int main()
{
double complex v, z;
double a = 0.0, b = 0.0;
puts("Calculate the inverse hyperbolic cosine of a complex number,"
" cacosh(z)\n");
puts("Enter the real and imaginary parts of a complex number:");
if ( scanf("%lf %lf", &a, &b) == 2)
{
z = a + b * I;
printf( "z = %.2f %+.2f*I.\n", creal(z), cimag(z) );
v = cacosh(z);
printf( "The cacosh(z) function yields %.2f %+.2f*I.\n",
creal(v), cimag(v) );
printf( "The inverse function, ccosh(cacosh(z)),"
" yields %.2f %+.2f*I.\n",
creal( ccosh(v)), cimag( ccosh(v)) );
}
else
printf("Invalid input.\n");
return 0;
}
double complex
ccos(double complex z)
{
/* ccos(z) = ccosh(I * z) */
return (ccosh(CMPLX(-cimag(z), creal(z))));
}
//## Complex Complex.ccoshf();
static KMETHOD Complex_ccoshf(KonohaContext *kctx, KonohaStack *sfp)
{
kComplex *kc = (kComplex *) sfp[0].asObject;
float _Complex zf = (float _Complex)kc->z;
float ret = ccosh(zf);
KReturnFloatValue(ret);
}
//## Complex Complex.ccoshl();
static KMETHOD Complex_ccoshl(KonohaContext *kctx, KonohaStack *sfp)
{
kComplex *kc = (kComplex *) sfp[0].asObject;
long double _Complex zl = (long double _Complex)kc->z;
long double ret = ccosh(zl);
KReturnFloatValue(ret);
}
dcomplex
ccos(dcomplex z) {
double x, y;
x = D_RE(z);
y = D_IM(z);
D_RE(z) = y;
D_IM(z) = -x;
return (ccosh(z));
}
void
cmplx (double _Complex z)
{
cabs (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 129 } */
cacos (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 131 } */
cacosh (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 133 } */
carg (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 135 } */
casin (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 137 } */
casinh (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 139 } */
catan (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 141 } */
catanh (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 143 } */
ccos (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 145 } */
ccosh (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 147 } */
cexp (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 149 } */
cimag (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 151 } */
clog (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 153 } */
conj (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 155 } */
cpow (z, z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 157 } */
cproj (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 159 } */
creal (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 161 } */
csin (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 163 } */
csinh (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 165 } */
csqrt (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 167 } */
ctan (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 169 } */
ctanh (z); /* { dg-warning "incompatible implicit" } */
/* { dg-message "include ..complex.h.." "" { target *-*-* } 171 } */
