initial commit / add all books

16 files changed, 304 insertions, 0 deletions

diff --git a/1332/CH9/EX9.1/9_1.pdf b/1332/CH9/EX9.1/9_1.pdf
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index 000000000..460aca796
--- /dev/null
+++ b/1332/CH9/EX9.1/9_1.pdf
diff --git a/1332/CH9/EX9.1/9_1.sce b/1332/CH9/EX9.1/9_1.sce
new file mode 100755
index 000000000..06416f8c5
--- /dev/null
+++ b/1332/CH9/EX9.1/9_1.sce
@@ -0,0 +1,11 @@
+//Example 9.1

+//Moore-Penrose Generalized Inverse

+//Page no. 292

+clc;clear;close;

+

+AT=[3,0,3;0,3,3];

+A=AT';           //transpose

+I=inv(AT*A);       //inverse

+disp(I,'Inverse of AT*A=',AT*A,'AT*A=',A,'A=',AT,'AT=');

+A#=I*AT;

+disp(A#,'Moore-Penrose Generalized Inverse of A=')
\ No newline at end of file
diff --git a/1332/CH9/EX9.2/9_2.pdf b/1332/CH9/EX9.2/9_2.pdf
new file mode 100755
index 000000000..81f76b7f6
--- /dev/null
+++ b/1332/CH9/EX9.2/9_2.pdf
diff --git a/1332/CH9/EX9.2/9_2.sce b/1332/CH9/EX9.2/9_2.sce
new file mode 100755
index 000000000..3d0d4911a
--- /dev/null
+++ b/1332/CH9/EX9.2/9_2.sce
@@ -0,0 +1,60 @@
+//Example 9.2

+//Curve Fitting

+//Page no. 293

+clc;clear;close;

+x(1)=0.25;

+for i=2:6

+    x(1,i)=x(1,i-1)+0.25;

+end               //x values

+y(1,1)=3.1;y(1,2)=1.7;y(1,3)=1;y(1,4)=0.68;y(1,5)=0.42;y(1,6)=0.26; //y values

+

+//construction of normal equations

+for i=1:6

+    Y(1,i)=log10(y(1,i));

+end

+Ex=0;

+for i=1:6

+    Ex=Ex+x(1,i);

+end

+EY=0;

+for i=1:6

+    EY=EY+Y(1,i);

+end

+Ex2=0;

+for i=1:6

+    Ex2=Ex2+x(1,i)^2;

+end

+ExY=0;

+for i=1:6

+    ExY=ExY+x(1,i)*Y(1,i);

+end

+printf('E x(k)\t\t y(k)\t\tE Y(k)\t\tE x2(k)\t\tE x(k)*Y(k)')

+printf('\n----------------------------------------------------------------------------')

+for i=1:6

+    printf('\n%f\t%f\t%f\t%f\t%f',x(1,i),y(1,i),Y(1,i),x(1,i)^2,x(1,i)*Y(1,i))

+end

+printf('\n----------------------------------------------------------------------------')

+printf('\n%f\t%f\t%f\t%f\t%f',Ex,0,EY,Ex2,ExY)

+printf('\n----------------------------------------------------------------------------\n\n')

+A=[6,Ex;Ex,Ex2];      //system of normal equations

+B=[EY;ExY];

+X=inv(A)*B;

+a=exp(X(1,1));

+b=-1*X(2,1);

+for i=1:2

+    for j=1:2

+        printf('%f    ',A(i,j))

+    end

+    if(i==1)

+        printf('  *')

+    end

+    

+    printf('\ta%i',i);

+    if(i==1)

+        printf('  =')

+    end

+    

+    printf('\t%f\n',B(i,1))

+end

+printf('\n\na1=%f\na2=%f\n\na=%f\nb=%f\n\n',X(1,1),X(2,1),a,b)

+printf('The fitted curve is:\n            %fx\ny=%f e',b,a)
\ No newline at end of file
diff --git a/1332/CH9/EX9.3/9_3.pdf b/1332/CH9/EX9.3/9_3.pdf
new file mode 100755
index 000000000..41156b47d
--- /dev/null
+++ b/1332/CH9/EX9.3/9_3.pdf
diff --git a/1332/CH9/EX9.3/9_3.sce b/1332/CH9/EX9.3/9_3.sce
new file mode 100755
index 000000000..9213721c0
--- /dev/null
+++ b/1332/CH9/EX9.3/9_3.sce
@@ -0,0 +1,61 @@
+//Example 9.3

+//Gram-Schmidt Orthogonalization/Orthonormalization Process

+//Page no. 294

+clc;clear;close;

+deff('y=f(x,a)','y=sqrt(x(1,a)^2+x(2,a)^2+x(3,a)^2+x(4,a)^2)');

+deff('y=f1(g,a,h,b)','y=g(1,a)*h(1,b)+g(2,a)*h(2,b)+g(3,a)*h(3,b)+g(4,a)*h(4,b)');

