def minmod(x, y, z): min_of_all = af.minof(af.minof(af.abs(x),af.abs(y)), af.abs(z)) # af.sign(x) = 1 for x<0 and sign(x) for x>0: signx = 1 - 2 * af.sign(x) signy = 1 - 2 * af.sign(y) signz = 1 - 2 * af.sign(z) result = 0.25 * af.abs(signx + signy) * (signx + signz) * min_of_all af.eval(result) return result
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))
# Copyright (c) 2015, ArrayFire # All rights reserved. # # This file is distributed under 3-clause BSD license. # The complete license agreement can be obtained at: # http://arrayfire.com/licenses/BSD-3-Clause ######################################################## import arrayfire as af af.info() ITERATIONS = 200 POINTS = int(10.0 * ITERATIONS) Z = 1 + af.range(POINTS) / ITERATIONS win = af.Window(800, 800, "3D Plot example using ArrayFire") t = 0.1 while not win.close(): X = af.cos(Z * t + t) / Z Y = af.sin(Z * t + t) / Z X = af.maxof(af.minof(X, 1), -1) Y = af.maxof(af.minof(Y, 1), -1) Pts = af.join(1, X, Y, Z) win.plot3(Pts) t = t + 0.01
af.display(c) af.display(a << b) af.display(a << 2) c = a c <<= 2 af.display(c) af.display(-a) af.display(+a) af.display(~a) af.display(a) af.display(af.cast(a, af.c32)) af.display(af.maxof(a, b)) af.display(af.minof(a, b)) af.display(af.rem(a, b)) a = af.randu(3, 3) - 0.5 b = af.randu(3, 3) - 0.5 af.display(af.abs(a)) af.display(af.arg(a)) af.display(af.sign(a)) af.display(af.round(a)) af.display(af.trunc(a)) af.display(af.floor(a)) af.display(af.ceil(a)) af.display(af.hypot(a, b)) af.display(af.sin(a)) af.display(af.cos(a))
def reconstruct_ppm(input_array, axis): if(axis == 0): x0_shift = 2; y0_shift = 0; z0_shift = 0 x1_shift = 1; y1_shift = 0; z1_shift = 0 x3_shift = -1; y3_shift = 0; z3_shift = 0 x4_shift = -2; y4_shift = 0; z4_shift = 0 elif(axis == 1): x0_shift = 0; y0_shift = 2; z0_shift = 0 x1_shift = 0; y1_shift = 1; z1_shift = 0 x3_shift = 0; y3_shift = -1; z3_shift = 0 x4_shift = 0; y4_shift = -2; z4_shift = 0 elif(axis == 2): x0_shift = 0; y0_shift = 0; z0_shift = 2 x1_shift = 0; y1_shift = 0; z1_shift = 1 x3_shift = 0; y3_shift = 0; z3_shift = -1 x4_shift = 0; y4_shift = 0; z4_shift = -2 else: raise Exception('Invalid choice for axis') y0 = af.shift(input_array, x0_shift, y0_shift, z0_shift) y1 = af.shift(input_array, x1_shift, y1_shift, z1_shift) y2 = input_array; y3 = af.shift(input_array, x3_shift, y3_shift, z3_shift) y4 = af.shift(input_array, x4_shift, y4_shift, z4_shift) # Approximants for slopes d0 = 2 * (y1-y0) d1 = 2 * (y2-y1) d2 = 2 * (y3-y2) d3 = 2 * (y4-y3) D1 = 0.5 * (y2-y0) D2 = 0.5 * (y3-y1) D3 = 0.5 * (y4-y2) cond_zero_slope1 = (d1 * d0 <= 0) sign1 = (D1 > 0) * 2 - 1 DQ1 = (1 - cond_zero_slope1) * sign1 * \ af.minof(af.abs(D1),af.minof(af.abs(d0),af.abs(d1))) cond_zero_slope2 = (d2 * d1 <= 0) sign2 = (D2 > 0) * 2 - 1 DQ2 = (1 - cond_zero_slope2) * sign2 * \ af.minof(af.abs(D2),af.minof(af.abs(d1),af.abs(d2))) cond_zero_slope3 = (d3 * d2 <= 0) sign3 = (D3 > 0) * 2 - 1; DQ3 = (1 - cond_zero_slope3) * sign3 * \ af.minof(af.abs(D3),af.minof(af.abs(d2),af.abs(d3))) # Base high-order PPM reconstruction left_value = 0.5 * (y2 + y1) - (DQ2-DQ1)/6 right_value = 0.5 * (y3 + y2) - (DQ3-DQ2)/6 # Corrections corr1 = ((right_value - y2) * (y2 - left_value) <= 0) qd = right_value - left_value qe = 6 * (y2 - 0.5 * (right_value + left_value)) corr2 = (qd * (qd - qe) < 0) corr3 = (qd * (qd + qe) < 0) left_value = left_value * (1 - corr1) + corr1 * y2; right_value = right_value * (1 - corr1) + corr1 * y2; left_value = left_value * (1 - corr2) + corr2 * (3 * y2 - 2 * right_value) right_value = right_value * corr2 + (1 - corr2) * right_value * (1 - corr3) + \ (1 - corr2) * corr3 * (3 * y2 - 2 * left_value) return(left_value, right_value)
