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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZHEGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, 2: $ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, 3: $ LWORK, RWORK, 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, LDA, LDB, LDZ, LWORK, M, N 13: DOUBLE PRECISION ABSTOL, VL, VU 14: * .. 15: * .. Array Arguments .. 16: INTEGER IFAIL( * ), IWORK( * ) 17: DOUBLE PRECISION RWORK( * ), W( * ) 18: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ), 19: $ Z( LDZ, * ) 20: * .. 21: * 22: * Purpose 23: * ======= 24: * 25: * ZHEGVX computes selected eigenvalues, and optionally, eigenvectors 26: * of a complex generalized Hermitian-definite eigenproblem, of the form 27: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and 28: * B are assumed to be Hermitian and B is also positive definite. 29: * Eigenvalues and eigenvectors can be selected by specifying either a 30: * range of values or a range of indices for the 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: * A (input/output) COMPLEX*16 array, dimension (LDA, N) 59: * On entry, the Hermitian matrix A. If UPLO = 'U', the 60: * leading N-by-N upper triangular part of A contains the 61: * upper triangular part of the matrix A. If UPLO = 'L', 62: * the leading N-by-N lower triangular part of A contains 63: * the lower triangular part of the matrix A. 64: * 65: * On exit, the lower triangle (if UPLO='L') or the upper 66: * triangle (if UPLO='U') of A, including the diagonal, is 67: * destroyed. 68: * 69: * LDA (input) INTEGER 70: * The leading dimension of the array A. LDA >= max(1,N). 71: * 72: * B (input/output) COMPLEX*16 array, dimension (LDB, N) 73: * On entry, the Hermitian matrix B. If UPLO = 'U', the 74: * leading N-by-N upper triangular part of B contains the 75: * upper triangular part of the matrix B. If UPLO = 'L', 76: * the leading N-by-N lower triangular part of B contains 77: * the lower triangular part of the matrix B. 78: * 79: * On exit, if INFO <= N, the part of B containing the matrix is 80: * overwritten by the triangular factor U or L from the Cholesky 81: * factorization B = U**H*U or B = L*L**H. 82: * 83: * LDB (input) INTEGER 84: * The leading dimension of the array B. LDB >= max(1,N). 85: * 86: * VL (input) DOUBLE PRECISION 87: * VU (input) DOUBLE PRECISION 88: * If RANGE='V', the lower and upper bounds of the interval to 89: * be searched for eigenvalues. VL < VU. 90: * Not referenced if RANGE = 'A' or 'I'. 91: * 92: * IL (input) INTEGER 93: * IU (input) INTEGER 94: * If RANGE='I', the indices (in ascending order) of the 95: * smallest and largest eigenvalues to be returned. 96: * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. 97: * Not referenced if RANGE = 'A' or 'V'. 98: * 99: * ABSTOL (input) DOUBLE PRECISION 100: * The absolute error tolerance for the eigenvalues. 101: * An approximate eigenvalue is accepted as converged 102: * when it is determined to lie in an interval [a,b] 103: * of width less than or equal to 104: * 105: * ABSTOL + EPS * max( |a|,|b| ) , 106: * 107: * where EPS is the machine precision. If ABSTOL is less than 108: * or equal to zero, then EPS*|T| will be used in its place, 109: * where |T| is the 1-norm of the tridiagonal matrix obtained 110: * by reducing A to tridiagonal form. 111: * 112: * Eigenvalues will be computed most accurately when ABSTOL is 113: * set to twice the underflow threshold 2*DLAMCH('S'), not zero. 114: * If this routine returns with INFO>0, indicating that some 115: * eigenvectors did not converge, try setting ABSTOL to 116: * 2*DLAMCH('S'). 117: * 118: * M (output) INTEGER 119: * The total number of eigenvalues found. 0 <= M <= N. 120: * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. 121: * 122: * W (output) DOUBLE PRECISION array, dimension (N) 123: * The first M elements contain the selected 124: * eigenvalues in ascending order. 125: * 126: * Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M)) 127: * If JOBZ = 'N', then Z is not referenced. 128: * If JOBZ = 'V', then if INFO = 0, the first M columns of Z 129: * contain the orthonormal eigenvectors of the matrix A 130: * corresponding to the selected eigenvalues, with the i-th 131: * column of Z holding the eigenvector associated with W(i). 132: * The eigenvectors are normalized as follows: 133: * if ITYPE = 1 or 2, Z**T*B*Z = I; 134: * if ITYPE = 3, Z**T*inv(B)*Z = I. 135: * 136: * If an eigenvector fails to converge, then that column of Z 137: * contains the latest approximation to the eigenvector, and the 138: * index of the eigenvector is returned in IFAIL. 139: * Note: the user must ensure that at least max(1,M) columns are 140: * supplied in the array Z; if RANGE = 'V', the exact value of M 141: * is not known in advance and an upper bound must be used. 142: * 143: * LDZ (input) INTEGER 144: * The leading dimension of the array Z. LDZ >= 1, and if 145: * JOBZ = 'V', LDZ >= max(1,N). 146: * 147: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 148: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 149: * 150: * LWORK (input) INTEGER 151: * The length of the array WORK. LWORK >= max(1,2*N). 152: * For optimal efficiency, LWORK >= (NB+1)*N, 153: * where NB is the blocksize for ZHETRD returned by ILAENV. 