irfpy.util.streamline

Tracing a field to make a stream line

Code author: Yoshifumi Futaana

Any vector field, $\mathbf{B}(x,y,z)$, is traced from a given point $(x_0,y_0,z_0)$.

See also the sample script at streamline_sample.

class irfpy.util.streamline.SimpleTracing(initpos, vector_field, dt)

Bases: object

Simple tracing

The differential equations are

$$dx=Bx(x,y,z)dtdy=By(x,y,z)dtdz=Bz(x,y,z)dt$$

For numerical calculation, we use Runge-Kutta 4.

$$r_{i+1}=r_i+\frac{\mathrm{\Delta }t}{6}(k_1+2k_2+2k_3+k_4)$$

where r denotes (x, y, z). Each coefficients are

$$k_1=B(r_i)k_2=B(r_i+\frac{\mathrm{\Delta }t}{2}{k}_1)k_3=B(r_i+\frac{\mathrm{\Delta }t}{2}{k}_2)k_4=B(r_i+\mathrm{\Delta }t{k}_3)$$

If one wants to backward trace, you may instance another object that gives -vector_field in the constructor.

An example is shown.

Assume a vector field as

$$Bx=xBy=0Bz=\sqrt{x^2+z^2}$$

The vector_field should be a function that returns a vector, i.e.,

>>> vfield = lambda p: np.array((p[0], 0, np.sqrt(p[0]**2+p[2]**2)))

The vector_field should take np.array, returning np.array() object.

>>> tracer = SimpleTracing([1, 0, 1], vfield, 0.001)
>>> tracer.step_forward()
>>> print(tracer.x, tracer.y, tracer.z, tracer.tlist[-1])
1.0010005001667084 0.0 1.0014150674450009 0.001

step_forward()

irfpy.util.streamline.doctests()