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/* -*- mode: C -*- */
/*
IGraph library.
Copyright (C) 2010-2012 Gabor Csardi <csardi.gabor@gmail.com>
334 Harvard street, Cambridge, MA 02139 USA
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301 USA
*/
#include "igraph_complex.h"
#include "igraph_math.h"
#include <math.h>
/**
* \example igraph_complex.c
*/
igraph_complex_t igraph_complex(igraph_real_t x, igraph_real_t y) {
igraph_complex_t res;
IGRAPH_REAL(res) = x;
IGRAPH_IMAG(res) = y;
return res;
}
igraph_complex_t igraph_complex_polar(igraph_real_t r, igraph_real_t theta) {
igraph_complex_t res;
IGRAPH_REAL(res) = r * cos(theta);
IGRAPH_IMAG(res) = r * sin(theta);
return res;
}
igraph_bool_t igraph_complex_eq_tol(igraph_complex_t z1,
igraph_complex_t z2,
igraph_real_t tol) {
if (fabs(IGRAPH_REAL(z1) - IGRAPH_REAL(z2)) > tol ||
fabs(IGRAPH_IMAG(z1) - IGRAPH_IMAG(z2)) > tol) {
return 0;
}
return 1;
}
igraph_real_t igraph_complex_mod(igraph_complex_t z) {
igraph_real_t x = IGRAPH_REAL(z);
igraph_real_t y = IGRAPH_IMAG(z);
return hypot(x, y);
}
igraph_real_t igraph_complex_arg(igraph_complex_t z) {
igraph_real_t x = IGRAPH_REAL(z);
igraph_real_t y = IGRAPH_IMAG(z);
if (x == 0.0 && y == 0.0) {
return 0.0;
}
return atan2(y, x);
}
igraph_complex_t igraph_complex_add(igraph_complex_t z1,
igraph_complex_t z2) {
igraph_complex_t res;
IGRAPH_REAL(res) = IGRAPH_REAL(z1) + IGRAPH_REAL(z2);
IGRAPH_IMAG(res) = IGRAPH_IMAG(z1) + IGRAPH_IMAG(z2);
return res;
}
igraph_complex_t igraph_complex_sub(igraph_complex_t z1,
igraph_complex_t z2) {
igraph_complex_t res;
IGRAPH_REAL(res) = IGRAPH_REAL(z1) - IGRAPH_REAL(z2);
IGRAPH_IMAG(res) = IGRAPH_IMAG(z1) - IGRAPH_IMAG(z2);
return res;
}
igraph_complex_t igraph_complex_mul(igraph_complex_t z1,
igraph_complex_t z2) {
igraph_complex_t res;
IGRAPH_REAL(res) = IGRAPH_REAL(z1) * IGRAPH_REAL(z2) -
IGRAPH_IMAG(z1) * IGRAPH_IMAG(z2);
IGRAPH_IMAG(res) = IGRAPH_REAL(z1) * IGRAPH_IMAG(z2) +
IGRAPH_IMAG(z1) * IGRAPH_REAL(z2);
return res;
}
igraph_complex_t igraph_complex_div(igraph_complex_t z1,
igraph_complex_t z2) {
igraph_complex_t res;
igraph_real_t z1r = IGRAPH_REAL(z1), z1i = IGRAPH_IMAG(z1);
igraph_real_t z2r = IGRAPH_REAL(z2), z2i = IGRAPH_IMAG(z2);
igraph_real_t s = 1.0 / igraph_complex_abs(z2);
igraph_real_t sz2r = s * z2r;
igraph_real_t sz2i = s * z2i;
IGRAPH_REAL(res) = (z1r * sz2r + z1i * sz2i) * s;
IGRAPH_IMAG(res) = (z1i * sz2r - z1r * sz2i) * s;
return res;
}
igraph_complex_t igraph_complex_add_real(igraph_complex_t z,
igraph_real_t x) {
igraph_complex_t res;
IGRAPH_REAL(res) = IGRAPH_REAL(z) + x;
IGRAPH_IMAG(res) = IGRAPH_IMAG(z);
return res;
}
igraph_complex_t igraph_complex_add_imag(igraph_complex_t z,
igraph_real_t y) {
igraph_complex_t res;
IGRAPH_REAL(res) = IGRAPH_REAL(z);
IGRAPH_IMAG(res) = IGRAPH_IMAG(z) + y;
return res;
}
igraph_complex_t igraph_complex_sub_real(igraph_complex_t z,
igraph_real_t x) {
igraph_complex_t res;
IGRAPH_REAL(res) = IGRAPH_REAL(z) - x;
IGRAPH_IMAG(res) = IGRAPH_IMAG(z);
return res;
}
igraph_complex_t igraph_complex_sub_imag(igraph_complex_t z,
igraph_real_t y) {
igraph_complex_t res;
IGRAPH_REAL(res) = IGRAPH_REAL(z);
IGRAPH_IMAG(res) = IGRAPH_IMAG(z) - y;
return res;
}
igraph_complex_t igraph_complex_mul_real(igraph_complex_t z,
