Linear Algebra and the C Language/a0n6

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as: c00f.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define ARRAY A3 /* ------------------------------------ */ #define RC RC3 /* ------------------------------------ */ void fun(void) { double **A = rsymmetric_mR( i_mR(RC,RC),999); double **AEVect = eigs_V_mR(A, i_mR(RC,RC)); double **InvAEVect = transpose_mR(AEVect, i_mR(RC,RC)); double **AEValue = eigs_mR(A, i_mR(RC,C1)); double **T = i_mR(RC,RC); double **a = i_mR(RC,RC); double **b [ARRAY]; double **r [ARRAY]; double **br [ARRAY]; double **EVabr[ARRAY]; int i; for(i=A0; i<ARRAY; i++) { b[i] = c_c_mR( AEVect,i+C1, i_mR(RC,C1),C1); r[i] = c_r_mR(InvAEVect,i+R1, i_mR(R1,RC),R1); br[i] = mul_mR(b[i],r[i], i_mR(RC,RC)); EVabr[i] = smul_mR(AEValue[i+R1][C1]*AEValue[i+R1][C1],br[i], i_mR(RC,RC)); } clrscrn(); printf(" A:"); p_mR(A, S10,P4,C6); printf(" AEVect: Eigenvectors of A"); p_mR(AEVect, S10,P4,C6); printf(" AEValue: Eigenvalues of A"); p_mR(AEValue, S10,P4,C6); stop(); clrscrn(); printf(" A**2:"); pow_mR(2, A, T); p_mR(T, S10,P0,C6); add_mR(EVabr[0], EVabr[1], T); add_mR( T, EVabr[2], a); printf(" We can calculate the nth power of A\n" " by simply taking the nth power of \n" " each of the eigenvalues. \n\n\n\n" " E1**2 b1r1 + E2**2 b2r2 + E3**2 b3r3 = A**2"); p_mR(a, S10,P0,C6); f_mR(A); f_mR(AEVect); f_mR(InvAEVect); f_mR(AEValue); f_mR(T); f_mR(a); for(i=A0; i<ARRAY; i++) { f_mR( b[i]); f_mR( r[i]); f_mR( br[i]); f_mR(EVabr[i]); } } /* ------------------------------------ */ int main(void) { time_t t; srand(time(&t)); do { fun(); } while(stop_w()); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ A property of spectral decomposition: E1**2 * b1r1 + E2**2 * b2r2 + E3**2 * b3r3 = A**2 E1**3 * b1r1 + E2**3 * b2r2 + E3**3 * b3r3 = A**3 ... E1**n * b1r1 + E2**n * b2r2 + E3**n * b3r3 = A**n We can calculate the nth power of A by simply taking the nth power of each of the eigenvalues. b: The columns of the eigenvectors of A r: The rows of eigenvectors of the inverse of A E: The eignvalues of A. b1r1 is obtained by multiplying the first column of the eigenvector of A by the first row of the eigenvector of the inverse of A. Screen output example: A: +28.0000 +729.0000 -82.0000 +729.0000 +419.0000 -499.0000 -82.0000 -499.0000 +507.0000 AEVect: Eigenvectors of A +0.4597 +0.7274 +0.5094 +0.7149 -0.6435 +0.2737 -0.5269 -0.2383 +0.8158 AEValue: Eigenvalues of A +1255.5856 -589.9704 +288.3848 Press return to continue. A**2: +538949 +366781 -407641 +366781 +956003 -521852 -407641 -521852 +512774 We can calculate the nth power of A by simply taking the nth power of each of the eigenvalues. E1**2 b1r1 + E2**2 b2r2 + E3**2 b3r3 = A**2 +538949 +366781 -407641 +366781 +956003 -521852 -407641 -521852 +512774 Press return to continue Press X return to stop