Linear Algebra and the C Language/a0lh

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as: c03a.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ /* ------------------------------------ */ #define RA R3 #define CA C2 /* ------------------------------------ */ /* ------------------------------------ */ int main(void) { double a[RA*(CA)]={ -2, -3, 1, 0, 0, 1 }; double x[RA*C1]={ -1, 2, -3 }; double **A = ca_A_mR(a, i_mR(RA,CA)); double **AT = transpose_mR(A, i_mR(CA,RA)); double **ATA = mul_mR(AT,A, i_mR(CA,CA)); double **invATA = invgj_mR(ATA, i_mR(CA,CA)); double **invATA_AT = mul_mR(invATA,AT, i_mR(CA,RA)); double **V = mul_mR(A,invATA_AT,i_mR(RA,RA)); /* A inv(AT A) AT */ double **X = ca_A_mR(x, i_mR(RA,C1)); double **VX = mul_mR(V,X, i_mR(RA,C1)); clrscrn(); printf(" A is subspace of R%d \n\n" " Find a transformation matrix for \n" " a projection onto R%d. \n\n" " Proj(x) = A inv(AT A) AT \n\n",RA,RA); printf(" A:"); p_mR(A,S5,P1,C7); stop(); clrscrn(); printf(" AT:"); p_mR(AT,S5,P1,C7); printf(" AT A:"); p_mR(ATA,S5,P1,C7); printf(" inv(ATA):"); p_mR(invATA,S5,P4,C7); printf(" inv(ATA)AT:"); p_mR(invATA_AT,S5,P4,C7); printf(" V = A inv(ATA)AT"); p_mR(V,S5,P4,C7); stop(); clrscrn(); printf(" V is transformation matrix for \n" " a projection onto a R%d subspace \n\n" " V:",RA); p_mR(V,S5,P4,C7); printf(" X:"); p_mR(X,S5,P1,C7); printf(" Proj(x) = A inv(ATA)AT x \n\n" " Proj(x) = V x Verify the result with the last C file"); p_mR(VX,S5,P4,C7); stop(); f_mR(A); f_mR(AT); f_mR(ATA); f_mR(invATA); f_mR(invATA_AT); f_mR(V); /* A inv(AT A) AT */ f_mR(X); f_mR(VX); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ Screen output example: A is subspace of R3 Find a transformation matrix for a projection onto R3 : Proj(x) = A inv(AT A) AT A: -2.0 -3.0 +1.0 +0.0 +0.0 +1.0 Press return to continue. AT: -2.0 +1.0 +0.0 -3.0 +0.0 +1.0 AT A: +5.0 +6.0 +6.0 +10.0 inv(ATA): +0.7143 -0.4286 -0.4286 +0.3571 inv(ATA)AT: -0.1429 +0.7143 -0.4286 -0.2143 -0.4286 +0.3571 V = A inv(ATA)AT +0.9286 -0.1429 -0.2143 -0.1429 +0.7143 -0.4286 -0.2143 -0.4286 +0.3571 Press return to continue. V is transformation matrix for a projection onto a R3 subspace. +0.9286 -0.1429 -0.2143 -0.1429 +0.7143 -0.4286 -0.2143 -0.4286 +0.3571 X: -1.0 +2.0 -3.0 Proj(x) = A inv(ATA)AT x Proj(x) = V x Verify the result with the last C file -0.5714 +2.8571 -1.7143 Press return to continue.