schrodinger.application.matsci.elasticity.strain module¶
This module provides classes and methods used to describe deformations and strains, including applying those deformations to structure objects and generating deformed structure sets for further calculations.
Copyright Schrodinger, LLC. All rights reserved.
-
class
schrodinger.application.matsci.elasticity.strain.
Deformation
¶ Bases:
schrodinger.application.matsci.elasticity.tensors.SquareTensor
Subclass of SquareTensor that describes the deformation gradient tensor
-
is_independent
(tol=1e-08)¶ checks to determine whether the deformation is independent
-
get_perturbed_indices
(tol=1e-08)¶ Gets indices of perturbed elements of the deformation gradient, i. e. those that differ from the identity
-
green_lagrange_strain
¶ calculates the euler-lagrange strain from the deformation gradient
-
apply_to_structure
(structure)¶ Apply the deformation gradient to a structure.
- Args:
- structure (Structure object): the structure object to
- be modified by the deformation
-
classmethod
from_index_amount
(matrixpos, amt)¶ Factory method for constructing a Deformation object from a matrix position and amount
- Args:
- matrixpos (tuple): tuple corresponding the matrix position to
- have a perturbation added
- amt (float): amount to add to the identity matrix at position
- matrixpos
-
T
¶ Same as self.transpose(), except that self is returned if self.ndim < 2.
>>> x = np.array([[1.,2.],[3.,4.]]) >>> x array([[ 1., 2.], [ 3., 4.]]) >>> x.T array([[ 1., 3.], [ 2., 4.]]) >>> x = np.array([1.,2.,3.,4.]) >>> x array([ 1., 2., 3., 4.]) >>> x.T array([ 1., 2., 3., 4.])
-
__contains__
¶ Return key in self.
-
__init__
¶ Initialize self. See help(type(self)) for accurate signature.
-
__len__
¶ Return len(self).
-
all
(axis=None, out=None, keepdims=False)¶ Returns True if all elements evaluate to True.
Refer to
numpy.all
for full documentation.numpy.all : equivalent function
-
any
(axis=None, out=None, keepdims=False)¶ Returns True if any of the elements of
a
evaluate to True.Refer to
numpy.any
for full documentation.numpy.any : equivalent function
-
argmax
(axis=None, out=None)¶ Return indices of the maximum values along the given axis.
Refer to
numpy.argmax
for full documentation.numpy.argmax : equivalent function
-
argmin
(axis=None, out=None)¶ Return indices of the minimum values along the given axis of
a
.Refer to
numpy.argmin
for detailed documentation.numpy.argmin : equivalent function
-
argpartition
(kth, axis=-1, kind='introselect', order=None)¶ Returns the indices that would partition this array.
Refer to
numpy.argpartition
for full documentation.New in version 1.8.0.
numpy.argpartition : equivalent function
-
argsort
(axis=-1, kind='quicksort', order=None)¶ Returns the indices that would sort this array.
Refer to
numpy.argsort
for full documentation.numpy.argsort : equivalent function
-
astype
(dtype, order='K', casting='unsafe', subok=True, copy=True)¶ Copy of the array, cast to a specified type.
- dtype : str or dtype
- Typecode or data-type to which the array is cast.
- order : {‘C’, ‘F’, ‘A’, ‘K’}, optional
- Controls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. Default is ‘K’.
- casting : {‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}, optional
Controls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility.
- ‘no’ means the data types should not be cast at all.
- ‘equiv’ means only byte-order changes are allowed.
- ‘safe’ means only casts which can preserve values are allowed.
- ‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.
- ‘unsafe’ means any data conversions may be done.
- subok : bool, optional
- If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array.
- copy : bool, optional
- By default, astype always returns a newly allocated array. If this
is set to false, and the
dtype
,order
, andsubok
requirements are satisfied, the input array is returned instead of a copy.
- arr_t : ndarray
- Unless
copy
is False and the other conditions for returning the input array are satisfied (see description forcopy
input parameter),arr_t
is a new array of the same shape as the input array, with dtype, order given bydtype
,order
.
Starting in NumPy 1.9, astype method now returns an error if the string dtype to cast to is not long enough in ‘safe’ casting mode to hold the max value of integer/float array that is being casted. Previously the casting was allowed even if the result was truncated.
- ComplexWarning
- When casting from complex to float or int. To avoid this,
one should use
a.real.astype(t)
.
>>> x = np.array([1, 2, 2.5]) >>> x array([ 1. , 2. , 2.5])
>>> x.astype(int) array([1, 2, 2])
-
base
¶ Base object if memory is from some other object.
The base of an array that owns its memory is None:
>>> x = np.array([1,2,3,4]) >>> x.base is None True
Slicing creates a view, whose memory is shared with x:
>>> y = x[2:] >>> y.base is x True
-
byteswap
(inplace=False)¶ Swap the bytes of the array elements
Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place.
- inplace : bool, optional
- If
True
, swap bytes in-place, default isFalse
.
- out : ndarray
- The byteswapped array. If
inplace
isTrue
, this is a view to self.
>>> A = np.array([1, 256, 8755], dtype=np.int16) >>> map(hex, A) ['0x1', '0x100', '0x2233'] >>> A.byteswap(inplace=True) array([ 256, 1, 13090], dtype=int16) >>> map(hex, A) ['0x100', '0x1', '0x3322']
Arrays of strings are not swapped
>>> A = np.array(['ceg', 'fac']) >>> A.byteswap() array(['ceg', 'fac'], dtype='|S3')
-
choose
(choices, out=None, mode='raise')¶ Use an index array to construct a new array from a set of choices.
Refer to
numpy.choose
for full documentation.numpy.choose : equivalent function
-
clip
(min=None, max=None, out=None)¶ Return an array whose values are limited to
[min, max]
. One of max or min must be given.Refer to
numpy.clip
for full documentation.numpy.clip : equivalent function
-
compress
(condition, axis=None, out=None)¶ Return selected slices of this array along given axis.
Refer to
numpy.compress
for full documentation.numpy.compress : equivalent function
-
conj
()¶ Complex-conjugate all elements.
Refer to
numpy.conjugate
for full documentation.numpy.conjugate : equivalent function
-
conjugate
()¶ Return the complex conjugate, element-wise.
Refer to
numpy.conjugate
for full documentation.numpy.conjugate : equivalent function
-
copy
(order='C')¶ Return a copy of the array.
- order : {‘C’, ‘F’, ‘A’, ‘K’}, optional
- Controls the memory layout of the copy. ‘C’ means C-order,
‘F’ means F-order, ‘A’ means ‘F’ if
a
is Fortran contiguous, ‘C’ otherwise. ‘K’ means match the layout ofa
as closely as possible. (Note that this function andnumpy.copy()
are very similar, but have different default values for their order= arguments.)
numpy.copy numpy.copyto
>>> x = np.array([[1,2,3],[4,5,6]], order='F')
>>> y = x.copy()
>>> x.fill(0)
>>> x array([[0, 0, 0], [0, 0, 0]])
>>> y array([[1, 2, 3], [4, 5, 6]])
>>> y.flags['C_CONTIGUOUS'] True
-
ctypes
¶ An object to simplify the interaction of the array with the ctypes module.
This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library.
None
- c : Python object
- Possessing attributes data, shape, strides, etc.
numpy.ctypeslib
Below are the public attributes of this object which were documented in “Guide to NumPy” (we have omitted undocumented public attributes, as well as documented private attributes):
- data: A pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byte-order. The memory area may not even be writeable. The array flags and data-type of this array should be respected when passing this attribute to arbitrary C-code to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as self._array_interface_[‘data’][0].
- shape (c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the C-integer corresponding to dtype(‘p’) on this platform. This base-type could be c_int, c_long, or c_longlong depending on the platform. The c_intp type is defined accordingly in numpy.ctypeslib. The ctypes array contains the shape of the underlying array.
- strides (c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.
- data_as(obj): Return the data pointer cast to a particular c-types object. For example, calling self._as_parameter_ is equivalent to self.data_as(ctypes.c_void_p). Perhaps you want to use the data as a pointer to a ctypes array of floating-point data: self.data_as(ctypes.POINTER(ctypes.c_double)).
- shape_as(obj): Return the shape tuple as an array of some other c-types type. For example: self.shape_as(ctypes.c_short).
- strides_as(obj): Return the strides tuple as an array of some other c-types type. For example: self.strides_as(ctypes.c_longlong).
Be careful using the ctypes attribute - especially on temporary arrays or arrays constructed on the fly. For example, calling
(a+b).ctypes.data_as(ctypes.c_void_p)
returns a pointer to memory that is invalid because the array created as (a+b) is deallocated before the next Python statement. You can avoid this problem using eitherc=a+b
orct=(a+b).ctypes
. In the latter case, ct will hold a reference to the array until ct is deleted or re-assigned.If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the as parameter attribute which will return an integer equal to the data attribute.
>>> import ctypes >>> x array([[0, 1], [2, 3]]) >>> x.ctypes.data 30439712 >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_long)) <ctypes.LP_c_long object at 0x01F01300> >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_long)).contents c_long(0) >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_longlong)).contents c_longlong(4294967296L) >>> x.ctypes.shape <numpy.core._internal.c_long_Array_2 object at 0x01FFD580> >>> x.ctypes.shape_as(ctypes.c_long) <numpy.core._internal.c_long_Array_2 object at 0x01FCE620> >>> x.ctypes.strides <numpy.core._internal.c_long_Array_2 object at 0x01FCE620> >>> x.ctypes.strides_as(ctypes.c_longlong) <numpy.core._internal.c_longlong_Array_2 object at 0x01F01300>
-
cumprod
(axis=None, dtype=None, out=None)¶ Return the cumulative product of the elements along the given axis.
Refer to
numpy.cumprod
for full documentation.numpy.cumprod : equivalent function
-
cumsum
(axis=None, dtype=None, out=None)¶ Return the cumulative sum of the elements along the given axis.
Refer to
numpy.cumsum
for full documentation.numpy.cumsum : equivalent function
-
data
¶ Python buffer object pointing to the start of the array’s data.
-
det
¶ shorthand for the determinant of the SquareTensor
-
diagonal
(offset=0, axis1=0, axis2=1)¶ Return specified diagonals. In NumPy 1.9 the returned array is a read-only view instead of a copy as in previous NumPy versions. In a future version the read-only restriction will be removed.
Refer to
numpy.diagonal()
for full documentation.numpy.diagonal : equivalent function
-
dot
(b, out=None)¶ Dot product of two arrays.
Refer to
numpy.dot
for full documentation.numpy.dot : equivalent function
>>> a = np.eye(2) >>> b = np.ones((2, 2)) * 2 >>> a.dot(b) array([[ 2., 2.], [ 2., 2.]])
This array method can be conveniently chained:
>>> a.dot(b).dot(b) array([[ 8., 8.], [ 8., 8.]])
-
dtype
¶ Data-type of the array’s elements.
None
d : numpy dtype object
numpy.dtype
>>> x array([[0, 1], [2, 3]]) >>> x.dtype dtype('int32') >>> type(x.dtype) <type 'numpy.dtype'>
-
dump
(file)¶ Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load.
- file : str
- A string naming the dump file.
-
dumps
()¶ Returns the pickle of the array as a string. pickle.loads or numpy.loads will convert the string back to an array.
None
-
einsum_sequence
(other_arrays, einsum_string=None)¶ Calculates the result of an einstein summation expression
-
fill
(value)¶ Fill the array with a scalar value.
- value : scalar
- All elements of
a
will be assigned this value.
>>> a = np.array([1, 2]) >>> a.fill(0) >>> a array([0, 0]) >>> a = np.empty(2) >>> a.fill(1) >>> a array([ 1., 1.])
-
flags
¶ Information about the memory layout of the array.
- C_CONTIGUOUS (C)
- The data is in a single, C-style contiguous segment.
- F_CONTIGUOUS (F)
- The data is in a single, Fortran-style contiguous segment.
- OWNDATA (O)
- The array owns the memory it uses or borrows it from another object.
- WRITEABLE (W)
- The data area can be written to. Setting this to False locks the data, making it read-only. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a non-writeable array raises a RuntimeError exception.
- ALIGNED (A)
- The data and all elements are aligned appropriately for the hardware.
- WRITEBACKIFCOPY (X)
- This array is a copy of some other array. The C-API function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.
- UPDATEIFCOPY (U)
- (Deprecated, use WRITEBACKIFCOPY) This array is a copy of some other array. When this array is deallocated, the base array will be updated with the contents of this array.
- FNC
- F_CONTIGUOUS and not C_CONTIGUOUS.
- FORC
- F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).
- BEHAVED (B)
- ALIGNED and WRITEABLE.
- CARRAY (CA)
- BEHAVED and C_CONTIGUOUS.
- FARRAY (FA)
- BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.
The
flags
object can be accessed dictionary-like (as ina.flags['WRITEABLE']
), or by using lowercased attribute names (as ina.flags.writeable
). Short flag names are only supported in dictionary access.Only the WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling
ndarray.setflags
.The array flags cannot be set arbitrarily:
- UPDATEIFCOPY can only be set
False
. - WRITEBACKIFCOPY can only be set
False
. - ALIGNED can only be set
True
if the data is truly aligned. - WRITEABLE can only be set
True
if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string.
Arrays can be both C-style and Fortran-style contiguous simultaneously. This is clear for 1-dimensional arrays, but can also be true for higher dimensional arrays.
Even for contiguous arrays a stride for a given dimension
arr.strides[dim]
may be arbitrary ifarr.shape[dim] == 1
or the array has no elements. It does not generally hold thatself.strides[-1] == self.itemsize
for C-style contiguous arrays orself.strides[0] == self.itemsize
for Fortran-style contiguous arrays is true.
-
flat
¶ A 1-D iterator over the array.
This is a
numpy.flatiter
instance, which acts similarly to, but is not a subclass of, Python’s built-in iterator object.flatten : Return a copy of the array collapsed into one dimension.
flatiter
>>> x = np.arange(1, 7).reshape(2, 3) >>> x array([[1, 2, 3], [4, 5, 6]]) >>> x.flat[3] 4 >>> x.T array([[1, 4], [2, 5], [3, 6]]) >>> x.T.flat[3] 5 >>> type(x.flat) <type 'numpy.flatiter'>
An assignment example:
>>> x.flat = 3; x array([[3, 3, 3], [3, 3, 3]]) >>> x.flat[[1,4]] = 1; x array([[3, 1, 3], [3, 1, 3]])
-
flatten
(order='C')¶ Return a copy of the array collapsed into one dimension.
- order : {‘C’, ‘F’, ‘A’, ‘K’}, optional
- ‘C’ means to flatten in row-major (C-style) order.
‘F’ means to flatten in column-major (Fortran-
style) order. ‘A’ means to flatten in column-major
order if
a
is Fortran contiguous in memory, row-major order otherwise. ‘K’ means to flattena
in the order the elements occur in memory. The default is ‘C’.
- y : ndarray
- A copy of the input array, flattened to one dimension.
ravel : Return a flattened array. flat : A 1-D flat iterator over the array.
>>> a = np.array([[1,2], [3,4]]) >>> a.flatten() array([1, 2, 3, 4]) >>> a.flatten('F') array([1, 3, 2, 4])
-
classmethod
from_values_indices
(values, indices, populate=False, structure=None, voigt_rank=None, vsym=True, verbose=False)¶ Creates a tensor from values and indices, with options for populating the remainder of the tensor.
- Args:
values (floats): numbers to place at indices indices (array-likes): indices to place values at populate (bool): whether to populate the tensor structure (Structure): structure to base population
or fit_to_structure on- voigt_rank (int): full tensor rank to indicate the
- shape of the resulting tensor. This is necessary if one provides a set of indices more minimal than the shape of the tensor they want, e.g. Tensor.from_values_indices((0, 0), 100)
- vsym (bool): whether to voigt symmetrize during the
- optimization procedure
verbose (bool): whether to populate verbosely
-
classmethod
from_voigt
(voigt_input)¶ Constructor based on the voigt notation vector or matrix.
- Args:
- voigt_input (array-like): voigt input for a given tensor
-
get_scaled
(scale_factor)¶ Scales the tensor by a certain multiplicative scale factor
- Args:
- scale_factor (float): scalar multiplier to be applied to the
- SquareTensor object
-
static
get_voigt_dict
(rank)¶ Returns a dictionary that maps indices in the tensor to those in a voigt representation based on input rank
- Args:
- rank (int): Tensor rank to generate the voigt map
-
getfield
(dtype, offset=0)¶ Returns a field of the given array as a certain type.
A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes.
- dtype : str or dtype
- The data type of the view. The dtype size of the view can not be larger than that of the array itself.
- offset : int
- Number of bytes to skip before beginning the element view.
>>> x = np.diag([1.+1.j]*2) >>> x[1, 1] = 2 + 4.j >>> x array([[ 1.+1.j, 0.+0.j], [ 0.+0.j, 2.+4.j]]) >>> x.getfield(np.float64) array([[ 1., 0.], [ 0., 2.]])
By choosing an offset of 8 bytes we can select the complex part of the array for our view:
>>> x.getfield(np.float64, offset=8) array([[ 1., 0.], [ 0., 4.]])
-
imag
¶ The imaginary part of the array.
>>> x = np.sqrt([1+0j, 0+1j]) >>> x.imag array([ 0. , 0.70710678]) >>> x.imag.dtype dtype('float64')
-
inv
¶ shorthand for matrix inverse on SquareTensor
-
is_fit_to_structure
(structure, tol=0.01)¶ Tests whether a tensor is invariant with respect to the symmetry operations of a particular structure by testing whether the residual of the symmetric portion is below a tolerance
- Args:
- structure (Structure): structure to be fit to tol (float): tolerance for symmetry testing
-
is_rotation
(tol=0.001, include_improper=True)¶ Test to see if tensor is a valid rotation matrix, performs a test to check whether the inverse is equal to the transpose and if the determinant is equal to one within the specified tolerance
- Args:
- tol (float): tolerance to both tests of whether the
- the determinant is one and the inverse is equal to the transpose
- include_improper (bool): whether to include improper
- rotations in the determination of validity
-
is_symmetric
(tol=1e-05)¶ Tests whether a tensor is symmetric or not based on the residual with its symmetric part, from self.symmetrized
- Args:
- tol (float): tolerance to test for symmetry
-
is_voigt_symmetric
(tol=1e-06)¶ Tests symmetry of tensor to that necessary for voigt-conversion by grouping indices into pairs and constructing a sequence of possible permutations to be used in a tensor transpose
-
item
(*args)¶ Copy an element of an array to a standard Python scalar and return it.
*args : Arguments (variable number and type)
- none: in this case, the method only works for arrays
with one element (
a.size == 1
), which element is copied into a standard Python scalar object and returned. - int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return.
- tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array.
- z : Standard Python scalar object
- A copy of the specified element of the array as a suitable Python scalar
When the data type of
a
is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned.item
is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python’s optimized math.>>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.item(3) 2 >>> x.item(7) 5 >>> x.item((0, 1)) 1 >>> x.item((2, 2)) 3
- none: in this case, the method only works for arrays
with one element (
-
itemset
(*args)¶ Insert scalar into an array (scalar is cast to array’s dtype, if possible)
There must be at least 1 argument, and define the last argument as item. Then,
a.itemset(*args)
is equivalent to but faster thana[args] = item
. The item should be a scalar value andargs
must select a single item in the arraya
.- \*args : Arguments
- If one argument: a scalar, only used in case
a
is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple.
Compared to indexing syntax,
itemset
provides some speed increase for placing a scalar into a particular location in anndarray
, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when usingitemset
(anditem
) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration.>>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[3, 1, 7], [2, 0, 3], [8, 5, 9]])
-
itemsize
¶ Length of one array element in bytes.
>>> x = np.array([1,2,3], dtype=np.float64) >>> x.itemsize 8 >>> x = np.array([1,2,3], dtype=np.complex128) >>> x.itemsize 16
-
max
(axis=None, out=None, keepdims=False)¶ Return the maximum along a given axis.
Refer to
numpy.amax
for full documentation.numpy.amax : equivalent function
-
mean
(axis=None, dtype=None, out=None, keepdims=False)¶ Returns the average of the array elements along given axis.
Refer to
numpy.mean
for full documentation.numpy.mean : equivalent function
-
min
(axis=None, out=None, keepdims=False)¶ Return the minimum along a given axis.
Refer to
numpy.amin
for full documentation.numpy.amin : equivalent function
-
nbytes
¶ Total bytes consumed by the elements of the array.
Does not include memory consumed by non-element attributes of the array object.
>>> x = np.zeros((3,5,2), dtype=np.complex128) >>> x.nbytes 480 >>> np.prod(x.shape) * x.itemsize 480
-
ndim
¶ Number of array dimensions.
>>> x = np.array([1, 2, 3]) >>> x.ndim 1 >>> y = np.zeros((2, 3, 4)) >>> y.ndim 3
-
newbyteorder
(new_order='S')¶ Return the array with the same data viewed with a different byte order.
Equivalent to:
arr.view(arr.dtype.newbytorder(new_order))
Changes are also made in all fields and sub-arrays of the array data type.
- new_order : string, optional
Byte order to force; a value from the byte order specifications below.
new_order
codes can be any of:- ‘S’ - swap dtype from current to opposite endian
- {‘<’, ‘L’} - little endian
- {‘>’, ‘B’} - big endian
- {‘=’, ‘N’} - native order
- {‘|’, ‘I’} - ignore (no change to byte order)
The default value (‘S’) results in swapping the current byte order. The code does a case-insensitive check on the first letter of
new_order
for the alternatives above. For example, any of ‘B’ or ‘b’ or ‘biggish’ are valid to specify big-endian.
- new_arr : array
- New array object with the dtype reflecting given change to the byte order.
-
nonzero
()¶ Return the indices of the elements that are non-zero.
Refer to
numpy.nonzero
for full documentation.numpy.nonzero : equivalent function
-
partition
(kth, axis=-1, kind='introselect', order=None)¶ Rearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined.
New in version 1.8.0.
- kth : int or sequence of ints
- Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order of all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once.
- axis : int, optional
- Axis along which to sort. Default is -1, which means sort along the last axis.
- kind : {‘introselect’}, optional
- Selection algorithm. Default is ‘introselect’.
- order : str or list of str, optional
- When
a
is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need to be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.
numpy.partition : Return a parititioned copy of an array. argpartition : Indirect partition. sort : Full sort.
See
np.partition
for notes on the different algorithms.>>> a = np.array([3, 4, 2, 1]) >>> a.partition(3) >>> a array([2, 1, 3, 4])
>>> a.partition((1, 3)) array([1, 2, 3, 4])
-
polar_decomposition
(side='right')¶ calculates matrices for polar decomposition
-
principal_invariants
¶ Returns a list of principal invariants for the tensor, which are the values of the coefficients of the characteristic polynomial for the matrix
-
prod
(axis=None, dtype=None, out=None, keepdims=False)¶ Return the product of the array elements over the given axis
Refer to
numpy.prod
for full documentation.numpy.prod : equivalent function
-
ptp
(axis=None, out=None, keepdims=False)¶ Peak to peak (maximum - minimum) value along a given axis.
Refer to
numpy.ptp
for full documentation.numpy.ptp : equivalent function
-
put
(indices, values, mode='raise')¶ Set
a.flat[n] = values[n]
for alln
in indices.Refer to
numpy.put
for full documentation.numpy.put : equivalent function
-
ravel
([order])¶ Return a flattened array.
Refer to
numpy.ravel
for full documentation.numpy.ravel : equivalent function
ndarray.flat : a flat iterator on the array.
-
real
¶ The real part of the array.
>>> x = np.sqrt([1+0j, 0+1j]) >>> x.real array([ 1. , 0.70710678]) >>> x.real.dtype dtype('float64')
numpy.real : equivalent function
-
refine_rotation
()¶ Helper method for refining rotation matrix by ensuring that second and third rows are perpindicular to the first. Gets new y vector from an orthogonal projection of x onto y and the new z vector from a cross product of the new x and y
- Args:
- tol to test for rotation
- Returns:
- new rotation matrix
-
repeat
(repeats, axis=None)¶ Repeat elements of an array.
Refer to
numpy.repeat
for full documentation.numpy.repeat : equivalent function
-
reshape
(shape, order='C')¶ Returns an array containing the same data with a new shape.
Refer to
numpy.reshape
for full documentation.numpy.reshape : equivalent function
Unlike the free function
numpy.reshape
, this method onndarray
allows the elements of the shape parameter to be passed in as separate arguments. For example,a.reshape(10, 11)
is equivalent toa.reshape((10, 11))
.
-
resize
(new_shape, refcheck=True)¶ Change shape and size of array in-place.
- new_shape : tuple of ints, or
n
ints - Shape of resized array.
- refcheck : bool, optional
- If False, reference count will not be checked. Default is True.
None
- ValueError
- If
a
does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist. - SystemError
- If the
order
keyword argument is specified. This behaviour is a bug in NumPy.
resize : Return a new array with the specified shape.
This reallocates space for the data area if necessary.
Only contiguous arrays (data elements consecutive in memory) can be resized.
The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set
refcheck
to False.Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped:
>>> a = np.array([[0, 1], [2, 3]], order='C') >>> a.resize((2, 1)) >>> a array([[0], [1]])
>>> a = np.array([[0, 1], [2, 3]], order='F') >>> a.resize((2, 1)) >>> a array([[0], [2]])
Enlarging an array: as above, but missing entries are filled with zeros:
>>> b = np.array([[0, 1], [2, 3]]) >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple >>> b array([[0, 1, 2], [3, 0, 0]])
Referencing an array prevents resizing…
>>> c = a >>> a.resize((1, 1)) Traceback (most recent call last): ... ValueError: cannot resize an array that has been referenced ...
Unless
refcheck
is False:>>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])
- new_shape : tuple of ints, or
-
rotate
(matrix, tol=0.001)¶ Applies a rotation directly, and tests input matrix to ensure a valid rotation.
- Args:
- matrix (3x3 array-like): rotation matrix to be applied to tensor tol (float): tolerance for testing rotation matrix validity
-
round
(decimals=0, out=None)¶ Return
a
with each element rounded to the given number of decimals.Refer to
numpy.around
for full documentation.numpy.around : equivalent function
-
searchsorted
(v, side='left', sorter=None)¶ Find indices where elements of v should be inserted in a to maintain order.
For full documentation, see
numpy.searchsorted
numpy.searchsorted : equivalent function
-
setfield
(val, dtype, offset=0)¶ Put a value into a specified place in a field defined by a data-type.
Place
val
intoa
’s field defined bydtype
and beginningoffset
bytes into the field.- val : object
- Value to be placed in field.
- dtype : dtype object
- Data-type of the field in which to place
val
. - offset : int, optional
- The number of bytes into the field at which to place
val
.
None
getfield
>>> x = np.eye(3) >>> x.getfield(np.float64) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) >>> x.setfield(3, np.int32) >>> x.getfield(np.int32) array([[3, 3, 3], [3, 3, 3], [3, 3, 3]]) >>> x array([[ 1.00000000e+000, 1.48219694e-323, 1.48219694e-323], [ 1.48219694e-323, 1.00000000e+000, 1.48219694e-323], [ 1.48219694e-323, 1.48219694e-323, 1.00000000e+000]]) >>> x.setfield(np.eye(3), np.int32) >>> x array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])
-
setflags
(write=None, align=None, uic=None)¶ Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY), respectively.
These Boolean-valued flags affect how numpy interprets the memory area used by
a
(see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The WRITEBACKIFCOPY and (deprecated) UPDATEIFCOPY flags can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.)- write : bool, optional
- Describes whether or not
a
can be written to. - align : bool, optional
- Describes whether or not
a
is aligned properly for its type. - uic : bool, optional
- Describes whether or not
a
is a copy of another “base” array.
Array flags provide information about how the memory area used for the array is to be interpreted. There are 7 Boolean flags in use, only four of which can be changed by the user: WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED.
WRITEABLE (W) the data area can be written to;
ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler);
UPDATEIFCOPY (U) (deprecated), replaced by WRITEBACKIFCOPY;
WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced by .base). When the C-API function PyArray_ResolveWritebackIfCopy is called, the base array will be updated with the contents of this array.
All flags can be accessed using the single (upper case) letter as well as the full name.
>>> y array([[3, 1, 7], [2, 0, 0], [8, 5, 9]]) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : True ALIGNED : True WRITEBACKIFCOPY : False UPDATEIFCOPY : False >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False WRITEBACKIFCOPY : False UPDATEIFCOPY : False >>> y.setflags(uic=1) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: cannot set WRITEBACKIFCOPY flag to True
-
shape
¶ Tuple of array dimensions.
The shape property is usually used to get the current shape of an array, but may also be used to reshape the array in-place by assigning a tuple of array dimensions to it. As with
numpy.reshape
, one of the new shape dimensions can be -1, in which case its value is inferred from the size of the array and the remaining dimensions. Reshaping an array in-place will fail if a copy is required.>>> x = np.array([1, 2, 3, 4]) >>> x.shape (4,) >>> y = np.zeros((2, 3, 4)) >>> y.shape (2, 3, 4) >>> y.shape = (3, 8) >>> y array([[ 0., 0., 0., 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0., 0., 0., 0.]]) >>> y.shape = (3, 6) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: total size of new array must be unchanged >>> np.zeros((4,2))[::2].shape = (-1,) Traceback (most recent call last): File "<stdin>", line 1, in <module> AttributeError: incompatible shape for a non-contiguous array
numpy.reshape : similar function ndarray.reshape : similar method
-
size
¶ Number of elements in the array.
Equal to
np.prod(a.shape)
, i.e., the product of the array’s dimensions.a.size
returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggestednp.prod(a.shape)
, which returns an instance ofnp.int_
), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.>>> x = np.zeros((3, 5, 2), dtype=np.complex128) >>> x.size 30 >>> np.prod(x.shape) 30
-
sort
(axis=-1, kind='quicksort', order=None)¶ Sort an array, in-place.
- axis : int, optional
- Axis along which to sort. Default is -1, which means sort along the last axis.
- kind : {‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional
- Sorting algorithm. Default is ‘quicksort’.
- order : str or list of str, optional
- When
a
is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.
numpy.sort : Return a sorted copy of an array. argsort : Indirect sort. lexsort : Indirect stable sort on multiple keys. searchsorted : Find elements in sorted array. partition: Partial sort.
See
sort
for notes on the different sorting algorithms.>>> a = np.array([[1,4], [3,1]]) >>> a.sort(axis=1) >>> a array([[1, 4], [1, 3]]) >>> a.sort(axis=0) >>> a array([[1, 3], [1, 4]])
Use the
order
keyword to specify a field to use when sorting a structured array:>>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) >>> a.sort(order='y') >>> a array([('c', 1), ('a', 2)], dtype=[('x', '|S1'), ('y', '<i4')])
-
squeeze
(axis=None)¶ Remove single-dimensional entries from the shape of
a
.Refer to
numpy.squeeze
for full documentation.numpy.squeeze : equivalent function
-
std
(axis=None, dtype=None, out=None, ddof=0, keepdims=False)¶ Returns the standard deviation of the array elements along given axis.
Refer to
numpy.std
for full documentation.numpy.std : equivalent function
-
strides
¶ Tuple of bytes to step in each dimension when traversing an array.
The byte offset of element
(i[0], i[1], ..., i[n])
in an arraya
is:offset = sum(np.array(i) * a.strides)
A more detailed explanation of strides can be found in the “ndarray.rst” file in the NumPy reference guide.
Imagine an array of 32-bit integers (each 4 bytes):
x = np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]], dtype=np.int32)
This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array
x
will be(20, 4)
.numpy.lib.stride_tricks.as_strided
>>> y = np.reshape(np.arange(2*3*4), (2,3,4)) >>> y array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]]) >>> y.strides (48, 16, 4) >>> y[1,1,1] 17 >>> offset=sum(y.strides * np.array((1,1,1))) >>> offset/y.itemsize 17
>>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0) >>> x.strides (32, 4, 224, 1344) >>> i = np.array([3,5,2,2]) >>> offset = sum(i * x.strides) >>> x[3,5,2,2] 813 >>> offset / x.itemsize 813
-
sum
(axis=None, dtype=None, out=None, keepdims=False)¶ Return the sum of the array elements over the given axis.
Refer to
numpy.sum
for full documentation.numpy.sum : equivalent function
-
swapaxes
(axis1, axis2)¶ Return a view of the array with
axis1
andaxis2
interchanged.Refer to
numpy.swapaxes
for full documentation.numpy.swapaxes : equivalent function
-
symmetrized
¶ Returns a generally symmetrized tensor, calculated by taking the sum of the tensor and its transpose with respect to all possible permutations of indices
-
take
(indices, axis=None, out=None, mode='raise')¶ Return an array formed from the elements of
a
at the given indices.Refer to
numpy.take
for full documentation.numpy.take : equivalent function
-
tobytes
(order='C')¶ Construct Python bytes containing the raw data bytes in the array.
Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object can be produced in either ‘C’ or ‘Fortran’, or ‘Any’ order (the default is ‘C’-order). ‘Any’ order means C-order unless the F_CONTIGUOUS flag in the array is set, in which case it means ‘Fortran’ order.
New in version 1.9.0.
- order : {‘C’, ‘F’, None}, optional
- Order of the data for multidimensional arrays: C, Fortran, or the same as for the original array.
- s : bytes
- Python bytes exhibiting a copy of
a
’s raw data.
>>> x = np.array([[0, 1], [2, 3]]) >>> x.tobytes() b'\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00' >>> x.tobytes('C') == x.tobytes() True >>> x.tobytes('F') b'\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00'
-
tofile
(fid, sep="", format="%s")¶ Write array to a file as text or binary (default).
Data is always written in ‘C’ order, independent of the order of
a
. The data produced by this method can be recovered using the function fromfile().- fid : file or str
- An open file object, or a string containing a filename.
- sep : str
- Separator between array items for text output.
If “” (empty), a binary file is written, equivalent to
file.write(a.tobytes())
. - format : str
- Format string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using “format” % item.
This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size.
When fid is a file object, array contents are directly written to the file, bypassing the file object’s
write
method. As a result, tofile cannot be used with files objects supporting compression (e.g., GzipFile) or file-like objects that do not supportfileno()
(e.g., BytesIO).
-
tolist
()¶ Return the array as a (possibly nested) list.
Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible Python type.
none
- y : list
- The possibly nested list of array elements.
The array may be recreated,
a = np.array(a.tolist())
.>>> a = np.array([1, 2]) >>> a.tolist() [1, 2] >>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]]
-
tostring
(order='C')¶ Construct Python bytes containing the raw data bytes in the array.
Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object can be produced in either ‘C’ or ‘Fortran’, or ‘Any’ order (the default is ‘C’-order). ‘Any’ order means C-order unless the F_CONTIGUOUS flag in the array is set, in which case it means ‘Fortran’ order.
This function is a compatibility alias for tobytes. Despite its name it returns bytes not strings.
- order : {‘C’, ‘F’, None}, optional
- Order of the data for multidimensional arrays: C, Fortran, or the same as for the original array.
- s : bytes
- Python bytes exhibiting a copy of
a
’s raw data.
>>> x = np.array([[0, 1], [2, 3]]) >>> x.tobytes() b'\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00' >>> x.tobytes('C') == x.tobytes() True >>> x.tobytes('F') b'\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00'
-
trace
(offset=0, axis1=0, axis2=1, dtype=None, out=None)¶ Return the sum along diagonals of the array.
Refer to
numpy.trace
for full documentation.numpy.trace : equivalent function
-
trans
¶ shorthand for transpose on SquareTensor
-
transform
(symm_op)¶ Applies a transformation (via a symmetry operation) to a tensor.
- Args:
- symm_op (SymmOp): a symmetry operation to apply to the tensor
-
transpose
(*axes)¶ Returns a view of the array with axes transposed.
For a 1-D array, this has no effect. (To change between column and row vectors, first cast the 1-D array into a matrix object.) For a 2-D array, this is the usual matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and
a.shape = (i[0], i[1], ... i[n-2], i[n-1])
, thena.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])
.axes : None, tuple of ints, or
n
ints- None or no argument: reverses the order of the axes.
- tuple of ints:
i
in thej
-th place in the tuple meansa
’si
-th axis becomesa.transpose()
’sj
-th axis. n
ints: same as an n-tuple of the same ints (this form is intended simply as a “convenience” alternative to the tuple form)
- out : ndarray
- View of
a
, with axes suitably permuted.
ndarray.T : Array property returning the array transposed.
>>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1, 0)) array([[1, 3], [2, 4]]) >>> a.transpose(1, 0) array([[1, 3], [2, 4]])
-
var
(axis=None, dtype=None, out=None, ddof=0, keepdims=False)¶ Returns the variance of the array elements, along given axis.
Refer to
numpy.var
for full documentation.numpy.var : equivalent function
-
view
(dtype=None, type=None)¶ New view of array with the same data.
- dtype : data-type or ndarray sub-class, optional
- Data-type descriptor of the returned view, e.g., float32 or int16. The
default, None, results in the view having the same data-type as
a
. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting thetype
parameter). - type : Python type, optional
- Type of the returned view, e.g., ndarray or matrix. Again, the default None results in type preservation.
a.view()
is used two different ways:a.view(some_dtype)
ora.view(dtype=some_dtype)
constructs a view of the array’s memory with a different data-type. This can cause a reinterpretation of the bytes of memory.a.view(ndarray_subclass)
ora.view(type=ndarray_subclass)
just returns an instance ofndarray_subclass
that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory.For
a.view(some_dtype)
, ifsome_dtype
has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the behavior of the view cannot be predicted just from the superficial appearance ofa
(shown byprint(a)
). It also depends on exactly howa
is stored in memory. Therefore ifa
is C-ordered versus fortran-ordered, versus defined as a slice or transpose, etc., the view may give different results.>>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])
Viewing array data using a different type and dtype:
>>> y = x.view(dtype=np.int16, type=np.matrix) >>> y matrix([[513]], dtype=int16) >>> print(type(y)) <class 'numpy.matrixlib.defmatrix.matrix'>
Creating a view on a structured array so it can be used in calculations
>>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) >>> xv = x.view(dtype=np.int8).reshape(-1,2) >>> xv array([[1, 2], [3, 4]], dtype=int8) >>> xv.mean(0) array([ 2., 3.])
Making changes to the view changes the underlying array
>>> xv[0,1] = 20 >>> print(x) [(1, 20) (3, 4)]
Using a view to convert an array to a recarray:
>>> z = x.view(np.recarray) >>> z.a array([1], dtype=int8)
Views share data:
>>> x[0] = (9, 10) >>> z[0] (9, 10)
Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.:
>>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) >>> y = x[:, 0:2] >>> y array([[1, 2], [4, 5]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: new type not compatible with array. >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 2)], [(4, 5)]], dtype=[('width', '<i2'), ('length', '<i2')])
-
voigt
¶ Returns the tensor in Voigt notation
-
voigt_symmetrized
¶ Returns a “voigt”-symmetrized tensor, i. e. a voigt-notation tensor such that it is invariant wrt permutation of indices
-
zeroed
(tol=0.001)¶ returns the matrix with all entries below a certain threshold (i.e. tol) set to zero
-
-
class
schrodinger.application.matsci.elasticity.strain.
DeformedStructureSet
(structure, norm_strains=None, shear_strains=None, symmetry=False)¶ Bases:
collections.abc.Sequence
class that generates a set of independently deformed structures that can be used to calculate linear stress-strain response
-
NORM_INDICES
= [(0, 0), (1, 1), (2, 2)]¶
-
NORM_STRAINS
= [-0.01, -0.005, 0.005, 0.01]¶
-
SHEAR_INDICES
= [(0, 1), (0, 2), (1, 2)]¶
-
SHEAR_STRAINS
= [-0.06, -0.03, 0.03, 0.06]¶
-
__init__
(structure, norm_strains=None, shear_strains=None, symmetry=False)¶ constructs the deformed geometries of a structure. Generates m + n deformed structures according to the supplied parameters.
- Args:
structure (Structure): structure to undergo deformation norm_strains (list of floats): strain values to apply
to each normal mode.- shear_strains (list of floats): strain values to apply
- to each shear mode.
symmetry (bool): whether or not to use symmetry reduction.
-
__len__
()¶
-
__contains__
(value)¶
-
count
(value) → integer -- return number of occurrences of value¶
-
index
(value[, start[, stop]]) → integer -- return first index of value.¶ Raises ValueError if the value is not present.
-
-
class
schrodinger.application.matsci.elasticity.strain.
Strain
¶ Bases:
schrodinger.application.matsci.elasticity.tensors.SquareTensor
Subclass of SquareTensor that describes the Green-Lagrange strain tensor.
-
classmethod
from_deformation
(deformation)¶ Factory method that returns a Strain object from a deformation gradient
- Args:
- deformation (3x3 array-like):
-
classmethod
from_index_amount
(idx, amount)¶ Like Deformation.from_index_amount, except generates a strain from the zero 3x3 tensor or voigt vector with the amount specified in the index location. Ensures symmetric strain.
- Args:
- idx (tuple or integer): index to be perturbed, can be voigt or
- full-tensor notation
amount (float): amount to perturb selected index
-
deformation_matrix
¶ returns the deformation matrix
-
T
¶ Same as self.transpose(), except that self is returned if self.ndim < 2.
>>> x = np.array([[1.,2.],[3.,4.]]) >>> x array([[ 1., 2.], [ 3., 4.]]) >>> x.T array([[ 1., 3.], [ 2., 4.]]) >>> x = np.array([1.,2.,3.,4.]) >>> x array([ 1., 2., 3., 4.]) >>> x.T array([ 1., 2., 3., 4.])
-
__contains__
¶ Return key in self.
-
__init__
¶ Initialize self. See help(type(self)) for accurate signature.
-
__len__
¶ Return len(self).
-
all
(axis=None, out=None, keepdims=False)¶ Returns True if all elements evaluate to True.
Refer to
numpy.all
for full documentation.numpy.all : equivalent function
-
any
(axis=None, out=None, keepdims=False)¶ Returns True if any of the elements of
a
evaluate to True.Refer to
numpy.any
for full documentation.numpy.any : equivalent function
-
argmax
(axis=None, out=None)¶ Return indices of the maximum values along the given axis.
Refer to
numpy.argmax
for full documentation.numpy.argmax : equivalent function
-
argmin
(axis=None, out=None)¶ Return indices of the minimum values along the given axis of
a
.Refer to
numpy.argmin
for detailed documentation.numpy.argmin : equivalent function
-
argpartition
(kth, axis=-1, kind='introselect', order=None)¶ Returns the indices that would partition this array.
Refer to
numpy.argpartition
for full documentation.New in version 1.8.0.
numpy.argpartition : equivalent function
-
argsort
(axis=-1, kind='quicksort', order=None)¶ Returns the indices that would sort this array.
Refer to
numpy.argsort
for full documentation.numpy.argsort : equivalent function
-
astype
(dtype, order='K', casting='unsafe', subok=True, copy=True)¶ Copy of the array, cast to a specified type.
- dtype : str or dtype
- Typecode or data-type to which the array is cast.
- order : {‘C’, ‘F’, ‘A’, ‘K’}, optional
- Controls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. Default is ‘K’.
- casting : {‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}, optional
Controls what kind of data casting may occur. Defaults to ‘unsafe’ for backwards compatibility.
- ‘no’ means the data types should not be cast at all.
- ‘equiv’ means only byte-order changes are allowed.
- ‘safe’ means only casts which can preserve values are allowed.
- ‘same_kind’ means only safe casts or casts within a kind, like float64 to float32, are allowed.
- ‘unsafe’ means any data conversions may be done.
- subok : bool, optional
- If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array.
- copy : bool, optional
- By default, astype always returns a newly allocated array. If this
is set to false, and the
dtype
,order
, andsubok
requirements are satisfied, the input array is returned instead of a copy.
- arr_t : ndarray
- Unless
copy
is False and the other conditions for returning the input array are satisfied (see description forcopy
input parameter),arr_t
is a new array of the same shape as the input array, with dtype, order given bydtype
,order
.
Starting in NumPy 1.9, astype method now returns an error if the string dtype to cast to is not long enough in ‘safe’ casting mode to hold the max value of integer/float array that is being casted. Previously the casting was allowed even if the result was truncated.
- ComplexWarning
- When casting from complex to float or int. To avoid this,
one should use
a.real.astype(t)
.
>>> x = np.array([1, 2, 2.5]) >>> x array([ 1. , 2. , 2.5])
>>> x.astype(int) array([1, 2, 2])
-
base
¶ Base object if memory is from some other object.
The base of an array that owns its memory is None:
>>> x = np.array([1,2,3,4]) >>> x.base is None True
Slicing creates a view, whose memory is shared with x:
>>> y = x[2:] >>> y.base is x True
-
byteswap
(inplace=False)¶ Swap the bytes of the array elements
Toggle between low-endian and big-endian data representation by returning a byteswapped array, optionally swapped in-place.
- inplace : bool, optional
- If
True
, swap bytes in-place, default isFalse
.
- out : ndarray
- The byteswapped array. If
inplace
isTrue
, this is a view to self.
>>> A = np.array([1, 256, 8755], dtype=np.int16) >>> map(hex, A) ['0x1', '0x100', '0x2233'] >>> A.byteswap(inplace=True) array([ 256, 1, 13090], dtype=int16) >>> map(hex, A) ['0x100', '0x1', '0x3322']
Arrays of strings are not swapped
>>> A = np.array(['ceg', 'fac']) >>> A.byteswap() array(['ceg', 'fac'], dtype='|S3')
-
choose
(choices, out=None, mode='raise')¶ Use an index array to construct a new array from a set of choices.
Refer to
numpy.choose
for full documentation.numpy.choose : equivalent function
-
clip
(min=None, max=None, out=None)¶ Return an array whose values are limited to
[min, max]
. One of max or min must be given.Refer to
numpy.clip
for full documentation.numpy.clip : equivalent function
-
compress
(condition, axis=None, out=None)¶ Return selected slices of this array along given axis.
Refer to
numpy.compress
for full documentation.numpy.compress : equivalent function
-
conj
()¶ Complex-conjugate all elements.
Refer to
numpy.conjugate
for full documentation.numpy.conjugate : equivalent function
-
conjugate
()¶ Return the complex conjugate, element-wise.
Refer to
numpy.conjugate
for full documentation.numpy.conjugate : equivalent function
-
copy
(order='C')¶ Return a copy of the array.
- order : {‘C’, ‘F’, ‘A’, ‘K’}, optional
- Controls the memory layout of the copy. ‘C’ means C-order,
‘F’ means F-order, ‘A’ means ‘F’ if
a
is Fortran contiguous, ‘C’ otherwise. ‘K’ means match the layout ofa
as closely as possible. (Note that this function andnumpy.copy()
are very similar, but have different default values for their order= arguments.)
numpy.copy numpy.copyto
>>> x = np.array([[1,2,3],[4,5,6]], order='F')
>>> y = x.copy()
>>> x.fill(0)
>>> x array([[0, 0, 0], [0, 0, 0]])
>>> y array([[1, 2, 3], [4, 5, 6]])
>>> y.flags['C_CONTIGUOUS'] True
-
ctypes
¶ An object to simplify the interaction of the array with the ctypes module.
This attribute creates an object that makes it easier to use arrays when calling shared libraries with the ctypes module. The returned object has, among others, data, shape, and strides attributes (see Notes below) which themselves return ctypes objects that can be used as arguments to a shared library.
None
- c : Python object
- Possessing attributes data, shape, strides, etc.
numpy.ctypeslib
Below are the public attributes of this object which were documented in “Guide to NumPy” (we have omitted undocumented public attributes, as well as documented private attributes):
- data: A pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byte-order. The memory area may not even be writeable. The array flags and data-type of this array should be respected when passing this attribute to arbitrary C-code to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as self._array_interface_[‘data’][0].
- shape (c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the C-integer corresponding to dtype(‘p’) on this platform. This base-type could be c_int, c_long, or c_longlong depending on the platform. The c_intp type is defined accordingly in numpy.ctypeslib. The ctypes array contains the shape of the underlying array.
- strides (c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.
- data_as(obj): Return the data pointer cast to a particular c-types object. For example, calling self._as_parameter_ is equivalent to self.data_as(ctypes.c_void_p). Perhaps you want to use the data as a pointer to a ctypes array of floating-point data: self.data_as(ctypes.POINTER(ctypes.c_double)).
- shape_as(obj): Return the shape tuple as an array of some other c-types type. For example: self.shape_as(ctypes.c_short).
- strides_as(obj): Return the strides tuple as an array of some other c-types type. For example: self.strides_as(ctypes.c_longlong).
Be careful using the ctypes attribute - especially on temporary arrays or arrays constructed on the fly. For example, calling
(a+b).ctypes.data_as(ctypes.c_void_p)
returns a pointer to memory that is invalid because the array created as (a+b) is deallocated before the next Python statement. You can avoid this problem using eitherc=a+b
orct=(a+b).ctypes
. In the latter case, ct will hold a reference to the array until ct is deleted or re-assigned.If the ctypes module is not available, then the ctypes attribute of array objects still returns something useful, but ctypes objects are not returned and errors may be raised instead. In particular, the object will still have the as parameter attribute which will return an integer equal to the data attribute.
>>> import ctypes >>> x array([[0, 1], [2, 3]]) >>> x.ctypes.data 30439712 >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_long)) <ctypes.LP_c_long object at 0x01F01300> >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_long)).contents c_long(0) >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_longlong)).contents c_longlong(4294967296L) >>> x.ctypes.shape <numpy.core._internal.c_long_Array_2 object at 0x01FFD580> >>> x.ctypes.shape_as(ctypes.c_long) <numpy.core._internal.c_long_Array_2 object at 0x01FCE620> >>> x.ctypes.strides <numpy.core._internal.c_long_Array_2 object at 0x01FCE620> >>> x.ctypes.strides_as(ctypes.c_longlong) <numpy.core._internal.c_longlong_Array_2 object at 0x01F01300>
-
cumprod
(axis=None, dtype=None, out=None)¶ Return the cumulative product of the elements along the given axis.
Refer to
numpy.cumprod
for full documentation.numpy.cumprod : equivalent function
-
cumsum
(axis=None, dtype=None, out=None)¶ Return the cumulative sum of the elements along the given axis.
Refer to
numpy.cumsum
for full documentation.numpy.cumsum : equivalent function
-
data
¶ Python buffer object pointing to the start of the array’s data.
-
det
¶ shorthand for the determinant of the SquareTensor
-
diagonal
(offset=0, axis1=0, axis2=1)¶ Return specified diagonals. In NumPy 1.9 the returned array is a read-only view instead of a copy as in previous NumPy versions. In a future version the read-only restriction will be removed.
Refer to
numpy.diagonal()
for full documentation.numpy.diagonal : equivalent function
-
dot
(b, out=None)¶ Dot product of two arrays.
Refer to
numpy.dot
for full documentation.numpy.dot : equivalent function
>>> a = np.eye(2) >>> b = np.ones((2, 2)) * 2 >>> a.dot(b) array([[ 2., 2.], [ 2., 2.]])
This array method can be conveniently chained:
>>> a.dot(b).dot(b) array([[ 8., 8.], [ 8., 8.]])
-
dtype
¶ Data-type of the array’s elements.
None
d : numpy dtype object
numpy.dtype
>>> x array([[0, 1], [2, 3]]) >>> x.dtype dtype('int32') >>> type(x.dtype) <type 'numpy.dtype'>
-
dump
(file)¶ Dump a pickle of the array to the specified file. The array can be read back with pickle.load or numpy.load.
- file : str
- A string naming the dump file.
-
dumps
()¶ Returns the pickle of the array as a string. pickle.loads or numpy.loads will convert the string back to an array.
None
-
einsum_sequence
(other_arrays, einsum_string=None)¶ Calculates the result of an einstein summation expression
-
fill
(value)¶ Fill the array with a scalar value.
- value : scalar
- All elements of
a
will be assigned this value.
>>> a = np.array([1, 2]) >>> a.fill(0) >>> a array([0, 0]) >>> a = np.empty(2) >>> a.fill(1) >>> a array([ 1., 1.])
-
flags
¶ Information about the memory layout of the array.
- C_CONTIGUOUS (C)
- The data is in a single, C-style contiguous segment.
- F_CONTIGUOUS (F)
- The data is in a single, Fortran-style contiguous segment.
- OWNDATA (O)
- The array owns the memory it uses or borrows it from another object.
- WRITEABLE (W)
- The data area can be written to. Setting this to False locks the data, making it read-only. A view (slice, etc.) inherits WRITEABLE from its base array at creation time, but a view of a writeable array may be subsequently locked while the base array remains writeable. (The opposite is not true, in that a view of a locked array may not be made writeable. However, currently, locking a base object does not lock any views that already reference it, so under that circumstance it is possible to alter the contents of a locked array via a previously created writeable view onto it.) Attempting to change a non-writeable array raises a RuntimeError exception.
- ALIGNED (A)
- The data and all elements are aligned appropriately for the hardware.
- WRITEBACKIFCOPY (X)
- This array is a copy of some other array. The C-API function PyArray_ResolveWritebackIfCopy must be called before deallocating to the base array will be updated with the contents of this array.
- UPDATEIFCOPY (U)
- (Deprecated, use WRITEBACKIFCOPY) This array is a copy of some other array. When this array is deallocated, the base array will be updated with the contents of this array.
- FNC
- F_CONTIGUOUS and not C_CONTIGUOUS.
- FORC
- F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).
- BEHAVED (B)
- ALIGNED and WRITEABLE.
- CARRAY (CA)
- BEHAVED and C_CONTIGUOUS.
- FARRAY (FA)
- BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.
The
flags
object can be accessed dictionary-like (as ina.flags['WRITEABLE']
), or by using lowercased attribute names (as ina.flags.writeable
). Short flag names are only supported in dictionary access.Only the WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED flags can be changed by the user, via direct assignment to the attribute or dictionary entry, or by calling
ndarray.setflags
.The array flags cannot be set arbitrarily:
- UPDATEIFCOPY can only be set
False
. - WRITEBACKIFCOPY can only be set
False
. - ALIGNED can only be set
True
if the data is truly aligned. - WRITEABLE can only be set
True
if the array owns its own memory or the ultimate owner of the memory exposes a writeable buffer interface or is a string.
Arrays can be both C-style and Fortran-style contiguous simultaneously. This is clear for 1-dimensional arrays, but can also be true for higher dimensional arrays.
Even for contiguous arrays a stride for a given dimension
arr.strides[dim]
may be arbitrary ifarr.shape[dim] == 1
or the array has no elements. It does not generally hold thatself.strides[-1] == self.itemsize
for C-style contiguous arrays orself.strides[0] == self.itemsize
for Fortran-style contiguous arrays is true.
-
flat
¶ A 1-D iterator over the array.
This is a
numpy.flatiter
instance, which acts similarly to, but is not a subclass of, Python’s built-in iterator object.flatten : Return a copy of the array collapsed into one dimension.
flatiter
>>> x = np.arange(1, 7).reshape(2, 3) >>> x array([[1, 2, 3], [4, 5, 6]]) >>> x.flat[3] 4 >>> x.T array([[1, 4], [2, 5], [3, 6]]) >>> x.T.flat[3] 5 >>> type(x.flat) <type 'numpy.flatiter'>
An assignment example:
>>> x.flat = 3; x array([[3, 3, 3], [3, 3, 3]]) >>> x.flat[[1,4]] = 1; x array([[3, 1, 3], [3, 1, 3]])
-
flatten
(order='C')¶ Return a copy of the array collapsed into one dimension.
- order : {‘C’, ‘F’, ‘A’, ‘K’}, optional
- ‘C’ means to flatten in row-major (C-style) order.
‘F’ means to flatten in column-major (Fortran-
style) order. ‘A’ means to flatten in column-major
order if
a
is Fortran contiguous in memory, row-major order otherwise. ‘K’ means to flattena
in the order the elements occur in memory. The default is ‘C’.
- y : ndarray
- A copy of the input array, flattened to one dimension.
ravel : Return a flattened array. flat : A 1-D flat iterator over the array.
>>> a = np.array([[1,2], [3,4]]) >>> a.flatten() array([1, 2, 3, 4]) >>> a.flatten('F') array([1, 3, 2, 4])
-
classmethod
from_values_indices
(values, indices, populate=False, structure=None, voigt_rank=None, vsym=True, verbose=False)¶ Creates a tensor from values and indices, with options for populating the remainder of the tensor.
- Args:
values (floats): numbers to place at indices indices (array-likes): indices to place values at populate (bool): whether to populate the tensor structure (Structure): structure to base population
or fit_to_structure on- voigt_rank (int): full tensor rank to indicate the
- shape of the resulting tensor. This is necessary if one provides a set of indices more minimal than the shape of the tensor they want, e.g. Tensor.from_values_indices((0, 0), 100)
- vsym (bool): whether to voigt symmetrize during the
- optimization procedure
verbose (bool): whether to populate verbosely
-
classmethod
from_voigt
(voigt_input)¶ Constructor based on the voigt notation vector or matrix.
- Args:
- voigt_input (array-like): voigt input for a given tensor
-
get_scaled
(scale_factor)¶ Scales the tensor by a certain multiplicative scale factor
- Args:
- scale_factor (float): scalar multiplier to be applied to the
- SquareTensor object
-
static
get_voigt_dict
(rank)¶ Returns a dictionary that maps indices in the tensor to those in a voigt representation based on input rank
- Args:
- rank (int): Tensor rank to generate the voigt map
-
getfield
(dtype, offset=0)¶ Returns a field of the given array as a certain type.
A field is a view of the array data with a given data-type. The values in the view are determined by the given type and the offset into the current array in bytes. The offset needs to be such that the view dtype fits in the array dtype; for example an array of dtype complex128 has 16-byte elements. If taking a view with a 32-bit integer (4 bytes), the offset needs to be between 0 and 12 bytes.
- dtype : str or dtype
- The data type of the view. The dtype size of the view can not be larger than that of the array itself.
- offset : int
- Number of bytes to skip before beginning the element view.
>>> x = np.diag([1.+1.j]*2) >>> x[1, 1] = 2 + 4.j >>> x array([[ 1.+1.j, 0.+0.j], [ 0.+0.j, 2.+4.j]]) >>> x.getfield(np.float64) array([[ 1., 0.], [ 0., 2.]])
By choosing an offset of 8 bytes we can select the complex part of the array for our view:
>>> x.getfield(np.float64, offset=8) array([[ 1., 0.], [ 0., 4.]])
-
imag
¶ The imaginary part of the array.
>>> x = np.sqrt([1+0j, 0+1j]) >>> x.imag array([ 0. , 0.70710678]) >>> x.imag.dtype dtype('float64')
-
inv
¶ shorthand for matrix inverse on SquareTensor
-
is_fit_to_structure
(structure, tol=0.01)¶ Tests whether a tensor is invariant with respect to the symmetry operations of a particular structure by testing whether the residual of the symmetric portion is below a tolerance
- Args:
- structure (Structure): structure to be fit to tol (float): tolerance for symmetry testing
-
is_rotation
(tol=0.001, include_improper=True)¶ Test to see if tensor is a valid rotation matrix, performs a test to check whether the inverse is equal to the transpose and if the determinant is equal to one within the specified tolerance
- Args:
- tol (float): tolerance to both tests of whether the
- the determinant is one and the inverse is equal to the transpose
- include_improper (bool): whether to include improper
- rotations in the determination of validity
-
is_symmetric
(tol=1e-05)¶ Tests whether a tensor is symmetric or not based on the residual with its symmetric part, from self.symmetrized
- Args:
- tol (float): tolerance to test for symmetry
-
is_voigt_symmetric
(tol=1e-06)¶ Tests symmetry of tensor to that necessary for voigt-conversion by grouping indices into pairs and constructing a sequence of possible permutations to be used in a tensor transpose
-
item
(*args)¶ Copy an element of an array to a standard Python scalar and return it.
*args : Arguments (variable number and type)
- none: in this case, the method only works for arrays
with one element (
a.size == 1
), which element is copied into a standard Python scalar object and returned. - int_type: this argument is interpreted as a flat index into the array, specifying which element to copy and return.
- tuple of int_types: functions as does a single int_type argument, except that the argument is interpreted as an nd-index into the array.
- z : Standard Python scalar object
- A copy of the specified element of the array as a suitable Python scalar
When the data type of
a
is longdouble or clongdouble, item() returns a scalar array object because there is no available Python scalar that would not lose information. Void arrays return a buffer object for item(), unless fields are defined, in which case a tuple is returned.item
is very similar to a[args], except, instead of an array scalar, a standard Python scalar is returned. This can be useful for speeding up access to elements of the array and doing arithmetic on elements of the array using Python’s optimized math.>>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.item(3) 2 >>> x.item(7) 5 >>> x.item((0, 1)) 1 >>> x.item((2, 2)) 3
- none: in this case, the method only works for arrays
with one element (
-
itemset
(*args)¶ Insert scalar into an array (scalar is cast to array’s dtype, if possible)
There must be at least 1 argument, and define the last argument as item. Then,
a.itemset(*args)
is equivalent to but faster thana[args] = item
. The item should be a scalar value andargs
must select a single item in the arraya
.- \*args : Arguments
- If one argument: a scalar, only used in case
a
is of size 1. If two arguments: the last argument is the value to be set and must be a scalar, the first argument specifies a single array element location. It is either an int or a tuple.
Compared to indexing syntax,
itemset
provides some speed increase for placing a scalar into a particular location in anndarray
, if you must do this. However, generally this is discouraged: among other problems, it complicates the appearance of the code. Also, when usingitemset
(anditem
) inside a loop, be sure to assign the methods to a local variable to avoid the attribute look-up at each loop iteration.>>> x = np.random.randint(9, size=(3, 3)) >>> x array([[3, 1, 7], [2, 8, 3], [8, 5, 3]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[3, 1, 7], [2, 0, 3], [8, 5, 9]])
-
itemsize
¶ Length of one array element in bytes.
>>> x = np.array([1,2,3], dtype=np.float64) >>> x.itemsize 8 >>> x = np.array([1,2,3], dtype=np.complex128) >>> x.itemsize 16
-
max
(axis=None, out=None, keepdims=False)¶ Return the maximum along a given axis.
Refer to
numpy.amax
for full documentation.numpy.amax : equivalent function
-
mean
(axis=None, dtype=None, out=None, keepdims=False)¶ Returns the average of the array elements along given axis.
Refer to
numpy.mean
for full documentation.numpy.mean : equivalent function
-
min
(axis=None, out=None, keepdims=False)¶ Return the minimum along a given axis.
Refer to
numpy.amin
for full documentation.numpy.amin : equivalent function
-
nbytes
¶ Total bytes consumed by the elements of the array.
Does not include memory consumed by non-element attributes of the array object.
>>> x = np.zeros((3,5,2), dtype=np.complex128) >>> x.nbytes 480 >>> np.prod(x.shape) * x.itemsize 480
-
ndim
¶ Number of array dimensions.
>>> x = np.array([1, 2, 3]) >>> x.ndim 1 >>> y = np.zeros((2, 3, 4)) >>> y.ndim 3
-
newbyteorder
(new_order='S')¶ Return the array with the same data viewed with a different byte order.
Equivalent to:
arr.view(arr.dtype.newbytorder(new_order))
Changes are also made in all fields and sub-arrays of the array data type.
- new_order : string, optional
Byte order to force; a value from the byte order specifications below.
new_order
codes can be any of:- ‘S’ - swap dtype from current to opposite endian
- {‘<’, ‘L’} - little endian
- {‘>’, ‘B’} - big endian
- {‘=’, ‘N’} - native order
- {‘|’, ‘I’} - ignore (no change to byte order)
The default value (‘S’) results in swapping the current byte order. The code does a case-insensitive check on the first letter of
new_order
for the alternatives above. For example, any of ‘B’ or ‘b’ or ‘biggish’ are valid to specify big-endian.
- new_arr : array
- New array object with the dtype reflecting given change to the byte order.
-
nonzero
()¶ Return the indices of the elements that are non-zero.
Refer to
numpy.nonzero
for full documentation.numpy.nonzero : equivalent function
-
partition
(kth, axis=-1, kind='introselect', order=None)¶ Rearranges the elements in the array in such a way that the value of the element in kth position is in the position it would be in a sorted array. All elements smaller than the kth element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined.
New in version 1.8.0.
- kth : int or sequence of ints
- Element index to partition by. The kth element value will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order of all elements in the partitions is undefined. If provided with a sequence of kth it will partition all elements indexed by kth of them into their sorted position at once.
- axis : int, optional
- Axis along which to sort. Default is -1, which means sort along the last axis.
- kind : {‘introselect’}, optional
- Selection algorithm. Default is ‘introselect’.
- order : str or list of str, optional
- When
a
is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need to be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.
numpy.partition : Return a parititioned copy of an array. argpartition : Indirect partition. sort : Full sort.
See
np.partition
for notes on the different algorithms.>>> a = np.array([3, 4, 2, 1]) >>> a.partition(3) >>> a array([2, 1, 3, 4])
>>> a.partition((1, 3)) array([1, 2, 3, 4])
-
polar_decomposition
(side='right')¶ calculates matrices for polar decomposition
-
principal_invariants
¶ Returns a list of principal invariants for the tensor, which are the values of the coefficients of the characteristic polynomial for the matrix
-
prod
(axis=None, dtype=None, out=None, keepdims=False)¶ Return the product of the array elements over the given axis
Refer to
numpy.prod
for full documentation.numpy.prod : equivalent function
-
ptp
(axis=None, out=None, keepdims=False)¶ Peak to peak (maximum - minimum) value along a given axis.
Refer to
numpy.ptp
for full documentation.numpy.ptp : equivalent function
-
put
(indices, values, mode='raise')¶ Set
a.flat[n] = values[n]
for alln
in indices.Refer to
numpy.put
for full documentation.numpy.put : equivalent function
-
ravel
([order])¶ Return a flattened array.
Refer to
numpy.ravel
for full documentation.numpy.ravel : equivalent function
ndarray.flat : a flat iterator on the array.
-
real
¶ The real part of the array.
>>> x = np.sqrt([1+0j, 0+1j]) >>> x.real array([ 1. , 0.70710678]) >>> x.real.dtype dtype('float64')
numpy.real : equivalent function
-
refine_rotation
()¶ Helper method for refining rotation matrix by ensuring that second and third rows are perpindicular to the first. Gets new y vector from an orthogonal projection of x onto y and the new z vector from a cross product of the new x and y
- Args:
- tol to test for rotation
- Returns:
- new rotation matrix
-
repeat
(repeats, axis=None)¶ Repeat elements of an array.
Refer to
numpy.repeat
for full documentation.numpy.repeat : equivalent function
-
reshape
(shape, order='C')¶ Returns an array containing the same data with a new shape.
Refer to
numpy.reshape
for full documentation.numpy.reshape : equivalent function
Unlike the free function
numpy.reshape
, this method onndarray
allows the elements of the shape parameter to be passed in as separate arguments. For example,a.reshape(10, 11)
is equivalent toa.reshape((10, 11))
.
-
resize
(new_shape, refcheck=True)¶ Change shape and size of array in-place.
- new_shape : tuple of ints, or
n
ints - Shape of resized array.
- refcheck : bool, optional
- If False, reference count will not be checked. Default is True.
None
- ValueError
- If
a
does not own its own data or references or views to it exist, and the data memory must be changed. PyPy only: will always raise if the data memory must be changed, since there is no reliable way to determine if references or views to it exist. - SystemError
- If the
order
keyword argument is specified. This behaviour is a bug in NumPy.
resize : Return a new array with the specified shape.
This reallocates space for the data area if necessary.
Only contiguous arrays (data elements consecutive in memory) can be resized.
The purpose of the reference count check is to make sure you do not use this array as a buffer for another Python object and then reallocate the memory. However, reference counts can increase in other ways so if you are sure that you have not shared the memory for this array with another Python object, then you may safely set
refcheck
to False.Shrinking an array: array is flattened (in the order that the data are stored in memory), resized, and reshaped:
>>> a = np.array([[0, 1], [2, 3]], order='C') >>> a.resize((2, 1)) >>> a array([[0], [1]])
>>> a = np.array([[0, 1], [2, 3]], order='F') >>> a.resize((2, 1)) >>> a array([[0], [2]])
Enlarging an array: as above, but missing entries are filled with zeros:
>>> b = np.array([[0, 1], [2, 3]]) >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple >>> b array([[0, 1, 2], [3, 0, 0]])
Referencing an array prevents resizing…
>>> c = a >>> a.resize((1, 1)) Traceback (most recent call last): ... ValueError: cannot resize an array that has been referenced ...
Unless
refcheck
is False:>>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])
- new_shape : tuple of ints, or
-
rotate
(matrix, tol=0.001)¶ Applies a rotation directly, and tests input matrix to ensure a valid rotation.
- Args:
- matrix (3x3 array-like): rotation matrix to be applied to tensor tol (float): tolerance for testing rotation matrix validity
-
round
(decimals=0, out=None)¶ Return
a
with each element rounded to the given number of decimals.Refer to
numpy.around
for full documentation.numpy.around : equivalent function
-
searchsorted
(v, side='left', sorter=None)¶ Find indices where elements of v should be inserted in a to maintain order.
For full documentation, see
numpy.searchsorted
numpy.searchsorted : equivalent function
-
setfield
(val, dtype, offset=0)¶ Put a value into a specified place in a field defined by a data-type.
Place
val
intoa
’s field defined bydtype
and beginningoffset
bytes into the field.- val : object
- Value to be placed in field.
- dtype : dtype object
- Data-type of the field in which to place
val
. - offset : int, optional
- The number of bytes into the field at which to place
val
.
None
getfield
>>> x = np.eye(3) >>> x.getfield(np.float64) array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]]) >>> x.setfield(3, np.int32) >>> x.getfield(np.int32) array([[3, 3, 3], [3, 3, 3], [3, 3, 3]]) >>> x array([[ 1.00000000e+000, 1.48219694e-323, 1.48219694e-323], [ 1.48219694e-323, 1.00000000e+000, 1.48219694e-323], [ 1.48219694e-323, 1.48219694e-323, 1.00000000e+000]]) >>> x.setfield(np.eye(3), np.int32) >>> x array([[ 1., 0., 0.], [ 0., 1., 0.], [ 0., 0., 1.]])
-
setflags
(write=None, align=None, uic=None)¶ Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY), respectively.
These Boolean-valued flags affect how numpy interprets the memory area used by
a
(see Notes below). The ALIGNED flag can only be set to True if the data is actually aligned according to the type. The WRITEBACKIFCOPY and (deprecated) UPDATEIFCOPY flags can never be set to True. The flag WRITEABLE can only be set to True if the array owns its own memory, or the ultimate owner of the memory exposes a writeable buffer interface, or is a string. (The exception for string is made so that unpickling can be done without copying memory.)- write : bool, optional
- Describes whether or not
a
can be written to. - align : bool, optional
- Describes whether or not
a
is aligned properly for its type. - uic : bool, optional
- Describes whether or not
a
is a copy of another “base” array.
Array flags provide information about how the memory area used for the array is to be interpreted. There are 7 Boolean flags in use, only four of which can be changed by the user: WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED.
WRITEABLE (W) the data area can be written to;
ALIGNED (A) the data and strides are aligned appropriately for the hardware (as determined by the compiler);
UPDATEIFCOPY (U) (deprecated), replaced by WRITEBACKIFCOPY;
WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced by .base). When the C-API function PyArray_ResolveWritebackIfCopy is called, the base array will be updated with the contents of this array.
All flags can be accessed using the single (upper case) letter as well as the full name.
>>> y array([[3, 1, 7], [2, 0, 0], [8, 5, 9]]) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : True ALIGNED : True WRITEBACKIFCOPY : False UPDATEIFCOPY : False >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False WRITEBACKIFCOPY : False UPDATEIFCOPY : False >>> y.setflags(uic=1) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: cannot set WRITEBACKIFCOPY flag to True
-
shape
¶ Tuple of array dimensions.
The shape property is usually used to get the current shape of an array, but may also be used to reshape the array in-place by assigning a tuple of array dimensions to it. As with
numpy.reshape
, one of the new shape dimensions can be -1, in which case its value is inferred from the size of the array and the remaining dimensions. Reshaping an array in-place will fail if a copy is required.>>> x = np.array([1, 2, 3, 4]) >>> x.shape (4,) >>> y = np.zeros((2, 3, 4)) >>> y.shape (2, 3, 4) >>> y.shape = (3, 8) >>> y array([[ 0., 0., 0., 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0., 0., 0., 0.]]) >>> y.shape = (3, 6) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: total size of new array must be unchanged >>> np.zeros((4,2))[::2].shape = (-1,) Traceback (most recent call last): File "<stdin>", line 1, in <module> AttributeError: incompatible shape for a non-contiguous array
numpy.reshape : similar function ndarray.reshape : similar method
-
size
¶ Number of elements in the array.
Equal to
np.prod(a.shape)
, i.e., the product of the array’s dimensions.a.size
returns a standard arbitrary precision Python integer. This may not be the case with other methods of obtaining the same value (like the suggestednp.prod(a.shape)
, which returns an instance ofnp.int_
), and may be relevant if the value is used further in calculations that may overflow a fixed size integer type.>>> x = np.zeros((3, 5, 2), dtype=np.complex128) >>> x.size 30 >>> np.prod(x.shape) 30
-
sort
(axis=-1, kind='quicksort', order=None)¶ Sort an array, in-place.
- axis : int, optional
- Axis along which to sort. Default is -1, which means sort along the last axis.
- kind : {‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional
- Sorting algorithm. Default is ‘quicksort’.
- order : str or list of str, optional
- When
a
is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties.
numpy.sort : Return a sorted copy of an array. argsort : Indirect sort. lexsort : Indirect stable sort on multiple keys. searchsorted : Find elements in sorted array. partition: Partial sort.
