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#include "rb_lapack.h"
extern VOID slaebz_(integer* ijob, integer* nitmax, integer* n, integer* mmax, integer* minp, integer* nbmin, real* abstol, real* reltol, real* pivmin, real* d, real* e, real* e2, integer* nval, real* ab, real* c, integer* mout, integer* nab, real* work, integer* iwork, integer* info);
static VALUE
rblapack_slaebz(int argc, VALUE *argv, VALUE self){
VALUE rblapack_ijob;
integer ijob;
VALUE rblapack_nitmax;
integer nitmax;
VALUE rblapack_minp;
integer minp;
VALUE rblapack_nbmin;
integer nbmin;
VALUE rblapack_abstol;
real abstol;
VALUE rblapack_reltol;
real reltol;
VALUE rblapack_pivmin;
real pivmin;
VALUE rblapack_d;
real *d;
VALUE rblapack_e;
real *e;
VALUE rblapack_e2;
real *e2;
VALUE rblapack_nval;
integer *nval;
VALUE rblapack_ab;
real *ab;
VALUE rblapack_c;
real *c;
VALUE rblapack_nab;
integer *nab;
VALUE rblapack_mout;
integer mout;
VALUE rblapack_info;
integer info;
VALUE rblapack_nval_out__;
integer *nval_out__;
VALUE rblapack_ab_out__;
real *ab_out__;
VALUE rblapack_c_out__;
real *c_out__;
VALUE rblapack_nab_out__;
integer *nab_out__;
real *work;
integer *iwork;
integer n;
integer mmax;
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 mout, info, nval, ab, c, nab = NumRu::Lapack.slaebz( ijob, nitmax, minp, nbmin, abstol, reltol, pivmin, d, e, e2, nval, ab, c, nab, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE SLAEBZ( IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL, RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT, NAB, WORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* SLAEBZ contains the iteration loops which compute and use the\n* function N(w), which is the count of eigenvalues of a symmetric\n* tridiagonal matrix T less than or equal to its argument w. It\n* performs a choice of two types of loops:\n*\n* IJOB=1, followed by\n* IJOB=2: It takes as input a list of intervals and returns a list of\n* sufficiently small intervals whose union contains the same\n* eigenvalues as the union of the original intervals.\n* The input intervals are (AB(j,1),AB(j,2)], j=1,...,MINP.\n* The output interval (AB(j,1),AB(j,2)] will contain\n* eigenvalues NAB(j,1)+1,...,NAB(j,2), where 1 <= j <= MOUT.\n*\n* IJOB=3: It performs a binary search in each input interval\n* (AB(j,1),AB(j,2)] for a point w(j) such that\n* N(w(j))=NVAL(j), and uses C(j) as the starting point of\n* the search. If such a w(j) is found, then on output\n* AB(j,1)=AB(j,2)=w. If no such w(j) is found, then on output\n* (AB(j,1),AB(j,2)] will be a small interval containing the\n* point where N(w) jumps through NVAL(j), unless that point\n* lies outside the initial interval.\n*\n* Note that the intervals are in all cases half-open intervals,\n* i.e., of the form (a,b] , which includes b but not a .\n*\n* To avoid underflow, the matrix should be scaled so that its largest\n* element is no greater than overflow**(1/2) * underflow**(1/4)\n* in absolute value. To assure the most accurate computation\n* of small eigenvalues, the matrix should be scaled to be\n* not much smaller than that, either.