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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DSPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU, 2: $ IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK, 3: $ 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 AP( * ), BP( * ), W( * ), WORK( * ), 18: $ Z( LDZ, * ) 19: * .. 20: * 21: * Purpose 22: * ======= 23: * 24: * DSPGVX computes selected eigenvalues, and optionally, eigenvectors 25: * of a real generalized symmetric-definite eigenproblem, of the form 26: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A 27: * and B are assumed to be symmetric, stored in packed storage, and B 28: * is also positive definite. Eigenvalues and eigenvectors can be 29: * selected by specifying either a range of values or a range of indices 30: * 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 triangle of A and B are stored; 53: * = 'L': Lower triangle of A and B are stored. 54: * 55: * N (input) INTEGER 56: * The order of the matrix pencil (A,B). N >= 0. 57: * 58: * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) 59: * On entry, the upper or lower triangle of the symmetric 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) DOUBLE PRECISION array, dimension (N*(N+1)/2) 68: * On entry, the upper or lower triangle of the symmetric 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**T*U or B = L*L**T, 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 A 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) DOUBLE PRECISION array, dimension (LDZ, max(1,M)) 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**T*B*Z = I; 126: * if ITYPE = 3, Z**T*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) DOUBLE PRECISION array, dimension (8*N) 140: * 141: * IWORK (workspace) INTEGER array, dimension (5*N) 142: * 143: * IFAIL (output) INTEGER array, dimension (N) 144: * If JOBZ = 'V', then if INFO = 0, the first M elements of 145: * IFAIL are zero. If INFO > 0, then IFAIL contains the 146: * indices of the eigenvectors that failed to converge. 147: * If JOBZ = 'N', then IFAIL is not referenced. 148: * 149: * INFO (output) INTEGER 150: * = 0: successful exit 151: * < 0: if INFO = -i, the i-th argument had an illegal value 152: * > 0: DPPTRF or DSPEVX returned an error code: 153: * <= N: if INFO = i, DSPEVX failed to converge; 154: * i eigenvectors failed to converge. Their indices 155: * are stored in array IFAIL. 156: * > N: if INFO = N + i, for 1 <= i <= N, then the leading 157: * minor of order i of B is not positive definite. 158: * The factorization of B could not be completed and 159: * no eigenvalues or eigenvectors were computed. 160: * 161: * Further Details 162: * =============== 163: * 164: * Based on contributions by 165: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 166: * 167: * ===================================================================== 168: * 169: * .. Local Scalars .. 170: LOGICAL ALLEIG, INDEIG, UPPER, VALEIG, WANTZ 171: CHARACTER TRANS 172: INTEGER J 173: * .. 174: * .. External Functions .. 175: LOGICAL LSAME 176: EXTERNAL LSAME 177: * .. 178: * .. External Subroutines .. 179: EXTERNAL DPPTRF, DSPEVX, DSPGST, DTPMV, DTPSV, XERBLA 180: * .. 181: * .. Intrinsic Functions .. 182: INTRINSIC MIN 183: * .. 184: * .. Executable Statements .. 185: * 186: * Test the input parameters. 187: * 188: UPPER = LSAME( UPLO, 'U' ) 189: WANTZ = LSAME( JOBZ, 'V' ) 190: ALLEIG = LSAME( RANGE, 'A' ) 191: VALEIG = LSAME( RANGE, 'V' ) 192: INDEIG = LSAME( RANGE, 'I' ) 193: * 194: INFO = 0 195: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 196: INFO = -1 197: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 198: INFO = -2 199: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN 200: INFO = -3 201: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 202: INFO = -4 203: ELSE IF( N.LT.0 ) THEN 204: INFO = -5 205: ELSE 206: IF( VALEIG ) THEN 207: IF( N.GT.0 .AND. VU.LE.VL ) THEN 208: INFO = -9 209: END IF 210: ELSE IF( INDEIG ) THEN 211: IF( IL.LT.1 ) THEN 212: INFO = -10 213: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN 214: INFO = -11 215: END IF 216: END IF 217: END IF 218: IF( INFO.EQ.0 ) THEN 219: IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 220: INFO = -16 221: END IF 222: END IF 223: * 224: IF( INFO.NE.0 ) THEN 225: CALL XERBLA( 'DSPGVX', -INFO ) 226: RETURN 227: END IF 228: * 229: * Quick return if possible 230: * 231: M = 0 232: IF( N.EQ.0 ) 233: $ RETURN 234: * 235: * Form a Cholesky factorization of B. 236: * 237: CALL DPPTRF( UPLO, N, BP, INFO ) 238: IF( INFO.NE.0 ) THEN 239: INFO = N + INFO 240: RETURN 241: END IF 242: * 243: * Transform problem to standard eigenvalue problem and solve. 244: * 245: CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO ) 246: CALL DSPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M, 247: $ W, Z, LDZ, WORK, IWORK, IFAIL, INFO ) 248: * 249: IF( WANTZ ) THEN 250: * 251: * Backtransform eigenvectors to the original problem. 252: * 253: IF( INFO.GT.0 ) 254: $ M = INFO - 1 255: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 256: * 257: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 258: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y 259: * 260: IF( UPPER ) THEN 261: TRANS = 'N' 262: ELSE 263: TRANS = 'T' 264: END IF 265: * 266: DO 10 J = 1, M 267: CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 268: $ 1 ) 269: 10 CONTINUE 270: * 271: ELSE IF( ITYPE.EQ.3 ) THEN 272: * 273: * For B*A*x=(lambda)*x; 274: * backtransform eigenvectors: x = L*y or U'*y 275: * 276: IF( UPPER ) THEN 277: TRANS = 'T' 278: ELSE 279: TRANS = 'N' 280: END IF 281: * 282: DO 20 J = 1, M 283: CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 284: $ 1 ) 285: 20 CONTINUE 286: END IF 287: END IF 288: * 289: RETURN 290: * 291: * End of DSPGVX 292: * 293: END