Linear Algebra and the C Language/a06l
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as : c00b.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define RC R3
#define Cb C3
/* ------------------------------------ */
int main(void)
{
double ta[RC*RC] ={ 4,2,3,
5,3,1,
8,2,2};
double tb[RC*Cb] ={ 3, 4, 9,
2, 5, 8,
1, 6, 7};
double **A = ca_A_mR(ta, i_mR(RC,RC));
double **B = ca_A_mR(tb, i_mR(RC,Cb));
double **InvA = inv_mR(A, i_mR(RC,RC));
double **X = mul_mR(InvA,B, i_mR(RC,Cb));
clrscrn();
printf(" \n");
printf(" Linear systems with common coefficient matrix.\n\n");
printf(" Ax1=b1 \n");
printf(" Ax2=b2 \n");
printf(" ... \n");
printf(" Axn=bn \n\n");
printf(" We can write these equalities in this maner. \n\n");
printf(" A|x1|x2|...|xn| = b1|b2|...|bn| \n\n");
printf(" or simply : \n\n");
printf(" AX = B \n\n");
printf(" where B = b1|b2|...|bn \n\n");
printf(" and X = x1|x2|...|xn \n\n");
stop();
clrscrn();
printf(" We want to find X such as, \n\n");
printf(" AX = B \n\n");
printf(" If A is a square matrix and, \n\n");
printf(" If A has an inverse matrix, \n\n");
printf(" you can find X by this method\n\n");
printf(" X = inv(A) B \n\n\n");
printf(" To verify the result you can \n\n");
printf(" multiply the matrix A by X. \n\n");
printf(" You must refind B. \n\n");
stop();
clrscrn();
printf(" A :");
p_mR(A, S5,P0,C6);
printf(" b1 b2 ... bn :");
p_mR(B, S9,P0,C6);
stop();
clrscrn();
printf(" inv(A):");
pE_mR(InvA, S1,P4,C6);
printf(" X = inv(A) B :\n\n");
printf(" x1 x2 ... xn");
p_mR(X, S9,P4,C6);
stop();
clrscrn();
printf(" b1 b2 ... bn :");
p_mR(B, S9,P0,C6);
printf(" Ax1 Ax2 ... Axn :");
p_mR(mul_mR(A,X,B), S9,P0,C6);
stop();
f_mR(X);
f_mR(B);
f_mR(InvA);
f_mR(A);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Screen output example:
Linear systems with common coefficient matrix.
Ax1=b1
Ax2=b2
...
Axn=bn
We can write these equalities in this maner.
A|x1|x2|...|xn| = b1|b2|...|bn|
or simply :
AX = B
where B = b1|b2|...|bn
and X = x1|x2|...|xn
Press return to continue.
We want to find X such as,
AX = B
If A is a square matrix and,
If A has an inverse matrix,
you can find X by this method
X = inv(A) B
To verify the result you can
multiply the matrix A by X.
You must refind B.
Press return to continue.
A :
+4 +2 +3
+5 +3 +1
+8 +2 +2
b1 b2 ... bn :
+3 +4 +9
+2 +5 +8
+1 +6 +7
Press return to continue.
inv(A) :
-1.3333e-01 -6.6667e-02 +2.3333e-01
+6.6667e-02 +5.3333e-01 -3.6667e-01
+4.6667e-01 -2.6667e-01 -6.6667e-02
X = inv(A) * B :
x1 x2 ... xn
-0.3000 +0.5333 -0.1000
+0.9000 +0.7333 +2.3000
+0.8000 +0.1333 +1.6000
Press return to continue.
b1 b2 ... bn :
+3 +4 +9
+2 +5 +8
+1 +6 +7
Ax1 Ax2 ... Axn :
+3 +4 +9
+2 +5 +8
+1 +6 +7
Press return to continue.