Package PyDSTool :: Package Toolbox :: Module mechmatlib
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Module mechmatlib

source code

Functions [hide private]
 
dot(a, b)
Dot product of two arrays.
 
augment_3_vector(v=array([ 0., 0., 0.]), free=False) source code
 
augment_3x3_matrix(M=matrix([[ 1., 0., 0..., disp=array([ 0., 0., 0.]), free=False) source code
 
make_disp(r)
Make 3D displacement
source code
 
make_rot(a)
Make 3D rotation (around z, then new x, then new y)
source code
 
make_T(r, a)
Make general 3D transformation (displacement then rotation)
source code
 
cross(a, b)
Cross product of two 3D vectors
source code
Variables [hide private]
  ZeroPos = array([ 0., 0., 0., 1.])
  Id = matrix([[ 1., 0., 0., 0...
Function Details [hide private]

dot(a, b)

 
Dot product of two arrays.

For 2-D arrays it is equivalent to matrix multiplication, and for 1-D
arrays to inner product of vectors (without complex conjugation). For
N dimensions it is a sum product over the last axis of `a` and
the second-to-last of `b`::

    dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])

Parameters
----------
a : array_like
    First argument.
b : array_like
    Second argument.

Returns
-------
output : ndarray
    Returns the dot product of `a` and `b`.  If `a` and `b` are both
    scalars or both 1-D arrays then a scalar is returned; otherwise
    an array is returned.

Raises
------
ValueError
    If the last dimension of `a` is not the same size as
    the second-to-last dimension of `b`.

See Also
--------
vdot : Complex-conjugating dot product.
tensordot : Sum products over arbitrary axes.

Examples
--------
>>> np.dot(3, 4)
12

Neither argument is complex-conjugated:

>>> np.dot([2j, 3j], [2j, 3j])
(-13+0j)

For 2-D arrays it's the matrix product:

>>> a = [[1, 0], [0, 1]]
>>> b = [[4, 1], [2, 2]]
>>> np.dot(a, b)
array([[4, 1],
       [2, 2]])

>>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
>>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
>>> np.dot(a, b)[2,3,2,1,2,2]
499128
>>> sum(a[2,3,2,:] * b[1,2,:,2])
499128


Variables Details [hide private]

Id

Value:
matrix([[ 1.,  0.,  0.,  0.],
        [ 0.,  1.,  0.,  0.],
        [ 0.,  0.,  1.,  0.],
        [ 0.,  0.,  0.,  1.]], dtype=float32)