Annotation of rpl/lapack/lapack/dsygvx.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
! 2: $ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
! 3: $ LWORK, 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 A( LDA, * ), B( LDB, * ), W( * ), WORK( * ),
! 18: $ Z( LDZ, * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * DSYGVX 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 and B is also positive definite.
! 28: * Eigenvalues and eigenvectors can be selected by specifying either a
! 29: * range of values or a range of indices for the desired eigenvalues.
! 30: *
! 31: * Arguments
! 32: * =========
! 33: *
! 34: * ITYPE (input) INTEGER
! 35: * Specifies the problem type to be solved:
! 36: * = 1: A*x = (lambda)*B*x
! 37: * = 2: A*B*x = (lambda)*x
! 38: * = 3: B*A*x = (lambda)*x
! 39: *
! 40: * JOBZ (input) CHARACTER*1
! 41: * = 'N': Compute eigenvalues only;
! 42: * = 'V': Compute eigenvalues and eigenvectors.
! 43: *
! 44: * RANGE (input) CHARACTER*1
! 45: * = 'A': all eigenvalues will be found.
! 46: * = 'V': all eigenvalues in the half-open interval (VL,VU]
! 47: * will be found.
! 48: * = 'I': the IL-th through IU-th eigenvalues will be found.
! 49: *
! 50: * UPLO (input) CHARACTER*1
! 51: * = 'U': Upper triangle of A and B are stored;
! 52: * = 'L': Lower triangle of A and B are stored.
! 53: *
! 54: * N (input) INTEGER
! 55: * The order of the matrix pencil (A,B). N >= 0.
! 56: *
! 57: * A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
! 58: * On entry, the symmetric matrix A. If UPLO = 'U', the
! 59: * leading N-by-N upper triangular part of A contains the
! 60: * upper triangular part of the matrix A. If UPLO = 'L',
! 61: * the leading N-by-N lower triangular part of A contains
! 62: * the lower triangular part of the matrix A.
! 63: *
! 64: * On exit, the lower triangle (if UPLO='L') or the upper
! 65: * triangle (if UPLO='U') of A, including the diagonal, is
! 66: * destroyed.
! 67: *
! 68: * LDA (input) INTEGER
! 69: * The leading dimension of the array A. LDA >= max(1,N).
! 70: *
! 71: * B (input/output) DOUBLE PRECISION array, dimension (LDA, N)
! 72: * On entry, the symmetric matrix B. If UPLO = 'U', the
! 73: * leading N-by-N upper triangular part of B contains the
! 74: * upper triangular part of the matrix B. If UPLO = 'L',
! 75: * the leading N-by-N lower triangular part of B contains
! 76: * the lower triangular part of the matrix B.
! 77: *
! 78: * On exit, if INFO <= N, the part of B containing the matrix is
! 79: * overwritten by the triangular factor U or L from the Cholesky
! 80: * factorization B = U**T*U or B = L*L**T.
! 81: *
! 82: * LDB (input) INTEGER
! 83: * The leading dimension of the array B. LDB >= max(1,N).
! 84: *
! 85: * VL (input) DOUBLE PRECISION
! 86: * VU (input) DOUBLE PRECISION
! 87: * If RANGE='V', the lower and upper bounds of the interval to
! 88: * be searched for eigenvalues. VL < VU.
! 89: * Not referenced if RANGE = 'A' or 'I'.
! 90: *
! 91: * IL (input) INTEGER
! 92: * IU (input) INTEGER
! 93: * If RANGE='I', the indices (in ascending order) of the
! 94: * smallest and largest eigenvalues to be returned.
! 95: * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
! 96: * Not referenced if RANGE = 'A' or 'V'.
! 97: *
! 98: * ABSTOL (input) DOUBLE PRECISION
! 99: * The absolute error tolerance for the eigenvalues.
! 100: * An approximate eigenvalue is accepted as converged
! 101: * when it is determined to lie in an interval [a,b]
! 102: * of width less than or equal to
! 103: *
! 104: * ABSTOL + EPS * max( |a|,|b| ) ,
! 105: *
! 106: * where EPS is the machine precision. If ABSTOL is less than
! 107: * or equal to zero, then EPS*|T| will be used in its place,
! 108: * where |T| is the 1-norm of the tridiagonal matrix obtained
! 109: * by reducing A to tridiagonal form.