}
double complex Heston::logCF(const double &S, const double complex &u) const {
double complex temp1,temp2,temp3, v1, v2,v3, gamma, result;
v1 = kappa-I*rho*sigma*u;
v2 = u*u+I*u;
v3 = kappa*theta/(sigma*sigma);
gamma = sigma*sigma*v2+v1*v1;
gamma = cpow(gamma,.5);
temp1 = cexp(I*u*(log(S)+(r-q)*T)+v3*T*v1);
temp2 = ccosh(gamma*T/2.0)+v1/gamma*csinh(gamma*T/2.0);
result = temp1/cpow(temp2,2.0*v3);
temp1 = v0*v2; //v0 is class variable defined in .h file
temp2 = gamma/ctanh(gamma*T/2.0)+v1;
temp3 = cexp(-temp1/temp2);
result = result*temp3;
return result;
}
int main()
{
double x,y;
double complex result;
#ifdef XXXXX
for (x = -10; x < 10; x += 0.5)
for (y=-10; y < 10; y += 0.5) {
result = ccosh(x + I *y);
printf("%f %f %f %f %f %f\n",x,y,(double)cosh(x)*cos(y),(double)creal(result),(double)sinh(x)*sin(y),(double)cimag(result));
}
for (x = -10; x < 10; x += 0.5)
for (y=-10; y < 10; y += 0.5) {
result = csinh(x + I *y);
printf("%f %f %f %f %f %f\n",x,y,(double)sinh(x)*cos(y),(double)creal(result),(double)cosh(x)*sin(y),(double)cimag(result));
}
#endif
for (x = -10; x < 10; x += 0.5)
for (y=-10; y < 10; y += 0.5) {
double d = coshl( 2.0L * x ) + cosl( 2.0L * y );
result = ctanh(x + I *y);
printf("%f %f %f %f %f %f\n",x,y,(double)sinh(2.0*x)/d,(double)creal(result),(double)sin(2.0*y)/d,(double)cimag(result));
}
}
TEST(complex, ccosh) {
ASSERT_EQ(1.0, ccosh(0));
}
double complex ccos(double complex z)
{
return ccosh(CMPLX(-cimag(z), creal(z)));
}
f = ctanf(f); ld = ctanl(ld); TEST_TRACE(C99 7.3.6.1) d = cacosh(d); f = cacoshf(f); ld = cacoshl(ld); TEST_TRACE(C99 7.3.6.2) d = casinh(d); f = casinhf(f); ld = casinhl(ld); TEST_TRACE(C99 7.3.6.3) d = catanh(d); f = catanhf(f); ld = catanhl(ld); TEST_TRACE(C99 7.3.6.4) d = ccosh(d); f = ccoshf(f); ld = ccoshl(ld); TEST_TRACE(C99 7.3.6.5) d = csinh(d); f = csinhf(f); ld = csinhl(ld); TEST_TRACE(C99 7.3.6.6) d = ctanh(d); f = ctanhf(f); ld = ctanhl(ld); TEST_TRACE(C99 7.3.7.1) d = cexp(d); f = cexpf(f); ld = cexpl(ld); TEST_TRACE(C99 7.3.7.2)
void
docomplex (void)
{
#ifndef NO_DOUBLE
complex double ca, cb, cc;
double f1;
ca = 1.0 + 1.0 * I;
cb = 1.0 - 1.0 * I;
f1 = cabs (ca);
fprintf (stdout, "cabs : %f\n", f1);
cc = cacos (ca);
fprintf (stdout, "cacos : %f %fi\n", creal (cc),
cimag (cc));
cc = cacosh (ca);
fprintf (stdout, "cacosh : %f %fi\n", creal (cc),
cimag (cc));
f1 = carg (ca);
fprintf (stdout, "carg : %f\n", f1);
cc = casin (ca);
fprintf (stdout, "casin : %f %fi\n", creal (cc),
cimag (cc));
cc = casinh (ca);
fprintf (stdout, "casinh : %f %fi\n", creal (cc),
cimag (cc));
cc = catan (ca);
fprintf (stdout, "catan : %f %fi\n", creal (cc),
cimag (cc));
cc = catanh (ca);
fprintf (stdout, "catanh : %f %fi\n", creal (cc),
cimag (cc));
cc = ccos (ca);
fprintf (stdout, "ccos : %f %fi\n", creal (cc),
cimag (cc));
cc = ccosh (ca);
fprintf (stdout, "ccosh : %f %fi\n", creal (cc),
cimag (cc));
cc = cexp (ca);
