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#include "rb_lapack.h"
extern VOID dlarrd_(char* range, char* order, integer* n, doublereal* vl, doublereal* vu, integer* il, integer* iu, doublereal* gers, doublereal* reltol, doublereal* d, doublereal* e, doublereal* e2, doublereal* pivmin, integer* nsplit, integer* isplit, integer* m, doublereal* w, doublereal* werr, doublereal* wl, doublereal* wu, integer* iblock, integer* indexw, doublereal* work, integer* iwork, integer* info);
static VALUE
rblapack_dlarrd(int argc, VALUE *argv, VALUE self){
VALUE rblapack_range;
char range;
VALUE rblapack_order;
char order;
VALUE rblapack_vl;
doublereal vl;
VALUE rblapack_vu;
doublereal vu;
VALUE rblapack_il;
integer il;
VALUE rblapack_iu;
integer iu;
VALUE rblapack_gers;
doublereal *gers;
VALUE rblapack_reltol;
doublereal reltol;
VALUE rblapack_d;
doublereal *d;
VALUE rblapack_e;
doublereal *e;
VALUE rblapack_e2;
doublereal *e2;
VALUE rblapack_pivmin;
doublereal pivmin;
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_wl;
doublereal wl;
VALUE rblapack_wu;
doublereal wu;
VALUE rblapack_iblock;
integer *iblock;
VALUE rblapack_indexw;
integer *indexw;
VALUE rblapack_info;
integer info;
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 m, w, werr, wl, wu, iblock, indexw, info = NumRu::Lapack.dlarrd( range, order, vl, vu, il, iu, gers, reltol, d, e, e2, pivmin, nsplit, isplit, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE DLARRD( RANGE, ORDER, N, VL, VU, IL, IU, GERS, RELTOL, D, E, E2, PIVMIN, NSPLIT, ISPLIT, M, W, WERR, WL, WU, IBLOCK, INDEXW, WORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* DLARRD computes the eigenvalues of a symmetric tridiagonal\n* matrix T to suitable accuracy. This is an auxiliary code to be\n* called from DSTEMR.\n* The user may ask for all eigenvalues, all eigenvalues\n* in the half-open interval (VL, VU], or the IL-th through IU-th\n* eigenvalues.\n*\n* To avoid overflow, the matrix must be scaled so that its\n* largest element is no greater than overflow**(1/2) *\n* underflow**(1/4) in absolute value, and for greatest\n* accuracy, it should not be much smaller than that.\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\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* ORDER (input) CHARACTER*1\n* = 'B': (\"By Block\") the eigenvalues will be grouped by\n* split-off block (see IBLOCK, ISPLIT) and\n* ordered from smallest to largest within\n* the block.\n* = 'E': (\"Entire matrix\")\n* the eigenvalues for the entire matrix\n* will be ordered from smallest to\n* largest.\n*\n* N (input) INTEGER\n* The order of the tridiagonal matrix T. N >= 0.\n*\n* VL (input) DOUBLE PRECISION\n* VU (input) DOUBLE PRECISION\n* If RANGE='V', the lower and upper bounds of the interval to\n* be searched for eigenvalues. Eigenvalues less than or equal\n* to VL, or greater than VU, will not be returned. 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; IL = 1 and IU = 0 if N = 0.\n* Not referenced if RANGE = 'A' or 'V'.\n*\n* GERS (input) 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* RELTOL (input) DOUBLE PRECISION\n* The minimum relative width of an interval. When an interval\n* is narrower 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* D (input) DOUBLE PRECISION array, dimension (N)\n* The n diagonal elements of the tridiagonal matrix T.\n*\n* E (input) DOUBLE PRECISION array, dimension (N-1)\n* The (n-1) off-diagonal elements of the tridiagonal matrix T.\n*\n* E2 (input) DOUBLE PRECISION array, dimension (N-1)\n* The (n-1) squared off-diagonal elements of the tridiagonal matrix T.\n*\n* PIVMIN (input) DOUBLE PRECISION\n* The minimum pivot allowed in the Sturm sequence for T.\n*\n* NSPLIT (input) INTEGER\n* The number of diagonal blocks in the matrix T.