#18 (03/31/2025)

Octave (Poor man's MATLAB)

M-files

Function m-files
A script file that has the definition of your own function saved under the same name as the function name with m as the extension
Automatically loaded into Octave/MATLAB as if it were a built-in function.
function y=myfunction(x) y=x^3-x+1; end
function [x, y]=myfunction2(z) x=z^2; y=z^3; end
[a,b]=myfunction2(3);
Script m-files
A batch files that contain a set of statements that you would otherwise type from the keyboard.
To load a script m-file, type the file name (without extension, m) from the prompt.

Conditional statement

if a>2 
 disp('a is larger than 2')
end

----------------------------

for k=0:2:10
 disp(2*k)
end

----------------------------

while x < 5
    fprintf('x is %d\n', x);
    x = x + 1; % Increment x
end

----------------------------

x = 3;
switch x
    case 1
        disp('x is 1');
    case 2
        disp('x is 2');
    case 3
        disp('x is 3');
    otherwise
        disp('x is something else');
end

Sketch of comparison between C and Octave (MATLAB)

Quadratic equation

/* This program computes roots 
for quadratic equation. */
#include <stdio.h>
#include <math.h>

int main()
{
double a, b, c, disc, x1, x2;

printf("Enter 3 coeffs separated by space =");
scanf("%lf %lf %lf", &a, &b, &c);

disc=b*b-4*a*c;

if (disc<0) 
  { printf("Imaginary roots !\n"); return 0;}

x1= (-b + sqrt(disc))/(2*a);
x2= (-b - sqrt(disc))/(2*a);

printf("The roots are %lf and %lf. \n", x1, x2);

return 0;
}

a=input('Enter a = ');
b=input('Enter b = ');
c=input('Enter c = ');

disc=b^2-4*a*c;

if disc<0 
 disp('Imaginary roots !'); 
 return;
end;

x1=(-b-sqrt(disc))/(2*a);
x2=(-b+sqrt(disc))/(2*a);

fprintf('Roots are %f %f.\n', x1,x2);

Series summation

#include <stdio.h>
#include <math.h>

int main()
{
  int i;
  double sum = 0.0;
  for (i=0; i<1000; i++) 
    sum+=pow(-1,i)/(double)(2*i+1);
  printf("approx= %f true value= %lf\n ",
   4*sum, 4*atan(1.0));
return 0;
}

sum=0;

for k=0:1000 
 sum=sum+(-1)^k/(2*k+1); 
end

fprintf('Approx and exact values = %f %f.\n', 4*sum, 4*atan(1));
%% Note that "sum" is a reserved function in MATLAB/Octave.

Array

#include <stdio.h>
#include <math.h>

#define N 10

int main()
{
  float x[]={ -4.0, 1.2, 1.3, 2.5, -12.7, 
   9.0, 1.41, 65.2, -2.1, 2.36};
  int i;
  float sum = 0.0, average, variance;

  for (i=0; i<N; i++) sum+=x[i];
  average=sum/N;

  for (i=0; i<N; i++) 
   variance += pow(x[i]-average, 2);
  variance = variance/(N-1);

  printf("avg.= %f std. dev. = %f \n ",
    average, sqrt(variance));
  return 0;
}


N=10;
x=[-4 1.2 1.3 2.5 -12.7 9 1.41 65.2 -2.1 2.36];
sum=0;

for k=1:N
 sum=sum+x(k)
end

ave=sum/N;

var=0;
for k=1:N 
 var=var+(x(k)-ave)^2
end

var=var/(N-1);

fprintf('Average = %f, Standard deviation= %f.\n', ave, sqrt(var));

