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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 11: Eigenvalues and Eigenvectors"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.10: LU_Method.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 11.10\n",
+"//LU Method\n",
+"//Page no. 363\n",
+"clc;close;clear;\n",
+"\n",
+"A=[120,80,40,-16;80,120,16,-40;40,16,120,-80;-16,-40,-80,120];\n",
+"disp(A,'A =')\n",
+"L=eye(4,4);\n",
+"for l=1:20\n",
+"for j=1:4\n",
+" for i=1:j\n",
+" k=0\n",
+" for p=1:i-1\n",
+" k=k-A(i,p)*A(p,j)\n",
+" end\n",
+" A(i,j)=A(i,j)+k\n",
+" end\n",
+" for i=j+1:4\n",
+" k=0;\n",
+" for p=1:j-1\n",
+" k=k-A(i,p)*A(p,j)\n",
+" end\n",
+" A(i,j)=(A(i,j)+k)/A(j,j) \n",
+" end\n",
+"end\n",
+"disp(A,'Modified A = ')\n",
+" for i=1:4\n",
+" for j=1:4\n",
+" if i>j then\n",
+" L(i,j)=A(i,j)\n",
+" else\n",
+" U(i,j)=A(i,j)\n",
+" end\n",
+" end\n",
+"end\n",
+"disp(U,'U =',L,'L =')\n",
+"A=U*L;\n",
+"printf('\n\nAfter %i iterations, matrix A =\n\n',l)\n",
+"for i=1:4\n",
+" for j=1:4\n",
+" printf(' %.2f\t',A(i,j))\n",
+" end\n",
+" printf('\n')\n",
+"end\n",
+"end\n",
+"printf('\n\nTherefore the eigenvalues are the diagonal elements f the transformed triangular matrix are:\n\n')\n",
+"for i=1:4\n",
+" printf(' %.2f,',A(i,i))\n",
+"end"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.11: Generalized_Eigenvalue_Problem.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 11.11\n",
+"//Generalized Eigenvalue Problem\n",
+"//Page no. 365\n",
+"clc;close;clear;\n",
+"\n",
+"A=[1,1,0.5;1,1,0.25;0.5,0.25,2]\n",
+"B=[2,2,2;2,5,5;2,5,11]\n",
+"disp(B,'B =',A,'A =')\n",
+"for i=1:3\n",
+" G(i,i)=sqrt(B(i,i))\n",
+"end\n",
+"G=[B;eye(3,3)];\n",
+"\n",
+"//transformation to frobenius matrix\n",
+"for k=3:-1:2\n",
+" g(k)=0;\n",
+" for j=1:k-1\n",
+" if(g(k)<G(k,j))\n",
+" g(k)=G(k,j)\n",
+" p=j;\n",
+" end\n",
+" end\n",
+" if(g(k)~=0)\n",
+" for j=1:3\n",
+" r(1,j)=G(k,j)\n",
+" end\n",
+" for i=1:6\n",
+" G(i,k-1)=G(i,k-1)/g(k)\n",
+" end\n",
+" for j=1:3\n",
+" if(j~=k-1)\n",
+" l=G(k,j)\n",
+" for i=1:6\n",
+" G(i,j)=G(i,j)-l*G(i,k-1)\n",
+" end\n",
+" end\n",
+" end\n",
+" end\n",
+" for j=1:3\n",
+" for i=1:3\n",
+" c(i,1)=G(i,j)\n",
+" end\n",
+" G(k-1,j)=0\n",
+" for i=1:3\n",
+" G(k-1,j)=G(k-1,j)+r(1,i)*c(i,1)\n",
+" end\n",
+" end\n",
+"end\n",
+"\n",
+"//partition g\n",
+"for i=4:6\n",
+" for j=1:3\n",
+" T(i-3,j)=G(i,j)\n",
+" end\n",
+"end\n",
+"\n",
+"//eigenvalues computation\n",
+"p=poly(B,'x')\n",
+"a=roots(p)\n",
+"printf('\n\nDiagonalized Matrix B = \n\n')\n",
+"for i=1:3\n",
+" for j=1:3\n",
+" if i~=j then\n",
+" B(i,j)=0\n",
+" else\n",
+" B(i,j)=a(i)\n",
+" end\n",
+" end\n",
+"end\n",
+"disp(B)\n",
+"//eigenvectors computation\n",
+"for k=1:3\n",
