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Diffstat (limited to 'SRC/chegv.f')
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diff --git a/SRC/chegv.f b/SRC/chegv.f new file mode 100644 index 00000000..f68db722 --- /dev/null +++ b/SRC/chegv.f @@ -0,0 +1,232 @@ + SUBROUTINE CHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, + $ LWORK, RWORK, INFO ) +* +* -- LAPACK driver routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER JOBZ, UPLO + INTEGER INFO, ITYPE, LDA, LDB, LWORK, N +* .. +* .. Array Arguments .. + REAL RWORK( * ), W( * ) + COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* CHEGV computes all the eigenvalues, and optionally, the eigenvectors +* of a complex generalized Hermitian-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 Hermitian and B is also +* positive definite. +* +* Arguments +* ========= +* +* ITYPE (input) 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 +* +* JOBZ (input) CHARACTER*1 +* = 'N': Compute eigenvalues only; +* = 'V': Compute eigenvalues and eigenvectors. +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangles of A and B are stored; +* = 'L': Lower triangles of A and B are stored. +* +* N (input) INTEGER +* The order of the matrices A and B. N >= 0. +* +* A (input/output) COMPLEX array, dimension (LDA, N) +* On entry, the Hermitian 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, if JOBZ = 'V', then if INFO = 0, A contains the +* matrix Z of eigenvectors. The eigenvectors are normalized +* as follows: +* if ITYPE = 1 or 2, Z**H*B*Z = I; +* if ITYPE = 3, Z**H*inv(B)*Z = I. +* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') +* or the lower triangle (if UPLO='L') of A, including the +* diagonal, is destroyed. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* B (input/output) COMPLEX array, dimension (LDB, N) +* On entry, the Hermitian positive definite 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**H*U or B = L*L**H. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* W (output) REAL array, dimension (N) +* If INFO = 0, the eigenvalues in ascending order. +* +* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The length of the array WORK. LWORK >= max(1,2*N-1). +* For optimal efficiency, LWORK >= (NB+1)*N, +* where NB is the blocksize for CHETRD 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. +* +* RWORK (workspace) REAL array, dimension (max(1, 3*N-2)) +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: CPOTRF or CHEEV returned an error code: +* <= N: if INFO = i, CHEEV failed to converge; +* i off-diagonal elements of an intermediate +* tridiagonal form did not converge to zero; +* > 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. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ONE + PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY, UPPER, WANTZ + CHARACTER TRANS + INTEGER LWKOPT, NB, NEIG +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL ILAENV, LSAME +* .. +* .. External Subroutines .. + EXTERNAL CHEEV, CHEGST, CPOTRF, CTRMM, CTRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + UPPER = LSAME( UPLO, 'U' ) + LQUERY = ( LWORK.EQ. -1 ) +* + INFO = 0 + IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN + INFO = -1 + ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -2 + ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN + INFO = -3 + ELSE IF( N.LT.0 ) THEN + INFO = -4 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -6 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -8 + END IF +* + IF( INFO.EQ.0 ) THEN + NB = ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 ) + LWKOPT = MAX( 1, ( NB + 1 )*N ) + WORK( 1 ) = LWKOPT +* + IF( LWORK.LT.MAX( 1, 2*N-1 ) .AND. .NOT.LQUERY ) THEN + INFO = -11 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CHEGV ', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Form a Cholesky factorization of B. +* + CALL CPOTRF( UPLO, N, B, LDB, INFO ) + IF( INFO.NE.0 ) THEN + INFO = N + INFO + RETURN + END IF +* +* Transform problem to standard eigenvalue problem and solve. +* + CALL CHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) + CALL CHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO ) +* + IF( WANTZ ) THEN +* +* Backtransform eigenvectors to the original problem. +* + NEIG = N + IF( INFO.GT.0 ) + $ NEIG = INFO - 1 + IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN +* +* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; +* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y +* + IF( UPPER ) THEN + TRANS = 'N' + ELSE + TRANS = 'C' + END IF +* + CALL CTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) +* + ELSE IF( ITYPE.EQ.3 ) THEN +* +* For B*A*x=(lambda)*x; +* backtransform eigenvectors: x = L*y or U'*y +* + IF( UPPER ) THEN + TRANS = 'C' + ELSE + TRANS = 'N' + END IF +* + CALL CTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, + $ B, LDB, A, LDA ) + END IF + END IF +* + WORK( 1 ) = LWKOPT +* + RETURN +* +* End of CHEGV +* + END |