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#include "rb_lapack.h"
extern VOID sstemr_(char* jobz, char* range, integer* n, real* d, real* e, real* vl, real* vu, integer* il, integer* iu, integer* m, real* w, real* z, integer* ldz, integer* nzc, integer* isuppz, logical* tryrac, real* work, integer* lwork, integer* iwork, integer* liwork, integer* info);
static VALUE
rblapack_sstemr(int argc, VALUE *argv, VALUE self){
VALUE rblapack_jobz;
char jobz;
VALUE rblapack_range;
char range;
VALUE rblapack_d;
real *d;
VALUE rblapack_e;
real *e;
VALUE rblapack_vl;
real vl;
VALUE rblapack_vu;
real vu;
VALUE rblapack_il;
integer il;
VALUE rblapack_iu;
integer iu;
VALUE rblapack_nzc;
integer nzc;
VALUE rblapack_tryrac;
logical tryrac;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_liwork;
integer liwork;
VALUE rblapack_m;
integer m;
VALUE rblapack_w;
real *w;
VALUE rblapack_z;
real *z;
VALUE rblapack_isuppz;
integer *isuppz;
VALUE rblapack_work;
real *work;
VALUE rblapack_iwork;
integer *iwork;
VALUE rblapack_info;
integer info;
VALUE rblapack_d_out__;
real *d_out__;
VALUE rblapack_e_out__;
real *e_out__;
integer n;
integer ldz;
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 m, w, z, isuppz, work, iwork, info, d, e, tryrac = NumRu::Lapack.sstemr( jobz, range, d, e, vl, vu, il, iu, nzc, tryrac, [:lwork => lwork, :liwork => liwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE SSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, IWORK, LIWORK, INFO )\n\n* Purpose\n* =======\n*\n* SSTEMR computes selected eigenvalues and, optionally, eigenvectors\n* of a real symmetric tridiagonal matrix T. Any such unreduced matrix has\n* a well defined set of pairwise different real eigenvalues, the corresponding\n* real eigenvectors are pairwise orthogonal.\n*\n* The spectrum may be computed either completely or partially by specifying\n* either an interval (VL,VU] or a range of indices IL:IU for the desired\n* eigenvalues.\n*\n* Depending on the number of desired eigenvalues, these are computed either\n* by bisection or the dqds algorithm. Numerically orthogonal eigenvectors are\n* computed by the use of various suitable L D L^T factorizations near clusters\n* of close eigenvalues (referred to as RRRs, Relatively Robust\n* Representations). An informal sketch of the algorithm follows.\n*\n* For each unreduced block (submatrix) of T,\n* (a) Compute T - sigma I = L D L^T, so that L and D\n* define all the wanted eigenvalues to high relative accuracy.\n* This means that small relative changes in the entries of D and L\n* cause only small relative changes in the eigenvalues and\n* eigenvectors. The standard (unfactored) representation of the\n* tridiagonal matrix T does not have this property in general.\n* (b) Compute the eigenvalues to suitable accuracy.\n* If the eigenvectors are desired, the algorithm attains full\n* accuracy of the computed eigenvalues only right before\n* the corresponding vectors have to be computed, see steps c) and d).\n* (c) For each cluster of close eigenvalues, select a new\n* shift close to the cluster, find a new factorization, and refine\n* the shifted eigenvalues to suitable accuracy.\n* (d) For each eigenvalue with a large enough relative separation compute\n* the corresponding eigenvector by forming a rank revealing twisted\n* factorization. Go back to (c) for any clusters that remain.\n*\n* For more details, see:\n* - Inderjit S. Dhillon and Beresford N. Parlett: \"Multiple representations\n* to compute orthogonal eigenvectors of symmetric tridiagonal matrices,\"\n* Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.\n* - Inderjit Dhillon and Beresford Parlett: \"Orthogonal Eigenvectors and\n* Relative Gaps,\" SIAM Journal on Matrix Analysis and Applications, Vol. 25,\n* 2004. Also LAPACK Working Note 154.\n* - Inderjit Dhillon: \"A new O(n^2) algorithm for the symmetric\n* tridiagonal eigenvalue/eigenvector problem\",\n* Computer Science Division Technical Report No. UCB/CSD-97-971,\n* UC Berkeley, May 1997.\n*\n* Further Details\n* 1.SSTEMR works only on machines which follow IEEE-754\n* floating-point standard in their handling of infinities and NaNs.\n* This permits the use of efficient inner loops avoiding a check for\n* zero divisors.\n*\n\n* Arguments\n* =========\n*\n* JOBZ (input) CHARACTER*1\n* = 'N': Compute eigenvalues only;\n* = 'V': Compute eigenvalues and eigenvectors.\n*\n* RANGE (input) CHARACTER*1\n* = 'A': all eigenvalues will be found.