\n*\n* See W. Kahan \"Accurate Eigenvalues of a Symmetric Tridiagonal\n* Matrix\", Report CS41, Computer Science Dept., Stanford\n* University, July 21, 1966\n*\n* Note: the arguments are, in general, *not* checked for unreasonable\n* values.\n*\n\n* Arguments\n* =========\n*\n* IJOB (input) INTEGER\n* Specifies what is to be done:\n* = 1: Compute NAB for the initial intervals.\n* = 2: Perform bisection iteration to find eigenvalues of T.\n* = 3: Perform bisection iteration to invert N(w), i.e.,\n* to find a point which has a specified number of\n* eigenvalues of T to its left.\n* Other values will cause SLAEBZ to return with INFO=-1.\n*\n* NITMAX (input) INTEGER\n* The maximum number of \"levels\" of bisection to be\n* performed, i.e., an interval of width W will not be made\n* smaller than 2^(-NITMAX) * W. If not all intervals\n* have converged after NITMAX iterations, then INFO is set\n* to the number of non-converged intervals.\n*\n* N (input) INTEGER\n* The dimension n of the tridiagonal matrix T. It must be at\n* least 1.\n*\n* MMAX (input) INTEGER\n* The maximum number of intervals. If more than MMAX intervals\n* are generated, then SLAEBZ will quit with INFO=MMAX+1.\n*\n* MINP (input) INTEGER\n* The initial number of intervals. It may not be greater than\n* MMAX.\n*\n* NBMIN (input) INTEGER\n* The smallest number of intervals that should be processed\n* using a vector loop. If zero, then only the scalar loop\n* will be used.\n*\n* ABSTOL (input) REAL\n* The minimum (absolute) width of an interval. When an\n* interval is narrower than ABSTOL, or than RELTOL times the\n* larger (in magnitude) endpoint, then it is considered to be\n* sufficiently small, i.e., converged. This must be at least\n* zero.\n*\n* RELTOL (input) REAL\n* The minimum relative width of an interval. When an interval\n* is narrower than ABSTOL, or than RELTOL times the larger (in\n* magnitude) endpoint, then it is considered to be\n* sufficiently small, i.e., converged. Note: this should\n* always be at least radix*machine epsilon.\n*\n* PIVMIN (input) REAL\n* The minimum absolute value of a \"pivot\" in the Sturm\n* sequence loop. This *must* be at least max |e(j)**2| *\n* safe_min and at least safe_min, where safe_min is at least\n* the smallest number that can divide one without overflow.\n*\n* D (input) REAL array, dimension (N)\n* The diagonal elements of the tridiagonal matrix T.\n*\n* E (input) REAL array, dimension (N)\n* The offdiagonal elements of the tridiagonal matrix T in\n* positions 1 through N-1. E(N) is arbitrary.\n*\n* E2 (input) REAL array, dimension (N)\n* The squares of the offdiagonal elements of the tridiagonal\n* matrix T. E2(N) is ignored.\n*\n* NVAL (input/output) INTEGER array, dimension (MINP)\n* If IJOB=1 or 2, not referenced.\n* If IJOB=3, the desired values of N(w). The elements of NVAL\n* will be reordered to correspond with the intervals in AB.\n* Thus, NVAL(j) on output will not, in general be the same as\n* NVAL(j) on input, but it will correspond with the interval\n* (AB(j,1),AB(j,2)] on output.