schrodinger.application.matsci.elasticity.tensors module¶
This module provides a base class for tensor-like objects and methods for basic tensor manipulation. It also provides a class, SquareTensor, that provides basic methods for creating and manipulating rank 2 tensors
Copyright Schrodinger, LLC. All rights reserved.
- class schrodinger.application.matsci.elasticity.tensors.Tensor(input_array, vscale=None, check_rank=None)¶
Bases:
numpy.ndarray
Base class for doing useful general operations on Nth order tensors, without restrictions on the type (stress, elastic, strain, piezo, etc.)
- zeroed(tol=0.001)¶
returns the matrix with all entries below a certain threshold (i.e. tol) set to zero
- 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
- 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
- einsum_sequence(other_arrays, einsum_string=None)¶
Calculates the result of an einstein summation expression
- property 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
- property voigt_symmetrized¶
Returns a “voigt”-symmetrized tensor, i. e. a voigt-notation tensor such that it is invariant wrt permutation of indices
- 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_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
- property voigt¶
Returns the tensor in Voigt notation
- 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
- 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
- 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
- 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.
- Parameters
values (list[float]) – numbers to place at indices
indices – array-like collection of 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
- T¶
View of the transposed array.
Same as
self.transpose()
.>>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.T array([[1, 3], [2, 4]])
>>> a = np.array([1, 2, 3, 4]) >>> a array([1, 2, 3, 4]) >>> a.T array([1, 2, 3, 4])
transpose
- __contains__(key, /)¶
Return key in self.
- __len__()¶
Return len(self).
- all(axis=None, out=None, keepdims=False, *, where=True)¶
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, *, where=True)¶
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, *, keepdims=False)¶
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, *, keepdims=False)¶
Return indices of the minimum values along the given axis.
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=None, 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.
- dtypestr 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.
- subokbool, optional
If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array.
- copybool, 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_tndarray
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
.
Changed in version 1.17.0: Casting between a simple data type and a structured one is possible only for “unsafe” casting. Casting to multiple fields is allowed, but casting from multiple fields is not.
Changed in version 1.9.0: Casting from numeric to string types in ‘safe’ casting mode requires that the string dtype length is long enough to store the max integer/float value converted.
- 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. Arrays of byte-strings are not swapped. The real and imaginary parts of a complex number are swapped individually.
- inplacebool, optional
If
True
, swap bytes in-place, default isFalse
.
- outndarray
The byteswapped array. If
inplace
isTrue
, this is a view to self.
>>> A = np.array([1, 256, 8755], dtype=np.int16) >>> list(map(hex, A)) ['0x1', '0x100', '0x2233'] >>> A.byteswap(inplace=True) array([ 256, 1, 13090], dtype=int16) >>> list(map(hex, A)) ['0x100', '0x1', '0x3322']
Arrays of byte-strings are not swapped
>>> A = np.array([b'ceg', b'fac']) >>> A.byteswap() array([b'ceg', b'fac'], dtype='|S3')
A.newbyteorder().byteswap()
produces an array with the same valuesbut different representation in memory
>>> A = np.array([1, 2, 3]) >>> A.view(np.uint8) array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0], dtype=uint8) >>> A.newbyteorder().byteswap(inplace=True) array([1, 2, 3]) >>> A.view(np.uint8) array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3], dtype=uint8)
- 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, **kwargs)¶
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, and this function always passes sub-classes through.)
numpy.copy : Similar function with different default behavior numpy.copyto
This function is the preferred method for creating an array copy. The function
numpy.copy()
is similar, but it defaults to using order ‘K’, and will not pass sub-classes through by default.>>> 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
- cPython 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):
- _ctypes.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]
.Note that unlike
data_as
, a reference will not be kept to the array: code likectypes.c_void_p((a + b).ctypes.data)
will result in a pointer to a deallocated array, and should be spelt(a + b).ctypes.data_as(ctypes.c_void_p)
- _ctypes.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 (seec_intp
). This base-type could bectypes.c_int
,ctypes.c_long
, orctypes.c_longlong
depending on the platform. The ctypes array contains the shape of the underlying array.
- _ctypes.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.
- _ctypes.data_as(obj)
Return the data pointer cast to a particular c-types object. For example, calling
self._as_parameter_
is equivalent toself.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))
.The returned pointer will keep a reference to the array.
- _ctypes.shape_as(obj)
Return the shape tuple as an array of some other c-types type. For example:
self.shape_as(ctypes.c_short)
.
- _ctypes.strides_as(obj)
Return the strides tuple as an array of some other c-types type. For example:
self.strides_as(ctypes.c_longlong)
.