+" m=2\n",
+" for l=1:3\n",
+" y(l,k)=a(k)^(m)\n",
+" m=m-1;\n",
+" end\n",
+"end\n",
+"printf('\n\n')\n",
+"\n",
+"\n",
+"for k=1:3\n",
+" for l=1:3\n",
+" y1(l,1)=y(l,1)\n",
+" y2(l,1)=y(l,2)\n",
+" y3(l,1)=y(l,3)\n",
+" end\n",
+" x1=T*y3;\n",
+" x2=T*y2;\n",
+" x3=T*y1;\n",
+"end\n",
+"printf('\n\nEigenvectors of B are :\n\n')\n",
+"for i=1:3\n",
+" printf('|%.5f|\t\t|%.5f|\t\t|%.5f|',x3(i,1),x2(i,1),x1(i,1))\n",
+" printf('\n')\n",
+"end\n",
+"x=[x3,x2,x1]\n",
+"\n",
+"\n",
+"\n",
+"\n",
+"\n",
+"B=[2,2,2;2,5,5;2,5,11]\n",
+"G=0\n",
+"for i=1:3\n",
+" for j=1:3\n",
+" if i==j then\n",
+" G(i,j)=sqrt(B(i,j))\n",
+" else\n",
+" G(i,j)=0;\n",
+" end\n",
+" end\n",
+"end\n",
+"\n",
+"B=inv(G)*x'*A*x*inv(G)\n",
+"disp(B,'Eigenvectors of A =')\n",
+"\n",
+"printf('\n\n\nNote : Computation Error in book in caculation of eigenvector of B thus for A')\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.1: Eigenvalues_and_Eigenvectors.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 11.1\n",
+"//Eigenvalues and Eigenvectors\n",
+"//Page no. 333\n",
+"clc;clear;close;\n",
+"\n",
+"A1=[0.6;0.2];A2=[-0.2;0.6];A3=[-0.6;-0.2];A4=[0.2;-0.6];\n",
+"T=[1.1,-0.3;-0.3,1.9];\n",
+"B1=T*A1;B2=T*A2;B3=T*A3;B4=T*A4;\n",
+"disp(B4,B3,B2,B1,'The transformed vectors are :')\n",
+"disp('These points lie on the ellipse:')\n",
+"printf(' 2 2\n(x-3y)+(3x+y)\n------ ------\n 16 4\n\n')\n",
+"A5=[0;2/sqrt(10)];\n",
+"disp('The vector (0,2/10^(1/2)) lies on the circle:')\n",
+"printf(' 2 2\nx + y = 4\n -\n 10\n\n')\n",
+"B5=T*A5;\n",
+"disp('Also lies on the same ellipse',B5)\n",
+"printf('\n\nWe can see that there is a linear relationship between the first 4 vectors and their respective transformend vectors through the scalars known as eigenvectors and eigenvalues respectively')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.2: Leverriers_Method.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 11.2\n",
+"//Leverrier's Method\n",
+"//Page no. 337\n",
+"clc;close;clear;\n",
+"\n",
+"A=[2,2,2;2,5,5;2,5,1];\n",
+"A1=A;\n",
+"C(1)=0;\n",
+" for j=1:3\n",
+" for k=1:3\n",
+" if(j==k)\n",
+" C(1)=C(1)+A1(j,k)\n",
+" end\n",
+" end\n",
+" end\n",
+" disp(A,'A=')\n",
+" disp(A1,'A1=')\n",
+" printf('\nC1=')\n",
+" disp(C(1));\n",
+"for i=2:3\n",
+" A2=A*(A1-C(i-1)*eye(3,3));\n",
+" printf('\n\n\nA%i=',i)\n",
+" disp(A2);\n",
+" C(i)=0;\n",
+" for j=1:3\n",
+" for k=1:3\n",
+" if(j==k)\n",
+" C(i)=C(i)+A2(j,k)/i\n",
+" end\n",
+" end\n",
+" end\n",
+" printf('\nC%i=',i)\n",
+" disp(C(i))\n",
+" A1=A2;\n",
+"end\n",
+"printf('\n\n\nTherefore the characteristic polynomial is:\n 3 2\nx - %ix - %ix %i = 0',C(1),C(2),C(3))\n",
+"\n",
+"//verification\n",
+"printf('\n\nVerification:')\n",
+"s=poly(0,'s');\n",
+"p=poly(A,'x');\n",