\n*\n* AB (input/output) REAL array, dimension (MMAX,2)\n* The endpoints of the intervals. AB(j,1) is a(j), the left\n* endpoint of the j-th interval, and AB(j,2) is b(j), the\n* right endpoint of the j-th interval. The input intervals\n* will, in general, be modified, split, and reordered by the\n* calculation.\n*\n* C (input/output) REAL array, dimension (MMAX)\n* If IJOB=1, ignored.\n* If IJOB=2, workspace.\n* If IJOB=3, then on input C(j) should be initialized to the\n* first search point in the binary search.\n*\n* MOUT (output) INTEGER\n* If IJOB=1, the number of eigenvalues in the intervals.\n* If IJOB=2 or 3, the number of intervals output.\n* If IJOB=3, MOUT will equal MINP.\n*\n* NAB (input/output) INTEGER array, dimension (MMAX,2)\n* If IJOB=1, then on output NAB(i,j) will be set to N(AB(i,j)).\n* If IJOB=2, then on input, NAB(i,j) should be set. It must\n* satisfy the condition:\n* N(AB(i,1)) <= NAB(i,1) <= NAB(i,2) <= N(AB(i,2)),\n* which means that in interval i only eigenvalues\n* NAB(i,1)+1,...,NAB(i,2) will be considered. Usually,\n* NAB(i,j)=N(AB(i,j)), from a previous call to SLAEBZ with\n* IJOB=1.\n* On output, NAB(i,j) will contain\n* max(na(k),min(nb(k),N(AB(i,j)))), where k is the index of\n* the input interval that the output interval\n* (AB(j,1),AB(j,2)] came from, and na(k) and nb(k) are the\n* the input values of NAB(k,1) and NAB(k,2).\n* If IJOB=3, then on output, NAB(i,j) contains N(AB(i,j)),\n* unless N(w) > NVAL(i) for all search points w , in which\n* case NAB(i,1) will not be modified, i.e., the output\n* value will be the same as the input value (modulo\n* reorderings -- see NVAL and AB), or unless N(w) < NVAL(i)\n* for all search points w , in which case NAB(i,2) will\n* not be modified. Normally, NAB should be set to some\n* distinctive value(s) before SLAEBZ is called.\n*\n* WORK (workspace) REAL array, dimension (MMAX)\n* Workspace.\n*\n* IWORK (workspace) INTEGER array, dimension (MMAX)\n* Workspace.\n*\n* INFO (output) INTEGER\n* = 0: All intervals converged.\n* = 1--MMAX: The last INFO intervals did not converge.\n* = MMAX+1: More than MMAX intervals were generated.\n*\n\n* Further Details\n* ===============\n*\n* This routine is intended to be called only by other LAPACK\n* routines, thus the interface is less user-friendly. It is intended\n* for two purposes:\n*\n* (a) finding eigenvalues. In this case, SLAEBZ should have one or\n* more initial intervals set up in AB, and SLAEBZ should be called\n* with IJOB=1. This sets up NAB, and also counts the eigenvalues.\n* Intervals with no eigenvalues would usually be thrown out at\n* this point. Also, if not all the eigenvalues in an interval i\n* are desired, NAB(i,1) can be increased or NAB(i,2) decreased.\n* For example, set NAB(i,1)=NAB(i,2)-1 to get the largest\n* eigenvalue. SLAEBZ is then called with IJOB=2 and MMAX\n* no smaller than the value of MOUT returned by the call with\n* IJOB=1. After this (IJOB=2) call, eigenvalues NAB(i,1)+1\n* through NAB(i,2) are approximately AB(i,1) (or AB(i,2)) to the\n* tolerance specified by ABSTOL and RELTOL.\n*\n* (b) finding an interval (a',b'] containing eigenvalues w(f),...,w(l).