Linear Algebra and the C Language/a0ls

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c05c.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define RAT R2 #define CAT C5 #define Cb C1 /* ------------------------------------ */ #define CFREEV Cb+C3 /* ------------------------------------ */ int main(void) { double a_Tb[RAT*(CAT+Cb)]={ 2,0,0,4,1,0, 0,3,0,5,0,0 }; double **ATb = ca_A_mR(a_Tb, i_Abr_Ac_bc_mR(RAT,CAT,Cb)); double **AT = c_Ab_A_mR(ATb, i_mR(RAT,CAT)); double **b = c_Ab_b_mR(ATb, i_mR(RAT,Cb)); double **ATb_free = i_Abr_Ac_bc_mR(CAT,CAT,CFREEV); double **B = i_mR(CAT,CFREEV); double **ATB = i_mR(RAT,CFREEV); clrscrn(); printf("Find a basis B for the orthogonal complement of AT.\n\n" " AT:"); p_mR(AT,S6,P1,C10); printf(" b:"); p_mR(b,S6,P1,C10); printf(" ATb:"); p_mR(ATb,S6,P1,C10); stop(); clrscrn(); printf(" ATb: gj_PP_mR(ATb,NO);"); p_mR(gj_PP_mR(ATb,NO),S7,P3,C10); put_zeroR_mR(ATb,ATb_free); put_freeV_mR(ATb_free); printf(" ATb_free: b CFREEV"); p_mR(gj_PP_mR(ATb_free,YES),S7,P3,C10); printf(" The free variables of the system above \n" " are a basis B for the orthogonal complement of AT. \n\n" " B: Copy the coefficients in the next C file."); P_mR(c_Ab_b_mR(ATb_free,B),S10,P12,C7); stop(); clrscrn(); printf("Verify if B is a basis for" " the orthogonal complement of AT\n\n" " AT:" ); p_mR(AT, S7,P3,C10); printf(" B:"); p_mR(B, S7,P3,C10); printf(" AT B: AT and B are orthogonal"); p_mR(mul_mR(AT,B,ATB), S7,P6,C10); stop(); f_mR(ATb); f_mR(AT); f_mR(b); f_mR(ATb_free); f_mR(B); f_mR(ATB); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ Screen output example: Find a basis B for the orthogonal complement of AT. AT: +2.0 +0.0 +0.0 +4.0 +1.0 +0.0 +3.0 +0.0 +5.0 +0.0 b: +0.0 +0.0 ATb: +2.0 +0.0 +0.0 +4.0 +1.0 +0.0 +0.0 +3.0 +0.0 +5.0 +0.0 +0.0 Press return to continue. ATb: gj_PP_mR(ATb,NO); +1.000 +0.000 +0.000 +2.000 +0.500 +0.000 +0.000 +1.000 +0.000 +1.667 +0.000 +0.000 ATb_free: b CFREEV +1.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 -2.000 -0.500 +0.000 +1.000 +0.000 +0.000 +0.000 +0.000 +0.000 -1.667 +0.000 +0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +1.000 The free variables of the system above are a basis B for the orthogonal complement of AT. B: Copy the coefficients in the next C file. +0.000000000000, +0.000000000000, -2.000000000000, -0.500000000000, +0.000000000000, +0.000000000000, -1.666666666667, +0.000000000000, +0.000000000000, +1.000000000000, +0.000000000000, +0.000000000000, +0.000000000000, +0.000000000000, +1.000000000000, +0.000000000000, +0.000000000000, +0.000000000000, +0.000000000000, +1.000000000000 Press return to continue. Verify if B is a basis for the orthogonal complement of AT AT: +2.000 +0.000 +0.000 +4.000 +1.000 +0.000 +3.000 +0.000 +5.000 +0.000 B: +0.000 +0.000 -2.000 -0.500 +0.000 +0.000 -1.667 +0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +0.000 +1.000 +0.000 +0.000 +0.000 +0.000 +1.000 AT B: AT and B are orthogonal +0.000000 +0.000000 +0.000000 +0.000000 +0.000000 +0.000000 +0.000000 +0.000000 Press return to continue.