154: * 155: * If LWORK = -1, then a workspace query is assumed; the routine 156: * only calculates the optimal size of the WORK array, returns 157: * this value as the first entry of the WORK array, and no error 158: * message related to LWORK is issued by XERBLA. 159: * 160: * RWORK (workspace) DOUBLE PRECISION array, dimension (7*N) 161: * 162: * IWORK (workspace) INTEGER array, dimension (5*N) 163: * 164: * IFAIL (output) INTEGER array, dimension (N) 165: * If JOBZ = 'V', then if INFO = 0, the first M elements of 166: * IFAIL are zero. If INFO > 0, then IFAIL contains the 167: * indices of the eigenvectors that failed to converge. 168: * If JOBZ = 'N', then IFAIL is not referenced. 169: * 170: * INFO (output) INTEGER 171: * = 0: successful exit 172: * < 0: if INFO = -i, the i-th argument had an illegal value 173: * > 0: ZPOTRF or ZHEEVX returned an error code: 174: * <= N: if INFO = i, ZHEEVX failed to converge; 175: * i eigenvectors failed to converge. Their indices 176: * are stored in array IFAIL. 177: * > N: if INFO = N + i, for 1 <= i <= N, then the leading 178: * minor of order i of B is not positive definite. 179: * The factorization of B could not be completed and 180: * no eigenvalues or eigenvectors were computed. 181: * 182: * Further Details 183: * =============== 184: * 185: * Based on contributions by 186: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 187: * 188: * ===================================================================== 189: * 190: * .. Parameters .. 191: COMPLEX*16 CONE 192: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) 193: * .. 194: * .. Local Scalars .. 195: LOGICAL ALLEIG, INDEIG, LQUERY, UPPER, VALEIG, WANTZ 196: CHARACTER TRANS 197: INTEGER LWKOPT, NB 198: * .. 199: * .. External Functions .. 200: LOGICAL LSAME 201: INTEGER ILAENV 202: EXTERNAL LSAME, ILAENV 203: * .. 204: * .. External Subroutines .. 205: EXTERNAL XERBLA, ZHEEVX, ZHEGST, ZPOTRF, ZTRMM, ZTRSM 206: * .. 207: * .. Intrinsic Functions .. 208: INTRINSIC MAX, MIN 209: * .. 210: * .. Executable Statements .. 211: * 212: * Test the input parameters. 213: * 214: WANTZ = LSAME( JOBZ, 'V' ) 215: UPPER = LSAME( UPLO, 'U' ) 216: ALLEIG = LSAME( RANGE, 'A' ) 217: VALEIG = LSAME( RANGE, 'V' ) 218: INDEIG = LSAME( RANGE, 'I' ) 219: LQUERY = ( LWORK.EQ.-1 ) 220: * 221: INFO = 0 222: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 223: INFO = -1 224: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 225: INFO = -2 226: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN 227: INFO = -3 228: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 229: INFO = -4 230: ELSE IF( N.LT.0 ) THEN 231: INFO = -5 232: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 233: INFO = -7 234: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 235: INFO = -9 236: ELSE 237: IF( VALEIG ) THEN 238: IF( N.GT.0 .AND. VU.LE.VL ) 239: $ INFO = -11 240: ELSE IF( INDEIG ) THEN 241: IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN 242: INFO = -12 243: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN 244: INFO = -13 245: END IF 246: END IF 247: END IF 248: IF (INFO.EQ.0) THEN 249: IF (LDZ.LT.1 .OR. (WANTZ .AND. LDZ.LT.N)) THEN 250: INFO = -18 251: END IF 252: END IF 253: * 254: IF( INFO.EQ.0 ) THEN 255: NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) 256: LWKOPT = MAX( 1, ( NB + 1 )*N ) 257: WORK( 1 ) = LWKOPT 258: * 259: IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN 260: INFO = -20 261: END IF 262: END IF 263: * 264: IF( INFO.NE.0 ) THEN 265: CALL XERBLA( 'ZHEGVX', -INFO ) 266: RETURN 267: ELSE IF( LQUERY ) THEN 268: RETURN 269: END IF 270: * 271: * Quick return if possible 272: * 273: M = 0 274: IF( N.EQ.0 ) THEN 275: RETURN 276: END IF 277: * 278: * Form a Cholesky factorization of B. 279: * 280: CALL ZPOTRF( UPLO, N, B, LDB, INFO ) 281: IF( INFO.NE.0 ) THEN 282: INFO = N + INFO 283: RETURN 284: END IF 285: * 286: * Transform problem to standard eigenvalue problem and solve. 287: * 288: CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 289: CALL ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, 290: $ M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, 291: $ INFO ) 292: * 293: IF( WANTZ ) THEN 294: * 295: * Backtransform eigenvectors to the original problem. 296: * 297: IF( INFO.GT.0 ) 298: $ M = INFO - 1 299: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 300: * 301: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 302: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y 303: * 304: IF( UPPER ) THEN 305: TRANS = 'N' 306: ELSE 307: TRANS = 'C' 308: END IF 309: * 310: CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, M, CONE, B, 311: $ LDB, Z, LDZ ) 312: * 313: ELSE IF( ITYPE.EQ.3 ) THEN 314: * 315: * For B*A*x=(lambda)*x; 316: * backtransform eigenvectors: x = L*y or U'*y 317: * 318: IF( UPPER ) THEN 319: TRANS = 'C' 320: ELSE 321: TRANS = 'N' 322: END IF 323: * 324: CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, M, CONE, B, 325: $ LDB, Z, LDZ ) 326: END IF 327: END IF 328: * 329: * Set WORK(1) to optimal complex workspace size. 330: * 331: WORK( 1 ) = LWKOPT 332: * 333: RETURN 334: * 335: * End of ZHEGVX 336: * 337: END