\n* In this case, start with a Gershgorin interval (a,b). Set up\n* AB to contain 2 search intervals, both initially (a,b). One\n* NVAL element should contain f-1 and the other should contain l\n* , while C should contain a and b, resp. NAB(i,1) should be -1\n* and NAB(i,2) should be N+1, to flag an error if the desired\n* interval does not lie in (a,b). SLAEBZ is then called with\n* IJOB=3. On exit, if w(f-1) < w(f), then one of the intervals --\n* j -- will have AB(j,1)=AB(j,2) and NAB(j,1)=NAB(j,2)=f-1, while\n* if, to the specified tolerance, w(f-k)=...=w(f+r), k > 0 and r\n* >= 0, then the interval will have N(AB(j,1))=NAB(j,1)=f-k and\n* N(AB(j,2))=NAB(j,2)=f+r. The cases w(l) < w(l+1) and\n* w(l-r)=...=w(l+k) are handled similarly.\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n mout, info, nval, ab, c, nab = NumRu::Lapack.slaebz( ijob, nitmax, minp, nbmin, abstol, reltol, pivmin, d, e, e2, nval, ab, c, nab, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 14 && argc != 14)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 14)", argc);
rblapack_ijob = argv[0];
rblapack_nitmax = argv[1];
rblapack_minp = argv[2];
rblapack_nbmin = argv[3];
rblapack_abstol = argv[4];
rblapack_reltol = argv[5];
rblapack_pivmin = argv[6];
rblapack_d = argv[7];
rblapack_e = argv[8];
rblapack_e2 = argv[9];
rblapack_nval = argv[10];
rblapack_ab = argv[11];
rblapack_c = argv[12];
rblapack_nab = argv[13];
if (argc == 14) {
} else if (rblapack_options != Qnil) {
} else {
}
ijob = NUM2INT(rblapack_ijob);
minp = NUM2INT(rblapack_minp);
abstol = (real)NUM2DBL(rblapack_abstol);
pivmin = (real)NUM2DBL(rblapack_pivmin);
if (!NA_IsNArray(rblapack_e))
rb_raise(rb_eArgError, "e (9th argument) must be NArray");
if (NA_RANK(rblapack_e) != 1)
rb_raise(rb_eArgError, "rank of e (9th argument) must be %d", 1);
n = NA_SHAPE0(rblapack_e);
if (NA_TYPE(rblapack_e) != NA_SFLOAT)
rblapack_e = na_change_type(rblapack_e, NA_SFLOAT);
e = NA_PTR_TYPE(rblapack_e, real*);
if (!NA_IsNArray(rblapack_nval))
rb_raise(rb_eArgError, "nval (11th argument) must be NArray");
if (NA_RANK(rblapack_nval) != 1)
rb_raise(rb_eArgError, "rank of nval (11th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_nval) != ((ijob==1||ijob==2) ? 0 : ijob==3 ? minp : 0))
rb_raise(rb_eRuntimeError, "shape 0 of nval must be %d", (ijob==1||ijob==2) ? 0 : ijob==3 ? minp : 0);
if (NA_TYPE(rblapack_nval) != NA_LINT)
rblapack_nval = na_change_type(rblapack_nval, NA_LINT);
nval = NA_PTR_TYPE(rblapack_nval, integer*);
if (!NA_IsNArray(rblapack_nab))
rb_raise(rb_eArgError, "nab (14th argument) must be NArray");
if (NA_RANK(rblapack_nab) != 2)
rb_raise(rb_eArgError, "rank of nab (14th argument) must be %d", 2);
mmax = NA_SHAPE0(rblapack_nab);
if (NA_SHAPE1(rblapack_nab) != (2))
rb_raise(rb_eRuntimeError, "shape 1 of nab must be %d", 2);
if (NA_TYPE(rblapack_nab) != NA_LINT)
rblapack_nab = na_change_type(rblapack_nab, NA_LINT);
nab = NA_PTR_TYPE(rblapack_nab, integer*);
nitmax = NUM2INT(rblapack_nitmax);
reltol = (real)NUM2DBL(rblapack_reltol);
if (!NA_IsNArray(rblapack_e2))
rb_raise(rb_eArgError, "e2 (10th argument) must be NArray");
if (NA_RANK(rblapack_e2) != 1)
rb_raise(rb_eArgError, "rank of e2 (10th 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_SFLOAT)
