimension (N) 146: * If JOBZ = 'V', then if INFO = 0, the first M elements of 147: * IFAIL are zero. If INFO > 0, then IFAIL contains the 148: * indices of the eigenvectors that failed to converge. 149: * If JOBZ = 'N', then IFAIL is not referenced. 150: * 151: * INFO (output) INTEGER 152: * = 0: successful exit 153: * < 0: if INFO = -i, the i-th argument had an illegal value 154: * > 0: ZPPTRF or ZHPEVX returned an error code: 155: * <= N: if INFO = i, ZHPEVX failed to converge; 156: * i eigenvectors failed to converge. Their indices 157: * are stored in array IFAIL. 158: * > N: if INFO = N + i, for 1 <= i <= n, then the leading 159: * minor of order i of B is not positive definite. 160: * The factorization of B could not be completed and 161: * no eigenvalues or eigenvectors were computed. 162: * 163: * Further Details 164: * =============== 165: * 166: * Based on contributions by 167: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 168: * 169: * ===================================================================== 170: * 171: * .. Local Scalars .. 172: LOGICAL ALLEIG, INDEIG, UPPER, VALEIG, WANTZ 173: CHARACTER TRANS 174: INTEGER J 175: * .. 176: * .. External Functions .. 177: LOGICAL LSAME 178: EXTERNAL LSAME 179: * .. 180: * .. External Subroutines .. 181: EXTERNAL XERBLA, ZHPEVX, ZHPGST, ZPPTRF, ZTPMV, ZTPSV 182: * .. 183: * .. Intrinsic Functions .. 184: INTRINSIC MIN 185: * .. 186: * .. Executable Statements .. 187: * 188: * Test the input parameters. 189: * 190: WANTZ = LSAME( JOBZ, 'V' ) 191: UPPER = LSAME( UPLO, 'U' ) 192: ALLEIG = LSAME( RANGE, 'A' ) 193: VALEIG = LSAME( RANGE, 'V' ) 194: INDEIG = LSAME( RANGE, 'I' ) 195: * 196: INFO = 0 197: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 198: INFO = -1 199: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 200: INFO = -2 201: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN 202: INFO = -3 203: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 204: INFO = -4 205: ELSE IF( N.LT.0 ) THEN 206: INFO = -5 207: ELSE 208: IF( VALEIG ) THEN 209: IF( N.GT.0 .AND. VU.LE.VL ) THEN 210: INFO = -9 211: END IF 212: ELSE IF( INDEIG ) THEN 213: IF( IL.LT.1 ) THEN 214: INFO = -10 215: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN 216: INFO = -11 217: END IF 218: END IF 219: END IF 220: IF( INFO.EQ.0 ) THEN 221: IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 222: INFO = -16 223: END IF 224: END IF 225: * 226: IF( INFO.NE.0 ) THEN 227: CALL XERBLA( 'ZHPGVX', -INFO ) 228: RETURN 229: END IF 230: * 231: * Quick return if possible 232: * 233: IF( N.EQ.0 ) 234: $ RETURN 235: * 236: * Form a Cholesky factorization of B. 237: * 238: CALL ZPPTRF( UPLO, N, BP, INFO ) 239: IF( INFO.NE.0 ) THEN 240: INFO = N + INFO 241: RETURN 242: END IF 243: * 244: * Transform problem to standard eigenvalue problem and solve. 245: * 246: CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO ) 247: CALL ZHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M, 248: $ W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO ) 249: * 250: IF( WANTZ ) THEN 251: * 252: * Backtransform eigenvectors to the original problem. 253: * 254: IF( INFO.GT.0 ) 255: $ M = INFO - 1 256: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 257: * 258: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 259: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y 260: * 261: IF( UPPER ) THEN 262: TRANS = 'N' 263: ELSE 264: TRANS = 'C' 265: END IF 266: * 267: DO 10 J = 1, M 268: CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 269: $ 1 ) 270: 10 CONTINUE 271: * 272: ELSE IF( ITYPE.EQ.3 ) THEN 273: * 274: * For B*A*x=(lambda)*x; 275: * backtransform eigenvectors: x = L*y or U'*y 276: * 277: IF( UPPER ) THEN 278: TRANS = 'C' 279: ELSE 280: TRANS = 'N' 281: END IF 282: * 283: DO 20 J = 1, M 284: CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 285: $ 1 ) 286: 20 CONTINUE 287: END IF 288: END IF 289: * 290: RETURN 291: * 292: * End of ZHPGVX 293: * 294: END