LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
dsygvx.f File Reference

Go to the source code of this file.

Functions/Subroutines

subroutine dsygvx (ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL, INFO)
 DSYGST More...
 

Function/Subroutine Documentation

subroutine dsygvx ( integer  ITYPE,
character  JOBZ,
character  RANGE,
character  UPLO,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision  VL,
double precision  VU,
integer  IL,
integer  IU,
double precision  ABSTOL,
integer  M,
double precision, dimension( * )  W,
double precision, dimension( ldz, * )  Z,
integer  LDZ,
double precision, dimension( * )  WORK,
integer  LWORK,
integer, dimension( * )  IWORK,
integer, dimension( * )  IFAIL,
integer  INFO 
)

DSYGST

Download DSYGVX + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DSYGVX computes selected eigenvalues, and optionally, eigenvectors
 of a real generalized symmetric-definite eigenproblem, of the form
 A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A
 and B are assumed to be symmetric and B is also positive definite.
 Eigenvalues and eigenvectors can be selected by specifying either a
 range of values or a range of indices for the desired eigenvalues.
Parameters
[in]ITYPE
          ITYPE is INTEGER
          Specifies the problem type to be solved:
          = 1:  A*x = (lambda)*B*x
          = 2:  A*B*x = (lambda)*x
          = 3:  B*A*x = (lambda)*x
[in]JOBZ
          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors.
[in]RANGE
          RANGE is CHARACTER*1
          = 'A': all eigenvalues will be found.
          = 'V': all eigenvalues in the half-open interval (VL,VU]
                 will be found.
          = 'I': the IL-th through IU-th eigenvalues will be found.
[in]UPLO
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A and B are stored;
          = 'L':  Lower triangle of A and B are stored.
[in]N
          N is INTEGER
          The order of the matrix pencil (A,B).  N >= 0.
[in,out]A
          A is DOUBLE PRECISION array, dimension (LDA, N)
          On entry, the symmetric matrix A.  If UPLO = 'U', the
          leading N-by-N upper triangular part of A contains the
          upper triangular part of the matrix A.  If UPLO = 'L',
          the leading N-by-N lower triangular part of A contains
          the lower triangular part of the matrix A.

          On exit, the lower triangle (if UPLO='L') or the upper
          triangle (if UPLO='U') of A, including the diagonal, is
          destroyed.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB, N)
          On entry, the symmetric matrix B.  If UPLO = 'U', the
          leading N-by-N upper triangular part of B contains the
          upper triangular part of the matrix B.  If UPLO = 'L',
          the leading N-by-N lower triangular part of B contains
          the lower triangular part of the matrix B.

          On exit, if INFO <= N, the part of B containing the matrix is
          overwritten by the triangular factor U or L from the Cholesky
          factorization B = U**T*U or B = L*L**T.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in]VL
          VL is DOUBLE PRECISION
[in]VU
          VU is DOUBLE PRECISION
          If RANGE='V', the lower and upper bounds of the interval to
          be searched for eigenvalues. VL < VU.
          Not referenced if RANGE = 'A' or 'I'.
[in]IL
          IL is INTEGER
[in]IU
          IU is INTEGER
          If RANGE='I', the indices (in ascending order) of the
          smallest and largest eigenvalues to be returned.
          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
          Not referenced if RANGE = 'A' or 'V'.
[in]ABSTOL
          ABSTOL is DOUBLE PRECISION
          The absolute error tolerance for the eigenvalues.
          An approximate eigenvalue is accepted as converged
          when it is determined to lie in an interval [a,b]
          of width less than or equal to

                  ABSTOL + EPS *   max( |a|,|b| ) ,

          where EPS is the machine precision.  If ABSTOL is less than
          or equal to zero, then  EPS*|T|  will be used in its place,
          where |T| is the 1-norm of the tridiagonal matrix obtained
          by reducing C to tridiagonal form, where C is the symmetric
          matrix of the standard symmetric problem to which the
          generalized problem is transformed.

