pyNastran/op2/vector_utils

This is the pyNastran.op2.vector_utils.rst file.

vector_utils Module

defines some methods for working with arrays:
  • filter1d(a, b=None, zero_tol=0.001)

  • where_searchsorted(a, v, side=’left’, x=None, y=None)

  • sortedsum1d(ids, values, axis=None)

  • iformat(format_old, precision=2)

  • abs_max_min_global(values)

  • abs_max_min_vector(values)

  • abs_max_min(values, global_abs_max=True)

  • principal_3d(o11, o22, o33, o12, o23, o13)

  • transform_force(force_in_local,

    coord_out, coords, nid_cd, i_transform)

  • transform_force_moment(force_in_local, moment_in_local,

    coord_out, coords, nid_cd, i_transform, xyz_cid0, summation_point_cid0=None, consider_rxf=True, debug=False, log=None)

  • transform_force_moment_sum(force_in_local, moment_in_local,

    coord_out, coords, nid_cd, i_transform, xyz_cid0, summation_point_cid0=None, consider_rxf=True, debug=False, log=None)

pyNastran.op2.vector_utils.abs_max_min(values, global_abs_max=True)[source]

Gets the maximum value of x and -x. This is used for getting the max/min principal stress.

pyNastran.op2.vector_utils.abs_max_min_global(values)[source]

This is useful for figuring out absolute max or min principal stresses across single/multiple elements and finding a global max/min value.

Parameters
values: ndarray/listtuple

an ND-array of values; common NDARRAY/list/tuple shapes:

  1. [nprincipal_stresses]

  2. [nelements, nprincipal_stresses]

Returns
abs_max_mins: int/float

an array of the max or min principal stress don’t input mixed types

nvalues >= 1
>>> element1 = [0.0, -1.0, 2.0]  # 2.0
>>> element2 = [0.0, -3.0, 2.0]  # -3.0
>>> values = abs_max_min_global([element1, element2])
>>> values
-3.0
>>> element1 = [0.0, -1.0, 2.0]  # 2.0
>>> values = abs_max_min_global([element1])
>>> values
2.0

Note

[3.0, 2.0, -3.0] will return 3.0, and [-3.0, 2.0, 3.0] will return 3.0

pyNastran.op2.vector_utils.abs_max_min_vector(values)[source]

This is useful for figuring out principal stresses across multiple elements.

Parameters
values: ndarray/listtuple

an array of values, where the rows are interated over and the columns are going to be compressed

common NDARRAY/list/tuple shapes:
  1. [nprincipal_stresses]

  2. [nelements, nprincipal_stresses]

Returns
abs_max_mins: NDARRAY shape=[nelements] with dtype=values.dtype

an array of the max or min principal stress don’t input mixed types

::
>>> element1 = [0.0,  1.0, 2.0]  # 2.0
>>> element2 = [0.0, -1.0, 2.0]  # 2.0
>>> element3 = [0.0, -3.0, 2.0]  # -3.0
>>> values = [element1 element2, element3]
>>> values0 = abs_max_min_vectorized(values)
>>> values0
[2.0, 2.0, -3.0]

Note

[3.0, 2.0, -3.0] will return 3.0, and [-3.0, 2.0, 3.0] will return 3.0

pyNastran.op2.vector_utils.filter1d(a: numpy.ndarray, b: Optional[numpy.ndarray] = None, zero_tol: float = 0.001)[source]

Filters a 1d numpy array of values near 0.

Parameters
a(n, ) float ndarray

a vector to compare

b(n, ) float ndarray; default=None

another vector to compare If b is defined, both a and b must be near 0 for a value to be removed.

zero_tolfloat; default=0.001

the zero tolerance value

Returns
k(m, ) int ndarray

the indices of the removed values

a = [1., 2., 0.1]
>>> i = filter(a, zero_tol=0.5)
    ..
a[i]
>>> [0, 1]
    ..
a = [1., 2., 0.1]
b = [1., -0.1, 0.1]
>>> i = filter(a, b, zero_tol=0.5)
    ..
[0, 1]
pyNastran.op2.vector_utils.iformat(format_old: str, precision: int = 2) → str[source]

Converts binary data types to size vector arrays.

Parameters
format_oldstr

the int/float data types in single precision format

precisionint; default=2

the precision to convert to 1 : single precision (no conversion) 2 : double precision

Returns
format_newstr

the int/float data types in single/double precision format

Examples

>>> iformat('8i6f10s', precision=1)
'8i6f10s'
>>> iformat('8i6f10s', precision=2)
'8l6d10q'
pyNastran.op2.vector_utils.principal_3d(o11, o22, o33, o12, o23, o13)[source]

http://www.continuummechanics.org/cm/principalstrain.html

pyNastran.op2.vector_utils.sortedsum1d(ids, values, axis=None)[source]

Sums the values in a sorted 1d/2d array.

Parameters
ids(n, ) int ndarray

the integer values in a sorted order that indicate what is to be summed

values(n, m) float ndarray

the values to be summed Presumably m is 2 because this function is intended to be used for summing forces and moments

axisNone or int or tuple of ints, optional

Axis or axes along which a sum is performed. The default (axis=None) is perform a sum over all the dimensions of the input array. axis may be negative, in which case it counts from the last to the first axis. If this is a tuple of ints, a sum is performed on multiple axes, instead of a single axis or all the axes as before.

Not actually supported…

Returns
out(nunique, m) float ndarray

the summed values

Examples

1D Example For an set of arrays, there are 5 values in sorted order.

..code-block :: python

ids = [1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5] values = 1.0 * ids

We want to sum the values such that: ..code-block :: python

out = [2.0, 4.0, 9.0, 4.0, 15.0]

2D Example ..code-block :: python

ids = [1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5] values = [

[1.0, 1.0, 2.0, 2.0, 3.0, 3.0], [1.0, 1.0, 2.0, 2.0, 3.0, 3.0],

]

values = 1.0 * ids For 2D

Todo

This could probably be more efficient

Todo

Doesn’t support axis

pyNastran.op2.vector_utils.transform_force(force_in_local, coord_out: CORDx, coords: Dict[int, CORDx], nid_cd: int, unused_icd_transform)[source]

Transforms force/moment from global to local and returns all the forces.

Supports cylindrical/spherical coordinate systems.

Parameters
force(N, 3) ndarray

forces in the local frame

coord_outCORD()

the desired local frame

coordsdict[int] = CORDx

all the coordinate systems key : int value : CORDx

nid_cd(M, 2) int ndarray

the (BDF.point_ids, cd) array

icd_transformdict[cd] = (Mi, ) int ndarray

the mapping for nid_cd

.. warning:: the function signature will change…
.. todo:: sum of moments about a point must have an rxF term to get the

same value as Patran.

Fglobal = Flocal @ T
Flocal = T.T @ Fglobal
Flocal2 = T2.T @ (Flocal1 @ T1)
pyNastran.op2.vector_utils.transform_force_moment(force_in_local, moment_in_local, coord_out: CORDx, coords: Dict[int, CORDx], nid_cd: int, icd_transform: Dict[int, ndarray], xyz_cid0: ndarray, summation_point_cid0: Optional[NDArray3float] = None, consider_rxf: bool = True, debug: bool = False, log: Optional[SimpleLogger] = None)[source]

Transforms force/moment from global to local and returns all the forces.

Parameters
force_in_local(N, 3) ndarray

forces in the local frame

moment_in_local(N, 3) ndarray

moments in the local frame

coord_outCORDx()

the desired local frame

coordsdict[int] = CORDx

all the coordinate systems key : int value : CORDx

nid_cd(M, 2) int ndarray

the (BDF.point_ids, cd) array

icd_transformdict[cd] = (Mi, ) int ndarray

the mapping for nid_cd

xyz_cid0(n, 3) ndarray

the nodes in the global frame

summation_point_cid0(3, ) ndarray

the summation point in the global frame???

consider_rxfbool; default=True

considers the r x F term

debugbool; default=False

debugging flag

loglog; default=None

a log object that gets used when debug=True

Returns
force_out(n, 3) float ndarray

the ith float components in the coord_out coordinate frame

moment_out(n, 3) float ndarray

the ith moment components about the summation point in the coord_out coordinate frame

Todo

doesn’t seem to handle cylindrical/spherical systems ..

https://flexiblelearning.auckland.ac.nz/sportsci303/13_3/forceplate_manual.pdf
xyz0 = T_1_to_0 @ xyz1
xyz1 = T_1_to_0.T @ xyz0
xyz2 = T_2_to_0.T @ xyz0
xyz2 = T_2_to_0.T @ T_1_to_0 @ xyz1
xyz_g = T_a2g @ xyz_a
xyz_g = T_b2g @ xyz_b
T_b2g @ xyz_b = T_a2g @ xyz_a
xyz_b = T_b2g.T @ T_a2g @ xyz_a = T_g2b @ T_a2g @ xyz_a
pyNastran.op2.vector_utils.transform_force_moment_sum(force_in_local: NDArrayN3float, moment_in_local: NDArrayN3float, coord_out: CORDx, coords: Dict[int, CORDx], nid_cd: NDArrayN2int, icd_transform: Dict[int, NDArrayNint], xyz_cid0, summation_point_cid0=None, consider_rxf=True, debug=False, log=None)[source]

Transforms force/moment from global to local and returns a sum of forces/moments.

Parameters
force_in_local(N, 3) ndarray

forces in the local frame

moment_in_local(N, 3) ndarray

moments in the local frame

coord_outCORDx()

the desired local frame

coordsdict[int] = CORDx

all the coordinate systems key : int value : CORDx

nid_cd(M, 2) int ndarray

the (BDF.point_ids, cd) array

icd_transformdict[cd] = (Mi, ) int ndarray

the mapping for nid_cd

xyz_cid0(nnodes + nspoints + nepoints, 3) ndarray

the grid locations in coordinate system 0

summation_point_cid0(3, ) ndarray

the summation point in the global frame

consider_rxfbool; default=True

considers the r x F term

debugbool; default=False

debugging flag

loglog; default=None

a log object that gets used when debug=True

Returns
force_out(n, 3) float ndarray

the ith float components in the coord_out coordinate frame

moment_out(n, 3) float ndarray

the ith moment components about the summation point in the coord_out coordinate frame

force_out_sum(3, ) float ndarray

the sum of forces in the coord_out coordinate frame

moment_out_sum(3, ) float ndarray

the sum of moments about the summation point in the coord_out coordinate frame

Todo

doesn’t seem to handle cylindrical/spherical systems ..

pyNastran.op2.vector_utils.where_searchsorted(a, v, side='left', x=None, y=None)[source]

Implements a np.where that assumes a sorted array set.