Linear Algebra

Linear Algebra

LINEAR_ALGEBRA contains methods to perform basic mathematical operations

sasmol.linear_algebra.calculate_angle(a, b, c)

Calculates the angle at point b formed by three points a, b, and c.

The angle is defined between the vectors(a - b) and (c - b).

Parameters

• a –

• list (float) –

• b –

• list –

• c –

• list –

Returns

• float

• angle in radians

Notes

Returns NaN or Inf if either vector has zero length.

Examples

>> > import numpy >> > import sasmol.linear_algebra as linear_algebra >> > a = numpy.array([1.0, 0.0, 0.0]) >> > b = numpy.array([0.0, 0.0, 0.0]) >> > c = numpy.array([0.0, 1.0, 0.0]) >> > linear_algebra.calculate_angle(a, b, c) 1.5707963267948966

sasmol.linear_algebra.cmp(a, b)

python 3 does not provide the cmp function from python 2.7

sasmol.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

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.])

sasmol.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

sasmol.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]])

sasmol.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.]]))

sasmol.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

sasmol.linear_algebra.vec_scale(a, b, c)

Scale vector c by scalar b and store the result in a.

Parameters

• a – float list : output vector

• b – float : scale factor

• c – float list : vector to scale

Return type

output vector a

sasmol.linear_algebra.vec_sub(a, b, c)

Subtract vector c from vector b and store the result in a.

Parameters

• a – float list : output vector

• b – float list : minuend vector

• c – float list : subtrahend vector

Return type

output vector a