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author | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
commit | e1d39294aee16fa6db9ba079b14442358217db71 (patch) | |
tree | 30e5aa04c1f6596991fda5334f63dfb9b8027849 /SRC/zhbgvx.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
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Integrating Doxygen in comments
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diff --git a/SRC/zhbgvx.f b/SRC/zhbgvx.f index d2a198c5..84f57ce9 100644 --- a/SRC/zhbgvx.f +++ b/SRC/zhbgvx.f @@ -1,11 +1,299 @@ +*> \brief \b ZHBGST +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZHBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, +* LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, +* LDZ, WORK, RWORK, IWORK, IFAIL, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, RANGE, UPLO +* INTEGER IL, INFO, IU, KA, KB, LDAB, LDBB, LDQ, LDZ, M, +* $ N +* DOUBLE PRECISION ABSTOL, VL, VU +* .. +* .. Array Arguments .. +* INTEGER IFAIL( * ), IWORK( * ) +* DOUBLE PRECISION RWORK( * ), W( * ) +* COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), Q( LDQ, * ), +* $ WORK( * ), Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZHBGVX 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. Eigenvalues and +*> eigenvectors can be selected by specifying either all eigenvalues, +*> a range of values or a range of indices for the desired eigenvalues. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] JOBZ +*> \verbatim +*> JOBZ is CHARACTER*1 +*> = 'N': Compute eigenvalues only; +*> = 'V': Compute eigenvalues and eigenvectors. +*> \endverbatim +*> +*> \param[in] RANGE +*> \verbatim +*> 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. +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangles of A and B are stored; +*> = 'L': Lower triangles of A and B are stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrices A and B. N >= 0. +*> \endverbatim +*> +*> \param[in] KA +*> \verbatim +*> KA is INTEGER +*> The number of superdiagonals of the matrix A if UPLO = 'U', +*> or the number of subdiagonals if UPLO = 'L'. KA >= 0. +*> \endverbatim +*> +*> \param[in] KB +*> \verbatim +*> KB is INTEGER +*> The number of superdiagonals of the matrix B if UPLO = 'U', +*> or the number of subdiagonals if UPLO = 'L'. KB >= 0. +*> \endverbatim +*> +*> \param[in,out] AB +*> \verbatim +*> AB is COMPLEX*16 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). +*> \endverbatim +*> \verbatim +*> On exit, the contents of AB are destroyed. +*> \endverbatim +*> +*> \param[in] LDAB +*> \verbatim +*> LDAB is INTEGER +*> The leading dimension of the array AB. LDAB >= KA+1. +*> \endverbatim +*> +*> \param[in,out] BB +*> \verbatim +*> BB is COMPLEX*16 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). +*> \endverbatim +*> \verbatim +*> On exit, the factor S from the split Cholesky factorization +*> B = S**H*S, as returned by ZPBSTF. +*> \endverbatim +*> +*> \param[in] LDBB +*> \verbatim +*> LDBB is INTEGER +*> The leading dimension of the array BB. LDBB >= KB+1. +*> \endverbatim +*> +*> \param[out] Q +*> \verbatim +*> Q is COMPLEX*16 array, dimension (LDQ, N) +*> If JOBZ = 'V', the n-by-n matrix used in the reduction of +*> A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x, +*> and consequently C to tridiagonal form. +*> If JOBZ = 'N', the array Q is not referenced. +*> \endverbatim +*> +*> \param[in] LDQ +*> \verbatim +*> LDQ is INTEGER +*> The leading dimension of the array Q. If JOBZ = 'N', +*> LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N). +*> \endverbatim +*> +*> \param[in] VL +*> \verbatim +*> VL is DOUBLE PRECISION +*> \param[in] VU +*> \verbatim +*> 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'. +*> \endverbatim +*> \endverbatim +*> +*> \param[in] IL +*> \verbatim +*> IL is INTEGER +*> \param[in] IU +*> \verbatim +*> 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'. +*> \endverbatim +*> \endverbatim +*> +*> \param[in] ABSTOL +*> \verbatim +*> 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 +*> \endverbatim +*> \verbatim +*> ABSTOL + EPS * max( |a|,|b| ) , +*> \endverbatim +*> \verbatim +*> 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 AP to tridiagonal form. +*> \endverbatim +*> \verbatim +*> 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'). +*> \endverbatim +*> +*> \param[out] M +*> \verbatim +*> 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. +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> If INFO = 0, the eigenvalues in ascending order. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is COMPLEX*16 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. +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of the array Z. LDZ >= 1, and if +*> JOBZ = 'V', LDZ >= N. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (N) +*> \endverbatim +*> +*> \param[out] RWORK +*> \verbatim +*> RWORK is DOUBLE PRECISION array, dimension (7*N) +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (5*N) +*> \endverbatim +*> +*> \param[out] IFAIL +*> \verbatim +*> 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. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = i, and i is: +*> <= N: then i eigenvectors failed to converge. Their +*> indices are stored in array IFAIL. +*> > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF +*> returned INFO = i: B is not positive definite. +*> The factorization of B could not be completed and +*> no eigenvalues or eigenvectors were computed. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHEReigen +* +* +* Further Details +* =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Based on contributions by +*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA +*> +*> \endverbatim +*> +* ===================================================================== SUBROUTINE ZHBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, $ LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, $ LDZ, WORK, RWORK, IWORK, IFAIL, INFO ) * -* -- LAPACK driver routine (version 3.2) -- +* -- LAPACK eigen routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* November 2011 * * .. Scalar Arguments .. CHARACTER JOBZ, RANGE, UPLO @@ -20,160 +308,6 @@ $ WORK( * ), Z( LDZ, * ) * .. * -* Purpose -* ======= -* -* ZHBGVX 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. Eigenvalues and -* eigenvectors can be selected by specifying either all eigenvalues, -* a range of values or a range of indices for the desired eigenvalues. -* -* Arguments -* ========= -* -* JOBZ (input) CHARACTER*1 -* = 'N': Compute eigenvalues only; -* = 'V': Compute eigenvalues and eigenvectors. -* -* RANGE (input) 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. -* -* 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*16 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*16 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 ZPBSTF. -* -* LDBB (input) INTEGER -* The leading dimension of the array BB. LDBB >= KB+1. -* -* Q (output) COMPLEX*16 array, dimension (LDQ, N) -* If JOBZ = 'V', the n-by-n matrix used in the reduction of -* A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x, -* and consequently C to tridiagonal form. -* If JOBZ = 'N', the array Q is not referenced. -* -* LDQ (input) INTEGER -* The leading dimension of the array Q. If JOBZ = 'N', -* LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N). -* -* VL (input) DOUBLE PRECISION -* VU (input) 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'. -* -* IL (input) INTEGER -* IU (input) 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'. -* -* ABSTOL (input) 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 AP to tridiagonal form. -* -* 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'). -* -* M (output) INTEGER -* The total number of eigenvalues found. 0 <= M <= N. -* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. -* -* W (output) DOUBLE PRECISION array, dimension (N) -* If INFO = 0, the eigenvalues in ascending order. -* -* Z (output) COMPLEX*16 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*16 array, dimension (N) -* -* RWORK (workspace) DOUBLE PRECISION array, dimension (7*N) -* -* IWORK (workspace) INTEGER array, dimension (5*N) -* -* IFAIL (output) 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. -* -* 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: then i eigenvectors failed to converge. Their -* indices are stored in array IFAIL. -* > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF -* returned INFO = i: B is not positive definite. -* The factorization of B could not be completed and -* no eigenvalues or eigenvectors were computed. -* -* Further Details -* =============== -* -* Based on contributions by -* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA -* * ===================================================================== * * .. Parameters .. |