Linear Algebra and the C Language/a0mb

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c04d.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define RCA RC4 /* ------------------------------------ */ /* ------------------------------------ */ int main(void) { double a[RCA*RCA]={ +9.825339522090, +7.309094034726, -3.954100051573, -1.198212136840, +7.309094034726, +5.437252879491, -2.941464672512, -0.891352931064, -3.954100051573, -2.941464672512, +1.591284167096, +0.482207323363, -1.198212136840, -0.891352931064, +0.482207323363, +0.146123431322 }; double v[RCA*RCA]={ -0.760237560476, -0.596864313004, +0.373340433764, +0.121054375311, -0.565542575476, +0.802342191251, +0.000000000000, +0.000000000000, +0.305949262143, +0.000000000000, +0.927694411171, +0.000000000000, +0.092711897619, +0.000000000000, +0.000000000000, +0.992645877551 }; double **A = ca_A_mR(a, i_mR(RCA,RCA)); double **V = ca_A_mR(v, i_mR(RCA,RCA)); double **invV = invgj_mR(V, i_mR(RCA,RCA)); double **EValue = eigs_mR(A, i_mR(RCA, RCA)); double **T = i_mR(RCA,RCA); clrscrn(); printf(" The eigenvectors associated with eigenvalues\n" " with multiple multiplicity are not unique. \n" " There exist several set of unit vectors that\n" " correspond to the same eigenspace. \n\n\n" " An eigenvector associated with an eigenvalue\n" " with single multiplicity is unique, up to a\n" " change in the sign. \n\n\n"); printf(" A:"); p_mR(A, S9,P5, C4); stop(); clrscrn(); printf(" V:"); p_mR(V, S9,P5, C4); printf(" EValue = invV A V"); mul_mR(invV,A,T); mul_mR(T,V,EValue); p_mR(clean_eye_mR(EValue), S9,P5, C4); printf(" A = V EValue invV"); mul_mR(V,EValue,T); mul_mR(T,invV,A); p_mR(A, S9,P5, C4); stop(); f_mR(A); f_mR(V); f_mR(invV); f_mR(T); f_mR(EValue); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ Screen output example: The eigenvectors associated with eigenvalues with multiple multiplicity are not unique. There exist several set of unit vectors that correspond to the same eigenspace. An eigenvector associated with an eigenvalue with single multiplicity is unique, up to a change in the sign. A: +9.82534 +7.30909 -3.95410 -1.19821 +7.30909 +5.43725 -2.94146 -0.89135 -3.95410 -2.94146 +1.59128 +0.48221 -1.19821 -0.89135 +0.48221 +0.14612 Press return to continue. V: -0.76024 -0.59686 +0.37334 +0.12105 -0.56554 +0.80234 +0.00000 +0.00000 +0.30595 +0.00000 +0.92769 +0.00000 +0.09271 +0.00000 +0.00000 +0.99265 EValue = invV A V +17.00000 +0.00000 +0.00000 +0.00000 +0.00000 -0.00000 +0.00000 +0.00000 +0.00000 +0.00000 -0.00000 +0.00000 +0.00000 +0.00000 +0.00000 +0.00000 A = V EValue invV +9.82534 +7.30909 -3.95410 -1.19821 +7.30909 +5.43725 -2.94146 -0.89135 -3.95410 -2.94146 +1.59128 +0.48221 -1.19821 -0.89135 +0.48221 +0.14612 Press return to continue.