EL VALOR DE PI USANDO EL MÉTODO MONTE CARLO EN FORTRAN, SCILAB 5.5 Y MATLAB
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This document describes using the Monte Carlo method to estimate the value of pi in Fortran, Scilab, MATLAB, and Scilab. It generates random points in a unit circle and square, counts the number that fall in the circle, and uses that to calculate an approximation of pi. Code examples are provided to generate the random points, classify them as inside or outside the circle, and calculate pi based on the results. Plots of the points are also generated.
![USANDO MATLAB TENEMOS:
rand('state',123)
n = 5000;
XY=rand(n,2)*2-1;
isin=sum(XY.^2,2)<1;
m=sum(isin);
piestimate=4*m/n;
pi;
figure('color',[1,1,1]);
plot(XY(isin,1),XY(isin,2),'b.');
axis equal;
USANDO SCILAB TENEMOS:
function [xy, isin, piest]=mcpi(n)
xy = rand(n,2);
xy = xy * 2 - 1;](https://image.slidesharecdn.com/montecarlo-150821210444-lva1-app6891/85/EL-VALOR-DE-PI-USANDO-EL-METODO-MONTE-CARLO-EN-FORTRAN-SCILAB-5-5-Y-MATLAB-5-320.jpg)
![isin = sum(xy .^ 2, 2) < 1;
m = sum(isin);
piest = 4 * m/n;
endfunction
[xy,isin,piest]=mcpi(5000);
plot(xy(isin,1),xy(isin,2),'b.');
mtlb_axis("equal");
disp('pi_estimado');
disp(piest);](https://image.slidesharecdn.com/montecarlo-150821210444-lva1-app6891/85/EL-VALOR-DE-PI-USANDO-EL-METODO-MONTE-CARLO-EN-FORTRAN-SCILAB-5-5-Y-MATLAB-6-320.jpg)
EL VALOR DE PI USANDO EL MÉTODO MONTE CARLO EN FORTRAN, SCILAB 5.5 Y MATLAB
- 1. Año de la Diversificación Productiva y del Fortalecimiento de la Educación UNIVERSIDAD NACIONAL DEL CALLAO FACULTAD DE CIENCIAS NATURALES Y MATEMÁTICA FÍSICA TEÓRICA COMPUTACIONAL II “EL VALOR DE PI USANDO EL MÉTODO MONTE CARLO EN FORTRAN Y SCILAB 5.5” MARCO ANTONIO ALPACA CHAMBA ESCUELA PROFESIONAL DE: FÍSICA PROGRAM IMPLICIT NONE REAL, INTEGER… 11 -06-2015
- 2. Encontrar el valor de pi por el Método MONTE CARLO: USANDO FORTRAN TENEMOS: PROGRAM MONTE_PI INTEGER::S,L REAL :: X,Y,PI,N,R OPEN(UNIT=12,FILE='DENTRO.TXT',STATUS='UNKNOWN',ACTION='WRITE') OPEN(UNIT=13,FILE='FUERA.TXT',STATUS='UNKNOWN',ACTION='WRITE') PRINT*,'' PRINT*, '=====================================================================' PRINT*,' EL VALOR DE PI USANDO EL METHODMONTE CARLO' PRINT*,'================================================================== ====' PRINT*,'' PRINT*, 'INGRESAR EL NUMBER DE HISTORIAS:' READ(5,*) N PRINT*,'' PRINT*,('*',I=1,79) PRINT '(5X,"RESULTADOS COMPUTACIONALES")' PRINT*,('*',I=1,79) DO J=1,N R=1 IF (MOD(J,500)==0) THEN !DO WHILE (K<N+1) S=0 D=0 CALL RANDOM_SEED() END IF ENDDO DO L=1,N CALL RANDOM_NUMBER(X) CALL RANDOM_NUMBER(Y) RALEAT=SQRT(X**2+Y**2) IF(RALEAT<=(R**2)) THEN S=S+1 WRITE(12,7)X,Y ELSE D=D+1 WRITE(13,9)X,Y END IF ENDDO PI=4*S/N 7 FORMAT(2X,2F8.4) 9 FORMAT(2X,2F8.4) PRINT*,'EL NUMBER APROXIMADO DE PI ES:',PI PRINT*,'' STOP END PROGRAM
- 3. USANDO SCILAB TENEMOS: A=read('DENTRO.txt',15654,2); x=A(:,1); y=A(:,2); B=read('FUERA.txt',4238,2); x1=B(:,1); y1=B(:,2); plot(x,y,'ro') plot(x1,y1,'b*') xlabel('coordenada aleatoria(X)','fontsize',4) ylabel('coordenada aleatoria (Y)','fontsize',4) title('EL VALOR DE PI USANDO MONTE CARLO','fontsize',5);
- 4. program rng_estimate_pi implicit none integer,parameter:: NUM_DRAWS_TOTAL =1e7 integer::countDrawsInCircle =0,i real :: randomPosition (2) integer:: seedArray (16) call date_and_time(values=seedArray (1:8)) call date_and_time(values=seedArray (9:16)) call random_seed(put=seedArray) do i=1,NUM_DRAWS_TOTAL call random_number( randomPosition ) if((randomPosition(1)**2 + randomPosition(2)**2)<1.0) then countDrawsInCircle = countDrawsInCircle + 1 end if end do print*,'' print*,"el valor estimado de pi es:=", & 4.0*(real(countDrawsInCircle )/ real(NUM_DRAWS_TOTAL )) end program rng_estimate_pi
- 5. USANDO MATLAB TENEMOS: rand('state',123) n = 5000; XY=rand(n,2)*2-1; isin=sum(XY.^2,2)<1; m=sum(isin); piestimate=4*m/n; pi; figure('color',[1,1,1]); plot(XY(isin,1),XY(isin,2),'b.'); axis equal; USANDO SCILAB TENEMOS: function [xy, isin, piest]=mcpi(n) xy = rand(n,2); xy = xy * 2 - 1;
- 6. isin = sum(xy .^ 2, 2) < 1; m = sum(isin); piest = 4 * m/n; endfunction [xy,isin,piest]=mcpi(5000); plot(xy(isin,1),xy(isin,2),'b.'); mtlb_axis("equal"); disp('pi_estimado'); disp(piest);