MAGMA  1.2.0
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Macros | Functions
dstedx.cpp File Reference
#include "common_magma.h"
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Macros

#define Z(ix, iy)   (z + (ix) + ldz * (iy))
#define lapackf77_dlanst   FORTRAN_NAME( dlanst, DLANST )

Functions

double lapackf77_dlanst (char *norm, magma_int_t *n, double *d, double *e)
magma_int_t get_dstedx_smlsize ()
magma_int_t magma_dstedx (char range, magma_int_t n, double vl, double vu, magma_int_t il, magma_int_t iu, double *d, double *e, double *z, magma_int_t ldz, double *work, magma_int_t lwork, magma_int_t *iwork, magma_int_t liwork, double *dwork, magma_int_t *info)

Macro Definition Documentation

#define lapackf77_dlanst   FORTRAN_NAME( dlanst, DLANST )

Definition at line 15 of file dstedx.cpp.

#define Z (   ix,
  iy 
)    (z + (ix) + ldz * (iy))

Definition at line 13 of file dstedx.cpp.

Function Documentation

magma_int_t get_dstedx_smlsize ( )

Definition at line 20 of file dstedx.cpp.

{
return 25;
}

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double lapackf77_dlanst ( char *  norm,
magma_int_t *  n,
double *  d,
double *  e 
)
magma_int_t magma_dstedx ( char  range,
magma_int_t  n,
double  vl,
double  vu,
magma_int_t  il,
magma_int_t  iu,
double *  d,
double *  e,
double *  z,
magma_int_t  ldz,
double *  work,
magma_int_t  lwork,
magma_int_t *  iwork,
magma_int_t  liwork,
double *  dwork,
magma_int_t *  info 
)

Definition at line 27 of file dstedx.cpp.

References __func__, blasf77_dswap(), get_dstedx_smlsize(), lapackf77_dlamch, lapackf77_dlanst, lapackf77_dlascl(), lapackf77_dlaset(), lapackf77_dsteqr(), lapackf77_lsame, MAGMA_D_ABS, magma_dlaex0(), MAGMA_ERR_ILLEGAL_VALUE, MAGMA_SUCCESS, magma_xerbla(), max, min, and Z.

