Linear Algebra and the C Language/a0a0
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as : c00b.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define RA R3
#define CA C3
#define Cb C5
/* ------------------------------------ */
int main(void)
{
double at[RA*CA]={
+10, -150, -148,
+207, -215, +997,
-858, +803, +289
};
double bt[RA*Cb]={
+437, -146, -175, -954, -432,
-233, +243, +772, +920, -98,
+444, -886, -604, -15, +946
};
double **A = ca_A_mR(at, i_mR(RA,CA));
double **B = ca_A_mR(bt, i_mR(RA,Cb));
double **InvA = invgj_mR(A, i_mR(RA,CA));
double **X = mul_mR(InvA,B, i_mR(RA,Cb)) ;
double **T = mul_mR(A,X, i_mR(RA,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(" InvA:");
pE_mR(InvA,S1,P3,C7);
printf(" X = InvA B:");
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(T,S9,P0,C6);
stop();
f_mR(T);
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 :
+10 -150 -148
+207 -215 +997
-858 +803 +289
b1 b2 ... bn :
+437 -146 -175 -954 -432
-233 +243 +772 +920 -98
+444 -886 -604 -15 +946
Press return to continue.
inv(A) :
-6.5676e-03 -5.7471e-04 -1.3807e-03
-6.9674e-03 -9.4468e-04 -3.0912e-04
-1.3892e-04 +9.1861e-04 +2.2000e-04
X = inv(A) * B :
x1 x2 ... xn
-3.3492 +2.0425 +1.5396 +5.7575 +1.5874
-2.9619 +1.0616 +0.6767 +5.7825 +2.8101
-0.1771 +0.0486 +0.6006 +0.9744 +0.1781
Press return to continue.
b1 b2 ... bn :
+437 -146 -175 -954 -432
-233 +243 +772 +920 -98
+444 -886 -604 -15 +946
Ax1 Ax2 ... Axn :
+437 -146 -175 -954 -432
-233 +243 +772 +920 -98
+444 -886 -604 -15 +946
Press return to continue.