Package Biskit :: Module mathUtils

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Module mathUtils

source code

general purpose math methods

Classes

[hide private]

MathUtilError

Test
Test case

Functions

[hide private]

float accumulate(a)
cumulative sum of a[0], a[0]+a[1], a[0]+a[1]+[a2], ... normalized by N.sum( a )

float variance(x, avg=None)
Variance, σ^2

float SD(x, avg=None)
Standard deviation, σ

array('f') or float wMean(x, w=None)
Weighted mean: Mean of data (x) weighted by (w).

array('f') or float wVar(x, w)
Variance of weighted (w) data (x).

array('f') or float wSD(x, w)
Standard deviation of weighted data.

array('f') or float cross(v, w)
Cross product between two coordinates.

list aboveDiagonal(pw_m)
Collect att the values above the diagonal in a square matrix.

1|0 arrayEqual(a, b)
Compare 2 arrays or lists of numbers for equality.

array pairwiseDistances(u, v)
Pairwise distances between two arrays.

array( 1|0 ) randomMask(nOnes, length)
Create random array of given lenght and number of ones.

2D array random2DArray(matrix, ranNr=1, mask=None)
Create randomized 2D array containing ones and zeros.

[ float ] runningAverage(x, interval=2, preserve_boundaries=0)
Running average (smoothing) over a given data window.

dict packBinaryMatrix(cm)
Compress sparse array of 0 and ones to list of one-positions (space saving function, upack with unpackBinaryMatrix).

2D array unpackBinaryMatrix(pcm, raveled=0)
Uncompress array of 0 and 1 that was compressed with packBinaryMatrix.

dict matrixToList(cm)
Convert matrix into standard python list remembering the dimensions.

listToMatrix(lcm)
Convert result of matrixToList back into Numeric array

array eulerRotation(alpha, beta, gamma)
Builds a rotation matrix from successive rotations:

array randomRotation()
Get random rotation matrix.

[any] intersection(a, b, optimize=1)
Intersection of the two lists (i.e.

[any] nonredundant(l)
All members of a list without duplicates noredundant( [any] ) -> [any]

[any] union(a, b)
Union of two lists (without duplicates) union( [any], [any] ) -> [any]

[any] difference(a, b)
All members of a that are not in b difference([any], [any]) -> [any]

[any] removeFromList(l, v, all=1)
Remove all or first occurrence(s) of v from l.

[int] randomRange(start, stop, n)
Creates a set of n unique integers randomly distributed between start and stop.

float, float, float linfit(x, y)
Calculate linear least-square fit to the points given by x and y.

array cartesianToPolar(xyz)
Convert cartesian coordinate array to polar coordinate array: x,y,z -> r, θ, φ

array polarToCartesian(rtp)
Convert polar coordinate array to cartesian coordinate array: r, θ, φ -> x,y,z

array projectOnSphere(xyz, radius=None, center=None)
Project the coordinates xyz on a sphere with a given radius around a given center.

Function Details

[hide private]

accumulate(a)

source code

cumulative sum of a[0], a[0]+a[1], a[0]+a[1]+[a2], ... normalized by N.sum( a )

Parameters:

a (array) - array('f') or float

Returns: float: float

variance(x, avg=None)

source code

Variance, σ^2

Parameters:

x (array('f') or float) - data
avg (float OR None) - use this average, otherwise calculated from x

Returns: float: float

SD(x, avg=None)

source code

Standard deviation, σ

Parameters:

x (array('f') or float) - data
avg (float OR None) - use this average, otherwise calculated from x

Returns: float: float

wMean(x, w=None)

source code

Weighted mean: Mean of data (x) weighted by (w).

Parameters:

x (array) - X-D array with numbers
w (array) - 1-D array of same length as x with weight factors

Returns: array('f') or float: array('f') or float

wVar(x, w)

source code

Variance of weighted (w) data (x).

Parameters:

x (array) - X-D array with numbers
w (array) - 1-D array of same length as x with weight factors

Returns: array('f') or float: array('f') or float

wSD(x, w)

source code

Standard deviation of weighted data.

Parameters:

x (array) - X-D array with numbers
w (array) - 1-D array of same length as x with weight factors

Returns: array('f') or float: array('f') or float

cross(v, w)

source code

Cross product between two coordinates.

Parameters:

v (list or array) - coordinate vector
w (list or array) - coordinate vector

Returns: array('f') or float: array('f') or float

aboveDiagonal(pw_m)

source code

Collect att the values above the diagonal in a square matrix.

Parameters:

pw_m (2-D array) - symmetric square matrix

Returns: list: raveled list of 'unique' values without diagonal

arrayEqual(a, b)

source code

Compare 2 arrays or lists of numbers for equality.

Parameters:

a (array / list) - first array (multi-dimensional is supported)
b (array / list) - second array (multi-dimensional is supported)

Returns: 1|0: 1 if array/list a equals array/list b

pairwiseDistances(u, v)

source code

Pairwise distances between two arrays.

Parameters:

u (array) - first array
v (array) - second array

Returns: array: Numeric.array( len(u) x len(v) ) of double

randomMask(nOnes, length)

source code

Create random array of given lenght and number of ones.

Parameters:

nOnes (int) - number of ones
length (int) - lenght of array

Returns: array( 1|0 ): array with ones and zeros

random2DArray(matrix, ranNr=1, mask=None)

source code

Create randomized 2D array containing ones and zeros.