+"A=A-eye(3,3)*%s;\n",
+"disp(p,'=',A)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.3: Danilevsky_Method.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 11.3\n",
+"//Danilevsky Method\n",
+"//Page no. 341\n",
+"clc;close;clear;\n",
+"\n",
+"A=[-1,0,0;1,-2,3;0,2,-3];\n",
+"G=[A;eye(3,3)];\n",
+"disp(G);\n",
+"//transformation to frobenius matrix\n",
+"for k=3:-1:2\n",
+" g(k)=0;\n",
+" for j=1:k-1\n",
+" if(g(k)<G(k,j))\n",
+" g(k)=G(k,j)\n",
+" p=j;\n",
+" end\n",
+" end\n",
+" if(g(k)~=0)\n",
+" for j=1:3\n",
+" r(1,j)=G(k,j)\n",
+" end\n",
+" for i=1:6\n",
+" G(i,k-1)=G(i,k-1)/g(k)\n",
+" end\n",
+" disp(G)\n",
+" for j=1:3\n",
+" if(j~=k-1)\n",
+" l=G(k,j)\n",
+" for i=1:6\n",
+" G(i,j)=G(i,j)-l*G(i,k-1)\n",
+" end\n",
+" end\n",
+" end\n",
+" disp(G)\n",
+" end\n",
+" for j=1:3\n",
+" for i=1:3\n",
+" c(i,1)=G(i,j)\n",
+" end\n",
+" G(k-1,j)=0\n",
+" for i=1:3\n",
+" G(k-1,j)=G(k-1,j)+r(1,i)*c(i,1)\n",
+" end\n",
+" end\n",
+" disp(G)\n",
+"end\n",
+"\n",
+"//partition g\n",
+"for i=4:6\n",
+" for j=1:3\n",
+" T(i-3,j)=G(i,j)\n",
+" end\n",
+"end\n",
+"disp(T,'T=')\n",
+"\n",
+"//eigenvalues computation\n",
+"printf('\n\n\nCharateristic polynomial:')\n",
+"p=poly(A,'x')\n",
+"disp(p)\n",
+"printf('\n\n\nEigenvalues:')\n",
+"a=roots(p)\n",
+"disp(a')\n",
+"//eigenvectors computation\n",
+"for k=1:3\n",
+" m=2\n",
+" for l=1:3\n",
+" y(l,k)=a(k,1)^(m)\n",
+" m=m-1;\n",
+" end\n",
+"end\n",
+"printf('\n\n')\n",
+"disp(y,'y=')\n",
+"\n",
+"//eigenvector computation\n",
+"\n",
+"for k=1:3\n",
+" for l=1:3\n",
+" y1(l,1)=y(l,1)\n",
+" y2(l,1)=y(l,2)\n",
+" y3(l,1)=y(l,3)\n",
+" end\n",
+" x1=T*y3;\n",
+" x2=T*y2;\n",
+" x3=T*y1;\n",
+"end\n",
+"printf('\n\nEigenvectors :\n')\n",
+"for i=1:3\n",
+" printf('|%.1f|\t\t|%.1f|\t\t|%.1f|',x1(i,1),x2(i,1),x3(i,1))\n",
+" printf('\n')\n",
+"end"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.4: Power_Method.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 11.4\n",
+"//Power Method\n",
+"//Page no. 345\n",
+"clc;close;clear;\n",
+"\n",
+"A=[1,2;3,4];\n",
+"e=0.001;\n",
+"q0=[1;1];\n",
+"for i=1:5\n",
+" q1=A*q0;\n",
+" a=max(q1)\n",
+" for j=1:2\n",
+" q2(j)=q1(j)/a;\n",
+" end\n",
+" printf('\nq(%i) = %.4f a = %.4f Scaled q(%i) = %.4f\n %.4f %i\n\n',i,q1(1),a,i,q2(1),q1(2),q2(2))\n",
+" q1=q2;\n",
+" q0=q1;\n",
+"end\n",
+"printf('Hence the largest eigenvalue is %.4f with the corresponding eigenvector as %.4f\n %i',a,q0(1),q0(2))"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.5: Inverse_Power_Method.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 11.5\n",
+"//Inverse Power Method\n",
+"//Page no. 347\n",
+"clc;close;clear;\n",
+"\n",
+"A=[7,6,-3;-12,-20,24;-6,-12,16];\n",
+"e=10^-6;\n",
+"X=[1;1;1];\n",
+"B=0;\n",