fprintf (stdout, "cexp : %f %fi\n", creal (cc),
cimag (cc));
f1 = cimag (ca);
fprintf (stdout, "cimag : %f\n", f1);
cc = clog (ca);
fprintf (stdout, "clog : %f %fi\n", creal (cc),
cimag (cc));
cc = conj (ca);
fprintf (stdout, "conj : %f %fi\n", creal (cc),
cimag (cc));
cc = cpow (ca, cb);
fprintf (stdout, "cpow : %f %fi\n", creal (cc),
cimag (cc));
cc = cproj (ca);
fprintf (stdout, "cproj : %f %fi\n", creal (cc),
cimag (cc));
f1 = creal (ca);
fprintf (stdout, "creal : %f\n", f1);
cc = csin (ca);
fprintf (stdout, "csin : %f %fi\n", creal (cc),
cimag (cc));
cc = csinh (ca);
fprintf (stdout, "csinh : %f %fi\n", creal (cc),
cimag (cc));
cc = csqrt (ca);
fprintf (stdout, "csqrt : %f %fi\n", creal (cc),
cimag (cc));
cc = ctan (ca);
fprintf (stdout, "ctan : %f %fi\n", creal (cc),
cimag (cc));
cc = ctanh (ca);
fprintf (stdout, "ctanh : %f %fi\n", creal (cc),
cimag (cc));
#endif
}
//FIXME
long double complex ccoshl(long double complex z)
{
return ccosh(z);
}
/*
void
traceless_herm_M_evalues(QLA_ColorMatrix *Q, double *u, double *w,
double *q1, double *q2, double *q3) {
QLA_Complex c0, c1;
QLA_ColorMatrix Q2;
QLA_M_eq_M_times_M(&Q2, Q, Q);
printf("Q^2 = \n"); printm(&Q2);
QLA_C_eq_det_M (&c0, Q); // c0 = det(Q)
QLA_C_eq_trace_M (&c1, &Q2); // c1 = tr(Q^2)
double athird = 1.0/3.0;
double cc0, cc1, cc0max;
cc0 = QLA_real(c0);
cc1 = 0.5 * QLA_real(c1);
cc0max = 2*sqrt(cc1 * athird)*(cc1 * athird); //c_0^max = 2 * (c1/3)^{3/2}
printf("c0 = %f\n", cc0);
printf("c1 = %f\n", cc1);
printf("c0_max = %f\n", cc0max);
double theta;
theta =acos(cc0/cc0max);
*u = sqrt(athird * cc1) * cos(athird * theta);
*w = sqrt(cc1) * sin(athird * theta);
*q1 = 2 * *u;
*q2 = -*u + *w;
*q3 = -*u - *w;
printf("u = %f, w = %f, q1 = %f, q2 = %f, q3 = %f\n", *u, *w, *q1, *q2, *q3);
}
void
get_f_coeffs(QLA_ColorMatrix *Q, double _Complex *f0, double _Complex *f1, double _Complex *f2){
double u, w, q1, q2, q3;
traceless_herm_M_evalues(Q, &u, &w, &q1, &q2, &q3);
printf("q1=\n"); printc99(&q1);
double _Complex e2iu, e_iu;
e2iu = cexp(2 * _Complex_I * u);
e_iu = cexp(-1.0 * _Complex_I * u);
double u2 = u*u;
double w2 = w*w;
double _Complex zeta0w;
if (fabs(w) > 0.05) {
zeta0w = sin(w)/w;
}
else {
zeta0w = 1 - w2/6. * (1-w2/20. * (1 - w2/42.));
}
double _Complex h0, h1, h2;
h0 = (u2 - w2) * e2iu + e_iu * ( 8 * u2 *cos(w) + 2*_Complex_I*u * (3*u2+w2)*zeta0w);
h1 = 2*u*e2iu - e_iu * (2 * u * cos(w) - _Complex_I * (3*u2-w2)*zeta0w);
h2 = e2iu - e_iu * ( cos(w) + 3*_Complex_I*u * zeta0w);
double fac = 1.0/(9*u2-w2);
*f0 = h0 * fac;
*f1 = h1 * fac;
*f2 = h2 * fac;
}
void
get_Bs(QLA_ColorMatrix *Q, QLA_ColorMatrix *Q2, QLA_ColorMatrix *B1, QLA_ColorMatrix *B2, double _Complex *f0, double _Complex *f1, double _Complex *f2) {
double u, w, q1, q2, q3;
traceless_herm_M_evalues(Q, &u, &w, &q1, &q2, &q3);
printf("q1=\n"); printc99(&q1);
double _Complex e2iu, e_iu;
e2iu = cexp(2 * _Complex_I * u);
e_iu = cexp(-1.0 * _Complex_I * u);
double u2 = u*u;
double w2 = w*w;
double _Complex zeta0w, zeta1w;
if (fabs(w) > 0.05) {
zeta0w = sin(w)/w;
zeta1w = (cos(w)-zeta0w)/w2;
}
else {
zeta0w = 1 - w2/6. * (1-w2/20. * (1 - w2/42.));
zeta1w = -(1 - w2/10. * (1 - w2/28.*(1 - w2/54.)))/3.0;
}
double _Complex h0, h1, h2;
h0 = (u2 - w2) * e2iu + e_iu * ( 8 * u2 *cos(w) + 2*_Complex_I*u * (3*u2+w2)*zeta0w);
h1 = 2*u*e2iu - e_iu * (2 * u * cos(w) - _Complex_I * (3*u2-w2)*zeta0w);
h2 = e2iu - e_iu * ( cos(w) + 3*_Complex_I*u * zeta0w);
double fac = 1.0/(9*u2-w2);
*f0 = h0 * fac;
*f1 = h1 * fac;
*f2 = h2 * fac;
double _Complex r01, r11, r21, r02, r12, r22, iu;
double cosw = cos(w);
iu = _Complex_I * u;
r01 = 2*(u + _Complex_I * (u2 - w2)) * e2iu
+ 2 * e_iu * ( 4*u*(2 - iu) * cosw + _Complex_I * (9 * u2 + w2 - iu * (3*u2 + w2))*zeta0w);
r11 = 2*(1 + 2*iu) * e2iu
+ e_iu * ( -2 * (1-iu) * cosw + _Complex_I * (6*u + _Complex_I * (w2 - 3*u2)) * zeta0w);
r21 = 2 * _Complex_I * e2iu + _Complex_I * e_iu * (cosw - 3*(1-iu)*zeta0w);
r02 = -2 * e2iu + 2 * iu * e_iu * (cosw + (1+4*iu) * zeta0w + 3 * u2 * zeta1w);
r12 = -_Complex_I * e_iu * ( cosw + (1+2*iu) * zeta0w - 3*u2 * zeta1w);
r22 = e_iu * (zeta0w - 3 * iu * zeta1w);
double _Complex b10, b11, b12, b20, b21, b22;
double fac1, fac2, fac3;
double mult = 0.5 * fac * fac;
fac1 = 2 * u;
fac2 = 3*u2 - w2;
fac3 = 2*(15*u2+w2);
b10 = fac1 * r01 + fac2 * r02 - fac3 * (*f0);
b10 *= mult;
b11 = fac1 * r11 + fac2 * r12 - fac3 * (*f1);
b11 *= mult;
b12 = fac1 * r21 + fac2 * r22 - fac3 * (*f2);
b12 *= mult;
fac2 = 3*u;
fac3 = 24*u;
b20 = r01 - fac2 * r02 - fac3 * (*f0);
b20 *= mult;
b21 = r11 - fac2 * r12 - fac3 * (*f1);
b21 *= mult;
b22 = r21 - fac2 * r22 - fac3 * (*f2);
b22 *= mult;
QLA_Complex qb10, qb11, qb12, qb20, qb21, qb22;
QLA_c_eq_c99(qb10, b10);
QLA_c_eq_c99(qb11, b11);
QLA_c_eq_c99(qb12, b12);
QLA_c_eq_c99(qb20, b20);
QLA_c_eq_c99(qb21, b21);
QLA_c_eq_c99(qb22, b22);
QLA_M_eq_c(B1, &qb10);
QLA_M_peq_c_times_M(B1, &qb11, Q);
QLA_M_peq_c_times_M(B1, &qb12, Q2);
QLA_M_eq_c(B2, &qb20);
QLA_M_peq_c_times_M(B2, &qb21, Q);
QLA_M_peq_c_times_M(B2, &qb22, Q2);
}
*/
int
main(void) {
QLA_ColorMatrix O, iQ, matI;
QLA_M_eq_zero(&matI);
for(int i=0; i<QLA_Nc; i++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(matI,i,i), 1.0, 0.0);
}
printm(&matI);
//QLA_Complex tr;
//QLA_Real half = 0.5;
for(int i=0; i<QLA_Nc; i++) {
for(int j=0; j<QLA_Nc; j++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(O,i,j), i+1, QLA_Nc*(j+1));
}
QLA_c_eq_r_plus_ir(QLA_elem_M(O,i,i), 2+1, 1);
}
printm(&O);
#if QDP_Colors == 3
QLA_ColorMatrix A;
QLA_M_eq_zero(&A);
for ( int m = 0; m < QLA_Nc; m++) {
for ( int n = 0; n < QLA_Nc; n++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(A, m, n), 3+m, 2-n);
}
QLA_c_eq_r_plus_ir(QLA_elem_M(A,m,m), 2+1, 1);
}
QLA_M_eq_antiherm_M(&A, &A);
printm(&A);
QLA_M_eq_zero(&A);
QLA_c_eq_r_plus_ir(QLA_elem_M(A,0,0),0,-1);
QLA_c_eq_r_plus_ir(QLA_elem_M(A,1,1),0,0.4);
QLA_c_eq_r_plus_ir(QLA_elem_M(A,2,2),0,0.6);
printm(&A);
QLA_Complex minus_i;
QLA_c_eq_r_plus_ir(minus_i, 0, -1);
QLA_ColorMatrix Q, Q2, expiQ, qla_expA;
QLA_M_eq_C_times_M(&Q, &minus_i, &matI);
QLA_M_eq_M_times_M(&Q2, &Q, &Q);
printf("Q=\n"); printm(&Q);
double _Complex f0, f1, f2;
QLA_ColorMatrix B1, B2;
get_Bs(&Q, &Q2, &B1, &B2, &f0, &f1, &f2);
printf("f0, f1, f2=\n");
printc99(&f0);
printc99(&f1);
printc99(&f2);
QLA_Complex qf0, qf1, qf2;
QLA_c_eq_c99(qf0, f0);
QLA_c_eq_c99(qf1, f1);
QLA_c_eq_c99(qf2, f2);
QLA_M_eq_c(&expiQ, &qf0);
QLA_M_peq_c_times_M(&expiQ, &qf1, &Q);
QLA_M_peq_c_times_M(&expiQ, &qf2, &Q2);
QLA_M_eq_exp_M(&qla_expA, &matI);
printf("my expiQ = \n");
printm(&expiQ);
printf("qla expA = \n");
printm(&qla_expA);
// derivative
QLA_Complex trB1M, trB2M;
QLA_ColorMatrix prod, deriv;
//tr(B_1 M)
QLA_M_eq_M_times_M (&prod, &B1, &matI); //B_1 M
QLA_C_eq_trace_M (&trB1M, &prod);
//tr(B_2 M);
QLA_M_eq_M_times_M (&prod, &B2, &matI); //B_2 M
QLA_C_eq_trace_M (&trB2M, &prod);
// deriv = Tr(B_1 M) Q
QLA_M_eq_c_times_M (&deriv, &trB1M, &Q);
// deriv += Tr(B_2 M) Q^2
QLA_M_peq_c_times_M (&deriv, &trB2M, &Q2);
// deriv += f1 M
QLA_M_peq_c_times_M (&deriv, &qf1, &matI);
// deriv += f2 Q M
QLA_M_eq_M_times_M (&prod, &Q, &matI); // Q M
QLA_M_peq_c_times_M (&deriv, &qf2, &prod);
// deriv += f2 M Q
QLA_M_eq_M_times_M (&prod, &matI, &Q); // M Q
QLA_M_peq_c_times_M (&deriv, &qf2, &prod);
QLA_M_eq_c_times_M (&deriv, &minus_i, &deriv);
printf("M = \n");
printm(&matI);
printf("deriv = \n");
printm(&deriv);
QLA_M_meq_M(&deriv, &expiQ);
printf("diff = \n");
printm(&deriv);
/*
printf("2/3f0 = \n");
f0 *= 2.0/3;
printc99(&f0);
printc(&qf0);
printc(&qf1);
printc(&qf2);
*/
#endif
#if QDP_Colors == 2
QLA_ColorMatrix expO;
QLA_Complex Tr, det;
QLA_c_eq_c_times_c(det, QLA_elem_M(O,0,0),QLA_elem_M(O,1,1));
QLA_c_meq_c_times_c(det, QLA_elem_M(O,0,1), QLA_elem_M(O,1,0));
QLA_C_eq_trace_M(&Tr, &O);
QLA_Complex qs, qt;
QLA_c_eq_r_times_c(qs, 0.5, Tr); // s=TrA/2
QLA_Complex qs2;
QLA_c_eq_c_times_c(qs2, qs, qs); //s2 = s^2
QLA_c_meq_c(qs2, det); //s2 = s^2 - detA
double _Complex t = QLA_real(qs2) + QLA_imag(qs2) * _Complex_I;
t = csqrt(t); // sqrt(s^2 - det A)
QLA_c_eq_r_plus_ir(qt, creal(t), cimag(t)); // t = sqrt(s^2 - det A)
printf(" Matrix O = \n"); printm(&O);
printf("TrO = "); printc(&Tr);
printf("detO = "); printc(&det);
printf("s = "); printc(&qs);
printf("t^2 = "); printc(&qs2);
printf("t = "); printc(&qt);
//use the QLA exp function
QLA_ColorMatrix qla_exp;
QLA_M_eq_exp_M(&qla_exp, &O); //exp(O)
double _Complex exps, cosht, sinht, sinht_t;
double _Complex s = QLA_real(qs) + QLA_imag(qs) * _Complex_I;
exps = cexp(s);
if(creal(t) == 0 && cimag(t) == 0) {
cosht = 1;
sinht = 0;
sinht_t = 1;
} else {
cosht = ccosh(t);
sinht = csinh(t);
sinht_t = sinht/t;
}
double _Complex f0, f1;
f1 = exps * sinht_t;
f0 = exps * cosht - s * f1;;
//derivative of the exponential
double _Complex f0s, f1s, f1t, f0t2, f1t2, t2;
t2 = t*t;
f0s = f0 - f1;
f1s = f1;
if (cabs(t) > 0.05) {
f1t = ((f0-f1) + s*f1)/t;
f1t2 = f1t/t;
}
else { //when |t| < 0.05, the error is O(10^{-14})
f1t = exps * t/3 * (1+t2/10*(1+t2/28));
f1t2 = exps / 3 * (1+t2/10*(1+t2/28));
}
// f0t = t * f1 - s * f1t;
f0t2 = f1 - s * f1t2;
printf("f0 = \n"); printc99(&f0);
printf("f1 = \n"); printc99(&f1);
printf("f0s = \n"); printc99(&f0s);
printf("f1s = \n"); printc99(&f1s);
printf("f1t = \n"); printc99(&f1t);
printf("f0t2 = \n"); printc99(&f0t2);
printf("f1t2 = \n"); printc99(&f1t2);
QLA_Complex qf0, qf1;
QLA_c_eq_r_plus_ir(qf0, creal(f0), cimag(f0));
QLA_c_eq_r_plus_ir(qf1, creal(f1), cimag(f1));
QLA_M_eq_c_times_M(&expO, &qf1, &O);
QLA_M_peq_c(&expO, &qf0);
printf("QLA exp = \n"); printm(&qla_exp);
printf("my expO = \n"); printm(&expO);
/*
QLA_Complex qf0s, qf0t, qf1s, qf1t;
QLA_c_eq_r_plus_ir(qf0s, creal(f0s), cimag(f0s));
QLA_c_eq_r_plus_ir(qf0t, creal(f0t), cimag(f0t));
QLA_c_eq_r_plus_ir(qf1s, creal(f1s), cimag(f1s));
QLA_c_eq_r_plus_ir(qf1t, creal(f1t), cimag(f1t));
*/
QLA_ColorMatrix deriv;
QLA_M_eq_zero(&deriv);
QLA_ColorMatrix B, AB;
QLA_M_eq_M(&B, &matI);
//QLA_c_eq_r_plus_ir(QLA_elem_M(B,1,0), 0.1, 0.2);
//QLA_c_eq_r_plus_ir(QLA_elem_M(B,0,1), 0.2, 0.1);
printf("B=\n"); printm(&B);
QLA_M_eq_M_times_M(&AB, &O, &B);
printf("AB=\n"); printm(&AB);
QLA_M_eq_c_times_M(&deriv, &qf1, &B); //f1 * B
printf("f1 B = \n"); printm(&deriv);
QLA_Complex trB, trAB;
QLA_C_eq_trace_M(&trB, &B);
QLA_C_eq_trace_M(&trAB, &AB);
double _Complex ctrB = QLA_real(trB) + _Complex_I * QLA_imag(trB);
double _Complex ctrAB = QLA_real(trAB) + _Complex_I * QLA_imag(trAB);
double _Complex coeff;
coeff = (f0s - f0t2 * s) * ctrB;
coeff += (f1s - f1t2 * s) * ctrAB;
coeff *= 0.5;
printf("coeff = "); printc99(&coeff);
QLA_Complex qc;
QLA_D_c_eq_c99(qc, coeff);
printc(&qc);
QLA_M_peq_c_times_M(&deriv, &qc, &matI); // f1 * B + () I
printf("f1B+()I=\n"); printm(&deriv);
coeff = 0.5 * (f0t2 * ctrB + f1t2 * ctrAB);
QLA_D_c_eq_c99(qc, coeff);
printc(&qc);
QLA_M_peq_c_times_M(&deriv, &qc, &O);
printm(&deriv);
exp_deriv_site(&deriv, &expO, &O, &B);
printm(&deriv);
#endif
return 0;
}
CAMLprim value math_ccosh(value x) {
CAMLparam1(x);
CAMLreturn(caml_copy_complex(ccosh(Complex_val(x))));
}
void test06 ( )
/******************************************************************************/
/*
Purpose:
TEST06: intrinsic functions for double complex variables.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
07 November 2010
Author:
John Burkardt
*/
{
double complex a = {1.0 + 2.0 * I};
printf ( "\n" );
printf ( "TEST06\n" );
printf ( " Apply intrinsic functions to DOUBLE COMPLEX variables\n" );
/*
Print them.
*/
printf ( "\n" );
/*
Note that "I" by itself is NOT a complex number, nor is it the
imaginary unit. You have to cast it to ( complex ) or ( double complex )
or multiply it by a float or double before it results in a numerical
result.