          Eigenvalues will be computed most accurately when ABSTOL is
          set to twice the underflow threshold 2*DLAMCH('S'), not zero.
          If this routine returns with INFO>0, indicating that some
          eigenvectors did not converge, try setting ABSTOL to
          2*DLAMCH('S').
[out]M
          M is INTEGER
          The total number of eigenvalues found.  0 <= M <= N.
          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
[out]W
          W is DOUBLE PRECISION array, dimension (N)
          On normal exit, the first M elements contain the selected
          eigenvalues in ascending order.
[out]Z
          Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M))
          If JOBZ = 'N', then Z is not referenced.
          If JOBZ = 'V', then if INFO = 0, the first M columns of Z
          contain the orthonormal eigenvectors of the matrix A
          corresponding to the selected eigenvalues, with the i-th
          column of Z holding the eigenvector associated with W(i).
          The eigenvectors are normalized as follows:
          if ITYPE = 1 or 2, Z**T*B*Z = I;
          if ITYPE = 3, Z**T*inv(B)*Z = I.

          If an eigenvector fails to converge, then that column of Z
          contains the latest approximation to the eigenvector, and the
          index of the eigenvector is returned in IFAIL.
          Note: the user must ensure that at least max(1,M) columns are
          supplied in the array Z; if RANGE = 'V', the exact value of M
          is not known in advance and an upper bound must be used.
[in]LDZ
          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1, and if
          JOBZ = 'V', LDZ >= max(1,N).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK >= max(1,8*N).
          For optimal efficiency, LWORK >= (NB+3)*N,
          where NB is the blocksize for DSYTRD returned by ILAENV.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]IWORK
          IWORK is INTEGER array, dimension (5*N)
[out]IFAIL
          IFAIL is INTEGER array, dimension (N)
          If JOBZ = 'V', then if INFO = 0, the first M elements of
          IFAIL are zero.  If INFO > 0, then IFAIL contains the
          indices of the eigenvectors that failed to converge.
          If JOBZ = 'N', then IFAIL is not referenced.
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  DPOTRF or DSYEVX returned an error code:
             <= N:  if INFO = i, DSYEVX failed to converge;
                    i eigenvectors failed to converge.  Their indices
                    are stored in array IFAIL.
             > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                    minor of order i of B is not positive definite.
                    The factorization of B could not be completed and
                    no eigenvalues or eigenvectors were computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011
Contributors:
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 292 of file dsygvx.f.