\n* = 'V': all eigenvalues in the half-open interval (VL,VU]\n* will be found.\n* = 'I': the IL-th through IU-th eigenvalues will be found.\n*\n* N (input) INTEGER\n* The order of the matrix. N >= 0.\n*\n* D (input/output) REAL array, dimension (N)\n* On entry, the N diagonal elements of the tridiagonal matrix\n* T. On exit, D is overwritten.\n*\n* E (input/output) REAL array, dimension (N)\n* On entry, the (N-1) subdiagonal elements of the tridiagonal\n* matrix T in elements 1 to N-1 of E. E(N) need not be set on\n* input, but is used internally as workspace.\n* On exit, E is overwritten.\n*\n* VL (input) REAL\n* VU (input) REAL\n* If RANGE='V', the lower and upper bounds of the interval to\n* be searched for eigenvalues. VL < VU.\n* Not referenced if RANGE = 'A' or 'I'.\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, if N > 0.\n* Not referenced if RANGE = 'A' or 'V'.\n*\n* M (output) INTEGER\n* The total number of eigenvalues found. 0 <= M <= N.\n* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.\n*\n* W (output) REAL array, dimension (N)\n* The first M elements contain the selected eigenvalues in\n* ascending order.\n*\n* Z (output) REAL array, dimension (LDZ, max(1,M) )\n* If JOBZ = 'V', and if INFO = 0, then the first M columns of Z\n* contain the orthonormal eigenvectors of the matrix T\n* corresponding to the selected eigenvalues, with the i-th\n* column of Z holding the eigenvector associated with W(i).\n* If JOBZ = 'N', then Z is not referenced.\n* Note: the user must ensure that at least max(1,M) columns are\n* supplied in the array Z; if RANGE = 'V', the exact value of M\n* is not known in advance and can be computed with a workspace\n* query by setting NZC = -1, see below.\n*\n* LDZ (input) INTEGER\n* The leading dimension of the array Z. LDZ >= 1, and if\n* JOBZ = 'V', then LDZ >= max(1,N).\n*\n* NZC (input) INTEGER\n* The number of eigenvectors to be held in the array Z.\n* If RANGE = 'A', then NZC >= max(1,N).\n* If RANGE = 'V', then NZC >= the number of eigenvalues in (VL,VU].\n* If RANGE = 'I', then NZC >= IU-IL+1.\n* If NZC = -1, then a workspace query is assumed; the\n* routine calculates the number of columns of the array Z that\n* are needed to hold the eigenvectors.\n* This value is returned as the first entry of the Z array, and\n* no error message related to NZC is issued by XERBLA.\n*\n* ISUPPZ (output) INTEGER ARRAY, dimension ( 2*max(1,M) )\n* The support of the eigenvectors in Z, i.e., the indices\n* indicating the nonzero elements in Z. The i-th computed eigenvector\n* is nonzero only in elements ISUPPZ( 2*i-1 ) through\n* ISUPPZ( 2*i ). This is relevant in the case when the matrix\n* is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.\n*\n* TRYRAC (input/output) LOGICAL\n* If TRYRAC.EQ..TRUE., indicates that the code should check whether\n* the tridiagonal matrix defines its eigenvalues to high relative\n* accuracy. If so, the code uses relative-accuracy preserving\n* algorithms that might be (a bit) slower depending on the matrix.\n* If the matrix does not define its eigenvalues to high relative\n* accuracy, the code can uses possibly faster algorithms.\n* If TRYRAC.EQ..FALSE., the code is not required to guarantee\n* relatively accurate eigenvalues and can use the fastest possible\n* techniques.\n* On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix\n* does not define its eigenvalues to high relative accuracy.\n*\n* WORK (workspace/output) REAL array, dimension (LWORK)\n* On exit, if INFO = 0, WORK(1) returns the optimal\n* (and minimal) LWORK.\n*\n* LWORK (input) INTEGER\n* The dimension of the array WORK. LWORK >= max(1,18*N)\n* if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.\n* If LWORK = -1, then a workspace query is assumed; the routine\n* only calculates the optimal size of the WORK array, returns\n* this value as the first entry of the WORK array, and no error\n* message related to LWORK is issued by XERBLA.\n*\n* IWORK (workspace/output) INTEGER array, dimension (LIWORK)\n* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.\n*\n* LIWORK (input) INTEGER\n* The dimension of the array IWORK. LIWORK >= max(1,10*N)\n* if the eigenvectors are desired, and LIWORK >= max(1,8*N)\n* if only the eigenvalues are to be computed.\n* If LIWORK = -1, then a workspace query is assumed; the\n* routine only calculates the optimal size of the IWORK array,\n* returns this value as the first entry of the IWORK array, and\n* no error message related to LIWORK is issued by XERBLA.