igraph_real_t x) {
igraph_complex_t res;
IGRAPH_REAL(res) = IGRAPH_REAL(z) * x;
IGRAPH_IMAG(res) = IGRAPH_IMAG(z) * x;
return res;
}
igraph_complex_t igraph_complex_mul_imag(igraph_complex_t z,
igraph_real_t y) {
igraph_complex_t res;
IGRAPH_REAL(res) = - IGRAPH_IMAG(z) * y;
IGRAPH_IMAG(res) = IGRAPH_REAL(z) * y;
return res;
}
igraph_complex_t igraph_complex_div_real(igraph_complex_t z,
igraph_real_t x) {
igraph_complex_t res;
IGRAPH_REAL(res) = IGRAPH_REAL(z) / x;
IGRAPH_IMAG(res) = IGRAPH_IMAG(z) / x;
return res;
}
igraph_complex_t igraph_complex_div_imag(igraph_complex_t z,
igraph_real_t y) {
igraph_complex_t res;
IGRAPH_REAL(res) = IGRAPH_IMAG(z) / y;
IGRAPH_IMAG(res) = - IGRAPH_REAL(z) / y;
return res;
}
igraph_complex_t igraph_complex_conj(igraph_complex_t z) {
igraph_complex_t res;
IGRAPH_REAL(res) = IGRAPH_REAL(z);
IGRAPH_IMAG(res) = - IGRAPH_IMAG(z);
return res;
}
igraph_complex_t igraph_complex_neg(igraph_complex_t z) {
igraph_complex_t res;
IGRAPH_REAL(res) = - IGRAPH_REAL(z);
IGRAPH_IMAG(res) = - IGRAPH_IMAG(z);
return res;
}
igraph_complex_t igraph_complex_inv(igraph_complex_t z) {
igraph_complex_t res;
igraph_real_t s = 1.0 / igraph_complex_abs(z);
IGRAPH_REAL(res) = (IGRAPH_REAL(z) * s) * s;
IGRAPH_IMAG(res) = - (IGRAPH_IMAG(z) * s) * s;
return res;
}
igraph_real_t igraph_complex_abs(igraph_complex_t z) {
return hypot(IGRAPH_REAL(z), IGRAPH_IMAG(z));
}
igraph_real_t igraph_complex_logabs(igraph_complex_t z) {
igraph_real_t xabs = fabs(IGRAPH_REAL(z));
igraph_real_t yabs = fabs(IGRAPH_IMAG(z));
igraph_real_t max, u;
if (xabs >= yabs) {
max = xabs;
u = yabs / xabs;
} else {
max = yabs;
u = xabs / yabs;
}
return log (max) + 0.5 * log1p (u * u);
}
igraph_complex_t igraph_complex_sqrt(igraph_complex_t z) {
igraph_complex_t res;
if (IGRAPH_REAL(z) == 0.0 && IGRAPH_IMAG(z) == 0.0) {
IGRAPH_REAL(res) = IGRAPH_IMAG(res) = 0.0;
} else {
igraph_real_t x = fabs (IGRAPH_REAL(z));
igraph_real_t y = fabs (IGRAPH_IMAG(z));
igraph_real_t w;
if (x >= y) {
igraph_real_t t = y / x;
w = sqrt (x) * sqrt (0.5 * (1.0 + sqrt (1.0 + t * t)));
} else {
igraph_real_t t = x / y;
w = sqrt (y) * sqrt (0.5 * (t + sqrt (1.0 + t * t)));
}
if (IGRAPH_REAL(z) >= 0.0) {
igraph_real_t ai = IGRAPH_IMAG(z);
IGRAPH_REAL(res) = w;
IGRAPH_IMAG(res) = ai / (2.0 * w);
} else {
igraph_real_t ai = IGRAPH_IMAG(z);
igraph_real_t vi = (ai >= 0) ? w : -w;
IGRAPH_REAL(res) = ai / (2.0 * vi);
IGRAPH_IMAG(res) = vi;
}
}
return res;
}
igraph_complex_t igraph_complex_sqrt_real(igraph_real_t x) {
igraph_complex_t res;
if (x >= 0) {
IGRAPH_REAL(res) = sqrt(x);
IGRAPH_IMAG(res) = 0.0;
} else {
IGRAPH_REAL(res) = 0.0;
IGRAPH_IMAG(res) = sqrt(-x);
}
return res;
}
igraph_complex_t igraph_complex_exp(igraph_complex_t z) {
igraph_real_t rho = exp(IGRAPH_REAL(z));
igraph_real_t theta = IGRAPH_IMAG(z);
igraph_complex_t res;
IGRAPH_REAL(res) = rho * cos(theta);
IGRAPH_IMAG(res) = rho * sin(theta);
return res;
}
igraph_complex_t igraph_complex_pow(igraph_complex_t z1,
igraph_complex_t z2) {
igraph_complex_t res;
if (IGRAPH_REAL(z1) == 0 && IGRAPH_IMAG(z1) == 0.0) {
if (IGRAPH_REAL(z2) == 0 && IGRAPH_IMAG(z2) == 0.0) {
IGRAPH_REAL(res) = 1.0;
IGRAPH_IMAG(res) = 0.0;
} else {
IGRAPH_REAL(res) = IGRAPH_IMAG(res) = 0.0;
