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Package csb :: Package numeric
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Package numeric

source code

Low level numeric / math utility functions.

Submodules

Classes
  InvertibleMatrix
Matrix object which is intended to save time in MCMC sampling algorithms involving repeated integration of Hamiltonian equations of motion and frequent draws from multivariate normal distributions involving mass matrices as covariance matrices.
  MatrixInitError
Functions
 
approx_psi(x) source code
tuple
axis_and_angle(r)
Calculate axis and angle of rotation from a three dimensional rotation matrix.		 source code
 
convolve(x, f) source code
 
correlate(x, y) source code
 
d_approx_psi(x) source code
 
degree2radian(x)
Convert randian angles to torsion angles.		 source code
 
dihedral_angle(a, b, c, d)
Calculate the dihedral angle between 4 vectors, representing 4 connected points.		 source code
 
euler(a, b, c)
Calculate a three dimensional rotation matrix from the euler angles.		 source code
 
euler_angles(r)
Calculate the euler angles from a three dimensional rotation matrix.		 source code
 
exp(x, x_min=-308, x_max=709)
Safe version of exp, clips argument such that overflow does not occur.		 source code
 
from_polar(x)
Reconstruct d-dimensional vector from polar coordinates.		 source code
 
from_polar3d(x)
Reconstruct 3-dimensional vector from polar coordinates.		 source code
(n,n) numpy.array
gower_matrix(X)
Gower, J.C.		 source code
 
inv_psi(y, tol=1e-10, n_iter=100, psi=<function psi at 0x7fe0c56ef578>)
Inverse digamma function		 source code
 
isreal(x, tol=1e-14)
Check if input array has no imaginary part.		 source code
 
log(x, x_min=1e-308, x_max=1e+308)
Safe version of log, clips argument such that overflow does not occur.		 source code
 
log_midpoint_rule_2d(log_f, x, y) source code
 
log_sum_exp(x, axis=0)
Return the logarithm of the sum of exponentials.		 source code
 
log_sum_exp_accumulate(x, axis=0)
Return the logarithm of the accumulated sums of exponentials.		 source code
 
log_trapezoidal(log_y, x=None)
Compute the logarithm of the 1D integral of x, using trepezoidal approximation.		 source code
 
log_trapezoidal_2d(log_f, x=None, y=None)
Compute the logarithm of the 1D integral of x, using trepezoidal approximation.		 source code
 
norm(x)
Calculate the Eucledian norm of a d-dimensional vector.		 source code
 
pad(x, s)
Add layers of zeros around grid.		 source code
 
polar(x)
Polar coordinate representation of a d-dimensional vector.		 source code
 
polar3d(x)
Polar coordinate representation of a three-dimensional vector.		 source code
 
psi(x)
Digamma function		 source code
 
radian2degree(x)
Convert radians angles to torsion angles.		 source code
 
reverse(array, axis=0)
Reverse the order of elements in an array.		 source code
(3,3) numpy.array
rotation_matrix(axis, angle)
Calculate a three dimensional rotation matrix for a rotation around the given angle and axis.		 source code
 
sign(x)
Return the sign of the input.		 source code
 
simpson_2d(f)
Approximate the integral of f from a to b in two dimensions, using Composite Simpson's rule.		 source code
 
trapezoidal(x, y) source code
 
trapezoidal_2d(f)
Approximate the integral of f from a to b in two dimensions, using trepezoidal approximation.		 source code
 
trim(x, s)
Remove additional layers.		 source code
 
zerofill(x, s) source code
Variables
  EULER_MASCHERONI = 0.577215664902
  EXP_MAX = 709
  EXP_MIN = -308
  LOG_MAX = 1e+308
  LOG_MIN = 1e-308
  __package__ = 'csb.numeric'
Function Details

axis_and_angle(r)

source code 

Calculate axis and angle of rotation from a three dimensional rotation matrix.

Parameters:
  • r - 3x3 Rotation matrix
Returns: tuple
axis unit vector as (3,) numpy.array and angle in radians as float

degree2radian(x)

source code 

Convert randian angles to torsion angles.

