GENERAL USE AND SHARED FUNCTIONS

Shared Functions

model.u0_hat_from_thetaE_hat(thetaE_hat, beta)

Calculate the closest approach vector direction. Define the beta sign convention as Andy Gould does with

• beta > 0 means u0_E > 0

• u0_amp > 0 mean u0_E > 0

See Gould 2004, pg 320, bottom right

u0 > 0 –> lens passes to the right side of the source as seen from Earth

\(thetaX0 = xS0 - xL0 = u0 * thetaE\)

which implies that:

• u0_E > 0 for u0 > 0

• u0_E < 0 for u0 < 0

which is what we use.

model.get_angular_einstein_radius(m, d1, d2)

model.get_unit_vector(x)

model.get_u0(thetaE_hat, beta, thetaE_amp)

model.get_uhat(thetaE_hat, beta)

model.get_einstein_time(theta, v, days)

model.get_thetas(source, lens)

model.get_amplitudes(vectors)

model.get_unit_vectors(vectors)

model.get_plus(amps, hats, pos, lens, radius)

model.get_minus(amps, hats, pos, lens, radius)

model.oned_int(centre, function1, function2, ymax, ymin, n, x, middle, centres)

model.twod_int(centre, function1, function2, xmax, xmin, ymax, ymin, nx, ny, middle, centres)

model.twod_cent_x_int(centre, function1, function2, xmax, xmin, ymax, ymin, nx, ny, middle, centres)

model.oned_x_int(centre, function1, function2, ymax, ymin, n, x, middle, centres)

model.twod_cent_y_int(centre, function1, function2, xmax, xmin, ymax, ymin, nx, ny, middle, centres)

model.oned_y_int(centre, function1, function2, ymax, ymin, n, x, middle, centres)

model.get_image(y0, m1, d, R)

Function to find the images of the star

Parameters:

y0:

position of the cente of the source star, in units of anguler Einstein radius

m1:

Mass of rightmost lens divided by the total mass

d:

separation of the lenses in angular Einstein radii

R:

angular radius of the source in angular Einstein radii