292 *
293 * -- LAPACK driver routine (version 3.4.0) --
294 * -- LAPACK is a software package provided by Univ. of Tennessee, --
295 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
296 * November 2011
297 *
298 * .. Scalar Arguments ..
299  CHARACTER jobz, range, uplo
300  INTEGER il, info, itype, iu, lda, ldb, ldz, lwork, m, n
301  DOUBLE PRECISION abstol, vl, vu
302 * ..
303 * .. Array Arguments ..
304  INTEGER ifail( * ), iwork( * )
305  DOUBLE PRECISION a( lda, * ), b( ldb, * ), w( * ), work( * ),
306  $ z( ldz, * )
307 * ..
308 *
309 * =====================================================================
310 *
311 * .. Parameters ..
312  DOUBLE PRECISION one
313  parameter( one = 1.0d+0 )
314 * ..
315 * .. Local Scalars ..
316  LOGICAL alleig, indeig, lquery, upper, valeig, wantz
317  CHARACTER trans
318  INTEGER lwkmin, lwkopt, nb
319 * ..
320 * .. External Functions ..
321  LOGICAL lsame
322  INTEGER ilaenv
323  EXTERNAL lsame, ilaenv
324 * ..
325 * .. External Subroutines ..
326  EXTERNAL dpotrf, dsyevx, dsygst, dtrmm, dtrsm, xerbla
327 * ..
328 * .. Intrinsic Functions ..
329  INTRINSIC max, min
330 * ..
331 * .. Executable Statements ..
332 *
333 * Test the input parameters.
334 *
335  upper = lsame( uplo, 'U' )
336  wantz = lsame( jobz, 'V' )
337  alleig = lsame( range, 'A' )
338  valeig = lsame( range, 'V' )
339  indeig = lsame( range, 'I' )
340  lquery = ( lwork.EQ.-1 )
341 *
342  info = 0
343  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
344  info = -1
345  ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
346  info = -2
347  ELSE IF( .NOT.( alleig .OR. valeig .OR. indeig ) ) THEN
348  info = -3
349  ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
350  info = -4
351  ELSE IF( n.LT.0 ) THEN
352  info = -5
353  ELSE IF( lda.LT.max( 1, n ) ) THEN
354  info = -7
355  ELSE IF( ldb.LT.max( 1, n ) ) THEN
356  info = -9
357  ELSE
358  IF( valeig ) THEN
359  IF( n.GT.0 .AND. vu.LE.vl )
360  $ info = -11
361  ELSE IF( indeig ) THEN
362  IF( il.LT.1 .OR. il.GT.max( 1, n ) ) THEN
363  info = -12
364  ELSE IF( iu.LT.min( n, il ) .OR. iu.GT.n ) THEN
365  info = -13
366  END IF
367  END IF
368  END IF
369  IF (info.EQ.0) THEN
370  IF (ldz.LT.1 .OR. (wantz .AND. ldz.LT.n)) THEN
371  info = -18
372  END IF
373  END IF
374 *
375  IF( info.EQ.0 ) THEN
376  lwkmin = max( 1, 8*n )
377  nb = ilaenv( 1, 'DSYTRD', uplo, n, -1, -1, -1 )
378  lwkopt = max( lwkmin, ( nb + 3 )*n )
379  work( 1 ) = lwkopt
380 *
381  IF( lwork.LT.lwkmin .AND. .NOT.lquery ) THEN
382  info = -20
383  END IF
384  END IF
385 *
386  IF( info.NE.0 ) THEN
387  CALL xerbla( 'DSYGVX', -info )
388  RETURN
389  ELSE IF( lquery ) THEN
390  RETURN
391  END IF
392 *
393 * Quick return if possible
394 *
395  m = 0
396  IF( n.EQ.0 ) THEN
397  RETURN
398  END IF
399 *
400 * Form a Cholesky factorization of B.
401 *
402  CALL dpotrf( uplo, n, b, ldb, info )
403  IF( info.NE.0 ) THEN
404  info = n + info
405  RETURN
406  END IF
407 *
408 * Transform problem to standard eigenvalue problem and solve.
409 *
410  CALL dsygst( itype, uplo, n, a, lda, b, ldb, info )
411  CALL dsyevx( jobz, range, uplo, n, a, lda, vl, vu, il, iu, abstol,
412  $ m, w, z, ldz, work, lwork, iwork, ifail, info )
413 *
414  IF( wantz ) THEN
415 *
416 * Backtransform eigenvectors to the original problem.
417 *
418  IF( info.GT.0 )
419  $ m = info - 1
420  IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
421 *
422 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
423 * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
424 *
425  IF( upper ) THEN
426  trans = 'N'
427  ELSE
428  trans = 'T'
429  END IF
430 *
431  CALL dtrsm( 'Left', uplo, trans, 'Non-unit', n, m, one, b,
432  $ ldb, z, ldz )
433 *
434  ELSE IF( itype.EQ.3 ) THEN
435 *
436 * For B*A*x=(lambda)*x;
437 * backtransform eigenvectors: x = L*y or U**T*y
438 *
439  IF( upper ) THEN
440  trans = 'T'
441  ELSE
442  trans = 'N'
443  END IF
444 *
445  CALL dtrmm( 'Left', uplo, trans, 'Non-unit', n, m, one, b,
446  $ ldb, z, ldz )
447  END IF
448  END IF
449 *
450 * Set WORK(1) to optimal workspace size.
451 *
452  work( 1 ) = lwkopt
453 *
454  RETURN
455 *
456 * End of DSYGVX
457 *
subroutine dsyevx(JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL, INFO)
DSYEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices ...
Definition: dsyevx.f:248
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:183
subroutine dsygst(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
DSYGST
Definition: dsygst.f:129
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
subroutine dpotrf(UPLO, N, A, LDA, INFO)
DPOTRF
Definition: dpotrf.f:109
subroutine dtrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM
Definition: dtrmm.f:179

Here is the call graph for this function:

Here is the caller graph for this function: