Package csb :: Package numeric
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Package numeric

source code

Low level numeric / math utility functions.

Submodules

Functions
 
approx_psi(x) 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 0x3febf50>)
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
 
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

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

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