Parameters:
  • x - torsion angle
Returns:
radian angle of x

dihedral_angle(a, b, c, d)

source code 

Calculate the dihedral angle between 4 vectors, representing 4 connected points. The angle is in range [-180, 180].

Parameters:
  • a (array) - the four points that define the dihedral angle
Returns:
angle in [-180, 180]

euler(a, b, c)

source code 

Calculate a three dimensional rotation matrix from the euler angles.

Parameters:
  • a - alpha, angle between the x-axis and the line of nodes
  • b - beta, angle between the z axis of the different coordinate systems
  • c - gamma, angle between the line of nodes and the X-axis

euler_angles(r)

source code 

Calculate the euler angles from a three dimensional rotation matrix.

Parameters:
  • r - 3x3 Rotation matrix

exp(x, x_min=-308, x_max=709)

source code 

Safe version of exp, clips argument such that overflow does not occur.

Parameters:
  • x (numpy array or float or int) - input
  • x_min (float) - lower value for clipping
  • x_max (float) - upper value for clipping

from_polar(x)

source code 

Reconstruct d-dimensional vector from polar coordinates.

Parameters:
  • x - vector (i.e. rank one array)
Returns:
position in d-dimensional space

from_polar3d(x)

source code 

Reconstruct 3-dimensional vector from polar coordinates.

Parameters:
  • x - vector (i.e. rank one array)
Returns:
position in 3-dimensional space

gower_matrix(X)

source code 

Gower, J.C. (1966). Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53: 325-338

Parameters:
  • X ((m,n,k) numpy.array) - ensemble coordinates
Returns: (n,n) numpy.array
symmetric dissimilarity matrix

isreal(x, tol=1e-14)

source code 

Check if input array has no imaginary part.

Parameters:
  • x (numpy array) - input array
  • tol (float) - tolerance to check for equality zero

log(x, x_min=1e-308, x_max=1e+308)

source code 

Safe version of log, clips argument such that overflow does not occur.

Parameters:
  • x (numpy array or float or int) - input
  • x_min (float) - lower value for clipping
  • x_max (float) - upper value for clipping

log_sum_exp(x, axis=0)

source code 

Return the logarithm of the sum of exponentials.

Parameters:
  • x (Numpy array)

log_sum_exp_accumulate(x, axis=0)

source code 

Return the logarithm of the accumulated sums of exponentials.

Parameters:
  • x (Numpy array)

log_trapezoidal(log_y, x=None)

source code 

Compute the logarithm of the 1D integral of x, using trepezoidal approximation. Assumes x is monotonically increasing.

log_trapezoidal_2d(log_f, x=None, y=None)

source code 

Compute the logarithm of the 1D integral of x, using trepezoidal approximation. Assumes x and y is monotonically increasing.

norm(x)

source code 

Calculate the Eucledian norm of a d-dimensional vector.

Parameters:
  • x - vector (i.e. rank one array)
Returns:
length of vector

polar(x)

source code 

Polar coordinate representation of a d-dimensional vector.

Parameters:
  • x - vector (i.e. rank one array)
Returns:
polar coordinates (radius and polar angles)

polar3d(x)

source code 

Polar coordinate representation of a three-dimensional vector.

Parameters:
  • x - vector (i.e. rank one array)
Returns:
polar coordinates (radius and polar angles)

radian2degree(x)

source code 

Convert radians angles to torsion angles.

Parameters:
  • x - radian angle
Returns:
torsion angle of x

rotation_matrix(axis, angle)

source code 

Calculate a three dimensional rotation matrix for a rotation around the given angle and axis.

Parameters:
  • angle (float) - angle in radians
  • axis ((3,) numpy array)
Returns: (3,3) numpy.array

simpson_2d(f)

source code 

Approximate the integral of f from a to b in two dimensions, using Composite Simpson's rule.

Parameters:
  • f - 2D numpy array of function values
Returns:
approximation of the definit integral

trapezoidal_2d(f)

source code 

Approximate the integral of f from a to b in two dimensions, using trepezoidal approximation.

Parameters:
  • f - 2D numpy array of function values at equally spaces positions
Returns:
approximation of the definit integral

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