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#include "rb_lapack.h"
extern VOID dlarre_(char* range, integer* n, doublereal* vl, doublereal* vu, integer* il, integer* iu, doublereal* d, doublereal* e, doublereal* e2, doublereal* rtol1, doublereal* rtol2, doublereal* spltol, integer* nsplit, integer* isplit, integer* m, doublereal* w, doublereal* werr, doublereal* wgap, integer* iblock, integer* indexw, doublereal* gers, doublereal* pivmin, doublereal* work, integer* iwork, integer* info);
static VALUE
rblapack_dlarre(int argc, VALUE *argv, VALUE self){
VALUE rblapack_range;
char range;
VALUE rblapack_vl;
doublereal vl;
VALUE rblapack_vu;
doublereal vu;
VALUE rblapack_il;
integer il;
VALUE rblapack_iu;
integer iu;
VALUE rblapack_d;
doublereal *d;
VALUE rblapack_e;
doublereal *e;
VALUE rblapack_e2;
doublereal *e2;
VALUE rblapack_rtol1;
doublereal rtol1;
VALUE rblapack_rtol2;
doublereal rtol2;
VALUE rblapack_spltol;
doublereal spltol;
VALUE rblapack_nsplit;
integer nsplit;
VALUE rblapack_isplit;
integer *isplit;
VALUE rblapack_m;
integer m;
VALUE rblapack_w;
doublereal *w;
VALUE rblapack_werr;
doublereal *werr;
VALUE rblapack_wgap;
doublereal *wgap;
VALUE rblapack_iblock;
integer *iblock;
VALUE rblapack_indexw;
integer *indexw;
VALUE rblapack_gers;
doublereal *gers;
VALUE rblapack_pivmin;
doublereal pivmin;
VALUE rblapack_info;
integer info;
VALUE rblapack_d_out__;
doublereal *d_out__;
VALUE rblapack_e_out__;
doublereal *e_out__;
VALUE rblapack_e2_out__;
doublereal *e2_out__;
doublereal *work;
integer *iwork;
integer n;
VALUE rblapack_options;
if (argc > 0 && TYPE(argv[argc-1]) == T_HASH) {
argc--;
rblapack_options = argv[argc];
if (rb_hash_aref(rblapack_options, sHelp) == Qtrue) {
printf("%s\n", "USAGE:\n nsplit, isplit, m, w, werr, wgap, iblock, indexw, gers, pivmin, info, vl, vu, d, e, e2 = NumRu::Lapack.dlarre( range, vl, vu, il, iu, d, e, e2, rtol1, rtol2, spltol, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE DLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2, RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M, W, WERR, WGAP, IBLOCK, INDEXW, GERS, PIVMIN, WORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* To find the desired eigenvalues of a given real symmetric\n* tridiagonal matrix T, DLARRE sets any \"small\" off-diagonal\n* elements to zero, and for each unreduced block T_i, it finds\n* (a) a suitable shift at one end of the block's spectrum,\n* (b) the base representation, T_i - sigma_i I = L_i D_i L_i^T, and\n* (c) eigenvalues of each L_i D_i L_i^T.\n* The representations and eigenvalues found are then used by\n* DSTEMR to compute the eigenvectors of T.\n* The accuracy varies depending on whether bisection is used to\n* find a few eigenvalues or the dqds algorithm (subroutine DLASQ2) to\n* conpute all and then discard any unwanted one.\n* As an added benefit, DLARRE also outputs the n\n* Gerschgorin intervals for the matrices L_i D_i L_i^T.\n*\n\n* Arguments\n* =========\n*\n* RANGE (input) CHARACTER*1\n* = 'A': (\"All\") all eigenvalues will be found.\n* = 'V': (\"Value\") all eigenvalues in the half-open interval\n* (VL, VU] will be found.\n* = 'I': (\"Index\") the IL-th through IU-th eigenvalues (of the\n* entire matrix) will be found.\n*\n* N (input) INTEGER\n* The order of the matrix. N > 0.\n*\n* VL (input/output) DOUBLE PRECISION\n* VU (input/output) DOUBLE PRECISION\n* If RANGE='V', the lower and upper bounds for the eigenvalues.\n* Eigenvalues less than or equal to VL, or greater than VU,\n* will not be returned. VL < VU.\n* If RANGE='I' or ='A', DLARRE computes bounds on the desired\n* part of the spectrum.\n*\n* IL (input) INTEGER\n* IU (input) INTEGER\n* If RANGE='I', the indices (in ascending order) of the\n* smallest and largest eigenvalues to be returned.\n* 1 <= IL <= IU <= N.\n*\n* D (input/output) DOUBLE PRECISION array, dimension (N)\n* On entry, the N diagonal elements of the tridiagonal\n* matrix T.\n* On exit, the N diagonal elements of the diagonal\n* matrices D_i.\n*\n* E (input/output) DOUBLE PRECISION array, dimension (N)\n* On entry, the first (N-1) entries contain the subdiagonal\n* elements of the tridiagonal matrix T; E(N) need not be set.\n* On exit, E contains the subdiagonal elements of the unit\n* bidiagonal matrices L_i. The entries E( ISPLIT( I ) ),\n* 1 <= I <= NSPLIT, contain the base points sigma_i on output.