Linear Algebra and the C Language/a0ni

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as: c00b.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define RCA RC5 /* ------------------------------------ */ /* ------------------------------------ */ double f( double x) { return(cosh(2*x)); } char feq[] = "cosh(2*x)"; /* ------------------------------------ */ double g( double x) { return(2*cosh(x)*cosh(x)-1); } char geq[] = "2*cosh(x)**2)-1"; /* ------------------------------------ */ /* ------------------------------------ */ void fun(void) { double **A = rEsymmetric_mR( i_mR(RCA,RCA),999,+1.E-4); double **cosh2A = i_mR(RCA,RCA); double **TwocoshA_P2_mns1 = i_mR(RCA,RCA); double **EVector = i_mR(RCA,RCA); double **EVectorT = i_mR(RCA,RCA); double **EValue = i_mR(RCA,RCA); double **cosh2A_EValue = i_mR(RCA,RCA); double **TwocoshA_P2_mns1_EValue = i_mR(RCA,RCA); double **T1 = i_mR(RCA,RCA); clrscrn(); printf(" A:"); p_mR(A, S10,P4,C6); stop(); clrscrn(); eigs_V_mR(A,EVector); transpose_mR(EVector,EVectorT); /* EValue = EVectorT A EVector */ mul_mR(EVectorT,A,T1); mul_mR(T1,EVector,EValue); printf(" cosh(2 A)"); f_eigs_mR(f,EValue,cosh2A_EValue); /* cosh2A = EVector cosh2A_EValue EVectorT */ mul_mR(EVector,cosh2A_EValue,T1); mul_mR(T1,EVectorT,cosh2A); pE_mR(cosh2A, S10,P4,C6); printf(" 2cosh(A)**2-1"); f_eigs_mR(g,EValue,TwocoshA_P2_mns1_EValue); /* TwocoshA_P2_mns1 = EVector TwocoshA_P2_mns1_EValue EVectorT */ mul_mR(EVector,TwocoshA_P2_mns1_EValue,T1); mul_mR(T1,EVectorT,TwocoshA_P2_mns1); pE_mR(TwocoshA_P2_mns1, S10,P4,C6); f_mR(A); f_mR(cosh2A); f_mR(TwocoshA_P2_mns1); f_mR(EVector); f_mR(EVectorT); f_mR(EValue); f_mR(TwocoshA_P2_mns1_EValue); f_mR(cosh2A_EValue); f_mR(T1); } /* ------------------------------------ */ int main(void) { time_t t; srand(time(&t)); do { fun(); } while(stop_w()); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ Let's check the equations: We know that: cosh(x+y) = cosh(x) cosh(y) + sinh(x) sinh(y) let x = y cosh(x+x) = cosh(x) cosh(x) + sinh(x) sinh(x) cosh(2x) = cosh(x)**2 + sinh(x)**2 cosh(x)**2-sinh(x)**2 = 1 sinh(x)**2 = cosh(x)**2-1 cosh(2x) = cosh(x)**2 + (cosh(x)**2-1) cosh(2x) = 2*cosh(x)**2 - 1 Screen output example: A: +0.0254 +0.0143 -0.0145 +0.0007 +0.0082 +0.0143 +0.0161 -0.0023 -0.0104 +0.0050 -0.0145 -0.0023 +0.0279 -0.0141 -0.0096 +0.0007 -0.0104 -0.0141 +0.0289 +0.0087 +0.0082 +0.0050 -0.0096 +0.0087 +0.0199 Press return to continue. cosh(2 A) +1.0023e+00 +1.3156e-03 -1.7893e-03 +3.3706e-04 +1.1817e-03 +1.3156e-03 +1.0012e+00 -4.1518e-04 -7.6214e-04 +4.5606e-04 -1.7893e-03 -4.1518e-04 +1.0026e+00 -1.7503e-03 -1.4305e-03 +3.3706e-04 -7.6214e-04 -1.7503e-03 +1.0024e+00 +1.0307e-03 +1.1817e-03 +4.5606e-04 -1.4305e-03 +1.0307e-03 +1.0013e+00 2cosh(A)**2-1 +1.0023e+00 +1.3156e-03 -1.7893e-03 +3.3706e-04 +1.1817e-03 +1.3156e-03 +1.0012e+00 -4.1518e-04 -7.6214e-04 +4.5606e-04 -1.7893e-03 -4.1518e-04 +1.0026e+00 -1.7503e-03 -1.4305e-03 +3.3706e-04 -7.6214e-04 -1.7503e-03 +1.0024e+00 +1.0307e-03 +1.1817e-03 +4.5606e-04 -1.4305e-03 +1.0307e-03 +1.0013e+00 Press return to continue Press X return to stop