308 lines
11 KiB
FortranFixed
308 lines
11 KiB
FortranFixed
SUBROUTINE CHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
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$ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
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*
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* -- LAPACK driver routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER JOBZ, UPLO
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INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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REAL RWORK( * ), W( * )
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COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* CHEGVD computes all the eigenvalues, and optionally, the eigenvectors
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* of a complex generalized Hermitian-definite eigenproblem, of the form
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* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
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* B are assumed to be Hermitian and B is also positive definite.
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* If eigenvectors are desired, it uses a divide and conquer algorithm.
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*
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* The divide and conquer algorithm makes very mild assumptions about
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* floating point arithmetic. It will work on machines with a guard
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* digit in add/subtract, or on those binary machines without guard
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* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
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* Cray-2. It could conceivably fail on hexadecimal or decimal machines
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* without guard digits, but we know of none.
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*
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* Arguments
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* =========
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*
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* ITYPE (input) INTEGER
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* Specifies the problem type to be solved:
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* = 1: A*x = (lambda)*B*x
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* = 2: A*B*x = (lambda)*x
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* = 3: B*A*x = (lambda)*x
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*
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* JOBZ (input) CHARACTER*1
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* = 'N': Compute eigenvalues only;
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* = 'V': Compute eigenvalues and eigenvectors.
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*
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* UPLO (input) CHARACTER*1
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* = 'U': Upper triangles of A and B are stored;
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* = 'L': Lower triangles of A and B are stored.
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*
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* N (input) INTEGER
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* The order of the matrices A and B. N >= 0.
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*
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* A (input/output) COMPLEX array, dimension (LDA, N)
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* On entry, the Hermitian matrix A. If UPLO = 'U', the
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* leading N-by-N upper triangular part of A contains the
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* upper triangular part of the matrix A. If UPLO = 'L',
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* the leading N-by-N lower triangular part of A contains
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* the lower triangular part of the matrix A.
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*
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* On exit, if JOBZ = 'V', then if INFO = 0, A contains the
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* matrix Z of eigenvectors. The eigenvectors are normalized
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* as follows:
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* if ITYPE = 1 or 2, Z**H*B*Z = I;
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* if ITYPE = 3, Z**H*inv(B)*Z = I.
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* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
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* or the lower triangle (if UPLO='L') of A, including the
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* diagonal, is destroyed.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,N).
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*
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* B (input/output) COMPLEX array, dimension (LDB, N)
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* On entry, the Hermitian matrix B. If UPLO = 'U', the
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* leading N-by-N upper triangular part of B contains the
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* upper triangular part of the matrix B. If UPLO = 'L',
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* the leading N-by-N lower triangular part of B contains
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* the lower triangular part of the matrix B.
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*
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* On exit, if INFO <= N, the part of B containing the matrix is
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* overwritten by the triangular factor U or L from the Cholesky
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* factorization B = U**H*U or B = L*L**H.
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*
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* LDB (input) INTEGER
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* The leading dimension of the array B. LDB >= max(1,N).
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*
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* W (output) REAL array, dimension (N)
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* If INFO = 0, the eigenvalues in ascending order.
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*
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* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*
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* LWORK (input) INTEGER
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* The length of the array WORK.
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* If N <= 1, LWORK >= 1.
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* If JOBZ = 'N' and N > 1, LWORK >= N + 1.
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* If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2.
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*
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* If LWORK = -1, then a workspace query is assumed; the routine
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* only calculates the optimal sizes of the WORK, RWORK and
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* IWORK arrays, returns these values as the first entries of
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* the WORK, RWORK and IWORK arrays, and no error message
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* related to LWORK or LRWORK or LIWORK is issued by XERBLA.
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*
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* RWORK (workspace/output) REAL array, dimension (MAX(1,LRWORK))
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* On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
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*
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* LRWORK (input) INTEGER
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* The dimension of the array RWORK.
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* If N <= 1, LRWORK >= 1.
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* If JOBZ = 'N' and N > 1, LRWORK >= N.
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* If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
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*
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* If LRWORK = -1, then a workspace query is assumed; the
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* routine only calculates the optimal sizes of the WORK, RWORK
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* and IWORK arrays, returns these values as the first entries
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* of the WORK, RWORK and IWORK arrays, and no error message
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* related to LWORK or LRWORK or LIWORK is issued by XERBLA.
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*
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* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
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* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
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*
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* LIWORK (input) INTEGER
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* The dimension of the array IWORK.