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 = np.array([[0, 1], [2, 3]], dtype=np.int32) >>> x array([[0, 1], [2, 3]], dtype=int32) >>> x.ctypes.data 31962608 # may vary >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)) <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents c_uint(0) >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents c_ulong(4294967296) >>> x.ctypes.shape <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary >>> x.ctypes.strides <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary
- 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.
- 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()¶
- dtype¶
Data-type of the array’s elements.
Warning
Setting
arr.dtype
is discouraged and may be deprecated in the future. Setting will replace thedtype
without modifying the memory (see alsondarray.view
andndarray.astype
).None
d : numpy dtype object
ndarray.astype : Cast the values contained in the array to a new data-type. ndarray.view : Create a view of the same data but a different data-type. 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.
- filestr or Path
A string naming the dump file.
Changed in version 1.17.0:
pathlib.Path
objects are now accepted.
- dumps()¶
Returns the pickle of the array as a string. pickle.loads will convert the string back to an array.
None
- fill(value)¶
Fill the array with a scalar value.
- valuescalar
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.])
Fill expects a scalar value and always behaves the same as assigning to a single array element. The following is a rare example where this distinction is important:
>>> a = np.array([None, None], dtype=object) >>> a[0] = np.array(3) >>> a array([array(3), None], dtype=object) >>> a.fill(np.array(3)) >>> a array([array(3), array(3)], dtype=object)
Where other forms of assignments will unpack the array being assigned:
>>> a[...] = np.array(3) >>> a array([3, 3], dtype=object)
- 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.
- 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, 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:
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) <class '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’.
- yndarray
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])
- 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.
- dtypestr or dtype
The data type of the view. The dtype size of the view can not be larger than that of the array itself.
- offsetint
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')
- 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.
- zStandard 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.>>> np.random.seed(123) >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[2, 2, 6], [1, 3, 6], [1, 0, 1]]) >>> x.item(3) 1 >>> x.item(7) 0 >>> x.item((0, 1)) 2 >>> x.item((2, 2)) 1
- 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
.- *argsArguments
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.>>> np.random.seed(123) >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[2, 2, 6], [1, 3, 6], [1, 0, 1]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[2, 2, 6], [1, 0, 6], [1, 0, 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, initial=<no value>, where=True)¶
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, *, where=True)¶
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, initial=<no value>, where=True)¶
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_orderstring, 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
{‘<’, ‘little’} - little endian
{‘>’, ‘big’} - big endian
{‘=’, ‘native’} - native order, equivalent to
sys.byteorder
{‘|’, ‘I’} - ignore (no change to byte order)
The default value (‘S’) results in swapping the current byte order.
- new_arrarray
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.
- kthint 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.
Deprecated since version 1.22.0: Passing booleans as index is deprecated.
- axisint, optional
Axis along which to sort. Default is -1, which means sort along the last axis.
- kind{‘introselect’}, optional
Selection algorithm. Default is ‘introselect’.
- orderstr 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 partitioned 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)) >>> a array([1, 2, 3, 4])
- prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)¶
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
- 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_shapetuple of ints, or
n
ints Shape of resized array.
- refcheckbool, 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 references or is referenced ...
Unless
refcheck
is False:>>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])
- new_shapetuple of ints, or
- 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.- valobject
Value to be placed in field.
- dtypedtype object
Data-type of the field in which to place
val
.- offsetint, 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]], dtype=int32) >>> x array([[1.0e+000, 1.5e-323, 1.5e-323], [1.5e-323, 1.0e+000, 1.5e-323], [1.5e-323, 1.5e-323, 1.0e+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, 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 flag 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.)- writebool, optional
Describes whether or not
a
can be written to.- alignbool, optional
Describes whether or not
a
is aligned properly for its type.- uicbool, 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, 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);
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 = np.array([[3, 1, 7], ... [2, 0, 0], ... [8, 5, 9]]) >>> 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 >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False WRITEBACKIFCOPY : 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.Warning
Setting
arr.shape
is discouraged and may be deprecated in the future. Usingndarray.reshape
is the preferred approach.>>> 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 in-place modification. Use `.reshape()` to make a copy with the desired shape.
numpy.shape : Equivalent getter function. numpy.reshape : Function similar to setting
shape
. ndarray.reshape : Method similar to settingshape
.
- 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=None, order=None)¶
Sort an array in-place. Refer to
numpy.sort
for full documentation.- axisint, optional
Axis along which to sort. Default is -1, which means sort along the last axis.
- kind{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional
Sorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort under the covers and, in general, the actual implementation will vary with datatype. The ‘mergesort’ option is retained for backwards compatibility.
Changed in version 1.15.0: The ‘stable’ option was added.
- orderstr 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. numpy.argsort : Indirect sort. numpy.lexsort : Indirect stable sort on multiple keys. numpy.searchsorted : Find elements in sorted array. numpy.partition: Partial sort.
