void w3j_sqrt_sq(mpq_t r, long j1, long j2, long j3, long m1, long m2, long m3)
{
mpz_t n,d,h;
mpz_init(n);
mpz_init(d);
mpz_init(h);
binomialCoefficient(n, 2*j1,j1-j2+j3);
binomialCoefficient(h, 2*j2,j1+j2-j3);
mpz_mul(n,n,h);
binomialCoefficient(h, 2*j3,-j1+j2+j3);
mpz_mul(n,n,h);;
mpq_set_z(r,n);
binomialCoefficient(d, 2*j1,j1+m1);
binomialCoefficient(h, 2*j2,j2+m2);
mpz_mul(d,d,h);
binomialCoefficient(h, 2*j3,j3+m3);
mpz_mul(d,d,h);
mpq_set_den(r,d);
mpq_canonicalize(r);
mpz_clear(d); mpz_clear(h); mpz_clear(n);
}
void Rational::mpqInit(mpq_t& mpq) const
{
mpz_t num, den;
numerator.mpzInit(num);
denominator.mpzInit(den);
mpq_init(mpq);
mpq_set_num(mpq, num);
mpq_set_den(mpq, den);
mpz_clear(num);
mpz_clear(den);
}
void ddd_mpq_set_si(mytype a,signed long b)
{
mpz_t nz, dz;
mpz_init(nz);
mpz_init(dz);
mpz_set_si(nz, b);
mpz_set_ui(dz, 1U);
mpq_set_num(a, nz);
mpq_set_den(a, dz);
mpz_clear(nz);
mpz_clear(dz);
}
/* Function to generate the hypergeometric pdf */
void hypergeometricpdf(mpfr_t *out,mpz_t mu, mpz_t d,unsigned int mi,unsigned int conns,unsigned int phi, mpz_t bc_b_ai[], mpz_t mu_bc[])
{
unsigned int dini=(unsigned int)conns;
unsigned int dmax=(unsigned int)conns;
mpz_t bcm_b_ai;
mpz_init(bcm_b_ai);
mpq_t quotient;
mpq_init(quotient);
unsigned int odex=0;
unsigned int di;
// unsigned int phi;
unsigned int bi;
unsigned int ai_cnt;
//loop over d, phi and beta
for(di=dini;di<=dmax;di=di++)
{
//for(phi=1;phi<=di;phi++)
//{
for(bi=0;bi<=mi;bi++)
{
for(ai_cnt=phi;ai_cnt<=di;ai_cnt++)
{
if((mi-bi)<=0) //Then the number of successful picks is the number of draws with probability 1
{
if(ai_cnt==di)
mpq_set_d(quotient,1);
else
mpq_set_d(quotient,0);
}
else
{
mpz_mul(bcm_b_ai,bc_b_ai[bi*(dmax+1)+(ai_cnt)],bc_b_ai[(mi-bi)*(dmax+1)+(di-ai_cnt)]);
mpq_set_num(quotient, bcm_b_ai);
mpq_set_den(quotient, mu_bc[di-1]);
mpq_canonicalize(quotient);
}
mpfr_set_q(*(out+odex),quotient,MPFR_RNDN);
odex++; //Address array with simple counter increment;
}
}
//}
}
mpz_clear(bcm_b_ai);
mpq_clear(quotient);
}
static CRATIONAL *_powf(CRATIONAL *a, double f, bool invert)
{
ulong p;
mpz_t num, den;
mpq_t n;
if (invert || (double)(int)f != f)
return NULL;
if (f < 0)
{
f = (-f);
invert = TRUE;
}
p = (ulong)f;
mpz_init(num);
mpz_pow_ui(num, mpq_numref(a->n), p);
mpz_init(den);
mpz_pow_ui(den, mpq_denref(a->n), p);
mpq_init(n);
