Linear Algebra and the C Language/a0n5

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as: c00e.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 **T = i_mR(RC,RC); double **b [ARRAY]; double **r [ARRAY]; double **br[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)); } clrscrn(); printf(" A:"); p_mR(A, S10,P4,C6); printf(" AEVect: Eigenvectors of A"); p_mR(AEVect, S10,P4,C6); transpose_mR(AEVect,InvAEVect); printf(" Inverse of AEVect = InvAEVect"); p_mR(InvAEVect, S10,P4,C6); stop(); clrscrn(); mul_mR(br[0], br[1], T); printf(" This simply materializes that our projectors\n" " bnrn are orthogonal to each other. \n\n\n\n" " b1r1 * b2r2"); p_mR(T, S10,P4,C6); mul_mR(br[0], br[2], T); printf(" b1r1 * b3r3"); p_mR(T, S10,P4,C6); mul_mR(br[1], br[2], T); printf(" b2r2 * b3r3"); p_mR(T, S10,P4,C6); f_mR(A); f_mR(AEVect); f_mR(InvAEVect); f_mR(T); for(i=A0; i<ARRAY; i++) { f_mR( b[i]); f_mR( r[i]); f_mR(br[i]); } } /* ------------------------------------ */ int main(void) { time_t t; srand(time(&t)); do { fun(); } while(stop_w()); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ A property of spectral decomposition: b1r1 * b2r2 = 0 b1r1 * b3r3 = 0 b2r2 * b3r3 = 0 This simply materializes that our projectors are orthogonal to each other. b: The columns of the eigenvectors of A r: The rows of eigenvectors of the inverse 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: +292.0000 +262.0000 -677.0000 +262.0000 -959.0000 -735.0000 -677.0000 -735.0000 -272.0000 AEVect: Eigenvectors of A +0.0995 +0.7319 +0.6741 +0.8154 +0.3283 -0.4768 +0.5703 -0.5971 +0.5641 Inverse of AEVect = InvAEVect +0.0995 +0.8154 +0.5703 +0.7319 +0.3283 -0.5971 +0.6741 -0.4768 +0.5641 Press return to continue. This simply materializes that our projectors bnrn are orthogonal to each other. b1r1 * b2r2 +0.0000 +0.0000 -0.0000 +0.0000 +0.0000 -0.0000 +0.0000 +0.0000 -0.0000 b1r1 * b3r3 -0.0000 +0.0000 -0.0000 -0.0000 +0.0000 -0.0000 -0.0000 +0.0000 -0.0000 b2r2 * b3r3 +0.0000 -0.0000 +0.0000 +0.0000 -0.0000 +0.0000 -0.0000 +0.0000 -0.0000 Press return to continue Press X return to stop