Linear Algebra and the C Language/a0id

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00e.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ void fun(int r) { double **A = rdefinite_positive_mR( i_mR(r,r), 99); double **SqrtA = i_mR(r,r); double **invSqrtA = i_mR(r,r); double **V = i_mR(r,r); double **VT = i_mR(r,r); double **EValue = i_mR(r,r); double **f_EValue = i_mR(r,r); double **T = i_mR(r,r); clrscrn(); printf(" A positive-matrix is ​​positive definite\n" " if and only if its positive square root\n" " is invertible.\n\n" " A:"); p_mR(A, S6,P0, C8); stop(); clrscrn(); /* Eigenvector */ eigs_V_mR(A,V); transpose_mR(V,VT); /* EigenValue = VT * A * V */ mul_mR(VT,A,T); mul_mR(T,V,EValue); printf(" sqrt(A) = V * sqrt(EValue) * VT\n"); f_eigs_mR(sqrt,EValue,f_EValue); mul_mR(V,f_EValue,T); mul_mR(T,VT, SqrtA); p_mR(SqrtA, S10,P4, C8); printf(" inv(sqrt(A)):"); inv_mR(SqrtA,invSqrtA); p_mR(invSqrtA, S10,P4, C8); printf(" IDE = sqrt(A) inv(sqrt(A))"); mul_mR(SqrtA,invSqrtA,T ); p_mR(T, S10,P4, C8); f_mR(A); f_mR(SqrtA); f_mR(invSqrtA); f_mR(V); f_mR(VT); f_mR(EValue); f_mR(f_EValue); f_mR(T); } /* ------------------------------------ */ int main(void) { time_t t; srand(time(&t)); do { fun(RC4); } while(stop_w()); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ A positive-matrix is ​​positive definite if and only if its positive square root is invertible. Screen output example: A positive-matrix is ​​positive definite if and only if its positive square root is invertible. A: +8879 +8199 -2826 -2143 +8199 +12315 -1166 +2745 -2826 -1166 +11572 +3808 -2143 +2745 +3808 +7469 Press return to continue. sqrt(A) = V * sqrt(EValue) * VT +77.3385 +48.9529 -12.1061 -18.8362 +48.9529 +97.1459 -4.9575 +21.3707 -12.1061 -4.9575 +104.8783 +20.0350 -18.8362 +21.3707 +20.0350 +79.0954 inv(sqrt(A)): +0.0245 -0.0144 +0.0003 +0.0097 -0.0144 +0.0196 +0.0010 -0.0090 +0.0003 +0.0010 +0.0101 -0.0028 +0.0097 -0.0090 -0.0028 +0.0181 IDE = sqrt(A) inv(sqrt(A)) +1.0000 +0.0000 -0.0000 +0.0000 +0.0000 +1.0000 -0.0000 +0.0000 -0.0000 -0.0000 +1.0000 +0.0000 +0.0000 -0.0000 -0.0000 +1.0000 Press return to continue Press X return to stop