rblapack_e2 = na_change_type(rblapack_e2, NA_SFLOAT);
e2 = NA_PTR_TYPE(rblapack_e2, real*);
nbmin = NUM2INT(rblapack_nbmin);
if (!NA_IsNArray(rblapack_ab))
rb_raise(rb_eArgError, "ab (12th argument) must be NArray");
if (NA_RANK(rblapack_ab) != 2)
rb_raise(rb_eArgError, "rank of ab (12th argument) must be %d", 2);
if (NA_SHAPE0(rblapack_ab) != mmax)
rb_raise(rb_eRuntimeError, "shape 0 of ab must be the same as shape 0 of nab");
if (NA_SHAPE1(rblapack_ab) != (2))
rb_raise(rb_eRuntimeError, "shape 1 of ab must be %d", 2);
if (NA_TYPE(rblapack_ab) != NA_SFLOAT)
rblapack_ab = na_change_type(rblapack_ab, NA_SFLOAT);
ab = NA_PTR_TYPE(rblapack_ab, real*);
if (!NA_IsNArray(rblapack_d))
rb_raise(rb_eArgError, "d (8th argument) must be NArray");
if (NA_RANK(rblapack_d) != 1)
rb_raise(rb_eArgError, "rank of d (8th 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_SFLOAT)
rblapack_d = na_change_type(rblapack_d, NA_SFLOAT);
d = NA_PTR_TYPE(rblapack_d, real*);
if (!NA_IsNArray(rblapack_c))
rb_raise(rb_eArgError, "c (13th argument) must be NArray");
if (NA_RANK(rblapack_c) != 1)
rb_raise(rb_eArgError, "rank of c (13th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_c) != (ijob==1 ? 0 : (ijob==2||ijob==3) ? mmax : 0))
rb_raise(rb_eRuntimeError, "shape 0 of c must be %d", ijob==1 ? 0 : (ijob==2||ijob==3) ? mmax : 0);
if (NA_TYPE(rblapack_c) != NA_SFLOAT)
rblapack_c = na_change_type(rblapack_c, NA_SFLOAT);
c = NA_PTR_TYPE(rblapack_c, real*);
{
na_shape_t shape[1];
shape[0] = (ijob==1||ijob==2) ? 0 : ijob==3 ? minp : 0;
rblapack_nval_out__ = na_make_object(NA_LINT, 1, shape, cNArray);
}
nval_out__ = NA_PTR_TYPE(rblapack_nval_out__, integer*);
MEMCPY(nval_out__, nval, integer, NA_TOTAL(rblapack_nval));
rblapack_nval = rblapack_nval_out__;
nval = nval_out__;
{
na_shape_t shape[2];
shape[0] = mmax;
shape[1] = 2;
rblapack_ab_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
ab_out__ = NA_PTR_TYPE(rblapack_ab_out__, real*);
MEMCPY(ab_out__, ab, real, NA_TOTAL(rblapack_ab));
rblapack_ab = rblapack_ab_out__;
ab = ab_out__;
{
na_shape_t shape[1];
shape[0] = ijob==1 ? 0 : (ijob==2||ijob==3) ? mmax : 0;
rblapack_c_out__ = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
c_out__ = NA_PTR_TYPE(rblapack_c_out__, real*);
MEMCPY(c_out__, c, real, NA_TOTAL(rblapack_c));
rblapack_c = rblapack_c_out__;
c = c_out__;
{
na_shape_t shape[2];
shape[0] = mmax;
shape[1] = 2;
rblapack_nab_out__ = na_make_object(NA_LINT, 2, shape, cNArray);
}
nab_out__ = NA_PTR_TYPE(rblapack_nab_out__, integer*);
MEMCPY(nab_out__, nab, integer, NA_TOTAL(rblapack_nab));
rblapack_nab = rblapack_nab_out__;
nab = nab_out__;
work = ALLOC_N(real, (mmax));
iwork = ALLOC_N(integer, (mmax));
slaebz_(&ijob, &nitmax, &n, &mmax, &minp, &nbmin, &abstol, &reltol, &pivmin, d, e, e2, nval, ab, c, &mout, nab, work, iwork, &info);
free(work);
free(iwork);
rblapack_mout = INT2NUM(mout);
rblapack_info = INT2NUM(info);
return rb_ary_new3(6, rblapack_mout, rblapack_info, rblapack_nval, rblapack_ab, rblapack_c, rblapack_nab);
}
void
init_lapack_slaebz(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "slaebz", rblapack_slaebz, -1);
}
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