--- rpl/lapack/lapack/dlaed0.f 2010/12/21 13:53:28 1.7 +++ rpl/lapack/lapack/dlaed0.f 2011/11/21 20:42:54 1.8 @@ -1,10 +1,181 @@ +*> \brief \b DLAED0 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAED0 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, +* WORK, IWORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ +* .. +* .. Array Arguments .. +* INTEGER IWORK( * ) +* DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), +* $ WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAED0 computes all eigenvalues and corresponding eigenvectors of a +*> symmetric tridiagonal matrix using the divide and conquer method. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] ICOMPQ +*> \verbatim +*> ICOMPQ is INTEGER +*> = 0: Compute eigenvalues only. +*> = 1: Compute eigenvectors of original dense symmetric matrix +*> also. On entry, Q contains the orthogonal matrix used +*> to reduce the original matrix to tridiagonal form. +*> = 2: Compute eigenvalues and eigenvectors of tridiagonal +*> matrix. +*> \endverbatim +*> +*> \param[in] QSIZ +*> \verbatim +*> QSIZ is INTEGER +*> The dimension of the orthogonal matrix used to reduce +*> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The dimension of the symmetric tridiagonal matrix. N >= 0. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, the main diagonal of the tridiagonal matrix. +*> On exit, its eigenvalues. +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N-1) +*> The off-diagonal elements of the tridiagonal matrix. +*> On exit, E has been destroyed. +*> \endverbatim +*> +*> \param[in,out] Q +*> \verbatim +*> Q is DOUBLE PRECISION array, dimension (LDQ, N) +*> On entry, Q must contain an N-by-N orthogonal matrix. +*> If ICOMPQ = 0 Q is not referenced. +*> If ICOMPQ = 1 On entry, Q is a subset of the columns of the +*> orthogonal matrix used to reduce the full +*> matrix to tridiagonal form corresponding to +*> the subset of the full matrix which is being +*> decomposed at this time. +*> If ICOMPQ = 2 On entry, Q will be the identity matrix. +*> On exit, Q contains the eigenvectors of the +*> tridiagonal matrix. +*> \endverbatim +*> +*> \param[in] LDQ +*> \verbatim +*> LDQ is INTEGER +*> The leading dimension of the array Q. If eigenvectors are +*> desired, then LDQ >= max(1,N). In any case, LDQ >= 1. +*> \endverbatim +*> +*> \param[out] QSTORE +*> \verbatim +*> QSTORE is DOUBLE PRECISION array, dimension (LDQS, N) +*> Referenced only when ICOMPQ = 1. Used to store parts of +*> the eigenvector matrix when the updating matrix multiplies +*> take place. +*> \endverbatim +*> +*> \param[in] LDQS +*> \verbatim +*> LDQS is INTEGER +*> The leading dimension of the array QSTORE. If ICOMPQ = 1, +*> then LDQS >= max(1,N). In any case, LDQS >= 1. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, +*> If ICOMPQ = 0 or 1, the dimension of WORK must be at least +*> 1 + 3*N + 2*N*lg N + 3*N**2 +*> ( lg( N ) = smallest integer k +*> such that 2^k >= N ) +*> If ICOMPQ = 2, the dimension of WORK must be at least +*> 4*N + N**2. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, +*> If ICOMPQ = 0 or 1, the dimension of IWORK must be at least +*> 6 + 6*N + 5*N*lg N. +*> ( lg( N ) = smallest integer k +*> such that 2^k >= N ) +*> If ICOMPQ = 2, the dimension of IWORK must be at least +*> 3 + 5*N. +*> \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 failed to compute an eigenvalue while +*> working on the submatrix lying in rows and columns +*> INFO/(N+1) through mod(INFO,N+1). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERcomputational +* +*> \par Contributors: +* ================== +*> +*> Jeff Rutter, Computer Science Division, University of California +*> at Berkeley, USA +* +* ===================================================================== SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, $ WORK, IWORK, 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 .. INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ @@ -15,93 +186,6 @@ $ WORK( * ) * .. * -* Purpose -* ======= -* -* DLAED0 computes all eigenvalues and corresponding eigenvectors of a -* symmetric tridiagonal matrix using the divide and conquer method. -* -* Arguments -* ========= -* -* ICOMPQ (input) INTEGER -* = 0: Compute eigenvalues only. -* = 1: Compute eigenvectors of original dense symmetric matrix -* also. On entry, Q contains the orthogonal matrix used -* to reduce the original matrix to tridiagonal form. -* = 2: Compute eigenvalues and eigenvectors of tridiagonal -* matrix. -* -* QSIZ (input) INTEGER -* The dimension of the orthogonal matrix used to reduce -* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. -* -* N (input) INTEGER -* The dimension of the symmetric tridiagonal matrix. N >= 0. -* -* D (input/output) DOUBLE PRECISION array, dimension (N) -* On entry, the main diagonal of the tridiagonal matrix. -* On exit, its eigenvalues. -* -* E (input) DOUBLE PRECISION array, dimension (N-1) -* The off-diagonal elements of the tridiagonal matrix. -* On exit, E has been destroyed. -* -* Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N) -* On entry, Q must contain an N-by-N orthogonal matrix. -* If ICOMPQ = 0 Q is not referenced. -* If ICOMPQ = 1 On entry, Q is a subset of the columns of the -* orthogonal matrix used to reduce the full -* matrix to tridiagonal form corresponding to -* the subset of the full matrix which is being -* decomposed at this time. -* If ICOMPQ = 2 On entry, Q will be the identity matrix. -* On exit, Q contains the eigenvectors of the -* tridiagonal matrix. -* -* LDQ (input) INTEGER -* The leading dimension of the array Q. If eigenvectors are -* desired, then LDQ >= max(1,N). In any case, LDQ >= 1. -* -* QSTORE (workspace) DOUBLE PRECISION array, dimension (LDQS, N) -* Referenced only when ICOMPQ = 1. Used to store parts of -* the eigenvector matrix when the updating matrix multiplies -* take place. -* -* LDQS (input) INTEGER -* The leading dimension of the array QSTORE. If ICOMPQ = 1, -* then LDQS >= max(1,N). In any case, LDQS >= 1. -* -* WORK (workspace) DOUBLE PRECISION array, -* If ICOMPQ = 0 or 1, the dimension of WORK must be at least -* 1 + 3*N + 2*N*lg N + 2*N**2 -* ( lg( N ) = smallest integer k -* such that 2^k >= N ) -* If ICOMPQ = 2, the dimension of WORK must be at least -* 4*N + N**2. -* -* IWORK (workspace) INTEGER array, -* If ICOMPQ = 0 or 1, the dimension of IWORK must be at least -* 6 + 6*N + 5*N*lg N. -* ( lg( N ) = smallest integer k -* such that 2^k >= N ) -* If ICOMPQ = 2, the dimension of IWORK must be at least -* 3 + 5*N. -* -* INFO (output) INTEGER -* = 0: successful exit. -* < 0: if INFO = -i, the i-th argument had an illegal value. -* > 0: The algorithm failed to compute an eigenvalue while -* working on the submatrix lying in rows and columns -* INFO/(N+1) through mod(INFO,N+1). -* -* Further Details -* =============== -* -* Based on contributions by -* Jeff Rutter, Computer Science Division, University of California -* at Berkeley, USA -* * ===================================================================== * * .. Parameters ..