noads.gam_jax.utils.math

A math toolbox for MARILib.

author:

DRUOT Thierry, original Scilab implementation

author:

ROCHES Pascal, portage to Python

noads.gam_jax.utils.math.angle(sin_a, cos_a, typ=2)

Calculate an angle from its sine and cosine coordinates if typ=1 then -180<a_<180, if typ=2 then 0<a_<360.

noads.gam_jax.utils.math.approx_jac(res, y, args=(), step=1e-07)

noads.gam_jax.utils.math.cross_op(v)

Build the skew-symmetric matrix of vector v.

noads.gam_jax.utils.math.get_jac_func(res, args=(), step=1e-06)

noads.gam_jax.utils.math.great_circle_distance(p1, p2)

Compute the great circle distance between 2 points p : (lat, long).

noads.gam_jax.utils.math.lin_interp_1d(x, X, Y)

Linear interpolation without any control.

Parameters:

• x – current position

• X – array of the abscissa of the known points

• Y – array of the known values at given abscissa

Returns:

y the interpolated value of Y at x

noads.gam_jax.utils.math.look_ahead_4_zero(xini, dx, *fct)

Look ahead for a zero of the function.

Parameters:

• xini – initial value of the variable.

• dx – fixed search step.

• fct – function with the signature : [‘function_name’,a1,a2,a3,…,an] and function_name(x,a1,a2,a3,…,an).

noads.gam_jax.utils.math.maximize_1d(xini, dx, *fct)

Optimize 1 single variable, no constraint.

Parameters:

• xini – initial value of the variable.

• dx – fixed search step.

• fct – function with the signature : [‘function_name’,a1,a2,a3,…,an] and function_name(x,a1,a2,a3,…,an).

noads.gam_jax.utils.math.newton_solve(res_func, x0, dres_dy=None, args=(), res_max=1e-12, relax=0.995, max_iter=50, full_output=False)

noads.gam_jax.utils.math.norm(x)

noads.gam_jax.utils.math.renorm(v)

noads.gam_jax.utils.math.rotate_point(pivot, axe, angle, p0)

Retrieve the point coming from the rotation of p0 of angle, around the axis defined by pivot and axe.

noads.gam_jax.utils.math.rotate_vector(vec, axe, cos_a, sin_a)

Retrieve the vector vec rotated by the angle a around axe, using Olinde-Rodrigues formula v_star = vec + sin_a * np.cross(axe, vec) + (1 - cos_a) * np.cross(axe, np.cross(axe, vec)).

noads.gam_jax.utils.math.trinome(A, Y)

Calculate trinome coefficients from 3 given points A = [X2, X, 1] (Vandermonde matrix).

noads.gam_jax.utils.math.vander3(X)

Return the vandermonde matrix of a dim 3 array A = [X^2, X, 1].

Functions

angle(sin_a, cos_a[, typ])	Calculate an angle from its sine and cosine coordinates if typ=1 then -180<a_<180, if typ=2 then 0<a_<360.
approx_jac(res, y[, args, step])
cross_op(v)	Build the skew-symmetric matrix of vector v.
get_jac_func(res[, args, step])
great_circle_distance(p1, p2)	Compute the great circle distance between 2 points p : (lat, long).
lin_interp_1d(x, X, Y)	Linear interpolation without any control.
look_ahead_4_zero(xini, dx, *fct)	Look ahead for a zero of the function.
maximize_1d(xini, dx, *fct)	Optimize 1 single variable, no constraint.
newton_solve(res_func, x0[, dres_dy, args, ...])
norm(x)
renorm(v)
rotate_point(pivot, axe, angle, p0)	Retrieve the point coming from the rotation of p0 of angle, around the axis defined by pivot and axe.
rotate_vector(vec, axe, cos_a, sin_a)	Retrieve the vector vec rotated by the angle a around axe, using Olinde-Rodrigues formula v_star = vec + sin_a * np.cross(axe, vec) + (1 - cos_a) * np.cross(axe, np.cross(axe, vec)).
trinome(A, Y)	Calculate trinome coefficients from 3 given points A = [X2, X, 1] (Vandermonde matrix).
vander3(X)	Return the vandermonde matrix of a dim 3 array A = [X^2, X, 1].