*/
printf ( " ( double complex ) I = (%14.6g,%14.6g)\n", ( double complex ) I );
printf ( " a = (%14.6g,%14.6g)\n", a );
printf ( " - a = (%14.6g,%14.6g)\n", - a );
printf ( " a + 3 = (%14.6g,%14.6g)\n", a + 3 );
printf ( " a + (0,5) = (%14.6g,%14.6g)\n", a + ( 0, 5 ) );
printf ( " 4 * a = (%14.6g,%14.6g)\n", 4 * a );
printf ( " a / 8 = (%14.6g,%14.6g)\n", a / 8 );
printf ( " a * a = (%14.6g,%14.6g)\n", a * a );
printf ( " cpow ( a, 2 ) = (%14.6g,%14.6g)\n", cpow ( a, 2 ) );
printf ( " cpow ( 2, a ) = (%14.6g,%14.6g)\n", cpow ( 2, a ) );
printf ( " cpow ( a, a ) = (%14.6g,%14.6g)\n", cpow ( a, a ) );
printf ( " 1/a = (%14.6g,%14.6g)\n", 1.0 / a );
printf ( "\n" );
printf ( " cabs(a) = %14.6g\n", cabs ( a ) );
printf ( " cacos(a) = (%14.6g,%14.6g)\n", cacos ( a ) );
printf ( " cacosh(a) = (%14.6g,%14.6g)\n", cacosh ( a ) );
printf ( " carg(a) = %14.6g\n", carg ( a ) );
printf ( " casin(a) = (%14.6g,%14.6g)\n", casin ( a ) );
printf ( " casinh(a) = (%14.6g,%14.6g)\n", casinh ( a ) );
printf ( " catan(a) = (%14.6g,%14.6g)\n",
creal ( catan ( a ) ), cimag ( catan ( a ) ) );
printf ( " catanh(a) = (%14.6g,%14.6g)\n",
creal ( catanh ( a ) ), cimag ( catanh ( a ) ) );
printf ( " ccos(a) = (%14.6g,%14.6g)\n",
creal ( ccos ( a ) ), cimag ( ccos ( a ) ) );
printf ( " ccosh(a) = (%14.6g,%14.6g)\n",
creal ( ccosh ( a ) ), cimag ( ccosh ( a ) ) );
printf ( " cexp(a) = (%14.6g,%14.6g)\n",
creal ( cexp ( a ) ), cimag ( cexp ( a ) ) );
printf ( " cimag(a) = %14.6g\n", cimag ( a ) );
printf ( " clog(a) = (%14.6g,%14.6g)\n",
creal ( clog ( a ) ), cimag ( clog ( a ) ) );
printf ( " (double complex)(1) = (%14.6g,%14.6g)\n",
creal ( ( double complex ) ( 1 ) ), cimag ( ( double complex ) ( 1 ) ) );
printf ( " (double complex)(4.0) = (%14.6g,%14.6g)\n",
creal ( ( double complex ) ( 4.0 ) ), cimag ( ( double complex ) ( 4.0 ) ) );
printf ( " conj(a) = (%14.6g,%14.6g)\n",
creal ( conj ( a ) ), cimag ( conj ( a ) ) );
printf ( " cproj(a) = (%14.6g,%14.6g)\n",
creal ( cproj ( a ) ), cimag ( cproj ( a ) ) );
printf ( " creal(a) = %14.6g\n", creal ( a ) );
printf ( " csin(a) = (%14.6g,%14.6g)\n",
creal ( csin ( a ) ), cimag ( csin ( a ) ) );
printf ( " csinh(a) = (%14.6g,%14.6g)\n",
creal ( csinh ( a ) ), cimag ( csinh ( a ) ) );
printf ( " csqrt(a) = (%14.6g,%14.6g)\n",
creal ( csqrt ( a ) ), cimag ( csqrt ( a ) ) );
printf ( " ctan(a) = (%14.6g,%14.6g)\n",
creal ( ctan ( a ) ), cimag ( ctan ( a ) ) );
printf ( " ctanh(a) = (%14.6g,%14.6g)\n",
creal ( ctanh ( a ) ), cimag ( ctanh ( a ) ) );
printf ( " (int)(a) = %10d\n", ( int ) ( a ) );
return;
}
int
main(void) {
QLA_ColorMatrix O, iQ, tmp, matI;