def reconstruct_ppm(input_array, axis): """ Reconstructs the input array using PPM reconstruction. Parameters ---------- input_array: af.Array Array holding the cells data. axis: int Axis along which the reconstruction method is to be applied. """ if (axis == 0): x0_shift = 2 y0_shift = 0 z0_shift = 0 w0_shift = 0 x1_shift = 1 y1_shift = 0 z1_shift = 0 w1_shift = 0 x3_shift = -1 y3_shift = 0 z3_shift = 0 w3_shift = 0 x4_shift = -2 y4_shift = 0 z4_shift = 0 w4_shift = 0 elif (axis == 1): x0_shift = 0 y0_shift = 2 z0_shift = 0 w0_shift = 0 x1_shift = 0 y1_shift = 1 z1_shift = 0 w1_shift = 0 x3_shift = 0 y3_shift = -1 z3_shift = 0 w3_shift = 0 x4_shift = 0 y4_shift = -2 z4_shift = 0 w4_shift = 0 elif (axis == 2): x0_shift = 0 y0_shift = 0 z0_shift = 2 w0_shift = 0 x1_shift = 0 y1_shift = 0 z1_shift = 1 w1_shift = 0 x3_shift = 0 y3_shift = 0 z3_shift = -1 w3_shift = 0 x4_shift = 0 y4_shift = 0 z4_shift = -2 w4_shift = 0 elif (axis == 3): x0_shift = 0 y0_shift = 0 z0_shift = 0 w0_shift = 2 x1_shift = 0 y1_shift = 0 z1_shift = 0 w1_shift = 1 x3_shift = 0 y3_shift = 0 z3_shift = 0 w3_shift = -1 x4_shift = 0 y4_shift = 0 z4_shift = 0 w4_shift = -2 else: raise Exception('Invalid choice for axis') y0 = af.shift(input_array, x0_shift, y0_shift, z0_shift, w0_shift) y1 = af.shift(input_array, x1_shift, y1_shift, z1_shift, w1_shift) y2 = input_array y3 = af.shift(input_array, x3_shift, y3_shift, z3_shift, w3_shift) y4 = af.shift(input_array, x4_shift, y4_shift, z4_shift, w4_shift) # Approximants for slopes d0 = 2 * (y1 - y0) d1 = 2 * (y2 - y1) d2 = 2 * (y3 - y2) d3 = 2 * (y4 - y3) D1 = 0.5 * (y2 - y0) D2 = 0.5 * (y3 - y1) D3 = 0.5 * (y4 - y2) cond_zero_slope1 = (d1 * d0 <= 0) sign1 = (D1 > 0) * 2 - 1 DQ1 = (1 - cond_zero_slope1) * sign1 * \ af.minof(af.abs(D1),af.minof(af.abs(d0),af.abs(d1))) cond_zero_slope2 = (d2 * d1 <= 0) sign2 = (D2 > 0) * 2 - 1 DQ2 = (1 - cond_zero_slope2) * sign2 * \ af.minof(af.abs(D2),af.minof(af.abs(d1),af.abs(d2))) cond_zero_slope3 = (d3 * d2 <= 0) sign3 = (D3 > 0) * 2 - 1 DQ3 = (1 - cond_zero_slope3) * sign3 * \ af.minof(af.abs(D3),af.minof(af.abs(d2),af.abs(d3))) # Base high-order PPM reconstruction left_value = 0.5 * (y2 + y1) - (DQ2 - DQ1) / 6 right_value = 0.5 * (y3 + y2) - (DQ3 - DQ2) / 6 # Corrections corr1 = ((right_value - y2) * (y2 - left_value) <= 0) qd = right_value - left_value qe = 6 * (y2 - 0.5 * (right_value + left_value)) corr2 = (qd * (qd - qe) < 0) corr3 = (qd * (qd + qe) < 0) left_value = left_value * (1 - corr1) + corr1 * y2 right_value = right_value * (1 - corr1) + corr1 * y2 left_value = left_value * (1 - corr2) + corr2 * (3 * y2 - 2 * right_value) right_value = right_value * corr2 + (1 - corr2) * right_value * (1 - corr3) + \ (1 - corr2) * corr3 * (3 * y2 - 2 * left_value) return (left_value, right_value)