+

+U=[1/sqrt(3),-2/sqrt(7),1,0,0,0;0,1/sqrt(7),0,1,0,0;1/sqrt(3),1/sqrt(7),0,0,1,0;-1/sqrt(3),-1/sqrt(7),0,0,0,1];

+for i=1:4

+        V(i,1)=U(i,1);

+end

+for i=1:4

+    if(f(V,1)~=0)

+        W(i,1)=V(i,1)/f(V,1);

+    else

+        W(i,1)=0;

+    end 

+end

+for j=2:6

+    for i=1:4

+        for l=1:4

+            k(l,1)=0;

+        end

+        for l=1:j-1

+            for m=1:4

+                w(m,1)=W(m,l);

+            end

+            k=k-(f1(U,j,W,l))*w;

+        end

+        V(i,j)=U(i,j)+k(i,1);

+    end

+    for i=1:4

+        if(j~=4)

+            if(f(V,j)~=0)

+                W(i,j)=V(i,j)/f(V,j);

+            else

+                W(i,j)=0;

+            end 

+        else

+            W(i,j)=0;

+        end

+    end

+    

+end

+disp(U,'U=')

+disp('W=')

+printf('\n')

+for i=1:4

+    for j=1:6

+        printf('%.4f\t\t',W(i,j))

+    end

+    printf('\n')

+end

+disp('V=')

+printf('\n')

+for i=1:4

+    for j=1:6

+        printf('%.4f\t\t',V(i,j))

+    end

+    printf('\n')

+end
\ No newline at end of file
diff --git a/1332/CH9/EX9.4/9_4.pdf b/1332/CH9/EX9.4/9_4.pdf
new file mode 100755
index 000000000..6996647bf
--- /dev/null
+++ b/1332/CH9/EX9.4/9_4.pdf
diff --git a/1332/CH9/EX9.4/9_4.sce b/1332/CH9/EX9.4/9_4.sce
new file mode 100755
index 000000000..624b0e36e
--- /dev/null
+++ b/1332/CH9/EX9.4/9_4.sce
@@ -0,0 +1,34 @@
+//Example 9.4

+//QR Decomposition

+//Page no. 296

+clc;clear;close;

+

+A=[2,1,1;1,3,1;1,1,4];

+B=A*A';

+disp(B,'AT*A=')

+//cholesky factorization to find R

+R(2,1)=0;R(3,1)=0;R(3,2)=0;     

+for i=1:3

+    for j=1:3

+        if(i==j)

+            k=0;

+            for m=1:i-1

+               k=k+R(m,i)^2; 

+            end

+            R(i,j)=sqrt(B(i,j)-k)

+        end

+        if(j>i)

+            k=0;

+            for m=1:i-1

+                k=k+R(m,j)*R(m,i);

+            end

+            R(i,j)=(B(i,j)-k)/R(i,i)

+        end

+    end

+end

+//cholesky factorization end

+disp(R,'Upper Triangular Matrix (R)=')

+R_1=inv(R);

+disp(R_1,'Inverse of R')

+Q=A*R_1;

+disp(Q,'Orthogonal Matrix Q=')
\ No newline at end of file
diff --git a/1332/CH9/EX9.5/9_5.pdf b/1332/CH9/EX9.5/9_5.pdf
new file mode 100755
index 000000000..d311586e4
--- /dev/null
+++ b/1332/CH9/EX9.5/9_5.pdf
diff --git a/1332/CH9/EX9.5/9_5.sce b/1332/CH9/EX9.5/9_5.sce
new file mode 100755
index 000000000..b08b08d88
--- /dev/null
+++ b/1332/CH9/EX9.5/9_5.sce
@@ -0,0 +1,32 @@
+//Example 9.5

+//Vector Computation

+//Page no. 299

+clc;clear;close;

+

+X=[2,3,0,1];

+n=X(1);

+for i=2:4

+    if(n<X(i))

+        n=X(i);

+    end

+end

+printf('\nMaximum Value (n)=%i\n',n)

+for i=1:4

+    X(i)=X(i)/n;

+end

+disp(X,'Normalized X=')

+k=0;

+for i=1:4

+    k=k+X(i)^2;

+end

+sigma=X(1)*abs(1/X(1))*sqrt(k);

+printf('\nsigma=%f\n',sigma);

+X(1)=X(1)+sigma;

+printf('\nModified x1 = %g\n',X(1))

+for i=1:4

+    U(1,i)=X(i);

+end

+disp(U,'U=')

+p=sigma*X(1);sigma=n*sigma;

+printf('\n p = %f\n\n sigma = %f',p,sigma);