! 110: *
! 111: * Eigenvalues will be computed most accurately when ABSTOL is
! 112: * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
! 113: * If this routine returns with INFO>0, indicating that some
! 114: * eigenvectors did not converge, try setting ABSTOL to
! 115: * 2*DLAMCH('S').
! 116: *
! 117: * M (output) INTEGER
! 118: * The total number of eigenvalues found. 0 <= M <= N.
! 119: * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
! 120: *
! 121: * W (output) DOUBLE PRECISION array, dimension (N)
! 122: * On normal exit, the first M elements contain the selected
! 123: * eigenvalues in ascending order.
! 124: *
! 125: * Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
! 126: * If JOBZ = 'N', then Z is not referenced.
! 127: * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
! 128: * contain the orthonormal eigenvectors of the matrix A
! 129: * corresponding to the selected eigenvalues, with the i-th
! 130: * column of Z holding the eigenvector associated with W(i).
! 131: * The eigenvectors are normalized as follows:
! 132: * if ITYPE = 1 or 2, Z**T*B*Z = I;
! 133: * if ITYPE = 3, Z**T*inv(B)*Z = I.
! 134: *
! 135: * If an eigenvector fails to converge, then that column of Z
! 136: * contains the latest approximation to the eigenvector, and the
! 137: * index of the eigenvector is returned in IFAIL.
! 138: * Note: the user must ensure that at least max(1,M) columns are
! 139: * supplied in the array Z; if RANGE = 'V', the exact value of M
! 140: * is not known in advance and an upper bound must be used.
! 141: *
! 142: * LDZ (input) INTEGER
! 143: * The leading dimension of the array Z. LDZ >= 1, and if
! 144: * JOBZ = 'V', LDZ >= max(1,N).
! 145: *
! 146: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 147: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 148: *
! 149: * LWORK (input) INTEGER
! 150: * The length of the array WORK. LWORK >= max(1,8*N).
! 151: * For optimal efficiency, LWORK >= (NB+3)*N,
! 152: * where NB is the blocksize for DSYTRD returned by ILAENV.
! 153: *
! 154: * If LWORK = -1, then a workspace query is assumed; the routine
! 155: * only calculates the optimal size of the WORK array, returns
! 156: * this value as the first entry of the WORK array, and no error
! 157: * message related to LWORK is issued by XERBLA.
! 158: *
! 159: * IWORK (workspace) INTEGER array, dimension (5*N)
! 160: *
! 161: * IFAIL (output) INTEGER array, dimension (N)
! 162: * If JOBZ = 'V', then if INFO = 0, the first M elements of
! 163: * IFAIL are zero. If INFO > 0, then IFAIL contains the
! 164: * indices of the eigenvectors that failed to converge.
! 165: * If JOBZ = 'N', then IFAIL is not referenced.
! 166: *
! 167: * INFO (output) INTEGER
! 168: * = 0: successful exit
! 169: * < 0: if INFO = -i, the i-th argument had an illegal value
! 170: * > 0: DPOTRF or DSYEVX returned an error code:
! 171: * <= N: if INFO = i, DSYEVX failed to converge;
! 172: * i eigenvectors failed to converge. Their indices
! 173: * are stored in array IFAIL.
! 174: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
! 175: * minor of order i of B is not positive definite.
! 176: * The factorization of B could not be completed and
! 177: * no eigenvalues or eigenvectors were computed.
! 178: *
! 179: * Further Details
! 180: * ===============
! 181: *
! 182: * Based on contributions by
! 183: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
! 184: *
! 185: * =====================================================================
! 186: *
! 187: * .. Parameters ..
! 188: DOUBLE PRECISION ONE
! 189: PARAMETER ( ONE = 1.0D+0 )
! 190: * ..
! 191: * .. Local Scalars ..
! 192: LOGICAL ALLEIG, INDEIG, LQUERY, UPPER, VALEIG, WANTZ
! 193: CHARACTER TRANS
! 194: INTEGER LWKMIN, LWKOPT, NB
! 195: * ..
! 196: * .. External Functions ..
! 197: LOGICAL LSAME
! 198: INTEGER ILAENV
! 199: EXTERNAL LSAME, ILAENV
! 200: * ..
! 201: * .. External Subroutines ..
! 202: EXTERNAL DPOTRF, DSYEVX, DSYGST, DTRMM, DTRSM, XERBLA
! 203: * ..