\n*\n* E2 (input/output) DOUBLE PRECISION array, dimension (N)\n* On entry, the first (N-1) entries contain the SQUARES of the\n* subdiagonal elements of the tridiagonal matrix T;\n* E2(N) need not be set.\n* On exit, the entries E2( ISPLIT( I ) ),\n* 1 <= I <= NSPLIT, have been set to zero\n*\n* RTOL1 (input) DOUBLE PRECISION\n* RTOL2 (input) DOUBLE PRECISION\n* Parameters for bisection.\n* An interval [LEFT,RIGHT] has converged if\n* RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )\n*\n* SPLTOL (input) DOUBLE PRECISION\n* The threshold for splitting.\n*\n* NSPLIT (output) INTEGER\n* The number of blocks T splits into. 1 <= NSPLIT <= N.\n*\n* ISPLIT (output) INTEGER array, dimension (N)\n* The splitting points, at which T breaks up into blocks.\n* The first block consists of rows/columns 1 to ISPLIT(1),\n* the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),\n* etc., and the NSPLIT-th consists of rows/columns\n* ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.\n*\n* M (output) INTEGER\n* The total number of eigenvalues (of all L_i D_i L_i^T)\n* found.\n*\n* W (output) DOUBLE PRECISION array, dimension (N)\n* The first M elements contain the eigenvalues. The\n* eigenvalues of each of the blocks, L_i D_i L_i^T, are\n* sorted in ascending order ( DLARRE may use the\n* remaining N-M elements as workspace).\n*\n* WERR (output) DOUBLE PRECISION array, dimension (N)\n* The error bound on the corresponding eigenvalue in W.\n*\n* WGAP (output) DOUBLE PRECISION array, dimension (N)\n* The separation from the right neighbor eigenvalue in W.\n* The gap is only with respect to the eigenvalues of the same block\n* as each block has its own representation tree.\n* Exception: at the right end of a block we store the left gap\n*\n* IBLOCK (output) INTEGER array, dimension (N)\n* The indices of the blocks (submatrices) associated with the\n* corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue\n* W(i) belongs to the first block from the top, =2 if W(i)\n* belongs to the second block, etc.\n*\n* INDEXW (output) INTEGER array, dimension (N)\n* The indices of the eigenvalues within each block (submatrix);\n* for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the\n* i-th eigenvalue W(i) is the 10-th eigenvalue in block 2\n*\n* GERS (output) DOUBLE PRECISION array, dimension (2*N)\n* The N Gerschgorin intervals (the i-th Gerschgorin interval\n* is (GERS(2*i-1), GERS(2*i)).\n*\n* PIVMIN (output) DOUBLE PRECISION\n* The minimum pivot in the Sturm sequence for T.\n*\n* WORK (workspace) DOUBLE PRECISION array, dimension (6*N)\n* Workspace.\n*\n* IWORK (workspace) INTEGER array, dimension (5*N)\n* Workspace.\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* > 0: A problem occurred in DLARRE.\n* < 0: One of the called subroutines signaled an internal problem.\n* Needs inspection of the corresponding parameter IINFO\n* for further information.\n*\n* =-1: Problem in DLARRD.\n* = 2: No base representation could be found in MAXTRY iterations.\n* Increasing MAXTRY and recompilation might be a remedy.\n* =-3: Problem in DLARRB when computing the refined root\n* representation for DLASQ2.\n* =-4: Problem in DLARRB when preforming bisection on the\n* desired part of the spectrum.\n* =-5: Problem in DLASQ2.\n* =-6: Problem in DLASQ2.\n*\n\n* Further Details\n* The base representations are required to suffer very little\n* element growth and consequently define all their eigenvalues to\n* high relative accuracy.\n* ===============\n*\n* Based on contributions by\n* Beresford Parlett, University of California, Berkeley, USA\n* Jim Demmel, University of California, Berkeley, USA\n* Inderjit Dhillon, University of Texas, Austin, USA\n* Osni Marques, LBNL/NERSC, USA\n* Christof Voemel, University of California, Berkeley, USA\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n nsplit, isplit, m, w, werr, wgap, iblock, indexw, gers, pivmin, info, vl, vu, d, e, e2 = NumRu::Lapack.dlarre( range, vl, vu, il, iu, d, e, e2, rtol1, rtol2, spltol, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 11 && argc != 11)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 11)", argc);
rblapack_range = argv[0];
rblapack_vl = argv[1];
rblapack_vu = argv[2];
rblapack_il = argv[3];
rblapack_iu = argv[4];
rblapack_d = argv[5];
rblapack_e = argv[6];
rblapack_e2 = argv[7];
rblapack_rtol1 = argv[8];
rblapack_rtol2 = argv[9];
