--- rpl/lapack/lapack/zsteqr.f 2010/12/21 13:53:55 1.7 +++ rpl/lapack/lapack/zsteqr.f 2011/11/21 20:43:21 1.8 @@ -1,9 +1,141 @@ +*> \brief \b ZSTEQR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZSTEQR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER COMPZ +* INTEGER INFO, LDZ, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), E( * ), WORK( * ) +* COMPLEX*16 Z( LDZ, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a +*> symmetric tridiagonal matrix using the implicit QL or QR method. +*> The eigenvectors of a full or band complex Hermitian matrix can also +*> be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this +*> matrix to tridiagonal form. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] COMPZ +*> \verbatim +*> COMPZ is CHARACTER*1 +*> = 'N': Compute eigenvalues only. +*> = 'V': Compute eigenvalues and eigenvectors of the original +*> Hermitian matrix. On entry, Z must contain the +*> unitary matrix used to reduce the original matrix +*> to tridiagonal form. +*> = 'I': Compute eigenvalues and eigenvectors of the +*> tridiagonal matrix. Z is initialized to the identity +*> matrix. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. N >= 0. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, the diagonal elements of the tridiagonal matrix. +*> On exit, if INFO = 0, the eigenvalues in ascending order. +*> \endverbatim +*> +*> \param[in,out] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N-1) +*> On entry, the (n-1) subdiagonal elements of the tridiagonal +*> matrix. +*> On exit, E has been destroyed. +*> \endverbatim +*> +*> \param[in,out] Z +*> \verbatim +*> Z is COMPLEX*16 array, dimension (LDZ, N) +*> On entry, if COMPZ = 'V', then Z contains the unitary +*> matrix used in the reduction to tridiagonal form. +*> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the +*> orthonormal eigenvectors of the original Hermitian matrix, +*> and if COMPZ = 'I', Z contains the orthonormal eigenvectors +*> of the symmetric tridiagonal matrix. +*> If COMPZ = '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 +*> eigenvectors are desired, then LDZ >= max(1,N). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) +*> If COMPZ = 'N', then WORK 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: the algorithm has failed to find all the eigenvalues in +*> a total of 30*N iterations; if INFO = i, then i +*> elements of E have not converged to zero; on exit, D +*> and E contain the elements of a symmetric tridiagonal +*> matrix which is unitarily similar to the original +*> matrix. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERcomputational +* +* ===================================================================== SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- LAPACK computational routine (version 3.4.0) -- * -- 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 COMPZ @@ -14,66 +146,6 @@ COMPLEX*16 Z( LDZ, * ) * .. * -* Purpose -* ======= -* -* ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a -* symmetric tridiagonal matrix using the implicit QL or QR method. -* The eigenvectors of a full or band complex Hermitian matrix can also -* be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this -* matrix to tridiagonal form. -* -* Arguments -* ========= -* -* COMPZ (input) CHARACTER*1 -* = 'N': Compute eigenvalues only. -* = 'V': Compute eigenvalues and eigenvectors of the original -* Hermitian matrix. On entry, Z must contain the -* unitary matrix used to reduce the original matrix -* to tridiagonal form. -* = 'I': Compute eigenvalues and eigenvectors of the -* tridiagonal matrix. Z is initialized to the identity -* matrix. -* -* N (input) INTEGER -* The order of the matrix. N >= 0. -* -* D (input/output) DOUBLE PRECISION array, dimension (N) -* On entry, the diagonal elements of the tridiagonal matrix. -* On exit, if INFO = 0, the eigenvalues in ascending order. -* -* E (input/output) DOUBLE PRECISION array, dimension (N-1) -* On entry, the (n-1) subdiagonal elements of the tridiagonal -* matrix. -* On exit, E has been destroyed. -* -* Z (input/output) COMPLEX*16 array, dimension (LDZ, N) -* On entry, if COMPZ = 'V', then Z contains the unitary -* matrix used in the reduction to tridiagonal form. -* On exit, if INFO = 0, then if COMPZ = 'V', Z contains the -* orthonormal eigenvectors of the original Hermitian matrix, -* and if COMPZ = 'I', Z contains the orthonormal eigenvectors -* of the symmetric tridiagonal matrix. -* If COMPZ = 'N', then Z is not referenced. -* -* LDZ (input) INTEGER -* The leading dimension of the array Z. LDZ >= 1, and if -* eigenvectors are desired, then LDZ >= max(1,N). -* -* WORK (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2)) -* If COMPZ = 'N', then WORK is not referenced. -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* > 0: the algorithm has failed to find all the eigenvalues in -* a total of 30*N iterations; if INFO = i, then i -* elements of E have not converged to zero; on exit, D -* and E contain the elements of a symmetric tridiagonal -* matrix which is unitarily similar to the original -* matrix. -* * ===================================================================== * * .. Parameters ..