Parameters:

matrix (2D array) - matrix to randomize
mask (list(1|0)) - mask OR None (default: None)
ranNr (integer) - number of matricies to add up (default: 1)

Returns: 2D array: 2D array or |ranNr| added contact matricies

Raises:

MathUtilError - if mask does not fit matrix

runningAverage(x, interval=2, preserve_boundaries=0)

source code

Running average (smoothing) over a given data window.

Parameters:

x (list of int/float) - data
interval (int) - window size (-(interval-1)/2 to +(interval-1)/2) (default: 2)
preserve_boundaries (0|1) - shrink window at edges to keep original start and end value (default: 0)

Returns: [ float ]: list of floats

packBinaryMatrix(cm)

source code

Compress sparse array of 0 and ones to list of one-positions (space saving function, upack with unpackBinaryMatrix).

Parameters:

cm (2D array) - X by Y array of int

Returns: dict: {'shape':(X,Y), 'nonzero':[int] }

unpackBinaryMatrix(pcm, raveled=0)

source code

Uncompress array of 0 and 1 that was compressed with packBinaryMatrix.

Parameters:

pcm (dict) - {'shape':(X,Y,..), 'nonzero':[int]}
raveled (1|0) - return raveled (default: 0)

Returns: 2D array: N.array(X by Y by ..) of int

matrixToList(cm)

source code

Convert matrix into standard python list remembering the dimensions. Unpack with listToMatrix.

Parameters:

cm (2D array) - array of int

Returns: dict: {'shape':(int,..), 'lst':[..] }

Note: Not used right now.

listToMatrix(lcm)

source code

Convert result of matrixToList back into Numeric array

Parameters:

lcm (dict) - {'shape':(int,..), 'lst':[..] }

Returns:: Numeric.array

Note: Not used right now.

eulerRotation(alpha, beta, gamma)

source code

Builds a rotation matrix from successive rotations:

rotation about y-axis by angle alpha

rotation about x-axis by angle beta

rotation about z-axis by angle gamma

Parameters:

alpha (float) - euler angle α
beta (float) - euler angle β
gamma (float) - euler angle γ

Returns: array: 3 x 3 array of float

Author: Michael Habeck

randomRotation()

source code

Get random rotation matrix.

Returns: array: 3 x 3 array of float

Author: Michael Habeck

intersection(a, b, optimize=1)

source code

Intersection of the two lists (i.e. all values common to both two lists). intersection( [any], [any] ) -> [any]

Parameters:

a ([any]) - first list
b ([any]) - second list
optimize (1|0) - result is sorted like the shorter of the two lists (default: 1)

Returns: [any]: list

nonredundant(l)

source code

All members of a list without duplicates

 noredundant( [any] ) 
  -> [any]

Parameters:

l ([any]) - list

Returns: [any]: list

union(a, b)

source code

Union of two lists (without duplicates)

 union( [any], [any] ) 
  -> [any]

Parameters:

a ([any]) - first list
b ([any]) - second list

Returns: [any]: list

difference(a, b)

source code

All members of a that are not in b

 difference([any], [any]) 
  -> [any]

Parameters:

a ([any]) - first list
b ([any]) - second list

Returns: [any]: list

removeFromList(l, v, all=1)

source code

Remove all or first occurrence(s) of v from l.

 removeFromList( 
  l, v, [all=1] )

Parameters:

l ([ any ]) - list
v (any or [ any ]) - remove these values
all (0|1) - remove all occurrences (1) or only first one (0) (default: 1)

Returns: [any]: list

randomRange(start, stop, n)

source code

Creates a set of n unique integers randomly distributed between start and stop.

Parameters:

start (int) - minimal index
stop (int) - 1+maximal index
n (int) - number of indices

Returns: [int]: set of unique integers evenly distributed between start and stop

linfit(x, y)

source code

Calculate linear least-square fit to the points given by x and y. see http://mathworld.wolfram.com/LeastSquaresFitting.html

Parameters:

x ([ float ]) - x-data
y ([ float ]) - y-data

Returns: float, float, float: float, float - m, n, r^2 (slope, intersection, corr. coefficient)

Raises:

BiskitError - if x and y have different number of elements

cartesianToPolar(xyz)

source code

Convert cartesian coordinate array to polar coordinate array:

 
  x,y,z -> r, θ, φ

Parameters:

xyz (array) - array of cartesian coordinates (x, y, z)

Returns: array: array of polar coordinates (r, theta, phi)

polarToCartesian(rtp)

source code

Convert polar coordinate array to cartesian coordinate array:

 
  r, θ, φ -> x,y,z

Parameters:

rtp (array) - array of cartesian coordinates (r, theta, phi)

Returns: array: array of cartesian coordinates (x, y, z)

projectOnSphere(xyz, radius=None, center=None)

source code

Project the coordinates xyz on a sphere with a given radius around a given center.

Parameters:

xyz (array N x 3 of float) - cartesian coordinates
radius (float) - radius of target sphere, if not provided the maximal distance to center will be used (default: None)
center (array 0 x 3 of float) - center of the sphere, if not given the average of xyz will be assigned to the center (default: None)

Returns: array: array of cartesian coordinates (x, y, z)