PRACTICAL No.3

1) Multiplication Table

#include <apop.h>int main(){

gsl_matrix *m = gsl_matrix_alloc (20, 15);gsl_matrix_set_all (m, 1);for (int i=0; i< m->size1; i++){

Apop_matrix_row(m, i, one_row);gsl_vector_scale(one_row, i+1);

}for (int i=0; i< m->size2; i++){

Apop_matrix_col(m, i, one_col);gsl_vector_scale(one_col, i+1);

}apop_matrix_show(m);gsl_matrix_free(m);

}

TAXES.C

#include <apop.h>double calc_taxes(double income){

double cutoffs[] = {0, 11200, 42650, 110100, 178350, 349700, INFINITY};double rates[] = {0, 0.10, .15, .25, .28, .33, .35};double tax = 0;int bracket = 1;income -= 7850; income -= 3400*3; while (income > 0){

tax += rates[bracket] * GSL_MIN(income, cutoffs[bracket]-cutoffs[bracket-1]);income -= cutoffs[bracket];bracket ++;

}return tax;}int main(){

apop_db_open("data-census.db");strncpy(apop_opts.db_name_column,"geo_name", 100);apop_data *d = apop_query_to_data("select geo_name, Household_median_in as income\from income where sumlevel = '040'\ order by household_median_in desc");apop_col_t(d, "income", income_vector);d->vector = apop_vector_map(income_vector, calc_taxes);apop_name_add(d->names, "tax owed", 'v');apop_data_show(d);

}

Practical 3

Plotting a vector

#include <apop.h>void plot_matrix_now(gsl_matrix *data){

static FILE *gp = NULL;if (!gp)gp = popen("gnuplot -persist", "w");if (!gp){

printf("Couldn't open Gnuplot.\n");return;

}fprintf(gp,"reset; plot '-' \n");apop_matrix_print(data, .output_pipe=gp);fflush(gp);

}int main(){

apop_db_open("data-climate.db");plot_matrix_now(apop_query_to_matrix("select (year*12+month)/12., temp from temp"));

}

Eigen vector

#include<apop.h>apop_data *query_data(){

apop_db_open("data-census.db");return apop_query_to_data(" select postcode as row_names,m_per_100_f, population/1e6 as population, median_age from geography, income,demos,postcodes where income.sumlevel= '040' and geography.geo_id = demos.geo_id and income.geo_name = postcodes.state and geography.geo_id = income.geo_id ");

}void show_projection(gsl_matrix *pc_space, apop_data *data){

fprintf(stderr,"The eigenvectors:\n");apop_matrix_print(pc_space, .output_pipe=stderr);apop_data *projected = apop_dot(data, apop_matrix_to_data(pc_space));printf("plot '-' using 2:3:1 with labels\n");apop_data_show(projected);

}int main()

{

apop_plot_lattice(query_data(), "out");

}

Practical 4

bernoulli distribution (bernoulli.c)

#include <stdio.h>#include <gsl/gsl_randist.h>intmain (void){

int i;double p = 0.6;float sum=0;/* prints probability distibution table*/printf("random variable|||probability |||cumulative prob.\n");printf("-------------------------------------------------------\n");for (i = 0; i <= 1; i++)

{float k = gsl_ran_bernoulli_pdf (i,p);sum=sum+k;printf("%d\t\t%f\t\t%f\n",i,k,sum);

}printf("\n");return 0;}

binomial distribution (binomial.c)

#include <stdio.h>#include <gsl/gsl_randist.h>Int main (void){

int i,n=5;double p = 0.6;float sum=0;/* prints probability distibution table*/printf("random variable|||probability |||cumulative prob.\n");printf("-------------------------------------------------------\n");for (i = 0; i <= n; i++){

float k = gsl_ran_binomial_pdf (i,p,n);sum=sum+k;printf("%d\t\t%f\t\t%f\n",i,k,sum);

}printf("\n");return 0;

}

Poisson distribution (poi.c)

#include <stdio.h>#include <gsl/gsl_randist.h>Int main (void){

int i, n = 10;double mu = 3.0;float sum=0;/* prints probability distibution table*/printf("random variable|||probability |||cumulative prob.\n");printf("-------------------------------------------------------\n");for (i = 0; i <= n; i++){

float k = gsl_ran_poisson_pdf (i,mu);sum=sum+k;printf("%d\t\t%f\t\t%f\n",i,k,sum);

}printf("\n");return 0;

}

Uniform distribution(uniform.c)

#include <stdio.h>#include <gsl/gsl_randist.h>Int main (void){

double x;int a,b ;printf("enter vaue for x ,a,b \n");scanf("%f",&x);scanf("%d",&a);scanf("%d",&b);float sum=0;/* prints probability distibution table*/printf("random variable|||probability \n");printf("-------------------------------------------------------\n");float k = (float)gsl_ran_flat_pdf (x,a,b);printf("%f\t\t%f\n",x,k);

return 0;