}
} else if (IGRAPH_REAL(z2) == 1.0 && IGRAPH_IMAG(z2) == 0.0) {
IGRAPH_REAL(res) = IGRAPH_REAL(z1);
IGRAPH_IMAG(res) = IGRAPH_IMAG(z1);
} else if (IGRAPH_REAL(z2) == -1.0 && IGRAPH_IMAG(z2) == 0.0) {
res = igraph_complex_inv(z1);
} else {
igraph_real_t logr = igraph_complex_logabs (z1);
igraph_real_t theta = igraph_complex_arg (z1);
igraph_real_t z2r = IGRAPH_REAL(z2), z2i = IGRAPH_IMAG(z2);
igraph_real_t rho = exp (logr * z2r - z2i * theta);
igraph_real_t beta = theta * z2r + z2i * logr;
IGRAPH_REAL(res) = rho * cos(beta);
IGRAPH_IMAG(res) = rho * sin(beta);
}
return res;
}
igraph_complex_t igraph_complex_pow_real(igraph_complex_t z,
igraph_real_t x) {
igraph_complex_t res;
if (IGRAPH_REAL(z) == 0.0 && IGRAPH_IMAG(z) == 0.0) {
if (x == 0) {
IGRAPH_REAL(res) = 1.0;
IGRAPH_IMAG(res) = 0.0;
} else {
IGRAPH_REAL(res) = IGRAPH_IMAG(res) = 0.0;
}
} else {
igraph_real_t logr = igraph_complex_logabs(z);
igraph_real_t theta = igraph_complex_arg(z);
igraph_real_t rho = exp (logr * x);
igraph_real_t beta = theta * x;
IGRAPH_REAL(res) = rho * cos(beta);
IGRAPH_IMAG(res) = rho * sin(beta);
}
return res;
}
igraph_complex_t igraph_complex_log(igraph_complex_t z) {
igraph_complex_t res;
IGRAPH_REAL(res) = igraph_complex_logabs(z);
IGRAPH_IMAG(res) = igraph_complex_arg(z);
return res;
}
igraph_complex_t igraph_complex_log10(igraph_complex_t z) {
return igraph_complex_mul_real(igraph_complex_log(z), 1 / log(10.0));
}
igraph_complex_t igraph_complex_log_b(igraph_complex_t z,
igraph_complex_t b) {
return igraph_complex_div (igraph_complex_log(z), igraph_complex_log(b));
}
igraph_complex_t igraph_complex_sin(igraph_complex_t z) {
igraph_real_t zr = IGRAPH_REAL(z);
igraph_real_t zi = IGRAPH_IMAG(z);
igraph_complex_t res;
if (zi == 0.0) {
IGRAPH_REAL(res) = sin(zr);
IGRAPH_IMAG(res) = 0.0;
} else {
IGRAPH_REAL(res) = sin(zr) * cosh(zi);
IGRAPH_IMAG(res) = cos(zr) * sinh(zi);
}
return res;
}
igraph_complex_t igraph_complex_cos(igraph_complex_t z) {
igraph_real_t zr = IGRAPH_REAL(z);
igraph_real_t zi = IGRAPH_IMAG(z);
igraph_complex_t res;
if (zi == 0.0) {
IGRAPH_REAL(res) = cos(zr);
IGRAPH_IMAG(res) = 0.0;
} else {
IGRAPH_REAL(res) = cos(zr) * cosh(zi);
IGRAPH_IMAG(res) = sin(zr) * sinh(-zi);
}
return res;
}
igraph_complex_t igraph_complex_tan(igraph_complex_t z) {
igraph_real_t zr = IGRAPH_REAL(z);
igraph_real_t zi = IGRAPH_IMAG(z);
igraph_complex_t res;
if (fabs (zi) < 1) {
igraph_real_t D = pow (cos (zr), 2.0) + pow (sinh (zi), 2.0);
IGRAPH_REAL(res) = 0.5 * sin (2 * zr) / D;
IGRAPH_IMAG(res) = 0.5 * sinh (2 * zi) / D;
} else {
igraph_real_t u = exp (-zi);
igraph_real_t C = 2 * u / (1 - pow (u, 2.0));
igraph_real_t D = 1 + pow (cos (zr), 2.0) * pow (C, 2.0);
igraph_real_t S = pow (C, 2.0);
igraph_real_t T = 1.0 / tanh (zi);
IGRAPH_REAL(res) = 0.5 * sin (2 * zr) * S / D;
IGRAPH_IMAG(res) = T / D;
}
return res;
}
igraph_complex_t igraph_complex_sec(igraph_complex_t z) {
return igraph_complex_inv(igraph_complex_cos(z));
}
igraph_complex_t igraph_complex_csc(igraph_complex_t z) {
return igraph_complex_inv(igraph_complex_sin(z));
}
igraph_complex_t igraph_complex_cot(igraph_complex_t z) {
return igraph_complex_inv(igraph_complex_tan(z));
}
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