Linear Algebra and the C Language/a06k
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as : c00a.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define Cb C6
/* ------------------------------------ */
void fun(int rc)
{
double **A = r_mR( i_mR(rc,rc),999.);
double **B = r_mR( i_mR(rc,Cb),999.);
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);
f_mR(X);
f_mR(B);
f_mR(InvA);
f_mR(A);
}
/* ------------------------------------ */
int main(void)
{
time_t t;
srand(time(&t));
do
{
fun(rp_I(RC5)+RC1);
} while(stop_w());
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 :
-173 +63 +636 -397 +559
-322 -522 -481 +873 -200
+244 +716 -765 +703 -845
+746 -16 -157 -486 +891
-639 -802 +614 +351 +663
b1 b2 ... bn :
-948 +537 -12 +266 -632 +903
+961 -111 +498 -963 -905 -481
+328 +357 +177 -483 +248 +897
-449 -252 -762 +362 -231 +182
-610 +824 +488 -28 +44 +696
Press return to continue.
inv(A) :
-5.9536e-03 -5.1707e-03 +1.5358e-03 +8.6743e-04 +4.2516e-03
+3.0622e-03 +1.3481e-03 +6.7659e-04 -2.5023e-05 -1.2793e-03
-4.3985e-03 -4.9138e-03 +1.4973e-03 -4.1461e-05 +4.1903e-03
-2.0700e-03 -2.1302e-03 +1.7881e-03 +4.2410e-04 +2.8117e-03
+3.1355e-03 +2.3257e-03 -3.4587e-05 +6.1964e-04 -1.3106e-03
X = inv(A) * B :
x1 x2 ... xn
-1.8042 +1.2099 -0.8179 +2.8489 +8.8097 +1.6056
-0.5939 +0.6885 +0.1492 -0.7837 -3.0381 +1.8287
-2.5987 +2.1812 -0.0528 +2.7065 +7.7921 +2.6436
-1.4038 +1.9732 +0.3295 +0.7119 +3.7052 +2.7934
-0.2276 +0.1772 +0.0027 -1.1278 -4.2958 +0.8823
Press return to continue.
b1 b2 ... bn :
-948 +537 -12 +266 -632 +903
+961 -111 +498 -963 -905 -481
+328 +357 +177 -483 +248 +897
-449 -252 -762 +362 -231 +182
-610 +824 +488 -28 +44 +696
Ax1 Ax2 ... Axn :
-948 +537 -12 +266 -632 +903
+961 -111 +498 -963 -905 -481
+328 +357 +177 -483 +248 +897
-449 -252 -762 +362 -231 +182
-610 +824 +488 -28 +44 +696
Press return to continue
Press X return to stop