if (invert)
mpz_swap(num, den);
if (mpz_cmp_si(den, 0) == 0)
{
GB.Error(GB_ERR_ZERO);
return NULL;
}
mpq_set_num(n, num);
mpq_set_den(n, den);
mpz_clear(num);
mpz_clear(den);
mpq_canonicalize(n);
return RATIONAL_create(n);
}
void __rat_approx_step(mpq_t res, mpz_t num, mpz_t den, mpz_t a,
mpz_t pnm2, mpz_t pnm1, mpz_t qnm2, mpz_t qnm1, mpz_t pn, mpz_t qn)
{
mpz_tdiv_qr(a,num,num,den);
/* pn = an pn-1 + pn-2
* qn = an qn-1 + qn-2 */
mpz_mul(pn,a,pnm1);
mpz_add(pn,pn,pnm2);
mpz_mul(qn,a,qnm1);
mpz_add(qn,qn,qnm2);
mpq_set_num(res,pn);
mpq_set_den(res,qn);
mpq_canonicalize(res);
/* Advance: pn-1 -> pn-2, pn -> pn-1, and for q */
mpz_set(pnm2,pnm1);
mpz_set(qnm2,qnm1);
mpz_set(pnm1,pn);
mpz_set(qnm1,qn);
mpz_swap(num,den);
}
static void
solve(char* file_name) {
ppl_Constraint_System_t ppl_cs;
#ifndef NDEBUG
ppl_Constraint_System_t ppl_cs_copy;
#endif
ppl_Generator_t optimum_location;
ppl_Linear_Expression_t ppl_le;
int dimension, row, num_rows, column, nz, i, j, type;
int* coefficient_index;
double lb, ub;
double* coefficient_value;
mpq_t rational_lb, rational_ub;
mpq_t* rational_coefficient;
mpq_t* objective;
ppl_Linear_Expression_t ppl_objective_le;
ppl_Coefficient_t optimum_n;
ppl_Coefficient_t optimum_d;
mpq_t optimum;
mpz_t den_lcm;
int optimum_found;
glp_mpscp glpk_mpscp;
glpk_lp = glp_create_prob();
glp_init_mpscp(&glpk_mpscp);
if (verbosity == 0) {
/* FIXME: find a way to suppress output from glp_read_mps. */
}
#ifdef PPL_LPSOL_SUPPORTS_TIMINGS
if (print_timings)
start_clock();
#endif /* defined(PPL_LPSOL_SUPPORTS_TIMINGS) */
if (glp_read_mps(glpk_lp, GLP_MPS_FILE, &glpk_mpscp, file_name) != 0)
fatal("cannot read MPS file `%s'", file_name);
#ifdef PPL_LPSOL_SUPPORTS_TIMINGS
if (print_timings) {
fprintf(stderr, "Time to read the input file: ");
print_clock(stderr);
fprintf(stderr, " s\n");
start_clock();
}
#endif /* defined(PPL_LPSOL_SUPPORTS_TIMINGS) */
glpk_lp_num_int = glp_get_num_int(glpk_lp);
if (glpk_lp_num_int > 0 && !no_mip && !use_simplex)
fatal("the enumeration solving method can not handle MIP problems");
dimension = glp_get_num_cols(glpk_lp);
/* Read variables constrained to be integer. */
if (glpk_lp_num_int > 0 && !no_mip && use_simplex) {
if (verbosity >= 4)
fprintf(output_file, "Integer variables:\n");
integer_variables = (ppl_dimension_type*)
malloc((glpk_lp_num_int + 1)*sizeof(ppl_dimension_type));
