Linear Algebra and the C Language/a0cz

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00c.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define RCA RC6 /* ------------------------------------ */ /* ------------------------------------ */ int main(void) { double a[RCA*RCA] ={ +0.567743563267, +0.304424089190, -0.059677700710, -0.203424101776, +0.267148131435, -0.190855616323, +0.304424089190, +0.785604057676, +0.042029055301, +0.143264950247, -0.188143702858, +0.134413376479, -0.059677700710, +0.042029055301, +0.991760844584, -0.028084908937, +0.036882704058, -0.026349692872, -0.203424101776, +0.143264950247, -0.028084908937, +0.904266630484, +0.125722520384, -0.089818517482, +0.267148131435, -0.188143702858, +0.036882704058, +0.125722520384, +0.834894016457, +0.117954799378, -0.190855616323, +0.134413376479, -0.026349692872, -0.089818517482, +0.117954799378, +0.915730887532 }; double v[RCA*RCA] ={ +0.575801565025, -0.136763612579, -0.425812987594, +0.525729633538, -0.403913441448, +0.657462118097, +0.817589479944, +0.000000000000, +0.000000000000, +0.000000000000, +0.000000000000, -0.463029094469, +0.000000000000, +0.990603712023, +0.000000000000, +0.000000000000, +0.000000000000, +0.090769793525, +0.000000000000, +0.000000000000, +0.904811195552, +0.000000000000, +0.000000000000, +0.309408095427, +0.000000000000, +0.000000000000, +0.000000000000, +0.850651722164, +0.000000000000, -0.406332356012, +0.000000000000, +0.000000000000, +0.000000000000, +0.000000000000, +0.914797208029, +0.290291426791 }; 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 = i_mR(RCA,RCA); double **T = i_mR(RCA,RCA); clrscrn(); printf(" A :"); p_mR(A, S8,P6, C6); printf(" V :"); p_mR(V, S9,P6, C6); printf(" EValue = invV * A * V"); mul_mR(invV,A,T); mul_mR(T,V,EValue); p_mR(EValue, S9,P6, C6); stop(); clrscrn(); printf(" A :"); p_mR(A, S8,P6, C6); printf(" A = V * EValue * invV (Just verify the computation)"); mul_mR(V,EValue,T); mul_mR(T,invV,A); p_mR(A, S8,P6, C6); stop(); clrscrn(); printf(" V1 V2 V3 V4 V5 V6 :"); p_mR(V, S9,P6, C6); printf(" EValue1 EValue2 EValue3 EValue4 EValue5 EValue6 "); p_mR(EValue, S9,P6, C6); printf(" det(V) = %.3e\n" " det(V) != 0.00 V1,V2,V3,V4,V5 and V6 are linearly independent\n\n", det_R(V)); stop(); clrscrn(); printf(" The matrix A projects the space in the direction\n" " of the eigenvector V6 on a hyperplan determined\n" " by the eigenvector V1,V2,V3,V4 and V5 if :\n\n" " The eigenvector V1 has its eigenvalue equal to one and \n" " The eigenvector V2 has its eigenvalue equal to one and \n" " The eigenvector V3 has its eigenvalue equal to one and \n" " The eigenvector V4 has its eigenvalue equal to one and \n" " The eigenvector V5 has its eigenvalue equal to one and \n" " The eigenvector V6 has its eigenvalue equal to zero and \n\n" " If The vectors V1,V2,V3,V4,V5 and V6 are linearly independent\n\n"); stop(); f_mR(A); f_mR(V); f_mR(invV); f_mR(T); f_mR(EValue); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ Screen output example: A : +0.567744 +0.304424 -0.059678 -0.203424 +0.267148 -0.190856 +0.304424 +0.785604 +0.042029 +0.143265 -0.188144 +0.134413 -0.059678 +0.042029 +0.991761 -0.028085 +0.036883 -0.026350 -0.203424 +0.143265 -0.028085 +0.904267 +0.125723 -0.089819 +0.267148 -0.188144 +0.036883 +0.125723 +0.834894 +0.117955 -0.190856 +0.134413 -0.026350 -0.089819 +0.117955 +0.915731 V : +0.575802 -0.136764 -0.425813 +0.525730 -0.403913 +0.657462 +0.817589 +0.000000 +0.000000 +0.000000 +0.000000 -0.463029 +0.000000 +0.990604 +0.000000 +0.000000 +0.000000 +0.090770 +0.000000 +0.000000 +0.904811 +0.000000 +0.000000 +0.309408 +0.000000 +0.000000 +0.000000 +0.850652 +0.000000 -0.406332 +0.000000 +0.000000 +0.000000 +0.000000 +0.914797 +0.290291 EValue = invV * A * V +1.000000 +0.000000 +0.000000 -0.000000 +0.000000 -0.000000 +0.000000 +1.000000 -0.000000 +0.000000 -0.000000 -0.000000 +0.000000 -0.000000 +1.000000 -0.000000 +0.000000 -0.000000 -0.000000 +0.000000 -0.000000 +1.000000 +0.000000 +0.000000 +0.000000 -0.000000 +0.000000 +0.000000 +1.000000 +0.000000 +0.000000 -0.000000 -0.000000 +0.000000 -0.000000 -0.000000 Press return to continue. A : +0.567744 +0.304424 -0.059678 -0.203424 +0.267148 -0.190856 +0.304424 +0.785604 +0.042029 +0.143265 -0.188144 +0.134413 -0.059678 +0.042029 +0.991761 -0.028085 +0.036883 -0.026350 -0.203424 +0.143265 -0.028085 +0.904267 +0.125723 -0.089819 +0.267148 -0.188144 +0.036883 +0.125723 +0.834894 +0.117955 -0.190856 +0.134413 -0.026350 -0.089819 +0.117955 +0.915731 A = V * EValue * invV (Just verify the computation) +0.567744 +0.304424 -0.059678 -0.203424 +0.267148 -0.190856 +0.304424 +0.785604 +0.042029 +0.143265 -0.188144 +0.134413 -0.059678 +0.042029 +0.991761 -0.028085 +0.036883 -0.026350 -0.203424 +0.143265 -0.028085 +0.904267 +0.125723 -0.089819 +0.267148 -0.188144 +0.036883 +0.125723 +0.834894 +0.117955 -0.190856 +0.134413 -0.026350 -0.089819 +0.117955 +0.915731 Press return to continue. V1 V2 V3 V4 V5 V6 : +0.575802 -0.136764 -0.425813 +0.525730 -0.403913 +0.657462 +0.817589 +0.000000 +0.000000 +0.000000 +0.000000 -0.463029 +0.000000 +0.990604 +0.000000 +0.000000 +0.000000 +0.090770 +0.000000 +0.000000 +0.904811 +0.000000 +0.000000 +0.309408 +0.000000 +0.000000 +0.000000 +0.850652 +0.000000 -0.406332 +0.000000 +0.000000 +0.000000 +0.000000 +0.914797 +0.290291 EValue1 EValue2 EValue3 EValue4 EValue5 EValue6 +1.000000 +0.000000 +0.000000 -0.000000 +0.000000 -0.000000 +0.000000 +1.000000 -0.000000 +0.000000 -0.000000 -0.000000 +0.000000 -0.000000 +1.000000 -0.000000 +0.000000 -0.000000 -0.000000 +0.000000 -0.000000 +1.000000 +0.000000 +0.000000 +0.000000 -0.000000 +0.000000 +0.000000 +1.000000 +0.000000 +0.000000 -0.000000 -0.000000 +0.000000 -0.000000 -0.000000 det(V) = -8.674e-01 det(V) != 0.00 V1,V2,V3,V4,V5 and V6 are linearly independent Press return to continue. The matrix A projects the space in the direction of the eigenvector V6 on a hyperplan determined by the eigenvector V1,V2,V3,V4 and V5 if : The eigenvector V1 has its eigenvalue equal to one and The eigenvector V2 has its eigenvalue equal to one and The eigenvector V3 has its eigenvalue equal to one and The eigenvector V4 has its eigenvalue equal to one and The eigenvector V5 has its eigenvalue equal to one and The eigenvector V6 has its eigenvalue equal to zero and If The vectors V1,V2,V3,V4,V5 and V6 are linearly independent Press return to continue.