+printf('\n\n\nNote : There is a computation error in calculation of U1')
\ No newline at end of file
diff --git a/1332/CH9/EX9.6/9_6.pdf b/1332/CH9/EX9.6/9_6.pdf
new file mode 100755
index 000000000..36a5c4c29
--- /dev/null
+++ b/1332/CH9/EX9.6/9_6.pdf
diff --git a/1332/CH9/EX9.6/9_6.sce b/1332/CH9/EX9.6/9_6.sce
new file mode 100755
index 000000000..6c9009740
--- /dev/null
+++ b/1332/CH9/EX9.6/9_6.sce
@@ -0,0 +1,24 @@
+//Example 9.6

+//House Holder Transformation

+//Page no. 300

+clc;clear;close;

+

+A=[4,2,1;2,5,-2;1,-2,7]

+disp(A,'A=')

+k=0;

+for j=2:3

+    k=k+A(j,1)^2;

+end

+a=A(2,1)*abs(1/A(2,1))*sqrt(k);

+disp(a,'alpha=')

+U=[0;a+A(2,1);A(3,1)];

+disp(U,'U=')

+U1=U'*U;

+disp(U1,'UT*U=')

+U2=U*U';

+disp(U2,'U*UT=')

+P=eye(3,3)-(2*U2)/U1;

+disp(P,'P=');

+B=P*A*P;

+disp(B,'B=');

+printf('\n\n\nThere are computation error in the answers given by the book in this example\n\n(a22 value error in U*UT)')
\ No newline at end of file
diff --git a/1332/CH9/EX9.7/9_7.pdf b/1332/CH9/EX9.7/9_7.pdf
new file mode 100755
index 000000000..b181eceb4
--- /dev/null
+++ b/1332/CH9/EX9.7/9_7.pdf
diff --git a/1332/CH9/EX9.7/9_7.sce b/1332/CH9/EX9.7/9_7.sce
new file mode 100755
index 000000000..cf497efe8
--- /dev/null
+++ b/1332/CH9/EX9.7/9_7.sce
@@ -0,0 +1,47 @@
+//Example 9.7

+//Givens QR Method

+//Page no. 303

+clc;clear;close;

+

+A=[4,2,1;2,5,-2;1,-2,7]

+deff('y=c(i,j)','y=A(j,j)/sqrt((A(i,j)^2+A(j,j)^2))')

+deff('y=s(i,j)','y=A(i,j)/sqrt((A(i,j)^2+A(j,j)^2))')

+disp(A,'A=')

+R=A;Q=eye(3,3);

+m=1;

+for j=1:2

+    for i=j+1:3

+        for k=1:3             //C matrix evaluation

+            for l=1:3

+                if(k==l)

+                    if(k==i | k==j)

+                        C(k,l)=c(i,j)

+                    else

+                        C(k,l)=1

+                    end

+                end

+                if(k>l)

+                    if(k==i & l==j)

+                        C(k,l)=-1*s(i,j)

+                    else

+                        C(k,l)=0

+                    end

+                end

+                if(k<l)

+                    if(k==j & l==i)

+                        C(k,l)=s(i,j)

+                    else

+                        C(k,l)=0

+                    end

+                end

+            end

+        end

+        printf('\n\n Iteration %i',m)

+        m=m+1

+        disp(C,'C=');

+        R=C*R;

+        Q=Q*C';

+        disp(Q,'Q=',R,'R=')

+    end

+end

+disp(Q*R,'Q*R=A=')            //verification
\ No newline at end of file
diff --git a/1332/CH9/EX9.8/9_8.pdf b/1332/CH9/EX9.8/9_8.pdf
new file mode 100755
index 000000000..47c8cbef2
--- /dev/null
+++ b/1332/CH9/EX9.8/9_8.pdf
diff --git a/1332/CH9/EX9.8/9_8.sce b/1332/CH9/EX9.8/9_8.sce
new file mode 100755
index 000000000..79e5f435f
--- /dev/null
+++ b/1332/CH9/EX9.8/9_8.sce
@@ -0,0 +1,35 @@
+//Example 9.8

+//Recursive Least-Square Method

+//Page no. 308

+clc;clear;close;

+

+A0=[3,0;0,3;3,3];

+B0=[2;2;2];

+A1=[6,3];B1=[6];

+A0T=A0';

+G0=A0T*A0;

+disp(G0,'G0=')

+G0_1=inv(G0);

+disp(G0_1,'Inverse of G0=')

+X0=G0_1*A0T*B0;

+disp(X0,'X0=')

+

+//by recursive least square algorithm

+G1=G0+A1'*A1;

+disp(G1,'G1=');

+G1_1=inv(G1);

+disp(G1_1,'Inverse of G1')

+X1=X0+G1_1*A1'*(B1-A1*X0);

+disp(X1,'X1=')

+

+//verification

+A=[3,0;0,3;3,3;6,3];

+B=[2;2;2;6];

+AT=A';

+G=AT*A;

+disp(G,'G=')

+G_1=inv(G);

+disp(G_1,'Inverse of G=')

+X=G_1*AT*B;

+disp(X,'X=')

+disp('Thus X and X1 are Same')
\ No newline at end of file