for (i = 0, j = 0; i < dimension; ++i) {
int col_kind = glp_get_col_kind(glpk_lp, i+1);
if (col_kind == GLP_IV || col_kind == GLP_BV) {
integer_variables[j] = i;
if (verbosity >= 4) {
ppl_io_fprint_variable(output_file, i);
fprintf(output_file, " ");
}
++j;
}
}
}
coefficient_index = (int*) malloc((dimension+1)*sizeof(int));
coefficient_value = (double*) malloc((dimension+1)*sizeof(double));
rational_coefficient = (mpq_t*) malloc((dimension+1)*sizeof(mpq_t));
ppl_new_Constraint_System(&ppl_cs);
mpq_init(rational_lb);
mpq_init(rational_ub);
for (i = 1; i <= dimension; ++i)
mpq_init(rational_coefficient[i]);
mpz_init(den_lcm);
if (verbosity >= 4)
fprintf(output_file, "\nConstraints:\n");
/* Set up the row (ordinary) constraints. */
num_rows = glp_get_num_rows(glpk_lp);
for (row = 1; row <= num_rows; ++row) {
/* Initialize the least common multiple computation. */
mpz_set_si(den_lcm, 1);
/* Set `nz' to the number of non-zero coefficients. */
nz = glp_get_mat_row(glpk_lp, row, coefficient_index, coefficient_value);
for (i = 1; i <= nz; ++i) {
set_mpq_t_from_double(rational_coefficient[i], coefficient_value[i]);
/* Update den_lcm. */
mpz_lcm(den_lcm, den_lcm, mpq_denref(rational_coefficient[i]));
}
lb = glp_get_row_lb(glpk_lp, row);
ub = glp_get_row_ub(glpk_lp, row);
set_mpq_t_from_double(rational_lb, lb);
set_mpq_t_from_double(rational_ub, ub);
mpz_lcm(den_lcm, den_lcm, mpq_denref(rational_lb));
mpz_lcm(den_lcm, den_lcm, mpq_denref(rational_ub));
ppl_new_Linear_Expression_with_dimension(&ppl_le, dimension);
for (i = 1; i <= nz; ++i) {
mpz_mul(tmp_z, den_lcm, mpq_numref(rational_coefficient[i]));
mpz_divexact(tmp_z, tmp_z, mpq_denref(rational_coefficient[i]));
ppl_assign_Coefficient_from_mpz_t(ppl_coeff, tmp_z);
ppl_Linear_Expression_add_to_coefficient(ppl_le, coefficient_index[i]-1,
ppl_coeff);
}
type = glp_get_row_type(glpk_lp, row);
add_constraints(ppl_le, type, rational_lb, rational_ub, den_lcm, ppl_cs);
ppl_delete_Linear_Expression(ppl_le);
}
free(coefficient_value);
for (i = 1; i <= dimension; ++i)
mpq_clear(rational_coefficient[i]);
free(rational_coefficient);
free(coefficient_index);
#ifndef NDEBUG
ppl_new_Constraint_System_from_Constraint_System(&ppl_cs_copy, ppl_cs);
#endif
/*
FIXME: here we could build the polyhedron and minimize it before
adding the variable bounds.
