Linear Algebra and the C Language/a0n7

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as: c00g.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(1./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(" inv(A):"); inv_mR(A, T); pE_mR(T, S10,P4,C6); add_mR(EVabr[0], EVabr[1], T); add_mR( T, EVabr[2], a); printf(" We can calculate the inverse of A\n" " by simply taking the inverse of \n" " each of the eigenvalues. \n\n\n\n" " 1/E1 b1r1 + 1/E2 b2r2 + 1/E3 b3r3 = inv(A)"); pE_mR(a, S10,P4,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: 1/E1 * b1r1 + 1/E2 * b2r2 + 1/E3 * b3r3 = inv(A) We can calculate the inverse of A by simply taking the inverse 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 eigenvalues 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: +426.0000 +704.0000 +935.0000 +704.0000 +66.0000 +22.0000 +935.0000 +22.0000 +823.0000 AEVect: Eigenvectors of A +0.6591 +0.6910 +0.2969 +0.2897 -0.5975 +0.7477 +0.6940 -0.4067 -0.5940 AEValue: Eigenvalues of A +1720.0870 -733.1394 +328.0524 Press return to continue. inv(A): -1.3013e-04 +1.3508e-03 +1.1173e-04 +1.3508e-03 +1.2657e-03 -1.5685e-03 +1.1173e-04 -1.5685e-03 +1.1301e-03 We can calculate the inverse of A by simply taking the inverse of each of the eigenvalues. 1/E1 b1r1 + 1/E2 b2r2 + 1/E3 b3r3 = inv(A) -1.3013e-04 +1.3508e-03 +1.1173e-04 +1.3508e-03 +1.2657e-03 -1.5685e-03 +1.1173e-04 -1.5685e-03 +1.1301e-03 Press return to continue Press X return to stop