411 REFERENCE · Wikibooks
Linear Algebra and the C Language/a09z
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
__NOTOC__
Install and compile this file in your working directory.
/* ------------------------------------ */
/* Save as : c00a.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define Cb C6
/* ------------------------------------ */
void fun(int r)
{
double **A = r_mR( i_mR(r,r ),999);
double **B = r_mR( i_mR(r,Cb),999);
double **InvA = invgj_mR(A, i_mR(r,r));
double **X = mul_mR(InvA,B, i_mR(r,Cb)) ;
double **T = mul_mR(A,X, i_mR(r,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);
f_mR(T);
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(C2)+C4);
} 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
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.
A :
-958 -989 +776 +885 -818
+506 +369 +41 -454 +292
-500 -728 +530 -442 +355
+415 -309 +606 +560 +786
-680 -747 +497 -332 -931
b1 b2 ... bn :
+375 +239 -694 +932 +35 +875
-557 -549 -530 +253 -322 -500
+957 -718 +115 -830 +898 +730
-770 -586 -115 +981 -197 -385
-758 +151 -633 -95 -667 +160
inv(A) :
-2.0406e-03 -1.7849e-03 -1.4648e-03 +2.0454e-03 +2.4014e-03
+2.8712e-03 +4.1837e-03 +7.2322e-04 -2.2605e-03 -2.8432e-03
+2.2049e-03 +3.6716e-03 +5.4489e-04 -8.4155e-04 -1.2884e-03
+4.0053e-04 -4.2286e-04 -4.0146e-04 +2.3031e-04 -4.4318e-04
+2.2088e-04 +5.7626e-05 +9.2362e-04 -2.1160e-04 -1.0766e-03
X = inv(A) * B :
x1 x2 ... xn
-4.5680 +0.7079 +0.4384 +0.6408 -2.8167 -2.3656
+3.3342 -1.2346 -2.0672 +1.1868 +1.7445 +1.3638
+0.9278 -1.5814 -2.5012 +1.8284 +0.4093 +0.6091
+0.1601 +0.4142 +0.1540 +0.8676 +0.0399 +0.1092
+1.9136 -0.6806 +0.6282 -0.6515 +1.5783 +0.7479
b1 b2 ... bn :
+375 +239 -694 +932 +35 +875
-557 -549 -530 +253 -322 -500
+957 -718 +115 -830 +898 +730
-770 -586 -115 +981 -197 -385
-758 +151 -633 -95 -667 +160
Ax1 Ax2 ... Axn :
+375 +239 -694 +932 +35 +875
-557 -549 -530 +253 -322 -500
+957 -718 +115 -830 +898 +730
-770 -586 -115 +981 -197 -385
-758 +151 -633 -95 -667 +160
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