QLA_M_eq_zero(&matI);
for(int i=0; i<QLA_Nc; i++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(matI,i,i), 1.0, 0.0);
}
printm(&matI);
QLA_Complex tr;
QLA_Real half = 0.5;
for(int i=0; i<QLA_Nc; i++) {
for(int j=0; j<QLA_Nc; j++) {
QLA_c_eq_r_plus_ir(QLA_elem_M(O,i,j), i+1, QLA_Nc*(j+1));
}
QLA_c_eq_r_plus_ir(QLA_elem_M(O,i,i), 2+1, 1);
}
#if QDP_Colors == 3
QLA_Complex ci;
QLA_c_eq_r_plus_ir(ci, 0, 1);
//use my own implementation
QLA_ColorMatrix expiQ;
QLA_ColorMatrix QQ;
QLA_ColorMatrix QQQ;
QLA_M_eq_M_times_M(&QQ, &iQ, &iQ); //-Q^2
QLA_M_eq_M_times_M(&QQQ, &QQ, &iQ); //-iQ^3
QLA_M_eq_c_times_M(&QQQ, &ci, &QQQ); //Q^3
QLA_Complex c0, c1;
QLA_C_eq_trace_M(&c0, &QQQ);
QLA_c_eq_r_times_c(c0, 0.3333333, c0);
QLA_C_eq_trace_M(&c1, &QQ);
QLA_c_eq_r_times_c(c1, -0.5, c1);
double _Complex tf0, tf1, tf2;
getfs(&tf0, &tf1, &tf2, QLA_real(c0), QLA_real(c1));
QLA_Complex f0, f1, f2;
f0 = tf0;
f1 = tf1;
f2 = tf2;
printm(&O);
printf("iQ = \n");
printm(&iQ);
printf("QLA: exp(iQ) = \n");
printm(&qla_exp);
printf("Q^3 = \n");
printm(&QQQ);
printf("c0 = "); printc(&c0);
printf("c1 = "); printc(&c1);
#endif
#if QDP_Colors == 2
QLA_ColorMatrix expO;
QLA_Complex Tr, det;
QLA_c_eq_c_times_c(det, QLA_elem_M(O,0,0),QLA_elem_M(O,1,1));
QLA_c_meq_c_times_c(det, QLA_elem_M(O,0,1), QLA_elem_M(O,1,0));
QLA_C_eq_trace_M(&Tr, &O);
QLA_Complex s, t;
QLA_c_eq_r_times_c(s, 0.5, Tr); // s=TrA/2
QLA_Complex s2;
QLA_c_eq_c_times_c(s2, s, s); //s2 = s^2
QLA_c_meq_c(s2, det); //s2 = s^2 - detA
double _Complex dc_t = QLA_real(s2) + QLA_imag(s2) * _Complex_I;
dc_t = csqrt(dc_t); // sqrt(s^2 - det A)
QLA_c_eq_r_plus_ir(t, creal(dc_t), cimag(dc_t)); // t = sqrt(s^2 - det A)
printf(" Matrix O = \n"); printm(&O);
printf("TrO = "); printc(&Tr);
printf("detO = "); printc(&det);
printf("s = "); printc(&s);
printf("t^2 = "); printc(&s2);
printf("t = "); printc(&t);
//use the QLA exp function
QLA_ColorMatrix qla_exp;
QLA_M_eq_exp_M(&qla_exp, &O); //exp(O)
double _Complex cosht, sinht, sinht_t;
if(QLA_real(t) == 0 && QLA_imag(t) == 0) {
cosht = 1;
sinht = 0;
sinht_t = 1;
} else {
cosht = ccosh(dc_t);
sinht = csinh(dc_t);
sinht_t = sinht/dc_t;
}
double _Complex dc_s = QLA_real(s) + QLA_imag(s) * _Complex_I;
double _Complex dc_f0, dc_f1;
dc_f0 = cexp(dc_s) * (cosht - dc_s * sinht_t);
dc_f1 = cexp(dc_s) * sinht_t;
QLA_Complex f0, f1;
QLA_c_eq_r_plus_ir(f0, creal(dc_f0), cimag(dc_f0));
QLA_c_eq_r_plus_ir(f1, creal(dc_f1), cimag(dc_f1));
QLA_M_eq_c_times_M(&expO, &f1, &O);
QLA_M_peq_c(&expO, &f0);
printf("QLA exp = \n"); printm(&qla_exp);
printf("my expO = \n"); printm(&expO);
#endif
return 0;
}