*/
/* Set up the columns constraints, i.e., variable bounds. */
for (column = 1; column <= dimension; ++column) {
lb = glp_get_col_lb(glpk_lp, column);
ub = glp_get_col_ub(glpk_lp, column);
set_mpq_t_from_double(rational_lb, lb);
set_mpq_t_from_double(rational_ub, ub);
/* Initialize the least common multiple computation. */
mpz_set_si(den_lcm, 1);
mpz_lcm(den_lcm, den_lcm, mpq_denref(rational_lb));
mpz_lcm(den_lcm, den_lcm, mpq_denref(rational_ub));
ppl_new_Linear_Expression_with_dimension(&ppl_le, dimension);
ppl_assign_Coefficient_from_mpz_t(ppl_coeff, den_lcm);
ppl_Linear_Expression_add_to_coefficient(ppl_le, column-1, ppl_coeff);
type = glp_get_col_type(glpk_lp, column);
add_constraints(ppl_le, type, rational_lb, rational_ub, den_lcm, ppl_cs);
ppl_delete_Linear_Expression(ppl_le);
}
mpq_clear(rational_ub);
mpq_clear(rational_lb);
/* Deal with the objective function. */
objective = (mpq_t*) malloc((dimension+1)*sizeof(mpq_t));
/* Initialize the least common multiple computation. */
mpz_set_si(den_lcm, 1);
mpq_init(objective[0]);
set_mpq_t_from_double(objective[0], glp_get_obj_coef(glpk_lp, 0));
for (i = 1; i <= dimension; ++i) {
mpq_init(objective[i]);
set_mpq_t_from_double(objective[i], glp_get_obj_coef(glpk_lp, i));
/* Update den_lcm. */
mpz_lcm(den_lcm, den_lcm, mpq_denref(objective[i]));
}
/* Set the ppl_objective_le to be the objective function. */
ppl_new_Linear_Expression_with_dimension(&ppl_objective_le, dimension);
/* Set value for objective function's inhomogeneous term. */
mpz_mul(tmp_z, den_lcm, mpq_numref(objective[0]));
mpz_divexact(tmp_z, tmp_z, mpq_denref(objective[0]));
ppl_assign_Coefficient_from_mpz_t(ppl_coeff, tmp_z);
ppl_Linear_Expression_add_to_inhomogeneous(ppl_objective_le, ppl_coeff);
/* Set values for objective function's variable coefficients. */
for (i = 1; i <= dimension; ++i) {
mpz_mul(tmp_z, den_lcm, mpq_numref(objective[i]));
mpz_divexact(tmp_z, tmp_z, mpq_denref(objective[i]));
ppl_assign_Coefficient_from_mpz_t(ppl_coeff, tmp_z);
ppl_Linear_Expression_add_to_coefficient(ppl_objective_le, i-1, ppl_coeff);
}
if (verbosity >= 4) {
fprintf(output_file, "Objective function:\n");
if (mpz_cmp_si(den_lcm, 1) != 0)
fprintf(output_file, "(");
ppl_io_fprint_Linear_Expression(output_file, ppl_objective_le);
}
for (i = 0; i <= dimension; ++i)
mpq_clear(objective[i]);
free(objective);
if (verbosity >= 4) {
if (mpz_cmp_si(den_lcm, 1) != 0) {
fprintf(output_file, ")/");
mpz_out_str(output_file, 10, den_lcm);
}
fprintf(output_file, "\n%s\n",
(maximize ? "Maximizing." : "Minimizing."));
}
ppl_new_Coefficient(&optimum_n);
ppl_new_Coefficient(&optimum_d);
ppl_new_Generator_zero_dim_point(&optimum_location);
optimum_found = use_simplex
? solve_with_simplex(ppl_cs,
ppl_objective_le,
optimum_n,
optimum_d,
optimum_location)
: solve_with_generators(ppl_cs,
ppl_objective_le,
optimum_n,
optimum_d,
optimum_location);
ppl_delete_Linear_Expression(ppl_objective_le);
if (glpk_lp_num_int > 0)
free(integer_variables);
if (optimum_found) {