See
numpy.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([(b'c', 1), (b'a', 2)], dtype=[('x', 'S1'), ('y', '<i8')])
- squeeze(axis=None)¶
Remove axes of length one from
a
.Refer to
numpy.squeeze
for full documentation.numpy.squeeze : equivalent function
- std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)¶
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.
Warning
Setting
arr.strides
is discouraged and may be deprecated in the future.numpy.lib.stride_tricks.as_strided
should be preferred to create a new view of the same data in a safer way.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, initial=0, where=True)¶
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
- 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 is produced in C-order by default. This behavior is controlled by the
order
parameter.New in version 1.9.0.
- order{‘C’, ‘F’, ‘A’}, optional
Controls the memory layout of the bytes object. ‘C’ means C-order, ‘F’ means F-order, ‘A’ (short for Any) means ‘F’ if
a
is Fortran contiguous, ‘C’ otherwise. Default is ‘C’.
- sbytes
Python bytes exhibiting a copy of
a
’s raw data.
- frombuffer
Inverse of this operation, construct a 1-dimensional array from Python bytes.
>>> x = np.array([[0, 1], [2, 3]], dtype='<u2') >>> x.tobytes() b'\x00\x00\x01\x00\x02\x00\x03\x00' >>> x.tobytes('C') == x.tobytes() True >>> x.tobytes('F') b'\x00\x00\x02\x00\x01\x00\x03\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().- fidfile or str or Path
An open file object, or a string containing a filename.
Changed in version 1.17.0:
pathlib.Path
objects are now accepted.- sepstr
Separator between array items for text output. If “” (empty), a binary file is written, equivalent to
file.write(a.tobytes())
.- formatstr
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 an
a.ndim
-levels deep nested list of Python scalars.Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible builtin Python type, via the
item
function.If
a.ndim
is 0, then since the depth of the nested list is 0, it will not be a list at all, but a simple Python scalar.none
- yobject, or list of object, or list of list of object, or …
The possibly nested list of array elements.
The array may be recreated via
a = np.array(a.tolist())
, although this may sometimes lose precision.For a 1D array,
a.tolist()
is almost the same aslist(a)
, except thattolist
changes numpy scalars to Python scalars:>>> a = np.uint32([1, 2]) >>> a_list = list(a) >>> a_list [1, 2] >>> type(a_list[0]) <class 'numpy.uint32'> >>> a_tolist = a.tolist() >>> a_tolist [1, 2] >>> type(a_tolist[0]) <class 'int'>
Additionally, for a 2D array,
tolist
applies recursively:>>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]]
The base case for this recursion is a 0D array:
>>> a = np.array(1) >>> list(a) Traceback (most recent call last): ... TypeError: iteration over a 0-d array >>> a.tolist() 1
- tostring(order='C')¶
A compatibility alias for
tobytes
, with exactly the same behavior.Despite its name, it returns
bytes
notstr
s.Deprecated since version 1.19.0.
- 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
- transpose(*axes)¶
Returns a view of the array with axes transposed.
Refer to
numpy.transpose
for full documentation.axes : None, tuple of ints, or
n
intsNone or no argument: reverses the order of the axes.
tuple of ints:
i
in thej
-th place in the tuple means that the array’si
-th axis becomes the transposed array’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).
- pndarray
View of the array with its axes suitably permuted.
transpose : Equivalent function. ndarray.T : Array property returning the array transposed. ndarray.reshape : Give a new shape to an array without changing its data.
>>> 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]])
>>> a = np.array([1, 2, 3, 4]) >>> a array([1, 2, 3, 4]) >>> a.transpose() array([1, 2, 3, 4])
- var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)¶
Returns the variance of the array elements, along given axis.
Refer to
numpy.var
for full documentation.numpy.var : equivalent function
- view([dtype][, type])¶
New view of array with the same data.
Note
Passing None for
dtype
is different from omitting the parameter, since the former invokesdtype(None)
which is an alias fordtype('float_')
.- dtypedata-type or ndarray sub-class, optional
Data-type descriptor of the returned view, e.g., float32 or int16. Omitting it 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).- typePython type, optional
Type of the returned view, e.g., ndarray or matrix. Again, omission of the parameter 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 last axis ofa
must be contiguous. This axis will be resized in the result.Changed in version 1.23.0: Only the last axis needs to be contiguous. Previously, the entire array had to be C-contiguous.