}

Multinomial distribution (multinomial.c)

#include <stdio.h>#include <gsl/gsl_randist.h>int main (void){

int k=3;const double p[]={0.2,0.4,0.4};const unsigned int n[]={2,3,4};/* prints probability */printf("random variable|||probability \n");printf("-------------------------------------------------------\n");double pmf =gsl_ran_multinomial_pdf(k,p,n);printf("%3.9f\n",pmf);return 0;

}

Hypergeometric distribution (hyper.c)

#include <stdio.h>#include <gsl/gsl_randist.h>int main (void){

int x,s,f,n;n=6;x=2;//random variables=13;//successf=39;//failure/* prints probability */printf("random variable|||probability \n");printf("-----------------------------------\n");double pmf =gsl_ran_hypergeometric_pdf(x,s,f,n);printf("%d %3.6f\n",x,pmf);return 0;

}

continous distributions (contdist.c)

#include <stdio.h>#include <math.h>#include <gsl/gsl_rng.h>#include <gsl/gsl_randist.h>#include <gsl/gsl_cdf.h>void normal();void beta();void gamma1();void exponential();void lognormal();int main(){

int choice;printf("continous distributions\n");printf("-----------------------\n");printf("1:Normal distribution\n");printf("2:Gamma distribution\n");printf("3:Exponential distribution\n");printf("4:Beta distribution\n");printf("5:Lognormal distribution\n");printf("enter your choice\n");scanf("%d",&choice);switch(choice){

case 1:normal();break;case 2:gamma1();break;case 3:exponential();break;case 4:beta();break;

case 5:lognormal();break;default:printf("wrong choice\n");

}return 0;

}void normal(){

double P, Q;double x = 10;double sigma=5;double pdf;printf("Normal distribution :x=%f sigma=%f\n",x,sigma);pdf = gsl_ran_gaussian_pdf (x,sigma);printf ("prob(x = %f) = %f\n", x, pdf);P = gsl_cdf_gaussian_P (x,sigma);printf ("prob(x < %f) = %f\n", x, P);Q = gsl_cdf_gaussian_Q (x,sigma);printf ("prob(x > %f) = %f\n", x, Q);x = gsl_cdf_gaussian_Pinv (P,sigma);printf ("Pinv(%f) = %f\n", P, x);x = gsl_cdf_gaussian_Qinv (Q,sigma);printf ("Qinv(%f) = %f\n", Q, x);

}void gamma1(){

double P, Q;double x = 1.5;double a=1;double b=2;double pdf; printf("Gamma distribution :x=%f a=%f b=%f\n",x,a,b);pdf = gsl_ran_gamma_pdf (x,a,b);printf ("prob(x = %f) = %f\n", x, pdf);P = gsl_cdf_gamma_P (x,a,b);

printf ("prob(x < %f) = %f\n", x, P);Q = gsl_cdf_gamma_Q (x,a,b);printf ("prob(x > %f) = %f\n", x, Q);x = gsl_cdf_gamma_Pinv (P,a,b);printf ("Pinv(%f) = %f\n", P, x);x = gsl_cdf_gamma_Qinv (Q,a,b);printf ("Qinv(%f) = %f\n", Q, x);

}void exponential(){

double P, Q;double x = 0.05;double lambda=2;double pdf;printf("Exponential distribution :x=%f lambda=%f\n",x,lambda);pdf = gsl_ran_exponential_pdf (x,lambda);printf ("prob(x = %f) = %f\n", x, pdf);P = gsl_cdf_exponential_P (x,lambda);printf ("prob(x < %f) = %f\n", x, P);Q = gsl_cdf_exponential_Q (x,lambda);printf ("prob(x > %f) = %f\n", x, Q);x = gsl_cdf_exponential_Pinv (P,lambda);printf ("Pinv(%f) = %f\n", P, x);x = gsl_cdf_exponential_Qinv (Q,lambda);printf ("Qinv(%f) = %f\n", Q, x);

}void beta(){

double P, Q;double x = 0.8;double a=0.5;double b=0.5;double pdf;printf("Beta distribution :x=%f a=%f b=%f\n",x,a,b);pdf = gsl_ran_beta_pdf (x,a,b);printf ("prob(x = %f) = %f\n", x, pdf);P = gsl_cdf_beta_P (x,a,b);

printf ("prob(x < %f) = %f\n", x, P);Q = gsl_cdf_beta_Q (x,a,b);printf ("prob(x > %f) = %f\n", x, Q);x = gsl_cdf_beta_Pinv (P,a,b);printf ("Pinv(%f) = %f\n", P, x);x = gsl_cdf_beta_Qinv (Q,a,b);printf ("Qinv(%f) = %f\n", Q, x);

