Linear Algebra

Linear Algebra

linear_algebra.calculate_angle(a, b, c)

Calculates the dihedral angle between three vectors

Parameters

a

float list : vector a

b

float list : vector b

c

float list : vector c

Returns:angle in radians Return type:float

Examples

>>> import sasmol.linear_algebra as linear_algebra
>>> a = numpy.array([1.0, 2.0, 3.0])
>>> b = numpy.array([-1.0, 6.0, 8.0])
>>> c = numpy.array([-4.0, -1.0, 4.0])
>>> linear_algebra.calculate_angle(a, b, c)
0.7556508878558726

linear_algebra.cross_product(a, b)

Returns cross product (vector product) on two vectors

Parameters

a

float list : vector a

b

float list : vector b

Returns: Return type:numpy.array of cross product

Examples

>>> import sasmol.linear_algebra as linear_algebra
>>> a = [1.0, 2.0, 3.0]
>>> b = [-1.0, 6.0, 8.0]
>>> linear_algebra.cross_product(a, b)
array([ -2., -11.,   8.])

linear_algebra.dihedral_angle(a1, a2, a3, a4)

Calculates the dihedral angle between four vectors

Parameters

a1

float list : vector a1

a2

float list : vector a2

a3

float list : vector a3

a4

float list : vector a4

Returns:dihedral angle in degrees Return type:float

Examples

>>> import sasmol.linear_algebra as linear_algebra
>>> a1 = numpy.array([1.0, 2.0, 3.0])
>>> a2 = numpy.array([-1.0, 6.0, 8.0])
>>> a3 = numpy.array([-4.0, -1.0, 4.0])
>>> a4 = numpy.array([-3.0, -41, 3.0])
>>> linear_algebra.dihedral_angle(a1, a2, a3, a4)
85.950635659264

linear_algebra.find_u(x, y)

Method to find the U matrix used to align two sets of 3 x 3 coordinate arrays

Parameters

x

numpy array : 3 x 3

y

numpy array : 3 x 3

Returns:containing U matrix for alignment of two vectors Return type:numpy.array

Examples

>>> import sasmol.linear_algebra as linear_algebra
>>> import numpy
>>> a = numpy.array([[[1.0, 2.0, 3.0],[1.0, 2.0, 3.0],[1.0, 2.0, 3.0]],[[1.0, 2.0, 3.0],[1.0, 2.0, 3.0],[1.0, 2.0, 3.0]],[[1.0, 2.0, 3.0],[1.0, 2.0, 3.0],[1.0, 2.0, 3.0]]])
>>> b = numpy.array([[[-1.0, 6.0, 8.0],[-1.0, 6.0, 8.0],[-1.0, 6.0, 8.0]],[[-1.0, 6.0, 8.0],[-1.0, 6.0, 8.0],[-1.0, 6.0, 8.0]],[[-1.0, 6.0, 8.0],[-1.0, 6.0, 8.0],[-1.0, 6.0, 8.0]]])
>>> b = [-1.0, 6.0, 8.0]
>>> linear_algebra.find_u(a, b)
array([[-0.33333333, -0.33333333, -0.33333333],
    [-0.33333333, -0.33333333, -0.33333333],
    [-0.33333333, -0.33333333, -0.33333333]])

linear_algebra.matrix_multiply(a, b)

Returns the result of multiplying matrix a by matrix b

Parameters

a

float list : matrix a

b

float list : matrix b

Returns:

error

list with error code (if error occurs)

numpy.array of matrix product

Return type:tuple

Examples

>>> import sasmol.linear_algebra as linear_algebra
>>> import numpy
>>> a=numpy.array([[5.0, 3.0, 1.0],[2.0, 3.0, 5.0]])
>>> b=numpy.array([[2.0, -4.0, 8.0]]).T
>>> linear_algebra.matrix_multiply(a, b)
([], array([[  6.],
   [ 32.]]))

linear_algebra.signed_angle(a, b, c)

This method calcultes the sign of the angle which is used in the calculation of a dihedral angle. As such, this method is not validated for other uses. It will fail if the basis atoms for the dihedral (atom 2 and atom 3) overlap.

Parameters

a

float list : vector a

b

float list : vector b

c

float list : vector c

Returns:signed angle in degrees Return type:float

Examples

>>> import sasmol.linear_algebra as linear_algebra
>>> a = [1.0, 2.0, 3.0]
>>> b = [-1.0, 6.0, 8.0]
>>> c = [-4.0, -1.0, 4]
>>> linear_algebra.signed_angle(a, b, c)
21.444512921997863