deeplearning/modulus/modulus-v2209/_modules/modulus/utils/sympy/functions.html

v22.09

Source code for modulus.utils.sympy.functions

"""simple Sympy helper functions """ from symengine import sqrt 
[docs]def line(x, point_x_1, point_y_1, point_x_2, point_y_2): """ line function from point intercepts Parameters ---------- x : Sympy Symbol/Exp the `x` in equation `y=a*x+b` point_x_1 : Sympy Symbol/Exp, float, int first intercept x position point_y_1 : Sympy Symbol/Exp, float, int first intercept y position point_x_2 : Sympy Symbol/Exp, float, int second intercept x position point_y_2 : Sympy Symbol/Exp, float, int second intercept y position Returns ------- y : Sympy Expr `y=slope*x+intercept` """ slope = (point_y_1 - point_y_2) / (point_x_1 - point_x_2) intercept = point_y_1 - slope * point_x_1 return slope * x + intercept
[docs]def parabola(x, inter_1, inter_2, height): """ parabola from point intercepts Parameters ---------- x : Sympy Symbol/Exp the `x` in equation `y=a*x*2+b*x+c` inter_1 : Sympy Symbol/Exp, float, int first intercept such that `y=0` when `x=inter_1` inter_2 : Sympy Symbol/Exp, float, int second intercept such that `y=0` when `x=inter_1` height : Sympy Symbol/Exp, float, int max height of parabola Returns ------- y : Sympy Expr `y=factor*(x-inter_1)*(x-+inter_2)` """ factor = (4 * height) / (-(inter_1**2) - inter_2**2 + 2 * inter_1 * inter_2) return factor * (x - inter_1) * (x - inter_2)
[docs]def parabola2D(x, y, inter_1_x, inter_2_x, inter_1_y, inter_2_y, height): """ square parabola from point intercepts Parameters ---------- x : Sympy Symbol/Exp the `x` in equation `z=parabola(x)*parabola(y)` y : Sympy Symbol/Exp the `y` in equation `z=a*x**2+b*y**2+c*xy+d*y+e*x+f` inter_1_x : Sympy Symbol/Exp, float, int first intercept such that `z=0` when `x=inter_1_x` inter_2_x : Sympy Symbol/Exp, float, int second intercept such that `z=0` when `x=inter_2_x` inter_1_y : Sympy Symbol/Exp, float, int first intercept such that `z=0` when `y=inter_1_y` inter_2_y : Sympy Symbol/Exp, float, int second intercept such that `z=0` when `y=inter_2_y` height : Sympy Symbol/Exp, float, int max height of parabola Returns ------- y : Sympy Expr `y=factor*(x-inter_1)*(x-+inter_2)` """ parabola_x = parabola(x, inter_1_x, inter_2_x, sqrt(height)) parabola_y = parabola(y, inter_1_y, inter_2_y, sqrt(height)) return parabola_x * parabola_y
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