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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/chpevx.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
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Integrating Doxygen in comments
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diff --git a/SRC/chpevx.f b/SRC/chpevx.f index 3d0fa42d..a234a4f0 100644 --- a/SRC/chpevx.f +++ b/SRC/chpevx.f @@ -1,11 +1,239 @@ +*> \brief <b> CHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b> +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE CHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, +* ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, +* IFAIL, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, RANGE, UPLO +* INTEGER IL, INFO, IU, LDZ, M, N +* REAL ABSTOL, VL, VU +* .. +* .. Array Arguments .. +* INTEGER IFAIL( * ), IWORK( * ) +* REAL RWORK( * ), W( * ) +* COMPLEX AP( * ), WORK( * ), Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> CHPEVX computes selected eigenvalues and, optionally, eigenvectors +*> of a complex Hermitian matrix A in packed storage. +*> Eigenvalues/vectors can be selected by specifying either 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 triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] AP +*> \verbatim +*> AP is COMPLEX array, dimension (N*(N+1)/2) +*> On entry, the upper or lower triangle of the Hermitian matrix +*> A, packed columnwise in a linear array. The j-th column of A +*> is stored in the array AP as follows: +*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; +*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. +*> \endverbatim +*> \verbatim +*> On exit, AP is overwritten by values generated during the +*> reduction to tridiagonal form. If UPLO = 'U', the diagonal +*> and first superdiagonal of the tridiagonal matrix T overwrite +*> the corresponding elements of A, and if UPLO = 'L', the +*> diagonal and first subdiagonal of T overwrite the +*> corresponding elements of A. +*> \endverbatim +*> +*> \param[in] VL +*> \verbatim +*> VL is REAL +*> \endverbatim +*> +*> \param[in] VU +*> \verbatim +*> VU is REAL +*> 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 +*> +*> \param[in] IL +*> \verbatim +*> IL is INTEGER +*> \endverbatim +*> +*> \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 +*> +*> \param[in] ABSTOL +*> \verbatim +*> ABSTOL is REAL +*> 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*SLAMCH('S'), not zero. +*> If this routine returns with INFO>0, indicating that some +*> eigenvectors did not converge, try setting ABSTOL to +*> 2*SLAMCH('S'). +*> \endverbatim +*> \verbatim +*> See "Computing Small Singular Values of Bidiagonal Matrices +*> with Guaranteed High Relative Accuracy," by Demmel and +*> Kahan, LAPACK Working Note #3. +*> \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 REAL array, dimension (N) +*> If INFO = 0, the selected eigenvalues in ascending order. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is COMPLEX array, dimension (LDZ, max(1,M)) +*> 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). +*> 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. +*> If JOBZ = 'N', then Z is not referenced. +*> 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. +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of the array Z. LDZ >= 1, and if +*> JOBZ = 'V', LDZ >= max(1,N). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] RWORK +*> \verbatim +*> RWORK is REAL 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, then i eigenvectors failed to converge. +*> Their indices are stored in array IFAIL. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complexOTHEReigen +* +* ===================================================================== SUBROUTINE CHPEVX( JOBZ, RANGE, UPLO, N, AP, 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 @@ -18,128 +246,6 @@ COMPLEX AP( * ), WORK( * ), Z( LDZ, * ) * .. * -* Purpose -* ======= -* -* CHPEVX computes selected eigenvalues and, optionally, eigenvectors -* of a complex Hermitian matrix A in packed storage. -* Eigenvalues/vectors can be selected by specifying either 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 triangle of A is stored; -* = 'L': Lower triangle of A is stored. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* AP (input/output) COMPLEX array, dimension (N*(N+1)/2) -* On entry, the upper or lower triangle of the Hermitian matrix -* A, packed columnwise in a linear array. The j-th column of A -* is stored in the array AP as follows: -* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; -* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -* -* On exit, AP is overwritten by values generated during the -* reduction to tridiagonal form. If UPLO = 'U', the diagonal -* and first superdiagonal of the tridiagonal matrix T overwrite -* the corresponding elements of A, and if UPLO = 'L', the -* diagonal and first subdiagonal of T overwrite the -* corresponding elements of A. -* -* VL (input) REAL -* -* VU (input) REAL -* 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) REAL -* 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*SLAMCH('S'), not zero. -* If this routine returns with INFO>0, indicating that some -* eigenvectors did not converge, try setting ABSTOL to -* 2*SLAMCH('S'). -* -* See "Computing Small Singular Values of Bidiagonal Matrices -* with Guaranteed High Relative Accuracy," by Demmel and -* Kahan, LAPACK Working Note #3. -* -* 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) REAL array, dimension (N) -* If INFO = 0, the selected eigenvalues in ascending order. -* -* Z (output) COMPLEX array, dimension (LDZ, max(1,M)) -* 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). -* 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. -* If JOBZ = 'N', then Z is not referenced. -* 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. -* -* LDZ (input) INTEGER -* The leading dimension of the array Z. LDZ >= 1, and if -* JOBZ = 'V', LDZ >= max(1,N). -* -* WORK (workspace) COMPLEX array, dimension (2*N) -* -* RWORK (workspace) REAL 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, then i eigenvectors failed to converge. -* Their indices are stored in array IFAIL. -* * ===================================================================== * * .. Parameters .. |