rblapack_spltol = argv[10];
if (argc == 11) {
} else if (rblapack_options != Qnil) {
} else {
}
range = StringValueCStr(rblapack_range)[0];
vu = NUM2DBL(rblapack_vu);
iu = NUM2INT(rblapack_iu);
if (!NA_IsNArray(rblapack_e))
rb_raise(rb_eArgError, "e (7th argument) must be NArray");
if (NA_RANK(rblapack_e) != 1)
rb_raise(rb_eArgError, "rank of e (7th argument) must be %d", 1);
n = NA_SHAPE0(rblapack_e);
if (NA_TYPE(rblapack_e) != NA_DFLOAT)
rblapack_e = na_change_type(rblapack_e, NA_DFLOAT);
e = NA_PTR_TYPE(rblapack_e, doublereal*);
rtol1 = NUM2DBL(rblapack_rtol1);
spltol = NUM2DBL(rblapack_spltol);
vl = NUM2DBL(rblapack_vl);
if (!NA_IsNArray(rblapack_d))
rb_raise(rb_eArgError, "d (6th argument) must be NArray");
if (NA_RANK(rblapack_d) != 1)
rb_raise(rb_eArgError, "rank of d (6th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_d) != n)
rb_raise(rb_eRuntimeError, "shape 0 of d must be the same as shape 0 of e");
if (NA_TYPE(rblapack_d) != NA_DFLOAT)
rblapack_d = na_change_type(rblapack_d, NA_DFLOAT);
d = NA_PTR_TYPE(rblapack_d, doublereal*);
rtol2 = NUM2DBL(rblapack_rtol2);
il = NUM2INT(rblapack_il);
if (!NA_IsNArray(rblapack_e2))
rb_raise(rb_eArgError, "e2 (8th argument) must be NArray");
if (NA_RANK(rblapack_e2) != 1)
rb_raise(rb_eArgError, "rank of e2 (8th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_e2) != n)
rb_raise(rb_eRuntimeError, "shape 0 of e2 must be the same as shape 0 of e");
if (NA_TYPE(rblapack_e2) != NA_DFLOAT)
rblapack_e2 = na_change_type(rblapack_e2, NA_DFLOAT);
e2 = NA_PTR_TYPE(rblapack_e2, doublereal*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_isplit = na_make_object(NA_LINT, 1, shape, cNArray);
}
isplit = NA_PTR_TYPE(rblapack_isplit, integer*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_w = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
w = NA_PTR_TYPE(rblapack_w, doublereal*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_werr = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
werr = NA_PTR_TYPE(rblapack_werr, doublereal*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_wgap = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
wgap = NA_PTR_TYPE(rblapack_wgap, doublereal*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_iblock = na_make_object(NA_LINT, 1, shape, cNArray);
}
iblock = NA_PTR_TYPE(rblapack_iblock, integer*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_indexw = na_make_object(NA_LINT, 1, shape, cNArray);
}
indexw = NA_PTR_TYPE(rblapack_indexw, integer*);
{
na_shape_t shape[1];
shape[0] = 2*n;
rblapack_gers = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
gers = NA_PTR_TYPE(rblapack_gers, doublereal*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_d_out__ = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
d_out__ = NA_PTR_TYPE(rblapack_d_out__, doublereal*);
MEMCPY(d_out__, d, doublereal, NA_TOTAL(rblapack_d));
rblapack_d = rblapack_d_out__;
d = d_out__;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_e_out__ = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
e_out__ = NA_PTR_TYPE(rblapack_e_out__, doublereal*);
MEMCPY(e_out__, e, doublereal, NA_TOTAL(rblapack_e));
rblapack_e = rblapack_e_out__;
e = e_out__;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_e2_out__ = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
e2_out__ = NA_PTR_TYPE(rblapack_e2_out__, doublereal*);
MEMCPY(e2_out__, e2, doublereal, NA_TOTAL(rblapack_e2));
rblapack_e2 = rblapack_e2_out__;
e2 = e2_out__;
work = ALLOC_N(doublereal, (6*n));
iwork = ALLOC_N(integer, (5*n));
dlarre_(&range, &n, &vl, &vu, &il, &iu, d, e, e2, &rtol1, &rtol2, &spltol, &nsplit, isplit, &m, w, werr, wgap, iblock, indexw, gers, &pivmin, work, iwork, &info);
free(work);
free(iwork);
rblapack_nsplit = INT2NUM(nsplit);
rblapack_m = INT2NUM(m);
rblapack_pivmin = rb_float_new((double)pivmin);
rblapack_info = INT2NUM(info);
rblapack_vl = rb_float_new((double)vl);
rblapack_vu = rb_float_new((double)vu);
return rb_ary_new3(16, rblapack_nsplit, rblapack_isplit, rblapack_m, rblapack_w, rblapack_werr, rblapack_wgap, rblapack_iblock, rblapack_indexw, rblapack_gers, rblapack_pivmin, rblapack_info, rblapack_vl, rblapack_vu, rblapack_d, rblapack_e, rblapack_e2);
}
void
init_lapack_dlarre(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "dlarre", rblapack_dlarre, -1);
}
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