Functions

#include <stdio.h>
#include <math.h>
#define EPS 1.0e-6

double f(double x)
{
	return x*x-2;
}

double fp(double x)
{
	return 2*x;
}

double newton(double x)
{
	return x - f(x)/fp(x);
}

int main()
{
	double x1, x2;
	int i;

	printf("Enter initial guess  =");
	scanf("%lf", &x1);

	if (fp(x1)==0.0) {
		printf("No convergence.\n");
		return;
	}

	for (i=0;i<100;i++)
	{
		x2=newton(x1);
		if (fabs(x1-x2)< EPS) break;
		x1=x2;
	}

	printf("iteration = %d\n", i);
	printf("x= %lf\n", x1);
	return 0;
}

function y=f(x)
 y=x*x-2;
end
%
% Save this file as f.m
%

function y=fp(x)
 y=2*x;
end
%
% Save this file as fp.m
%

function y=newton(x)
 y=x-f(x)/fp(x);
end
%
% Save this file as newton.m
%

x1=input('Enter initial guess = ');

if fp(x1) <eps disp('No convergence !');return; end

for i=0:1:99 
 x2=newton(x1);
 if abs(x1-x2)<1e-10 break; end
 x1=x2;
end

fprintf('Iteration = %d\n', i);
fprintf('x = %f\n', x1);

File handling

#include <stdio.h>
int main()
{
   FILE *fp1, *fp2; 
   float a,b,c;
   fp1=fopen("junk1.dat","r");
   fscanf(fp1, "%f", &a);
   fclose(fp1)

   fp2=fopen("junk2.dat","w");
   fprintf(fp2,"This is the first file.\n");
   fclose(fp2);

   return 0;
}

fp1=fopen('junk1.dat', 'r');
a=fscanf(fp1, '%f');
fclose(fp1);

fp2=fopen('junk2.dat', 'w');
fprintf(fp2, 'This is the first line.\n');
fclose(fp2);

Example

Using the fft (Fast Fourier Transform) and ifft (Inverse Fourier Transform) functions in MATLAB/OCTAVE, remove the noise from the data above and restore the original signal.

To import the data for the graph above into Octave/MATLAB, copy the following line and paste it into an Octave/MATLAB window.