+"Y=[0;0;0]\n",
+"a=0;l=0;\n",
+"for i=1:2\n",
+" printf('When a=%i\n',a);\n",
+" C=A-a*eye();\n",
+" disp(C,'C=')\n",
+" C_1=inv(C);\n",
+" disp(C_1,'Inverse of C=');\n",
+" printf('\n\nItr lambda X')\n",
+" printf('\n------------------------------------------------------------------\n')\n",
+" for j=1:10\n",
+" printf('\n%i %f %f %f %f',j-1,l,X(1),X(2),X(3));\n",
+" Y=C_1*X;\n",
+" B=max(Y);\n",
+" e1=abs(l-B);\n",
+" X=Y/B;\n",
+" m=0;\n",
+" for k=1:3\n",
+" m=m+(Y(k)-X(k))^2;\n",
+" end\n",
+" e2=sqrt(m);\n",
+" er=max(e1,e2);\n",
+" if(er<e)\n",
+" break\n",
+" end\n",
+" l=B;\n",
+" \n",
+" end\n",
+" a=-3;\n",
+" printf('\n\n\n\n')\n",
+"end\n",
+"printf('\n\n\nNote : Computation of Y is wrong given in the book')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.6: Rayleigh_Quotient.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 11.6\n",
+"//Rayleigh Quotient\n",
+"//Page no. 348\n",
+"clc;close;clear;\n",
+"\n",
+"A=[10,7,8,7;7,5,6,5;8,6,10,9;7,5,9,10];\n",
+"q0=[1;1;1;1];\n",
+"for i=0:4\n",
+" X=(A^i)*q0;\n",
+" l=(X'*A*X)/(X'*X)\n",
+" printf('\nLambda(%i) = %f\n',i+1,l)\n",
+"end\n",
+"printf('\n\nDominant Eigenvalue = %f\n\n\n',l)\n",
+"\n",
+"e=0.001;\n",
+"for i=1:5\n",
+" q1=A*q0;\n",
+" a=max(q1)\n",
+" for j=1:4\n",
+" q2(j)=q1(j)/a;\n",
+" end\n",
+"\n",
+" q1=q2;\n",
+" q0=q1;\n",
+"end\n",
+"disp(q2,'Corresponding Eigenvector = ')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.7: Jacobi_Method.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 11.7\n",
+"//Jacobi's Method\n",
+"//Page no. 355\n",
+"clc;close;clear;\n",
+"\n",
+"A=[1,1,1/2;1,1,1/4;1/2,1/4,2];\n",
+"C=A;\n",
+"V=[sqrt(2),0,1/2;sqrt(2),0,1/4;3/(4*sqrt(2)),-1/(4*sqrt(2)),2]\n",
+"S=eye(3,3)\n",
+"disp(A,'A =')\n",
+"VI=0;\n",
+"for i=1:3\n",
+" for j=1:3\n",
+" if(i~=j)\n",
+" VI=VI+A(i,j)^2 //initial off diag norm\n",
+" end\n",
+" end\n",
+"end\n",
+"VI=sqrt(VI);\n",
+"VF=VI*10^-7; //final threshold\n",
+"V1=VI/3;\n",
+"o=poly(0,'o');\n",
+"for i=1:3\n",
+"for q=2:3\n",
+" for p=q-1:-1:1\n",
+" if(A(p,q)>V1)\n",
+" a=-A(p,q);\n",
+" b=(A(p,p)-A(q,q))/2\n",
+" if(b~=0)\n",
+" w=b*abs(1/b)*(a/sqrt(a^2+b^2));\n",
+" else\n",
+" w=(a/sqrt(a^2+b^2));\n",
+" end\n",
+" sin0=w/sqrt(2*(1+sqrt(1-w^2)));\n",
+" cos0=sqrt(1-sin0^2)\n",
+" end\n",
+" B(p,p)=A(p,p)*cos0^2+A(q,q)*sin0^2-2*A(p,q)*sin0*cos0\n",
+" B(q,q)=A(p,p)*sin0^2+A(q,q)*cos0^2+2*A(p,q)*sin0*cos0\n",
+" B(p,q)=(A(p,p)-A(q,q))*sin0*cos0+A(p,q)*(cos0^2-sin0^2)\n",
+" S(i,i)=S(i,i)\n",
+" S(i,p)=S(i,p)*cos0-S(i,q)*sin0\n",
+" S(i,q)=S(i,p)*sin0+S(i,q)*cos0\n",
+" \n",
+" end\n",
+"end\n",
+"end\n",
+"disp(B,'B =')\n",
+"disp(S,'S =')\n",
+"printf('\n\n\nComputation error in the solution provided by book')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.8: Recursive_Formula.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 11.8\n",
