def initialize_f(q1, q2, v1, v2, v3, params): m = params.mass k = params.boltzmann_constant q2_minus = 0.5 q2_plus = 1.5 regulator = 20 # larger value makes the transition sharper n = 1 + 0.5 * (af.tanh((q2 - q2_minus) * regulator) - af.tanh( (q2 - q2_plus) * regulator)) v1_bulk = (af.tanh((q2 - q2_minus) * regulator) - af.tanh( (q2 - q2_plus) * regulator) - 1) v2_bulk = 0.01 * af.sin(2 * np.pi * q1) *\ ( af.exp(-25 * (q2 - q2_minus)**2) + af.exp(-25 * (q2 - q2_plus )**2) ) T = (10 / n) f = n * (m / (2 * np.pi * k * T)) \ * af.exp(-m * (v1 - v1_bulk)**2 / (2 * k * T)) \ * af.exp(-m * (v2 - v2_bulk)**2 / (2 * k * T)) af.eval(f) return (f)
def initialize_f(q1, q2, p1, p2, p3, params): m = params.mass k = params.boltzmann_constant q2_minus = 0.5 q2_plus = 1.5 regulator = 20 # larger value makes the transition sharper rho = 1 + 0.5 * ( af.tanh(( q2 - q2_minus)*regulator) - af.tanh(( q2 - q2_plus )*regulator) ) p1_bulk = ( af.tanh(( q2 - q2_minus)*regulator) - af.tanh(( q2 - q2_plus )*regulator) - 1 ) p2_bulk = 0.5 * af.sin(2*np.pi*q1) *\ ( af.exp(-25 * (q2 - q2_minus)**2) + af.exp(-25 * (q2 - q2_plus )**2) ) T = (10 / rho) f = rho * (m / (2 * np.pi * k * T))**(3 / 2) \ * af.exp(-m * (p1 - p1_bulk)**2 / (2 * k * T)) \ * af.exp(-m * (p2 - p2_bulk)**2 / (2 * k * T)) \ * af.exp(-m * (p3)**2 / (2 * k * T)) af.eval(f) return (f)
def lowpass_filter(f): f_hat = af.fft(f) dp1 = (domain.p1_end[0] - domain.p1_start[0]) / domain.N_p1 k_v = af.tile(af.to_array(np.fft.fftfreq(domain.N_p1, dp1)), 1, 1, f.shape[2], f.shape[3]) # Applying the filter: f_hat_filtered = 0.5 * (f_hat * (af.tanh( (k_v + 0.9 * af.max(k_v)) / 0.5) - af.tanh( (k_v + 0.9 * af.min(k_v)) / 0.5))) f_hat = af.select(af.abs(k_v) < 0.8 * af.max(k_v), f_hat, f_hat_filtered) f = af.real(af.ifft(f_hat)) return (f)
def tanh(x): if isinstance(x, afnumpy.ndarray): s = arrayfire.tanh(x.d_array) return afnumpy.ndarray(x.shape, dtype=pu.typemap(s.dtype()), af_array=s) else: return numpy.tanh(x)
def get_cartesian_coords(q1, q2): #x = q1 #y = q2*(1 + q1) weight = 0.5 * (1 + af.tanh(q2)) #x = (1. - weight)*q1 + weight*q1*(1 - 0.5*q2) x = q1 * (1 - 0.5 * q2) #x = q1*(2 + q2) y = q2 return (x, y)
def get_cartesian_coords(q1, q2): weight = 0.5 * (1 + af.tanh(10 * q2)) x = q1 #(1. - weight)*q1 + weight*q1*(1 - 0.5*q2) #x = q1*(2 + q2) y = q2 #a = 0.125; k = 2*np.pi #x = q1 + a*af.cos(k*q2) #y = q2 - a*af.sin(k*q1) return (x, y)
def simple_arith(verbose = False): display_func = _util.display_func(verbose) print_func = _util.print_func(verbose) a = af.randu(3,3,dtype=af.Dtype.u32) b = af.constant(4, 3, 3, dtype=af.Dtype.u32) display_func(a) display_func(b) c = a + b d = a d += b display_func(c) display_func(d) display_func(a + 2) display_func(3 + a) c = a - b d = a d -= b display_func(c) display_func(d) display_func(a - 2) display_func(3 - a) c = a * b d = a d *= b display_func(c * 2) display_func(3 * d) display_func(a * 2) display_func(3 * a) c = a / b d = a d /= b display_func(c / 2.0) display_func(3.0 / d) display_func(a / 2) display_func(3 / a) c = a % b d = a d %= b display_func(c % 2.0) display_func(3.0 % d) display_func(a % 2) display_func(3 % a) c = a ** b d = a d **= b display_func(c ** 2.0) display_func(3.0 ** d) display_func(a ** 2) display_func(3 ** a) display_func(a < b) display_func(a < 0.5) display_func(0.5 < a) display_func(a <= b) display_func(a <= 0.5) display_func(0.5 <= a) display_func(a > b) display_func(a > 0.5) display_func(0.5 > a) display_func(a >= b) display_func(a >= 0.5) display_func(0.5 >= a) display_func(a != b) display_func(a != 0.5) display_func(0.5 != a) display_func(a == b) display_func(a == 0.5) display_func(0.5 == a) display_func(a & b) display_func(a & 2) c = a c &= 2 display_func(c) display_func(a | b) display_func(a | 2) c = a c |= 2 display_func(c) display_func(a >> b) display_func(a >> 2) c = a c >>= 2 display_func(c) display_func(a << b) display_func(a << 2) c = a c <<= 2 display_func(c) display_func(-a) display_func(+a) display_func(~a) display_func(a) display_func(af.cast(a, af.Dtype.c32)) display_func(af.maxof(a,b)) display_func(af.minof(a,b)) display_func(af.rem(a,b)) a = af.randu(3,3) - 0.5 b = af.randu(3,3) - 0.5 display_func(af.abs(a)) display_func(af.arg(a)) display_func(af.sign(a)) display_func(af.round(a)) display_func(af.trunc(a)) display_func(af.floor(a)) display_func(af.ceil(a)) display_func(af.hypot(a, b)) display_func(af.sin(a)) display_func(af.cos(a)) display_func(af.tan(a)) display_func(af.asin(a)) display_func(af.acos(a)) display_func(af.atan(a)) display_func(af.atan2(a, b)) c = af.cplx(a) d = af.cplx(a,b) display_func(c) display_func(d) display_func(af.real(d)) display_func(af.imag(d)) display_func(af.conjg(d)) display_func(af.sinh(a)) display_func(af.cosh(a)) display_func(af.tanh(a)) display_func(af.asinh(a)) display_func(af.acosh(a)) display_func(af.atanh(a)) a = af.abs(a) b = af.abs(b) display_func(af.root(a, b)) display_func(af.pow(a, b)) display_func(af.pow2(a)) display_func(af.exp(a)) display_func(af.expm1(a)) display_func(af.erf(a)) display_func(af.erfc(a)) display_func(af.log(a)) display_func(af.log1p(a)) display_func(af.log10(a)) display_func(af.log2(a)) display_func(af.sqrt(a)) display_func(af.cbrt(a)) a = af.round(5 * af.randu(3,3) - 1) b = af.round(5 * af.randu(3,3) - 1) display_func(af.factorial(a)) display_func(af.tgamma(a)) display_func(af.lgamma(a)) display_func(af.iszero(a)) display_func(af.isinf(a/b)) display_func(af.isnan(a/a)) a = af.randu(5, 1) b = af.randu(1, 5) c = af.broadcast(lambda x,y: x+y, a, b) display_func(a) display_func(b) display_func(c) @af.broadcast def test_add(aa, bb): return aa + bb display_func(test_add(a, b))
def simple_arith(verbose=False): display_func = _util.display_func(verbose) print_func = _util.print_func(verbose) a = af.randu(3, 3) b = af.constant(4, 3, 3) display_func(a) display_func(b) c = a + b d = a d += b display_func(c) display_func(d) display_func(a + 2) display_func(3 + a) c = a - b d = a d -= b display_func(c) display_func(d) display_func(a - 2) display_func(3 - a) c = a * b d = a d *= b display_func(c * 2) display_func(3 * d) display_func(a * 2) display_func(3 * a) c = a / b d = a d /= b display_func(c / 2.0) display_func(3.0 / d) display_func(a / 2) display_func(3 / a) c = a % b d = a d %= b display_func(c % 2.0) display_func(3.0 % d) display_func(a % 2) display_func(3 % a) c = a**b d = a d **= b display_func(c**2.0) display_func(3.0**d) display_func(a**2) display_func(3**a) display_func(a < b) display_func(a < 0.5) display_func(0.5 < a) display_func(a <= b) display_func(a <= 0.5) display_func(0.5 <= a) display_func(a > b) display_func(a > 0.5) display_func(0.5 > a) display_func(a >= b) display_func(a >= 0.5) display_func(0.5 >= a) display_func(a != b) display_func(a != 0.5) display_func(0.5 != a) display_func(a == b) display_func(a == 0.5) display_func(0.5 == a) a = af.randu(3, 3, dtype=af.Dtype.u32) b = af.constant(4, 3, 3, dtype=af.Dtype.u32) display_func(a & b) display_func(a & 2) c = a c &= 2 display_func(c) display_func(a | b) display_func(a | 2) c = a c |= 2 display_func(c) display_func(a >> b) display_func(a >> 2) c = a c >>= 2 display_func(c) display_func(a << b) display_func(a << 2) c = a c <<= 2 display_func(c) display_func(-a) display_func(+a) display_func(~a) display_func(a) display_func(af.cast(a, af.Dtype.c32)) display_func(af.maxof(a, b)) display_func(af.minof(a, b)) display_func(af.rem(a, b)) a = af.randu(3, 3) - 0.5 b = af.randu(3, 3) - 0.5 display_func(af.abs(a)) display_func(af.arg(a)) display_func(af.sign(a)) display_func(af.round(a)) display_func(af.trunc(a)) display_func(af.floor(a)) display_func(af.ceil(a)) display_func(af.hypot(a, b)) display_func(af.sin(a)) display_func(af.cos(a)) display_func(af.tan(a)) display_func(af.asin(a)) display_func(af.acos(a)) display_func(af.atan(a)) display_func(af.atan2(a, b)) c = af.cplx(a) d = af.cplx(a, b) display_func(c) display_func(d) display_func(af.real(d)) display_func(af.imag(d)) display_func(af.conjg(d)) display_func(af.sinh(a)) display_func(af.cosh(a)) display_func(af.tanh(a)) display_func(af.asinh(a)) display_func(af.acosh(a)) display_func(af.atanh(a)) a = af.abs(a) b = af.abs(b) display_func(af.root(a, b)) display_func(af.pow(a, b)) display_func(af.pow2(a)) display_func(af.sigmoid(a)) display_func(af.exp(a)) display_func(af.expm1(a)) display_func(af.erf(a)) display_func(af.erfc(a)) display_func(af.log(a)) display_func(af.log1p(a)) display_func(af.log10(a)) display_func(af.log2(a)) display_func(af.sqrt(a)) display_func(af.cbrt(a)) a = af.round(5 * af.randu(3, 3) - 1) b = af.round(5 * af.randu(3, 3) - 1) display_func(af.factorial(a)) display_func(af.tgamma(a)) display_func(af.lgamma(a)) display_func(af.iszero(a)) display_func(af.isinf(a / b)) display_func(af.isnan(a / a)) a = af.randu(5, 1) b = af.randu(1, 5) c = af.broadcast(lambda x, y: x + y, a, b) display_func(a) display_func(b) display_func(c) @af.broadcast def test_add(aa, bb): return aa + bb display_func(test_add(a, b))
af.display(af.asin(a)) af.display(af.acos(a)) af.display(af.atan(a)) af.display(af.atan2(a, b)) c = af.cplx(a) d = af.cplx(a, b) af.display(c) af.display(d) af.display(af.real(d)) af.display(af.imag(d)) af.display(af.conjg(d)) af.display(af.sinh(a)) af.display(af.cosh(a)) af.display(af.tanh(a)) af.display(af.asinh(a)) af.display(af.acosh(a)) af.display(af.atanh(a)) a = af.abs(a) b = af.abs(b) af.display(af.root(a, b)) af.display(af.pow(a, b)) af.display(af.pow2(a)) af.display(af.exp(a)) af.display(af.expm1(a)) af.display(af.erf(a)) af.display(af.erfc(a)) af.display(af.log(a))
def _tanh(x): return af.tanh(x)
af.display(af.asin(a)) af.display(af.acos(a)) af.display(af.atan(a)) af.display(af.atan2(a, b)) c = af.cplx(a) d = af.cplx(a,b) af.display(c) af.display(d) af.display(af.real(d)) af.display(af.imag(d)) af.display(af.conjg(d)) af.display(af.sinh(a)) af.display(af.cosh(a)) af.display(af.tanh(a)) af.display(af.asinh(a)) af.display(af.acosh(a)) af.display(af.atanh(a)) a = af.abs(a) b = af.abs(b) af.display(af.root(a, b)) af.display(af.pow(a, b)) af.display(af.pow2(a)) af.display(af.exp(a)) af.display(af.expm1(a)) af.display(af.erf(a)) af.display(af.erfc(a)) af.display(af.log(a))