\n* 1 <= NSPLIT <= N.\n*\n* ISPLIT (input) INTEGER array, dimension (N)\n* The splitting points, at which T breaks up into submatrices.\n* The first submatrix 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* (Only the first NSPLIT elements will actually be used, but\n* since the user cannot know a priori what value NSPLIT will\n* have, N words must be reserved for ISPLIT.)\n*\n* M (output) INTEGER\n* The actual number of eigenvalues found. 0 <= M <= N.\n* (See also the description of INFO=2,3.)\n*\n* W (output) DOUBLE PRECISION array, dimension (N)\n* On exit, the first M elements of W will contain the\n* eigenvalue approximations. DLARRD computes an interval\n* I_j = (a_j, b_j] that includes eigenvalue j. The eigenvalue\n* approximation is given as the interval midpoint\n* W(j)= ( a_j + b_j)/2. The corresponding error is bounded by\n* WERR(j) = abs( a_j - b_j)/2\n*\n* WERR (output) DOUBLE PRECISION array, dimension (N)\n* The error bound on the corresponding eigenvalue approximation\n* in W.\n*\n* WL (output) DOUBLE PRECISION\n* WU (output) DOUBLE PRECISION\n* The interval (WL, WU] contains all the wanted eigenvalues.\n* If RANGE='V', then WL=VL and WU=VU.\n* If RANGE='A', then WL and WU are the global Gerschgorin bounds\n* on the spectrum.\n* If RANGE='I', then WL and WU are computed by DLAEBZ from the\n* index range specified.\n*\n* IBLOCK (output) INTEGER array, dimension (N)\n* At each row/column j where E(j) is zero or small, the\n* matrix T is considered to split into a block diagonal\n* matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which\n* block (from 1 to the number of blocks) the eigenvalue W(i)\n* belongs. (DLARRD may use the remaining N-M elements as\n* workspace.)\n*\n* INDEXW (output) INTEGER array, dimension (N)\n* The indices of the eigenvalues within each block (submatrix);\n* for example, INDEXW(i)= j and IBLOCK(i)=k imply that the\n* i-th eigenvalue W(i) is the j-th eigenvalue in block k.\n*\n* WORK (workspace) DOUBLE PRECISION array, dimension (4*N)\n*\n* IWORK (workspace) INTEGER array, dimension (3*N)\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: if INFO = -i, the i-th argument had an illegal value\n* > 0: some or all of the eigenvalues failed to converge or\n* were not computed:\n* =1 or 3: Bisection failed to converge for some\n* eigenvalues; these eigenvalues are flagged by a\n* negative block number. The effect is that the\n* eigenvalues may not be as accurate as the\n* absolute and relative tolerances. This is\n* generally caused by unexpectedly inaccurate\n* arithmetic.\n* =2 or 3: RANGE='I' only: Not all of the eigenvalues\n* IL:IU were found.\n* Effect: M < IU+1-IL\n* Cause: non-monotonic arithmetic, causing the\n* Sturm sequence to be non-monotonic.\n* Cure: recalculate, using RANGE='A', and pick\n* out eigenvalues IL:IU. In some cases,\n* increasing the PARAMETER \"FUDGE\" may\n* make things work.\n* = 4: RANGE='I', and the Gershgorin interval\n* initially used was too small. No eigenvalues\n* were computed.\n* Probable cause: your machine has sloppy\n* floating-point arithmetic.\n* Cure: Increase the PARAMETER \"FUDGE\",\n* recompile, and try again.\n*\n* Internal Parameters\n* ===================\n*\n* FUDGE DOUBLE PRECISION, default = 2\n* A \"fudge factor\" to widen the Gershgorin intervals. Ideally,\n* a value of 1 should work, but on machines with sloppy\n* arithmetic, this needs to be larger. The default for\n* publicly released versions should be large enough to handle\n* the worst machine around. Note that this has no effect\n* on accuracy of the solution.\n*\n* Based on contributions by\n* W. Kahan, University of California, Berkeley, USA\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\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n m, w, werr, wl, wu, iblock, indexw, info = NumRu::Lapack.dlarrd( range, order, vl, vu, il, iu, gers, reltol, d, e, e2, pivmin, nsplit, isplit, [: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_range = argv[0];