See
sort
for notes on the different sorting algorithms.>>> a = np.array([[1,4], [3,1]]) >>> a.sort(axis=1) >>> a array([[1, 4], [1, 3]]) >>> a.sort(axis=0) >>> a array([[1, 3], [1, 4]])
Use the
order
keyword to specify a field to use when sorting a structured array:>>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) >>> a.sort(order='y') >>> a array([('c', 1), ('a', 2)], dtype=[('x', '|S1'), ('y', '<i4')])
-
squeeze
(axis=None)¶ Remove single-dimensional entries from the shape of
a
.Refer to
numpy.squeeze
for full documentation.numpy.squeeze : equivalent function
-
std
(axis=None, dtype=None, out=None, ddof=0, keepdims=False)¶ Returns the standard deviation of the array elements along given axis.
Refer to
numpy.std
for full documentation.numpy.std : equivalent function
-
strides
¶ Tuple of bytes to step in each dimension when traversing an array.
The byte offset of element
(i[0], i[1], ..., i[n])
in an arraya
is:offset = sum(np.array(i) * a.strides)
A more detailed explanation of strides can be found in the “ndarray.rst” file in the NumPy reference guide.
Imagine an array of 32-bit integers (each 4 bytes):
x = np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]], dtype=np.int32)
This array is stored in memory as 40 bytes, one after the other (known as a contiguous block of memory). The strides of an array tell us how many bytes we have to skip in memory to move to the next position along a certain axis. For example, we have to skip 4 bytes (1 value) to move to the next column, but 20 bytes (5 values) to get to the same position in the next row. As such, the strides for the array
x
will be(20, 4)
.numpy.lib.stride_tricks.as_strided
>>> y = np.reshape(np.arange(2*3*4), (2,3,4)) >>> y array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]]) >>> y.strides (48, 16, 4) >>> y[1,1,1] 17 >>> offset=sum(y.strides * np.array((1,1,1))) >>> offset/y.itemsize 17
>>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0) >>> x.strides (32, 4, 224, 1344) >>> i = np.array([3,5,2,2]) >>> offset = sum(i * x.strides) >>> x[3,5,2,2] 813 >>> offset / x.itemsize 813
-
sum
(axis=None, dtype=None, out=None, keepdims=False)¶ Return the sum of the array elements over the given axis.
Refer to
numpy.sum
for full documentation.numpy.sum : equivalent function
-
swapaxes
(axis1, axis2)¶ Return a view of the array with
axis1
andaxis2
interchanged.Refer to
numpy.swapaxes
for full documentation.numpy.swapaxes : equivalent function
-
symmetrized
¶ Returns a generally symmetrized tensor, calculated by taking the sum of the tensor and its transpose with respect to all possible permutations of indices
-
take
(indices, axis=None, out=None, mode='raise')¶ Return an array formed from the elements of
a
at the given indices.Refer to
numpy.take
for full documentation.numpy.take : equivalent function
-
tobytes
(order='C')¶ Construct Python bytes containing the raw data bytes in the array.
Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object can be produced in either ‘C’ or ‘Fortran’, or ‘Any’ order (the default is ‘C’-order). ‘Any’ order means C-order unless the F_CONTIGUOUS flag in the array is set, in which case it means ‘Fortran’ order.
New in version 1.9.0.
- order : {‘C’, ‘F’, None}, optional
- Order of the data for multidimensional arrays: C, Fortran, or the same as for the original array.
- s : bytes
- Python bytes exhibiting a copy of
a
’s raw data.
>>> x = np.array([[0, 1], [2, 3]]) >>> x.tobytes() b'\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00' >>> x.tobytes('C') == x.tobytes() True >>> x.tobytes('F') b'\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00'
-
tofile
(fid, sep="", format="%s")¶ Write array to a file as text or binary (default).
Data is always written in ‘C’ order, independent of the order of
a
. The data produced by this method can be recovered using the function fromfile().- fid : file or str
- An open file object, or a string containing a filename.
- sep : str
- Separator between array items for text output.
If “” (empty), a binary file is written, equivalent to
file.write(a.tobytes())
. - format : str
- Format string for text file output. Each entry in the array is formatted to text by first converting it to the closest Python type, and then using “format” % item.
This is a convenience function for quick storage of array data. Information on endianness and precision is lost, so this method is not a good choice for files intended to archive data or transport data between machines with different endianness. Some of these problems can be overcome by outputting the data as text files, at the expense of speed and file size.
When fid is a file object, array contents are directly written to the file, bypassing the file object’s
write
method. As a result, tofile cannot be used with files objects supporting compression (e.g., GzipFile) or file-like objects that do not supportfileno()
(e.g., BytesIO).
-
tolist
()¶ Return the array as a (possibly nested) list.
Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible Python type.
none
- y : list
- The possibly nested list of array elements.
The array may be recreated,
a = np.array(a.tolist())
.>>> a = np.array([1, 2]) >>> a.tolist() [1, 2] >>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]]
-
tostring
(order='C')¶ Construct Python bytes containing the raw data bytes in the array.
Constructs Python bytes showing a copy of the raw contents of data memory. The bytes object can be produced in either ‘C’ or ‘Fortran’, or ‘Any’ order (the default is ‘C’-order). ‘Any’ order means C-order unless the F_CONTIGUOUS flag in the array is set, in which case it means ‘Fortran’ order.
This function is a compatibility alias for tobytes. Despite its name it returns bytes not strings.
- order : {‘C’, ‘F’, None}, optional
- Order of the data for multidimensional arrays: C, Fortran, or the same as for the original array.
- s : bytes
- Python bytes exhibiting a copy of
a
’s raw data.
>>> x = np.array([[0, 1], [2, 3]]) >>> x.tobytes() b'\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00' >>> x.tobytes('C') == x.tobytes() True >>> x.tobytes('F') b'\x00\x00\x00\x00\x02\x00\x00\x00\x01\x00\x00\x00\x03\x00\x00\x00'
-
trace
(offset=0, axis1=0, axis2=1, dtype=None, out=None)¶ Return the sum along diagonals of the array.
Refer to
numpy.trace
for full documentation.numpy.trace : equivalent function
-
trans
¶ shorthand for transpose on SquareTensor
-
transform
(symm_op)¶ Applies a transformation (via a symmetry operation) to a tensor.
- Args:
- symm_op (SymmOp): a symmetry operation to apply to the tensor
-
transpose
(*axes)¶ Returns a view of the array with axes transposed.
For a 1-D array, this has no effect. (To change between column and row vectors, first cast the 1-D array into a matrix object.) For a 2-D array, this is the usual matrix transpose. For an n-D array, if axes are given, their order indicates how the axes are permuted (see Examples). If axes are not provided and
a.shape = (i[0], i[1], ... i[n-2], i[n-1])
, thena.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])
.axes : None, tuple of ints, or
n
ints- None or no argument: reverses the order of the axes.
- tuple of ints:
i
in thej
-th place in the tuple meansa
’si
-th axis becomesa.transpose()
’sj
-th axis. n
ints: same as an n-tuple of the same ints (this form is intended simply as a “convenience” alternative to the tuple form)
- out : ndarray
- View of
a
, with axes suitably permuted.
ndarray.T : Array property returning the array transposed.
>>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.transpose() array([[1, 3], [2, 4]]) >>> a.transpose((1, 0)) array([[1, 3], [2, 4]]) >>> a.transpose(1, 0) array([[1, 3], [2, 4]])
-
var
(axis=None, dtype=None, out=None, ddof=0, keepdims=False)¶ Returns the variance of the array elements, along given axis.
Refer to
numpy.var
for full documentation.numpy.var : equivalent function
-
view
(dtype=None, type=None)¶ New view of array with the same data.
- dtype : data-type or ndarray sub-class, optional
- Data-type descriptor of the returned view, e.g., float32 or int16. The
default, None, results in the view having the same data-type as
a
. This argument can also be specified as an ndarray sub-class, which then specifies the type of the returned object (this is equivalent to setting thetype
parameter). - type : Python type, optional
- Type of the returned view, e.g., ndarray or matrix. Again, the default None results in type preservation.
a.view()
is used two different ways:a.view(some_dtype)
ora.view(dtype=some_dtype)
constructs a view of the array’s memory with a different data-type. This can cause a reinterpretation of the bytes of memory.a.view(ndarray_subclass)
ora.view(type=ndarray_subclass)
just returns an instance ofndarray_subclass
that looks at the same array (same shape, dtype, etc.) This does not cause a reinterpretation of the memory.For
a.view(some_dtype)
, ifsome_dtype
has a different number of bytes per entry than the previous dtype (for example, converting a regular array to a structured array), then the behavior of the view cannot be predicted just from the superficial appearance ofa
(shown byprint(a)
). It also depends on exactly howa
is stored in memory. Therefore ifa
is C-ordered versus fortran-ordered, versus defined as a slice or transpose, etc., the view may give different results.>>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])
Viewing array data using a different type and dtype:
>>> y = x.view(dtype=np.int16, type=np.matrix) >>> y matrix([[513]], dtype=int16) >>> print(type(y)) <class 'numpy.matrixlib.defmatrix.matrix'>
Creating a view on a structured array so it can be used in calculations
>>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) >>> xv = x.view(dtype=np.int8).reshape(-1,2) >>> xv array([[1, 2], [3, 4]], dtype=int8) >>> xv.mean(0) array([ 2., 3.])
Making changes to the view changes the underlying array
>>> xv[0,1] = 20 >>> print(x) [(1, 20) (3, 4)]
Using a view to convert an array to a recarray:
>>> z = x.view(np.recarray) >>> z.a array([1], dtype=int8)
Views share data:
>>> x[0] = (9, 10) >>> z[0] (9, 10)
Views that change the dtype size (bytes per entry) should normally be avoided on arrays defined by slices, transposes, fortran-ordering, etc.:
>>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) >>> y = x[:, 0:2] >>> y array([[1, 2], [4, 5]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): File "<stdin>", line 1, in <module> ValueError: new type not compatible with array. >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 2)], [(4, 5)]], dtype=[('width', '<i2'), ('length', '<i2')])
-
voigt
¶ Returns the tensor in Voigt notation
-
voigt_symmetrized
¶ Returns a “voigt”-symmetrized tensor, i. e. a voigt-notation tensor such that it is invariant wrt permutation of indices
-
von_mises_strain
¶ Equivalent strain to Von Mises Stress
-
zeroed
(tol=0.001)¶ returns the matrix with all entries below a certain threshold (i.e. tol) set to zero
-
classmethod
-
schrodinger.application.matsci.elasticity.strain.
convert_strain_to_deformation
(strain, shape='upper')¶ This function converts a strain to a deformation gradient that will produce that strain. Supports three methods:
- Args:
strain (3x3 array-like): strain matrix shape: (string): method for determining deformation, supports
“upper” produces an upper triangular defo “lower” produces a lower triangular defo “symmetric” produces a symmetric defo