mpq_init(optimum);
ppl_Coefficient_to_mpz_t(optimum_n, tmp_z);
mpq_set_num(optimum, tmp_z);
ppl_Coefficient_to_mpz_t(optimum_d, tmp_z);
mpz_mul(tmp_z, tmp_z, den_lcm);
mpq_set_den(optimum, tmp_z);
if (verbosity == 1)
fprintf(output_file, "Optimized problem.\n");
if (verbosity >= 2)
fprintf(output_file, "Optimum value: %.10g\n", mpq_get_d(optimum));
if (verbosity >= 3) {
fprintf(output_file, "Optimum location:\n");
ppl_Generator_divisor(optimum_location, ppl_coeff);
ppl_Coefficient_to_mpz_t(ppl_coeff, tmp_z);
for (i = 0; i < dimension; ++i) {
mpz_set(mpq_denref(tmp1_q), tmp_z);
ppl_Generator_coefficient(optimum_location, i, ppl_coeff);
ppl_Coefficient_to_mpz_t(ppl_coeff, mpq_numref(tmp1_q));
ppl_io_fprint_variable(output_file, i);
fprintf(output_file, " = %.10g\n", mpq_get_d(tmp1_q));
}
}
#ifndef NDEBUG
{
ppl_Polyhedron_t ph;
unsigned int relation;
ppl_new_C_Polyhedron_recycle_Constraint_System(&ph, ppl_cs_copy);
ppl_delete_Constraint_System(ppl_cs_copy);
relation = ppl_Polyhedron_relation_with_Generator(ph, optimum_location);
ppl_delete_Polyhedron(ph);
assert(relation == PPL_POLY_GEN_RELATION_SUBSUMES);
}
#endif
maybe_check_results(PPL_MIP_PROBLEM_STATUS_OPTIMIZED,
mpq_get_d(optimum));
mpq_clear(optimum);
}
ppl_delete_Constraint_System(ppl_cs);
ppl_delete_Coefficient(optimum_d);
ppl_delete_Coefficient(optimum_n);
ppl_delete_Generator(optimum_location);
glp_delete_prob(glpk_lp);
}
/* Function to calculate the expected number of unique codes
within each input success class */
void uniquecodes(mpfr_t *ucodes, int psiz, mpz_t n, unsigned long int mu, mpz_t ncodes ,mpfr_t *pdf,mpfr_prec_t prec)
{
//200 bits precision gives log[2^200] around 60 digits decimal precision
mpfr_t unity;
mpfr_init2(unity,prec);
mpfr_set_ui(unity,(unsigned long int) 1,MPFR_RNDN);
mpfr_t nunity;
mpfr_init2(nunity,prec);
mpfr_set_si(nunity,(signed long int) -1,MPFR_RNDN);
mpz_t bcnum;
mpz_init(bcnum);
mpfr_t bcnumf;
mpfr_init2(bcnumf,prec);
mpq_t cfrac;
mpq_init(cfrac);
mpfr_t cfracf;
mpfr_init2(cfracf,prec);
mpfr_t expargr;
mpfr_init2(expargr,prec);
mpfr_t r1;
mpfr_init2(r1,prec);
mpfr_t r2;
mpfr_init2(r2,prec);
// mpfr_t pdf[mu];
unsigned long int i;
int pdex;
int addr;
// for(i=0;i<=mu;i++)
// mpfr_init2(pdf[i],prec);
// inpdf(pdf,n,pin,mu,bcs,prec);
for(pdex=0;pdex<=psiz-1;pdex++)
{
for(i=0;i<=mu;i++)
{
addr=pdex*(mu+1)+i;
mpz_bin_ui(bcnum,n,i);
mpq_set_num(cfrac,ncodes);
mpq_set_den(cfrac,bcnum);
mpq_canonicalize(cfrac);
mpfr_set_q(cfracf,cfrac,MPFR_RNDN);
mpfr_mul(expargr,cfracf,*(pdf+addr),MPFR_RNDN);
mpfr_mul(expargr,expargr,nunity,MPFR_RNDN);
mpfr_exp(r1,expargr,MPFR_RNDN);
mpfr_sub(r1,unity,r1,MPFR_RNDN);
mpfr_set_z(bcnumf,bcnum,MPFR_RNDN);
mpfr_mul(r2,bcnumf,r1,MPFR_RNDN);
mpfr_set((*ucodes+addr),r2,MPFR_RNDN);
mpfr_round((*ucodes+addr),(*ucodes+addr));
}
}
mpfr_clear(unity);
mpfr_clear(nunity);
mpz_clear(bcnum);
mpfr_clear(bcnumf);
mpq_clear(cfrac);
mpfr_clear(cfracf);
mpfr_clear(expargr);
mpfr_clear(r1);
mpfr_clear(r2);
// for(i=0;i<=mu;i++)
// mpfr_clear(pdf[i]);
}