af.display(c) af.display(a << b) af.display(a << 2) c = a c <<= 2 af.display(c) af.display(-a) af.display(+a) af.display(~a) af.display(a) af.display(af.cast(a, af.c32)) af.display(af.maxof(a,b)) af.display(af.minof(a,b)) af.display(af.rem(a,b)) a = af.randu(3,3) - 0.5 b = af.randu(3,3) - 0.5 af.display(af.abs(a)) af.display(af.arg(a)) af.display(af.sign(a)) af.display(af.round(a)) af.display(af.trunc(a)) af.display(af.floor(a)) af.display(af.ceil(a)) af.display(af.hypot(a, b)) af.display(af.sin(a)) af.display(af.cos(a))
def advection_step(u, v): ''' done - Matching u_new and v_new ''' u_w_bc, v_w_bc = add_boundary_conditions(u, v) u = af.moddims(u_w_bc, params.n, params.n) v = af.moddims(v_w_bc, params.n, params.n) u_tile = u[1:-1, 1:-1] v_tile = v[1:-1, 1:-1] u_new = af.np_to_af_array(np.zeros([params.n, params.n])) v_new = af.np_to_af_array(np.zeros([params.n, params.n])) x0_tile = af.tile(af.np_to_af_array(np.linspace(0, 1, params.n)), 1, params.n)[1:-1, 1:-1] y0_tile = af.transpose(x0_tile) reference_0_tile = af.constant(0, params.n - 2, params.n - 2, dtype=af.Dtype.f64) reference_1_tile = af.constant(1, params.n - 2, params.n - 2, dtype=af.Dtype.f64) x1_tile = af.minof( af.maxof(x0_tile - params.delta_t * u_tile, reference_0_tile), reference_1_tile) y1_tile = af.minof( af.maxof(y0_tile - params.delta_t * v_tile, reference_0_tile), reference_1_tile) i_left_tile = af.minof(af.cast(x1_tile * (params.n - 1), af.Dtype.s64), (params.n - 2) * reference_1_tile) i_left_flat = af.flat(i_left_tile) i_right_tile = i_left_tile + 1 i_right_flat = af.flat(i_right_tile) j_bottom_tile = af.minof(af.cast(y1_tile * (params.n - 1), af.Dtype.s64), (params.n - 2) * reference_1_tile) j_bottom_flat = af.flat(j_bottom_tile * params.n) j_top_tile = j_bottom_tile + 1 j_top_flat = af.flat(j_top_tile * params.n) x_left_tile = i_left_tile / (params.n - 1) x_right_tile = i_right_tile / (params.n - 1) y_bottom_tile = j_bottom_tile / (params.n - 1) y_top_tile = j_top_tile / (params.n - 1) print(x_left_tile) flat_u = af.flat(u) flat_v = af.flat(v) u_top_left_tile = af.moddims(flat_u[i_left_flat + j_top_flat], params.n - 2, params.n - 2) u_top_right_tile = af.moddims(flat_u[i_right_flat + j_top_flat], params.n - 2, params.n - 2) u_bottom_left_tile = af.moddims(flat_u[i_left_flat + j_bottom_flat], params.n - 2, params.n - 2) u_bottom_right_tile = af.moddims(flat_u[i_right_flat + j_bottom_flat], params.n - 2, params.n - 2) v_top_left_tile = af.moddims(flat_v[i_left_flat + j_top_flat], params.n - 2, params.n - 2) v_top_right_tile = af.moddims(flat_v[i_right_flat + j_top_flat], params.n - 2, params.n - 2) v_bottom_left_tile = af.moddims(flat_v[i_left_flat + j_bottom_flat], params.n - 2, params.n - 2) v_bottom_right_tile = af.moddims(flat_v[i_right_flat + j_bottom_flat], params.n - 2, params.n - 2) u_upper_tile = u_top_left_tile\ + (u_top_right_tile - u_top_left_tile)\ * (x1_tile - x_left_tile) / params.delta_x u_lower_tile = u_bottom_right_tile\ + (u_bottom_left_tile - u_bottom_right_tile)\ * (x1_tile - x_left_tile) / params.delta_x u_new_tile = u_lower_tile + (u_upper_tile - u_lower_tile)\ * (y1_tile - y_bottom_tile) / params.delta_x v_upper_tile = v_top_left_tile + (v_top_right_tile - v_top_left_tile)\ * (x1_tile - x_left_tile) / params.delta_x v_lower_tile = v_bottom_right_tile + (v_bottom_left_tile - v_bottom_right_tile)\ * (x1_tile - x_left_tile) / params.delta_x v_new_tile = v_lower_tile + (v_upper_tile - v_lower_tile)\ * (y1_tile - y_bottom_tile) / params.delta_x u_new = af.flat(u_new_tile) v_new = af.flat(v_new_tile) return u_new, v_new