Linear Algebra and the C Language/a0hp

__NOTOC__ The Maclaurin series of the exponential function is : Exp(A) = Ide + A + (1/2) A2 + (1/6) A3 + ... + 1/(n-1)! A(n-1) Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00b.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define RCA RC4 /* ------------------------------------ */ void fun(void) { int n = 10; int i = 0; double **A = rE_mR(i_mR(RCA,RCA),999,+1.E-3); double **A_n = i_mR(RCA,RCA); double **sA = i_mR(RCA,RCA); double **ExpA = i_mR(RCA,RCA); double **NewExpA = i_mR(RCA,RCA); clrscrn(); printf(" Copy/Paste into the octave window. \n\n"); p_Octave_mR(A, "A", P3); printf(" expm (A)\n\n"); stop(); clrscrn(); printf(" A:"); p_mR(A, S4,P4,C6); for(i = 0; i <= n; i++) { pow_mR(i, A, A_n); smul_mR(1./factorial(i), A_n, sA); add_mR(ExpA,sA,NewExpA); printf(" NewExpA n = %d:",i); p_mR(NewExpA, S8,P6,C6); c_mR(NewExpA,ExpA); stop(); } clrscrn(); printf(" ExpA:"); p_mR(ExpA, S8,P4,C6); f_mR(A); f_mR(A_n); f_mR(sA); f_mR(ExpA); f_mR(NewExpA); } /* ------------------------------------ */ int main(void) { time_t t; srand(time(&t)); do { fun(); } while(stop_w()); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ Screen output example: Copy/Paste into the octave window. A=[ +0.127,+0.018,-0.685,+0.637; +0.063,+0.368,-0.814,+0.623; -0.898,-0.068,+0.520,-0.615; +0.040,-0.744,+0.700,+0.268] expm (A) Press return to continue. A: +0.1270 +0.0180 -0.6850 +0.6370 +0.0630 +0.3680 -0.8140 +0.6230 -0.8980 -0.0680 +0.5200 -0.6150 +0.0400 -0.7440 +0.7000 +0.2680 NewExpA n = 0: +1.000000 +0.000000 +0.000000 +0.000000 +0.000000 +1.000000 +0.000000 +0.000000 +0.000000 +0.000000 +1.000000 +0.000000 +0.000000 +0.000000 +0.000000 +1.000000 Press return to continue. NewExpA n = 1: +1.127000 +0.018000 -0.685000 +0.637000 +0.063000 +1.368000 -0.814000 +0.623000 -0.898000 -0.068000 +1.520000 -0.615000 +0.040000 -0.744000 +0.700000 +1.268000 Press return to continue. NewExpA n = 2: +1.455936 -0.191219 -0.690974 +0.979052 +0.456539 +1.232199 -0.978944 +1.091484 -1.202945 +0.122506 +1.775191 -1.164505 -0.289836 -1.004032 +1.264908 +0.869646 Press return to continue. NewExpA n = 3: +1.471817 -0.299603 -0.630536 +1.037230 +0.525966 +1.105457 -0.951231 +1.222509 -1.295568 +0.274538 +1.709145 -1.291097 -0.483667 -0.951921 +1.415744 +0.594218 Press return to continue. NewExpA n = 4: +1.457627 -0.321351 -0.593161 +1.017483 +0.521263 +1.069267 -0.910797 +1.218343 -1.282552 +0.312777 +1.663328 -1.280495 -0.525617 -0.899334 +1.409742 +0.529822 Press return to continue. NewExpA n = 5: +1.450122 -0.320573 -0.586554 +1.007310 +0.513392 +1.066656 -0.900639 +1.208038 -1.273427 +0.314684 +1.652039 -1.267868 -0.525457 -0.885951 +1.397288 +0.528317 Press return to continue. NewExpA n = 6: +1.448915 -0.319361 -0.586417 +1.005463 +0.511609 +1.067635 -0.899708 +1.205430 -1.271440 +0.313390 +1.651233 -1.264980 -0.523460 -0.884801 +1.394199 +0.530933 Press return to continue. NewExpA n = 7: +1.448876 -0.319106 -0.586615 +1.005378 +0.511451 +1.067950 -0.899839 +1.205173 -1.271295 +0.313028 +1.651418 -1.264733 -0.523002 -0.884984 +1.393902 +0.531588 Press return to continue. NewExpA n = 8: +1.448899 -0.319085 -0.586657 +1.005407 +0.511465 +1.067990 -0.899889 +1.205187 -1.271315 +0.312987 +1.651476 -1.264756 -0.522959 -0.885050 +1.393920 +0.531655 Press return to continue. NewExpA n = 9: +1.448904 -0.319086 -0.586661 +1.005414 +0.511470 +1.067991 -0.899895 +1.205194 -1.271322 +0.312987 +1.651483 -1.264765 -0.522961 -0.885058 +1.393929 +0.531655 Press return to continue. NewExpA n = 10: +1.448904 -0.319086 -0.586661 +1.005415 +0.511471 +1.067990 -0.899895 +1.205195 -1.271323 +0.312988 +1.651483 -1.264766 -0.522962 -0.885058 +1.393930 +0.531654 Press return to continue. ExpA: +1.4489 -0.3191 -0.5867 +1.0054 +0.5115 +1.0680 -0.8999 +1.2052 -1.2713 +0.3130 +1.6515 -1.2648 -0.5230 -0.8851 +1.3939 +0.5317 Press return to continue Press X return to stop