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Diffstat (limited to 'SRC/chbgv.f')
-rw-r--r-- | SRC/chbgv.f | 191 |
1 files changed, 191 insertions, 0 deletions
diff --git a/SRC/chbgv.f b/SRC/chbgv.f new file mode 100644 index 00000000..0230cda9 --- /dev/null +++ b/SRC/chbgv.f @@ -0,0 +1,191 @@ + SUBROUTINE CHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, + $ LDZ, WORK, 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, KA, KB, LDAB, LDBB, LDZ, N +* .. +* .. Array Arguments .. + REAL RWORK( * ), W( * ) + COMPLEX AB( LDAB, * ), BB( LDBB, * ), WORK( * ), + $ Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +* CHBGV computes all the eigenvalues, and optionally, the eigenvectors +* of a complex generalized Hermitian-definite banded eigenproblem, of +* the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian +* and banded, and B is also positive definite. +* +* Arguments +* ========= +* +* 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. +* +* KA (input) INTEGER +* The number of superdiagonals of the matrix A if UPLO = 'U', +* or the number of subdiagonals if UPLO = 'L'. KA >= 0. +* +* KB (input) INTEGER +* The number of superdiagonals of the matrix B if UPLO = 'U', +* or the number of subdiagonals if UPLO = 'L'. KB >= 0. +* +* AB (input/output) COMPLEX array, dimension (LDAB, N) +* On entry, the upper or lower triangle of the Hermitian band +* matrix A, stored in the first ka+1 rows of the array. The +* j-th column of A is stored in the j-th column of the array AB +* as follows: +* if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; +* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). +* +* On exit, the contents of AB are destroyed. +* +* LDAB (input) INTEGER +* The leading dimension of the array AB. LDAB >= KA+1. +* +* BB (input/output) COMPLEX array, dimension (LDBB, N) +* On entry, the upper or lower triangle of the Hermitian band +* matrix B, stored in the first kb+1 rows of the array. The +* j-th column of B is stored in the j-th column of the array BB +* as follows: +* if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; +* if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). +* +* On exit, the factor S from the split Cholesky factorization +* B = S**H*S, as returned by CPBSTF. +* +* LDBB (input) INTEGER +* The leading dimension of the array BB. LDBB >= KB+1. +* +* W (output) REAL array, dimension (N) +* If INFO = 0, the eigenvalues in ascending order. +* +* Z (output) COMPLEX array, dimension (LDZ, N) +* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of +* eigenvectors, with the i-th column of Z holding the +* eigenvector associated with W(i). The eigenvectors are +* normalized so that Z**H*B*Z = I. +* If JOBZ = 'N', then Z is not referenced. +* +* LDZ (input) INTEGER +* The leading dimension of the array Z. LDZ >= 1, and if +* JOBZ = 'V', LDZ >= N. +* +* WORK (workspace) COMPLEX array, dimension (N) +* +* RWORK (workspace) REAL array, dimension (3*N) +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: if INFO = i, and i is: +* <= N: the algorithm 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 CPBSTF +* returned INFO = i: B is not positive definite. +* The factorization of B could not be completed and +* no eigenvalues or eigenvectors were computed. +* +* ===================================================================== +* +* .. Local Scalars .. + LOGICAL UPPER, WANTZ + CHARACTER VECT + INTEGER IINFO, INDE, INDWRK +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL CHBGST, CHBTRD, CPBSTF, CSTEQR, SSTERF, XERBLA +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + UPPER = LSAME( UPLO, 'U' ) +* + INFO = 0 + IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -1 + ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( KA.LT.0 ) THEN + INFO = -4 + ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN + INFO = -5 + ELSE IF( LDAB.LT.KA+1 ) THEN + INFO = -7 + ELSE IF( LDBB.LT.KB+1 ) THEN + INFO = -9 + ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN + INFO = -12 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CHBGV ', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Form a split Cholesky factorization of B. +* + CALL CPBSTF( UPLO, N, KB, BB, LDBB, INFO ) + IF( INFO.NE.0 ) THEN + INFO = N + INFO + RETURN + END IF +* +* Transform problem to standard eigenvalue problem. +* + INDE = 1 + INDWRK = INDE + N + CALL CHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ, + $ WORK, RWORK( INDWRK ), IINFO ) +* +* Reduce to tridiagonal form. +* + IF( WANTZ ) THEN + VECT = 'U' + ELSE + VECT = 'N' + END IF + CALL CHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z, + $ LDZ, WORK, IINFO ) +* +* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEQR. +* + IF( .NOT.WANTZ ) THEN + CALL SSTERF( N, W, RWORK( INDE ), INFO ) + ELSE + CALL CSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ, + $ RWORK( INDWRK ), INFO ) + END IF + RETURN +* +* End of CHBGV +* + END |