{
/*
-- MAGMA (version 1.2.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
May 2012
.. Scalar Arguments ..
CHARACTER RANGE
INTEGER IL, IU, INFO, LDZ, LIWORK, LWORK, N
DOUBLE PRECISION VL, VU
..
.. Array Arguments ..
INTEGER IWORK( * )
DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ),
$ DWORK ( * )
..
Purpose
=======
DSTEDX computes some eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method.
This code makes very mild assumptions about floating point
arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits
which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none. See DLAEX3 for details.
Arguments
=========
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.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
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'.
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 subdiagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
On exit, if INFO = 0, Z contains the orthonormal eigenvectors
of the symmetric tridiagonal matrix.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N).
WORK (workspace/output) DOUBLE PRECISION array,
dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If N > 1 then LWORK must be at least ( 1 + 4*N + N**2 ).
Note that if N is less than or
equal to the minimum divide size, usually 25, then LWORK need
only be max(1,2*(N-1)).
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
LIWORK must be at least ( 3 + 5*N ).
Note that if N is less than or
equal to the minimum divide size, usually 25, then LIWORK
need only be 1.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the IWORK array,
returns this value as the first entry of the IWORK array, and
no error message related to LIWORK is issued by XERBLA.
DWORK (device workspace) DOUBLE PRECISION array, dimension (3*N*N/2+3*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
Modified by Francoise Tisseur, University of Tennessee.
=====================================================================
*/
char range_[2] = {range, 0};
double d_zero = 0.;
double d_one = 1.;
magma_int_t izero = 0;
magma_int_t ione = 1;
magma_int_t alleig, indeig, valeig, lquery;
magma_int_t i, j, k, m;
magma_int_t liwmin, lwmin;
magma_int_t start, end, smlsiz;
double eps, orgnrm, p, tiny;
// Test the input parameters.
alleig = lapackf77_lsame(range_, "A");
valeig = lapackf77_lsame(range_, "V");
indeig = lapackf77_lsame(range_, "I");
lquery = lwork == -1 || liwork == -1;
*info = 0;
if (! (alleig || valeig || indeig)) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldz < max(1,n)) {
*info = -10;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -4;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -5;
} else if (iu < min(n,il) || iu > n) {
*info = -6;
}
}
}
if (*info == 0) {
// Compute the workspace requirements
smlsiz = get_dstedx_smlsize();
if( n <= 1 ){
lwmin = 1;
liwmin = 1;
} else {
lwmin = 1 + 4*n + n*n;
liwmin = 3 + 5*n;
}
work[0] = lwmin;
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -12;
} else if (liwork < liwmin && ! lquery) {
*info = -14;
}
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return MAGMA_ERR_ILLEGAL_VALUE;
} else if (lquery) {
return MAGMA_SUCCESS;
}
// Quick return if possible
if(n==0)
return MAGMA_SUCCESS;
if(n==1){
*z = 1.;
return MAGMA_SUCCESS;
}
// If N is smaller than the minimum divide size (SMLSIZ+1), then
// solve the problem with another solver.
if (n < smlsiz){
char char_I[]= {'I', 0};
lapackf77_dsteqr(char_I, &n, d, e, z, &ldz, work, info);
} else {
char char_F[]= {'F', 0};
lapackf77_dlaset(char_F, &n, &n, &d_zero, &d_one, z, &ldz);
//Scale.
char char_M[]= {'M', 0};
orgnrm = lapackf77_dlanst(char_M, &n, d, e);
if (orgnrm == 0){
work[0] = lwmin;
iwork[0] = liwmin;
return MAGMA_SUCCESS;
}
eps = lapackf77_dlamch( "Epsilon" );
if (alleig){
start = 0;
while ( start < n ){
// Let FINISH be the position of the next subdiagonal entry
// such that E( END ) <= TINY or FINISH = N if no such
// subdiagonal exists. The matrix identified by the elements
// between START and END constitutes an independent
// sub-problem.
for(end = start+1; end < n; ++end){
tiny = eps * sqrt( MAGMA_D_ABS(d[end-1]*d[end]));
if (MAGMA_D_ABS(e[end-1]) <= tiny)
break;
}
// (Sub) Problem determined. Compute its size and solve it.
m = end - start;
if (m==1){
start = end;
continue;
}
if (m > smlsiz){
// Scale
char char_G[] = {'G', 0};
orgnrm = lapackf77_dlanst(char_M, &m, &d[start], &e[start]);
lapackf77_dlascl(char_G, &izero, &izero, &orgnrm, &d_one, &m, &ione, &d[start], &m, info);
magma_int_t mm = m-1;
lapackf77_dlascl(char_G, &izero, &izero, &orgnrm, &d_one, &mm, &ione, &e[start], &mm, info);
magma_dlaex0( m, &d[start], &e[start], Z(start, start), ldz, work, iwork, dwork, 'A', vl, vu, il, iu, info);
if( *info != 0) {
return MAGMA_SUCCESS;
}
// Scale Back
lapackf77_dlascl(char_G, &izero, &izero, &d_one, &orgnrm, &m, &ione, &d[start], &m, info);
} else {
char char_I[]= {'I', 0};
lapackf77_dsteqr( char_I, &m, &d[start], &e[start], Z(start, start), &ldz, work, info);
if (*info != 0){
*info = (start+1) *(n+1) + end;
}
}
start = end;
}
// If the problem split any number of times, then the eigenvalues
// will not be properly ordered. Here we permute the eigenvalues
// (and the associated eigenvectors) into ascending order.
if (m < n){
// Use Selection Sort to minimize swaps of eigenvectors
for (i = 1; i < n; ++i){
k = i-1;
p = d[i-1];
for (j = i; j < n; ++j){
if (d[j] < p){
k = j;
p = d[j];
}
}
if(k != i-1) {
d[k] = d[i-1];
d[i-1] = p;
blasf77_dswap(&n, Z(0,i-1), &ione, Z(0,k), &ione);
}
}
}
} else {
// Scale
char char_G[] = {'G', 0};
lapackf77_dlascl(char_G, &izero, &izero, &orgnrm, &d_one, &n, &ione, d, &n, info);
magma_int_t nm = n-1;
lapackf77_dlascl(char_G, &izero, &izero, &orgnrm, &d_one, &nm, &ione, e, &nm, info);
magma_dlaex0( n, d, e, z, ldz, work, iwork, dwork, range, vl, vu, il, iu, info);
if( *info != 0) {
return MAGMA_SUCCESS;
}
// Scale Back
lapackf77_dlascl(char_G, &izero, &izero, &d_one, &orgnrm, &n, &ione, d, &n, info);
}
}
work[0] = lwmin;
iwork[0] = liwmin;
return MAGMA_SUCCESS;
} /* dstedx */

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