}void lognormal(){

double P, Q;double x = 4;double zeta=2;double sigma=1.5;double pdf;printf("Lognormal distribution :x=%f zeta=%f sigma=%f\n",x,zeta,sigma);pdf = gsl_ran_lognormal_pdf (x,zeta,sigma);printf ("prob(x = %f) = %f\n", x, pdf);P = gsl_cdf_lognormal_P (x,zeta,sigma);printf ("prob(x < %f) = %f\n", x, P);Q = gsl_cdf_lognormal_Q (x,zeta,sigma);printf ("prob(x > %f) = %f\n", x, Q);x = gsl_cdf_lognormal_Pinv (P,zeta,sigma);printf ("Pinv(%f) = %f\n", P, x);

x = gsl_cdf_lognormal_Qinv (Q,zeta,sigma);printf ("Qinv(%f) = %f\n", Q, x);

}

Practical No. 5

Implementing regression

#include <stdio.h>#include <gsl/gsl_fit.h>int main (void){

int i, n = 4;double x[4] = { 1970, 1980, 1990, 2000 };double y[4] = { 12, 11, 14, 13 };double w[4] = { 0.1, 0.2, 0.3, 0.4 };

double c0, c1, cov00, cov01, cov11, chisq;gsl_fit_wlinear (x, 1, w, 1, y, 1, n,&c0, &c1, &cov00, &cov01, &cov11,&chisq);printf ("# best fit: Y = %g + %g X\n", c0, c1);printf ("# covariance matrix:\n");printf ("# [ %g, %g\n# %g, %g]\n",cov00, cov01, cov01, cov11);printf ("# chisq = %g\n", chisq);for (i = 0; i < n; i++)printf ("data: %g %g %g\n",x[i], y[i], 1/sqrt(w[i]));printf ("\n");for (i = -30; i < 130; i++){

double xf = x[0] + (i/100.0) * (x[n-1] - x[0]);double yf, yf_err;gsl_fit_linear_est (xf,c0, c1,cov00, cov01, cov11,&yf, &yf_err);printf ("fit: %g %g\n", xf, yf);printf ("hi : %g %g\n", xf, yf + yf_err);printf ("lo : %g %g\n", xf, yf - yf_err)

}return 0;

}

Implementing goodness of fit Chi Square

#include <apop.h>int main(){

apop_db_open("data-climate.db");apop_data *precip = apop_query_to_data("select PCP from precip");apop_model *est = apop_estimate(precip, apop_normal);apop_data *precip_binned = apop_data_to_bins(precip/*,.bin_count=180*/);apop_model *datahist = apop_estimate(precip_binned, apop_pmf);apop_model *modelhist = apop_model_to_pmf(.model=est,.binspec=apop_data_get_page(precip_binned, "<binspec>"), .draws=1e5);double scaling = apop_sum(datahist->data->weights)/apop_sum(modelhist->data->weights);gsl_vector_scale(modelhist->data->weights, scaling);apop_data_show(apop_histograms_test_goodness_of_fit(datahist,modelhist));

}

Implement testing with likelihood

#include <apop.h>double sin_square(apop_data *data, apop_model *m){

double x = apop_data_get(m->parameters, 0, -1);return -sin(x)*gsl_pow_2(x);

}apop_model sin_sq_model ={"-sin(x) times x^2",1, .p = sin_square};void do_search(int number, char *name, char *trace){

apop_model *out;

double p[] = {0};double result;char *outf;asprintf(&outf, "localmax_out/%s.gplot", trace);Apop_model_add_group(&sin_sq_model, apop_mle,.starting_pt= p,.method= number, .tolerance= 1e-4,.mu_t= 1.25, .trace_path= outf);out = apop_estimate(NULL, sin_sq_model);result = gsl_vector_get(out->parameters->vector, 0);printf("The %s algorithm found %g.\n", name, result);Apop_settings_rm_group(&sin_sq_model, apop_mle);

}int main(){

system ("mkdir -p localmax_out; rm -f localmax_out/*.gplot");apop_opts.verbose ++;do_search(APOP_SIMPLEX_NM, "N-M Simplex", "simplex");do_search(APOP_CG_FR, "F-R Conjugate gradient", "fr");do_search(APOP_SIMAN, "Simulated annealing", "siman");do_search(APOP_RF_NEWTON, "Root-finding", "root");fflush(NULL);system("sed -i \"1iplot '-'\" localmax_out/*.gplot");