! 204: * .. Intrinsic Functions ..
! 205: INTRINSIC MAX, MIN
! 206: * ..
! 207: * .. Executable Statements ..
! 208: *
! 209: * Test the input parameters.
! 210: *
! 211: UPPER = LSAME( UPLO, 'U' )
! 212: WANTZ = LSAME( JOBZ, 'V' )
! 213: ALLEIG = LSAME( RANGE, 'A' )
! 214: VALEIG = LSAME( RANGE, 'V' )
! 215: INDEIG = LSAME( RANGE, 'I' )
! 216: LQUERY = ( LWORK.EQ.-1 )
! 217: *
! 218: INFO = 0
! 219: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
! 220: INFO = -1
! 221: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 222: INFO = -2
! 223: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
! 224: INFO = -3
! 225: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 226: INFO = -4
! 227: ELSE IF( N.LT.0 ) THEN
! 228: INFO = -5
! 229: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 230: INFO = -7
! 231: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 232: INFO = -9
! 233: ELSE
! 234: IF( VALEIG ) THEN
! 235: IF( N.GT.0 .AND. VU.LE.VL )
! 236: $ INFO = -11
! 237: ELSE IF( INDEIG ) THEN
! 238: IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
! 239: INFO = -12
! 240: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
! 241: INFO = -13
! 242: END IF
! 243: END IF
! 244: END IF
! 245: IF (INFO.EQ.0) THEN
! 246: IF (LDZ.LT.1 .OR. (WANTZ .AND. LDZ.LT.N)) THEN
! 247: INFO = -18
! 248: END IF
! 249: END IF
! 250: *
! 251: IF( INFO.EQ.0 ) THEN
! 252: LWKMIN = MAX( 1, 8*N )
! 253: NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
! 254: LWKOPT = MAX( LWKMIN, ( NB + 3 )*N )
! 255: WORK( 1 ) = LWKOPT
! 256: *
! 257: IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
! 258: INFO = -20
! 259: END IF
! 260: END IF
! 261: *
! 262: IF( INFO.NE.0 ) THEN
! 263: CALL XERBLA( 'DSYGVX', -INFO )
! 264: RETURN
! 265: ELSE IF( LQUERY ) THEN
! 266: RETURN
! 267: END IF
! 268: *
! 269: * Quick return if possible
! 270: *
! 271: M = 0
! 272: IF( N.EQ.0 ) THEN
! 273: RETURN
! 274: END IF
! 275: *
! 276: * Form a Cholesky factorization of B.
! 277: *
! 278: CALL DPOTRF( UPLO, N, B, LDB, INFO )
! 279: IF( INFO.NE.0 ) THEN
! 280: INFO = N + INFO
! 281: RETURN
! 282: END IF
! 283: *
! 284: * Transform problem to standard eigenvalue problem and solve.
! 285: *
! 286: CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
! 287: CALL DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL,
! 288: $ M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL, INFO )
! 289: *
! 290: IF( WANTZ ) THEN
! 291: *
! 292: * Backtransform eigenvectors to the original problem.
! 293: *
! 294: IF( INFO.GT.0 )
! 295: $ M = INFO - 1
! 296: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
! 297: *
! 298: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
! 299: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
! 300: *
! 301: IF( UPPER ) THEN
! 302: TRANS = 'N'
! 303: ELSE
! 304: TRANS = 'T'
! 305: END IF
! 306: *
! 307: CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, M, ONE, B,
! 308: $ LDB, Z, LDZ )
! 309: *
! 310: ELSE IF( ITYPE.EQ.3 ) THEN
! 311: *
! 312: * For B*A*x=(lambda)*x;
! 313: * backtransform eigenvectors: x = L*y or U'*y
! 314: *
! 315: IF( UPPER ) THEN
! 316: TRANS = 'T'
! 317: ELSE
! 318: TRANS = 'N'
! 319: END IF
! 320: *
! 321: CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, M, ONE, B,
! 322: $ LDB, Z, LDZ )
! 323: END IF
! 324: END IF
! 325: *
! 326: * Set WORK(1) to optimal workspace size.
! 327: *
! 328: WORK( 1 ) = LWKOPT
! 329: *
! 330: RETURN
! 331: *
! 332: * End of DSYGVX
! 333: *
! 334: END
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