+"//Recursive Formula\n",
+"//Page no. 357\n",
+"clc;close;clear;\n",
+"\n",
+"A=[2,-1,0,0;-1,2,-1,0;0,-1,2,-1;0,0,-1,2];\n",
+"l=poly(0,'l');\n",
+"p0=1;\n",
+"p1=A(1,1)-l;\n",
+"for i=2:4\n",
+" p2=(A(i,i)-l)*p1-A(i,i-1)^2*p0;\n",
+" p0=p1;\n",
+" p1=p2;\n",
+" printf('\n\np%i(l) = ',i);\n",
+" disp(p2)\n",
+"end"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 11.9: QR_Method.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 11.9\n",
+"//QR Method\n",
+"//Page no. 360\n",
+"clc;close;clear;\n",
+"\n",
+"A=[2,-1,0;-1,2,-1;0,-1,2];\n",
+"deff('y=c(i,j)','y=A(j,j)/sqrt((A(i,j)^2+A(j,j)^2))')\n",
+"deff('y=s2(i,j)','y=A(i,j)/sqrt((A(i,j)^2+A(j,j)^2))')\n",
+"disp(A,'A=')\n",
+"l0=0;f=1;m=0;s=0;w=0;\n",
+"for n=1:5\n",
+" for j=1:2\n",
+" for k=1:2\n",
+" V(j,k)=A(j,k)\n",
+" end\n",
+" end\n",
+" disp(V,'V=')\n",
+" p=poly(V,'x');\n",
+" disp('=0',p);\n",
+" a=roots(p);\n",
+" for j=1:2\n",
+" printf('\na(%i) = %f',j,a(j))\n",
+" end\n",
+" if(abs(a(1)-V(1,1))<=abs(a(2)-V(1,1)))\n",
+" a=a(1)\n",
+" else\n",
+" a=a(2)\n",
+" end\n",
+" printf('\na = %f\n',a)\n",
+" s=s+a;\n",
+" A=A-a*eye()\n",
+" R=A;Q=eye(3,3);\n",
+" \n",
+" for j=1:2\n",
+" for i=j+1:3\n",
+" for k=1:3 //C matrix evaluation\n",
+" for l=1:3\n",
+" if(k==l)\n",
+" if(k==i | k==j)\n",
+" C(k,l)=c(i,j)\n",
+" else\n",
+" C(k,l)=1\n",
+" end\n",
+" end\n",
+" if(k>l)\n",
+" if(k==i & l==j)\n",
+" C(k,l)=-1*s2(i,j)\n",
+" else\n",
+" C(k,l)=0\n",
+" end\n",
+" end\n",
+" if(k<l)\n",
+" if(k==j & l==i)\n",
+" C(k,l)=s2(i,j)\n",
+" else\n",
+" C(k,l)=0\n",
+" end\n",
+" end\n",
+" end\n",
+" end\n",
+" \n",
+" R=C*R;\n",
+" Q=Q*C';\n",
+" \n",
+" end\n",
+" end\n",
+"disp(Q,'Q=',R,'R=')\n",
+"disp(Q*R,'Q*R=')\n",
+"A=R*Q;\n",
+"disp(A,'A=')\n",
+"end\n",
+"l1=l0+s;\n",
+"for i=2:3\n",
+" for j=2:3\n",
+" V(i-1,j-1)=A(i,j)\n",
+" end\n",
+"end\n",
+"disp(V,'V=')\n",
+" p=poly(V,'x');\n",
+" disp('=0',p);\n",
+" a=roots(p);\n",
+" for j=1:2\n",
+" printf('\na(%i) = %f',j,a(j))\n",
+" end\n",
+" l2=l1+a(1)\n",
+" l3=l1+a(2)\n",
+" disp(l3,'l3=',l2,'l2=',l1,'l1=')\n",
+"printf('\n\n\nNote : Values of V varies in each step resulting in different results due to error in book calculation')"
+ ]
+ }
+],
+"metadata": {
+ "kernelspec": {
+ "display_name": "Scilab",
+ "language": "scilab",
+ "name": "scilab"
+ },
+ "language_info": {
+ "file_extension": ".sce",
+ "help_links": [
+ {
+ "text": "MetaKernel Magics",
+ "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+ }
+ ],
+ "mimetype": "text/x-octave",
+ "name": "scilab",
+ "version": "0.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
generated by cgit (git 2.34.1) at 2025-07-12 21:37:09 +0000