y=[10.5998892219547 6.32715963943755 10.7418564397819 2.9411380441864 3.92528722303704 2.71618105372149 8.4617982675031 2.88080944171953 10.4141369874892 8.476032583145489 8.964925641878001 2.67576180217924 2.85081602904105 4.85231952204638 9.38358373297042 5.16481823892903 3.14070937711815 8.699875412947099 7.21927535505636 2.47218681863012 10.2726165797325 8.500254531789301 11.1978723384108 4.05021576256659 5.77322285188005 11.7074336020358 9.400871264109419 3.71878673302725 2.78562995675663 10.2401630961987 5.84306139392084 8.82789975382806 10.3993315932854 6.74306607935596 8.750462753122729 5.90480261238712 2.06109189130585 4.40535088299872 2.41192556568313 11.8214297012451 7.44250415683415 10.032769833142 6.28901765997294 3.08186615850219 6.76595055198963 1.87944040723309 11.502034897292 2.44379054233261 8.128891862212489 6.34299932572315 11.4665531337537 1.86621678597553 1.75517155481136 5.19324241215718 10.5420445171336 5.82311606131353 3.92802666444074 9.77260830545065 8.76106471812958 6.54554696769744 1.4624210554122 2.92068844004011 4.48263396519447 8.739554957492571 3.33478186865148 6.24348148116228 5.87860301757644 9.666406406463951 2.70299316464037 5.01601721808914 9.26536386544738 5.09532896085959 2.62513156468079 2.21732831519875 1.99448077033047 2.62844514632015 3.79686487481322 3.24327464459272 1.2326443145944 1.45988948327978 7.1131310391548 10.0220774080567 3.93470053413877 0.894329071535874 8.60989560717546 9.63540704314247 3.00857673282652 2.79007156060591 3.15054286446995 4.53048193808516 5.38399703002467 9.4833604924008 0.6953758598942 5.19383112351193 0.844822890049153 1.34649332130299 2.98525367766063 3.31627989414972 6.76285368200212 7.04875327912278 0.251045988826941 1.9108517787023 3.69941930619919 1.52517099472442 4.831074892421 7.11794613059188 8.72763093617244 9.078887558695371 5.89633680306463 1.24117091269616 9.850706571849731 7.44945101897683 1.24091019808261 4.18876971107157 1.9176033724533 9.995859008983791 4.06138975672046 1.15781821760705 6.39682907701427 9.58794591991612 2.2193562129817 8.15089615664534 6.25502635127747 2.54857914360014 9.129606203212679 2.4736245862179 3.56168512084511 4.43958848222138 6.8931750450365 3.37222234736257 3.90894160047792 7.00239599243425 7.36043668237722 5.72237545873726 6.02879296664729 9.802065832144031 8.575987244312429 9.897577054258401 6.18523789886617 5.69121169822893 2.46963366954875 9.129229771930889 10.8952016844065 4.04009660589757 10.3743854729916 7.86000365182057 4.62415698798384 10.6214785584302 11.4224951621026 5.67326994393055 4.08637580957679 8.65738342494789 3.19239876321067 11.5201022637337 10.636312915602 9.82811239395342 3.70890071720701 11.5798531399931 11.3079723127561 2.91023922097878 4.62563348751362 1.94134261430337 10.1199743509774 3.39739911000981 6.74500334449411 8.170425024996179 5.56015657871609 7.5183998639944 9.724435694474771 6.0923080693899 3.59482558370596 6.31863247939307 4.52463371931999 4.10296747447814 9.695171467636451 4.18461466022538 5.80815539286633 8.77375948273572 3.89726672007424 2.4379111867341 2.53028144217005 8.599734675735849 5.73721564890586 9.31292716873403 2.30164223598104 10.1205267404267 6.46257375724972 1.61357790565941 8.83703123702375 9.241195975932539 1.39848359552096 4.04514624784499 4.45713558113789 5.40256645503303 9.458465543021051 10.1594053991668 1.57320417124056 10.025068241083 8.050843440082611 7.57425636264847 4.99279654689739 1.14890755632154 8.48815583223322 0.513616604704808 8.20951495224771 7.36944262027792 2.28314474381409 9.61805543347821 6.38395393390104 3.82496380452266 8.716233740636451 0.624777553892277 2.13639412542771 2.67182229714328 0.960693039360867 7.94782117163402 6.97092617961824 5.54658352916538 9.25358919832107 -0.0518943288602689 4.09372366108078 3.0771241498034 0.9687056105548451 7.58002335011327 0.964153518012499 4.05886921736417 1.30771587473559 7.28546269899251 2.60725514587506 0.181148813423656 7.50124107556926 1.78225486901118 7.93044999804643 8.726414919885549 8.64856640820909 1.81661636398602 8.15011697120986 7.48520651711012 8.821324599765621 6.77111885101838 4.83400122253399 2.39038025124365 3.22625506903038 1.55735245264944 4.56184163155081 1.75825250678772 0.269608991651202 0.197345665382678 4.06499325144136 6.52779016528276 8.09415174197148 2.37792649587988 8.6329654872403 7.66695265328003 1.99742029842287 0.0182366166899817];

To change the working directory, issue


cd c:/tmp

The following commands may be useful:


cd c:/tmp
% CD to the "c:/tmp" directory
%
plot(y);
f1=fft(y); % Fast Fourier Transform of y, i.e. frequency domain expression of y
plot(abs(f1)); % Since f1 is a set of complex numbers, we take only the absolute values.
%
% Examine the graph of f1 (in frequency) and determine the cut-off values.
%
% Passing only low frequency data (low pass filter)
%
for i=1:256
 if abs(f1(i)) < (your guess)
   f1(i)=0;
 end;
end;
%
% Inverse FFT on f1
%
y2=ifft(f1);
%
% y2 is real but there is some dust so chop them off.
%
y2=abs(y2);

plot(y2);

File translated from T_EX by T_TH, version 4.03.
On 30 Mar 2025, 19:15.