Linear Algebra and the C Language/a08k

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00a.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define RA R4 #define CA C6 #define Cb C1 #define RB R3 /* B : a basis for the rows space of A */ /* ------------------------------------ */ int main(void) { double ab[RA*(CA+Cb)]={ +2, -6, +8, -4, +10, +8, 0, +10, -30, +45, -5, +40, +10, 0, +14, -42, +63, -7, +63, +49, 0, -3, +9, -12, +6, -15, -12, 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); c_r_mR(A,R2,B,R2); c_r_mR(A,R3,B,R3); 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 : +2.0 -6.0 +8.0 -4.0 +10.0 +8.0 +10.0 -30.0 +45.0 -5.0 +40.0 +10.0 +14.0 -42.0 +63.0 -7.0 +63.0 +49.0 -3.0 +9.0 -12.0 +6.0 -15.0 -12.0 b : +0.0 +0.0 +0.0 +0.0 Ab : +2.0 -6.0 +8.0 -4.0 +10.0 +8.0 +0.0 +10.0 -30.0 +45.0 -5.0 +40.0 +10.0 +0.0 +14.0 -42.0 +63.0 -7.0 +63.0 +49.0 +0.0 -3.0 +9.0 -12.0 +6.0 -15.0 -12.0 +0.0 Press return to continue. The nonzero rows vectors of Ab without b form a basis for the row space of A Ab : +2.000 -6.000 +8.000 -4.000 +10.000 +8.000 +0.000 +10.000 -30.000 +45.000 -5.000 +40.000 +10.000 +0.000 +14.000 -42.000 +63.000 -7.000 +63.000 +49.000 +0.000 -3.000 +9.000 -12.000 +6.000 -15.000 -12.000 +0.000 gj_PP_mR(Ab,NO) : +1.000 -3.000 +4.500 -0.500 +4.500 +3.500 +0.000 +0.000 +0.000 +1.000 +3.000 -1.000 -1.000 +0.000 -0.000 -0.000 -0.000 -0.000 +1.000 +5.000 -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 -3.000 +4.500 -0.500 +4.500 +3.500 +0.000 +0.000 +1.000 +3.000 -1.000 -1.000 -0.000 -0.000 -0.000 -0.000 +1.000 +5.000 Press return to continue.