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* If N <= 1, LIWORK >= 1.
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* If JOBZ = 'N' and N > 1, LIWORK >= 1.
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* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
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*
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* If LIWORK = -1, then a workspace query is assumed; the
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* routine only calculates the optimal sizes of the WORK, RWORK
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* and IWORK arrays, returns these values as the first entries
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* of the WORK, RWORK and IWORK arrays, and no error message
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* related to LWORK or LRWORK or LIWORK is issued by XERBLA.
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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* > 0: CPOTRF or CHEEVD returned an error code:
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* <= N: if INFO = i and JOBZ = 'N', then the algorithm
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* failed to converge; i off-diagonal elements of an
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* intermediate tridiagonal form did not converge to
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* zero;
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* if INFO = i and JOBZ = 'V', then the algorithm
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* failed to compute an eigenvalue while working on
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* the submatrix lying in rows and columns INFO/(N+1)
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* through mod(INFO,N+1);
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* > N: if INFO = N + i, for 1 <= i <= N, then the leading
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* minor of order i of B is not positive definite.
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* The factorization of B could not be completed and
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* no eigenvalues or eigenvectors were computed.
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*
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* Further Details
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* ===============
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*
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* Based on contributions by
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* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
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*
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* Modified so that no backsubstitution is performed if CHEEVD fails to
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* converge (NEIG in old code could be greater than N causing out of
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* bounds reference to A - reported by Ralf Meyer). Also corrected the
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* description of INFO and the test on ITYPE. Sven, 16 Feb 05.
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX CONE
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PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY, UPPER, WANTZ
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CHARACTER TRANS
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INTEGER LIOPT, LIWMIN, LOPT, LROPT, LRWMIN, LWMIN
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL CHEEVD, CHEGST, CPOTRF, CTRMM, CTRSM, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, REAL
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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WANTZ = LSAME( JOBZ, 'V' )
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UPPER = LSAME( UPLO, 'U' )
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LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
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*
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INFO = 0
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IF( N.LE.1 ) THEN
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LWMIN = 1
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LRWMIN = 1
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LIWMIN = 1
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ELSE IF( WANTZ ) THEN
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LWMIN = 2*N + N*N
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LRWMIN = 1 + 5*N + 2*N*N
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LIWMIN = 3 + 5*N
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ELSE
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LWMIN = N + 1
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LRWMIN = N
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LIWMIN = 1
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END IF
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LOPT = LWMIN
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LROPT = LRWMIN
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LIOPT = LIWMIN
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IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
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INFO = -1
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ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
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INFO = -2
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ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -6
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -8
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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WORK( 1 ) = LOPT
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RWORK( 1 ) = LROPT
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IWORK( 1 ) = LIOPT
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*
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IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -11
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ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -13
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ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -15
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END IF
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CHEGVD', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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* Form a Cholesky factorization of B.
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*
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CALL CPOTRF( UPLO, N, B, LDB, INFO )
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IF( INFO.NE.0 ) THEN
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INFO = N + INFO
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RETURN
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END IF
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*
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* Transform problem to standard eigenvalue problem and solve.
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*
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CALL CHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
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CALL CHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK,
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$ IWORK, LIWORK, INFO )
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LOPT = MAX( REAL( LOPT ), REAL( WORK( 1 ) ) )
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LROPT = MAX( REAL( LROPT ), REAL( RWORK( 1 ) ) )
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LIOPT = MAX( REAL( LIOPT ), REAL( IWORK( 1 ) ) )
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*
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IF( WANTZ .AND. INFO.EQ.0 ) THEN
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*
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* Backtransform eigenvectors to the original problem.
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*
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IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
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*
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* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
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* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
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*
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IF( UPPER ) THEN
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TRANS = 'N'
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ELSE
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TRANS = 'C'
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END IF
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*
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CALL CTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE,
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$ B, LDB, A, LDA )
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*
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ELSE IF( ITYPE.EQ.3 ) THEN
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*
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* For B*A*x=(lambda)*x;
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* backtransform eigenvectors: x = L*y or U'*y
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*
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IF( UPPER ) THEN
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TRANS = 'C'
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ELSE
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TRANS = 'N'
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END IF
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*
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CALL CTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE,
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$ B, LDB, A, LDA )
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END IF
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END IF
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*
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WORK( 1 ) = LOPT
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RWORK( 1 ) = LROPT
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IWORK( 1 ) = LIOPT
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*
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RETURN
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*
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* End of CHEGVD
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*
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END
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