\n*\n* INFO (output) INTEGER\n* On exit, INFO\n* = 0: successful exit\n* < 0: if INFO = -i, the i-th argument had an illegal value\n* > 0: if INFO = 1X, internal error in SLARRE,\n* if INFO = 2X, internal error in SLARRV.\n* Here, the digit X = ABS( IINFO ) < 10, where IINFO is\n* the nonzero error code returned by SLARRE or\n* SLARRV, respectively.\n*\n*\n\n* Further Details\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 m, w, z, isuppz, work, iwork, info, d, e, tryrac = NumRu::Lapack.sstemr( jobz, range, d, e, vl, vu, il, iu, nzc, tryrac, [:lwork => lwork, :liwork => liwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 10 && argc != 12)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 10)", argc);
rblapack_jobz = argv[0];
rblapack_range = argv[1];
rblapack_d = argv[2];
rblapack_e = argv[3];
rblapack_vl = argv[4];
rblapack_vu = argv[5];
rblapack_il = argv[6];
rblapack_iu = argv[7];
rblapack_nzc = argv[8];
rblapack_tryrac = argv[9];
if (argc == 12) {
rblapack_lwork = argv[10];
rblapack_liwork = argv[11];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
rblapack_liwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("liwork")));
} else {
rblapack_lwork = Qnil;
rblapack_liwork = Qnil;
}
jobz = StringValueCStr(rblapack_jobz)[0];
if (!NA_IsNArray(rblapack_d))
rb_raise(rb_eArgError, "d (3th argument) must be NArray");
if (NA_RANK(rblapack_d) != 1)
rb_raise(rb_eArgError, "rank of d (3th argument) must be %d", 1);
n = NA_SHAPE0(rblapack_d);
if (NA_TYPE(rblapack_d) != NA_SFLOAT)
rblapack_d = na_change_type(rblapack_d, NA_SFLOAT);
d = NA_PTR_TYPE(rblapack_d, real*);
vl = (real)NUM2DBL(rblapack_vl);
il = NUM2INT(rblapack_il);
nzc = NUM2INT(rblapack_nzc);
range = StringValueCStr(rblapack_range)[0];
vu = (real)NUM2DBL(rblapack_vu);
tryrac = (rblapack_tryrac == Qtrue);
if (!NA_IsNArray(rblapack_e))
rb_raise(rb_eArgError, "e (4th argument) must be NArray");
if (NA_RANK(rblapack_e) != 1)
rb_raise(rb_eArgError, "rank of e (4th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_e) != n)
rb_raise(rb_eRuntimeError, "shape 0 of e must be the same as shape 0 of d");
if (NA_TYPE(rblapack_e) != NA_SFLOAT)
rblapack_e = na_change_type(rblapack_e, NA_SFLOAT);
e = NA_PTR_TYPE(rblapack_e, real*);
if (rblapack_lwork == Qnil)
lwork = lsame_(&jobz,"V") ? 18*n : lsame_(&jobz,"N") ? 12*n : 0;
else {
lwork = NUM2INT(rblapack_lwork);
}
ldz = lsame_(&jobz,"V") ? MAX(1,n) : 1;
iu = NUM2INT(rblapack_iu);
m = lsame_(&range,"A") ? n : lsame_(&range,"I") ? iu-il+1 : 0;
if (rblapack_liwork == Qnil)
liwork = lsame_(&jobz,"V") ? 10*n : lsame_(&jobz,"N") ? 8*n : 0;
else {
liwork = NUM2INT(rblapack_liwork);
}
{
na_shape_t shape[1];
shape[0] = n;
rblapack_w = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
w = NA_PTR_TYPE(rblapack_w, real*);
{
na_shape_t shape[2];
shape[0] = ldz;
shape[1] = MAX(1,m);
rblapack_z = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
z = NA_PTR_TYPE(rblapack_z, real*);
{
na_shape_t shape[1];
shape[0] = 2*MAX(1,m);
rblapack_isuppz = na_make_object(NA_LINT, 1, shape, cNArray);
}
isuppz = NA_PTR_TYPE(rblapack_isuppz, integer*);
{
na_shape_t shape[1];
shape[0] = MAX(1,lwork);
rblapack_work = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, real*);
{
na_shape_t shape[1];
shape[0] = MAX(1,liwork);
rblapack_iwork = na_make_object(NA_LINT, 1, shape, cNArray);
}
iwork = NA_PTR_TYPE(rblapack_iwork, integer*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_d_out__ = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
d_out__ = NA_PTR_TYPE(rblapack_d_out__, real*);
MEMCPY(d_out__, d, real, 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_SFLOAT, 1, shape, cNArray);
}
e_out__ = NA_PTR_TYPE(rblapack_e_out__, real*);
MEMCPY(e_out__, e, real, NA_TOTAL(rblapack_e));
rblapack_e = rblapack_e_out__;
e = e_out__;
sstemr_(&jobz, &range, &n, d, e, &vl, &vu, &il, &iu, &m, w, z, &ldz, &nzc, isuppz, &tryrac, work, &lwork, iwork, &liwork, &info);
rblapack_m = INT2NUM(m);
rblapack_info = INT2NUM(info);
rblapack_tryrac = tryrac ? Qtrue : Qfalse;
return rb_ary_new3(10, rblapack_m, rblapack_w, rblapack_z, rblapack_isuppz, rblapack_work, rblapack_iwork, rblapack_info, rblapack_d, rblapack_e, rblapack_tryrac);
}
void
init_lapack_sstemr(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "sstemr", rblapack_sstemr, -1);
}
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