Linear Algebra and the C Language/a08m

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00c.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define RA R4 #define CA C6 #define Cb C1 #define RB R1 /* B : a basis for the rows space of A */ /* ------------------------------------ */ int main(void) { double ab[RA*(CA+Cb)]={ +9, -15, +21, -18, +6, +27, +0, -18, +30, -42, +36, -12, -54, +0, +21, -35, +49, -42, +14, +63, +0, -6, +10, -14, +12, -4, -18, +0 }; double **Ab = ca_A_mR(ab,i_Abr_Ac_bc_mR(RA,CA,Cb)); double **A = c_Ab_A_mR(Ab, i_mR(RA,CA)); double **b = c_Ab_b_mR(Ab, i_mR(RA,Cb)); double **B = i_mR(RB,CA); clrscrn(); printf("Basis for a Row Space by Row Reduction :\n\n"); printf(" A :"); p_mR(A,S6,P1,C10); printf(" b :"); p_mR(b,S6,P1,C10); printf(" Ab :"); p_mR(Ab,S6,P1,C10); stop(); clrscrn(); printf(" The nonzero rows vectors of Ab without b\n" " form a basis for the row space of A \n\n" " Ab :"); p_mR(Ab,S7,P3,C10); printf(" gj_PP_mR(Ab,NO) :"); gj_PP_mR(Ab,NO); p_mR(Ab,S7,P3,C10); c_Ab_A_mR(Ab,A); c_r_mR(A,R1,B,R1); printf(" B : Basis for a Row Space of A by Row Reduction"); p_mR(B,S7,P3,C10); stop(); f_mR(Ab); f_mR(b); f_mR(A); f_mR(B); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ The position of the pivots of Ab gives the position of the rows of A which form a basis for the row space of A. Screen output example: Basis for a Row Space by Row Reduction : A : +9.0 -15.0 +21.0 -18.0 +6.0 +27.0 -18.0 +30.0 -42.0 +36.0 -12.0 -54.0 +21.0 -35.0 +49.0 -42.0 +14.0 +63.0 -6.0 +10.0 -14.0 +12.0 -4.0 -18.0 b : +0.0 +0.0 +0.0 +0.0 Ab : +9.0 -15.0 +21.0 -18.0 +6.0 +27.0 +0.0 -18.0 +30.0 -42.0 +36.0 -12.0 -54.0 +0.0 +21.0 -35.0 +49.0 -42.0 +14.0 +63.0 +0.0 -6.0 +10.0 -14.0 +12.0 -4.0 -18.0 +0.0 Press return to continue. The nonzero rows vectors of Ab without b form a basis for the row space of A Ab : +9.000 -15.000 +21.000 -18.000 +6.000 +27.000 +0.000 -18.000 +30.000 -42.000 +36.000 -12.000 -54.000 +0.000 +21.000 -35.000 +49.000 -42.000 +14.000 +63.000 +0.000 -6.000 +10.000 -14.000 +12.000 -4.000 -18.000 +0.000 gj_PP_mR(Ab,NO) : +1.000 -1.667 +2.333 -2.000 +0.667 +3.000 +0.000 +0.000 +0.000 -0.000 +0.000 +0.000 +0.000 +0.000 +0.000 -0.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 +0.000 -0.000 +0.000 +0.000 +0.000 +0.000 B : Basis for a Row Space of A by Row Reduction +1.000 -1.667 +2.333 -2.000 +0.667 +3.000 Press return to continue.