}

Comparing 2 models using likelihood ratio#include <apop.h>apop_model * dummies(int slope_dummies){

apop_data *d = apop_query_to_mixed_data("mmt", "select riders, year-1977, line \from riders, lines \where riders.station=lines.station");apop_data *dummified = apop_data_to_dummies(d, 0, 't', .append='y',.remove='y');if (slope_dummies){

apop_col(d, 1, yeardata);for(int i=0; i < dummified->matrix->size2; i ++){apop_col(dummified, i, c);gsl_vector_mul(c, yeardata);

}}apop_model *out = apop_estimate(dummified, apop_ols);apop_model_show(out);return out;}int main(){

apop_db_open("data-metro.db");printf("With constant dummies:\n"); dummies(0);printf("With slope dummies:\n"); dummies(1);

}void show_normal_test(apop_model *unconstrained, apop_model*constrained, int n){

double statistic = (apop_data_get(unconstrained->info, .rowname="loglikelihood")- apop_data_get(constrained->info, .rowname="loglikelihood"))/sqrt(n);double confidence = gsl_cdf_gaussian_P(fabs(statistic), 1); //one-tailed.printf("The Normal statistic is: %g, so reject the null of no differencebetween models ""with %g%% confidence.\n", statistic, confidence*100);

}int main(){

apop_db_open("data-metro.db");apop_model *m0 = dummies(0);apop_model *m1 = dummies(1);show_normal_test(m0, m1, m0->data->matrix->size1);

}

PRACTICAL NO.-6

Generate random numbers using Monte Carlo method using#include <stdio.h>#include <gsl/gsl_rng.h>gsl_rng * r; /* global generator */int main (void){

const gsl_rng_type * T;gsl_rng_env_setup();T = gsl_rng_default;r = gsl_rng_alloc (T);printf ("generator type: %s\n", gsl_rng_name (r));printf ("seed = %lu\n", gsl_rng_default_seed);printf ("first value = %lu\n", gsl_rng_get (r));gsl_rng_free (r);return 0;

}

using exponential distribution#include <stdio.h>#include <stdlib.h>#include <math.h>#include <gsl/gsl_rng.h>#include <gsl/gsl_randist.h>int main(int argc, char *argv[]){

int i,n;float x,alpha;gsl_rng *r=gsl_rng_alloc(gsl_rng_mt19937); /* initialises GSL RNG */n=atoi(argv[1]);alpha=atof(argv[2]);x=0;for (i=0;i<n;i++){x=alpha*x + gsl_ran_exponential(r,1);

printf(" %2.4f \n",x);}return(0);}

Generating uniform random numbers in the range [0.0, 1.0) using uniformDistribution

#include <stdio.h>#include <gsl/gsl_rng.h>int main (void){

const gsl_rng_type * T;gsl_rng * r;int i, n = 10;gsl_rng_env_setup();T = gsl_rng_default;r = gsl_rng_alloc (T);for (i = 0; i < n; i++){

double u = gsl_rng_uniform (r);printf ("%.5f\n", u);

}gsl_rng_free (r);return 0;

}

Using binomial distribution#include <stdio.h>#include <gsl/gsl_rng.h>#include <gsl/gsl_randist.h>int main (void){

const gsl_rng_type * T;gsl_rng * r;int i, n = 10;/* create a generator chosen by the

environment variable GSL_RNG_TYPE */gsl_rng_env_setup();T = gsl_rng_default;r = gsl_rng_alloc (T);float p=0.3;/* print n random variates chosen fromthe binomial distribution with meanparameter mu */for (i = 0; i < n; i++){

unsigned int k = gsl_ran_binomial(r, p,n);printf (" %u", k);

}printf ("\n");gsl_rng_free (r);return 0;

}

Practical No. 7T-Test#include <apop.h>int main(){

apop_db_open("data-census.db");gsl_vector *n = apop_query_to_vector("select in_per_capita fromincome ""where state= (select state from geography where name ='NorthDakota')");gsl_vector *s = apop_query_to_vector("select in_per_capita from income""where state= (select state from geography where name ='SouthDakota')");apop_data *t = apop_t_test(n,s);apop_data_show(t); //show the whole output set...printf ("\n confidence: %g\n", apop_data_get(t, .rowname="conf.*2tail")); //...or just one value.

}

F-TEST#include "eigenbox.h"int main(){

double line[] = {0, 0, 0, 1};apop_data *constr = apop_line_to_data(line, 1, 1, 3);apop_data *d = query_data();apop_model *est = apop_estimate(d, apop_ols);apop_model_show(est);apop_data_show(apop_f_test(est, constr));

}

Practical No 8ANOVA#include <apop.h>int main(){apop_db_open("data-metro.db");char joinedtab[] = "(select year, riders, line \from riders, lines \where riders.station = lines.station)";apop_data_show(apop_anova(joinedtab, "riders", "line", "year"));}