rblapack_order = argv[1];
rblapack_vl = argv[2];
rblapack_vu = argv[3];
rblapack_il = argv[4];
rblapack_iu = argv[5];
rblapack_gers = argv[6];
rblapack_reltol = argv[7];
rblapack_d = argv[8];
rblapack_e = argv[9];
rblapack_e2 = argv[10];
rblapack_pivmin = argv[11];
rblapack_nsplit = argv[12];
rblapack_isplit = argv[13];
if (argc == 14) {
} else if (rblapack_options != Qnil) {
} else {
}
range = StringValueCStr(rblapack_range)[0];
vl = NUM2DBL(rblapack_vl);
il = NUM2INT(rblapack_il);
reltol = NUM2DBL(rblapack_reltol);
pivmin = NUM2DBL(rblapack_pivmin);
if (!NA_IsNArray(rblapack_isplit))
rb_raise(rb_eArgError, "isplit (14th argument) must be NArray");
if (NA_RANK(rblapack_isplit) != 1)
rb_raise(rb_eArgError, "rank of isplit (14th argument) must be %d", 1);
n = NA_SHAPE0(rblapack_isplit);
if (NA_TYPE(rblapack_isplit) != NA_LINT)
rblapack_isplit = na_change_type(rblapack_isplit, NA_LINT);
isplit = NA_PTR_TYPE(rblapack_isplit, integer*);
order = StringValueCStr(rblapack_order)[0];
iu = NUM2INT(rblapack_iu);
if (!NA_IsNArray(rblapack_d))
rb_raise(rb_eArgError, "d (9th argument) must be NArray");
if (NA_RANK(rblapack_d) != 1)
rb_raise(rb_eArgError, "rank of d (9th 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 isplit");
if (NA_TYPE(rblapack_d) != NA_DFLOAT)
rblapack_d = na_change_type(rblapack_d, NA_DFLOAT);
d = NA_PTR_TYPE(rblapack_d, doublereal*);
if (!NA_IsNArray(rblapack_e2))
rb_raise(rb_eArgError, "e2 (11th argument) must be NArray");
if (NA_RANK(rblapack_e2) != 1)
rb_raise(rb_eArgError, "rank of e2 (11th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_e2) != (n-1))
rb_raise(rb_eRuntimeError, "shape 0 of e2 must be %d", n-1);
if (NA_TYPE(rblapack_e2) != NA_DFLOAT)
rblapack_e2 = na_change_type(rblapack_e2, NA_DFLOAT);
e2 = NA_PTR_TYPE(rblapack_e2, doublereal*);
vu = NUM2DBL(rblapack_vu);
if (!NA_IsNArray(rblapack_e))
rb_raise(rb_eArgError, "e (10th argument) must be NArray");
if (NA_RANK(rblapack_e) != 1)
rb_raise(rb_eArgError, "rank of e (10th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_e) != (n-1))
rb_raise(rb_eRuntimeError, "shape 0 of e must be %d", n-1);
if (NA_TYPE(rblapack_e) != NA_DFLOAT)
rblapack_e = na_change_type(rblapack_e, NA_DFLOAT);
e = NA_PTR_TYPE(rblapack_e, doublereal*);
if (!NA_IsNArray(rblapack_gers))
rb_raise(rb_eArgError, "gers (7th argument) must be NArray");
if (NA_RANK(rblapack_gers) != 1)
rb_raise(rb_eArgError, "rank of gers (7th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_gers) != (2*n))
rb_raise(rb_eRuntimeError, "shape 0 of gers must be %d", 2*n);
if (NA_TYPE(rblapack_gers) != NA_DFLOAT)
rblapack_gers = na_change_type(rblapack_gers, NA_DFLOAT);
gers = NA_PTR_TYPE(rblapack_gers, doublereal*);
nsplit = NUM2INT(rblapack_nsplit);
{
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_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*);
work = ALLOC_N(doublereal, (4*n));
iwork = ALLOC_N(integer, (3*n));
dlarrd_(&range, &order, &n, &vl, &vu, &il, &iu, gers, &reltol, d, e, e2, &pivmin, &nsplit, isplit, &m, w, werr, &wl, &wu, iblock, indexw, work, iwork, &info);
free(work);
free(iwork);
rblapack_m = INT2NUM(m);
rblapack_wl = rb_float_new((double)wl);
rblapack_wu = rb_float_new((double)wu);
rblapack_info = INT2NUM(info);
return rb_ary_new3(8, rblapack_m, rblapack_w, rblapack_werr, rblapack_wl, rblapack_wu, rblapack_iblock, rblapack_indexw, rblapack_info);
}
void
init_lapack_dlarrd(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "dlarrd", rblapack_dlarrd, -1);
}
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