>>> 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.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 >>> x array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])
Using a view to convert an array to a recarray:
>>> z = x.view(np.recarray) >>> z.a array([1, 3], 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[:, ::2] >>> y array([[1, 3], [4, 6]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): ... ValueError: To change to a dtype of a different size, the last axis must be contiguous >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 3)], [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])
However, views that change dtype are totally fine for arrays with a contiguous last axis, even if the rest of the axes are not C-contiguous:
>>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4) >>> x.transpose(1, 0, 2).view(np.int16) array([[[ 256, 770], [3340, 3854]], [[1284, 1798], [4368, 4882]], [[2312, 2826], [5396, 5910]]], dtype=int16)
- class schrodinger.application.matsci.elasticity.tensors.TensorCollection(tensor_list, base_class=<class 'schrodinger.application.matsci.elasticity.tensors.Tensor'>)¶
Bases:
collections.abc.Sequence
A sequence of tensors that can be used for fitting data or for having a tensor expansion
- __init__(tensor_list, base_class=<class 'schrodinger.application.matsci.elasticity.tensors.Tensor'>)¶
- __len__()¶
- zeroed(tol=0.001)¶
- transform(symm_op)¶
- rotate(matrix, tol=0.001)¶
- property symmetrized¶
- is_symmetric(tol=1e-05)¶
- fit_to_structure(structure, symprec=0.1)¶
- is_fit_to_structure(structure, tol=0.01)¶
- property voigt¶
- property ranks¶
- is_voigt_symmetric(tol=1e-06)¶
- classmethod from_voigt(voigt_input_list, base_class=<class 'schrodinger.application.matsci.elasticity.tensors.Tensor'>)¶
- convert_to_ieee(structure, initial_fit=True, refine_rotation=True)¶
- __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.
Supporting start and stop arguments is optional, but recommended.
- class schrodinger.application.matsci.elasticity.tensors.SquareTensor(input_array, vscale=None)¶
Bases:
schrodinger.application.matsci.elasticity.tensors.Tensor
Base class for doing useful general operations on second rank tensors (stress, strain etc.).
- property trans¶
shorthand for transpose on SquareTensor
- property inv¶
shorthand for matrix inverse on SquareTensor
- property det¶
shorthand for the determinant of the SquareTensor
- 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
- 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
- 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
- property 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
- polar_decomposition(side='right')¶
calculates matrices for polar decomposition
- T¶
View of the transposed array.
Same as
self.transpose()
.>>> a = np.array([[1, 2], [3, 4]]) >>> a array([[1, 2], [3, 4]]) >>> a.T array([[1, 3], [2, 4]])
>>> a = np.array([1, 2, 3, 4]) >>> a array([1, 2, 3, 4]) >>> a.T array([1, 2, 3, 4])
transpose
- __contains__(key, /)¶
Return key in self.
- __len__()¶
Return len(self).
- all(axis=None, out=None, keepdims=False, *, where=True)¶
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, *, where=True)¶
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, *, keepdims=False)¶
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, *, keepdims=False)¶
Return indices of the minimum values along the given axis.
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=None, 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.
- dtypestr 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.
- subokbool, optional
If True, then sub-classes will be passed-through (default), otherwise the returned array will be forced to be a base-class array.
- copybool, 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_tndarray
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
.
Changed in version 1.17.0: Casting between a simple data type and a structured one is possible only for “unsafe” casting. Casting to multiple fields is allowed, but casting from multiple fields is not.
Changed in version 1.9.0: Casting from numeric to string types in ‘safe’ casting mode requires that the string dtype length is long enough to store the max integer/float value converted.
- 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. Arrays of byte-strings are not swapped. The real and imaginary parts of a complex number are swapped individually.
- inplacebool, optional
If
True
, swap bytes in-place, default isFalse
.
- outndarray
The byteswapped array. If
inplace
isTrue
, this is a view to self.
>>> A = np.array([1, 256, 8755], dtype=np.int16) >>> list(map(hex, A)) ['0x1', '0x100', '0x2233'] >>> A.byteswap(inplace=True) array([ 256, 1, 13090], dtype=int16) >>> list(map(hex, A)) ['0x100', '0x1', '0x3322']
Arrays of byte-strings are not swapped
>>> A = np.array([b'ceg', b'fac']) >>> A.byteswap() array([b'ceg', b'fac'], dtype='|S3')
A.newbyteorder().byteswap()
produces an array with the same valuesbut different representation in memory
>>> A = np.array([1, 2, 3]) >>> A.view(np.uint8) array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0], dtype=uint8) >>> A.newbyteorder().byteswap(inplace=True) array([1, 2, 3]) >>> A.view(np.uint8) array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3], dtype=uint8)
- 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, **kwargs)¶
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, and this function always passes sub-classes through.)
numpy.copy : Similar function with different default behavior numpy.copyto
This function is the preferred method for creating an array copy. The function
numpy.copy()
is similar, but it defaults to using order ‘K’, and will not pass sub-classes through by default.>>> 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
- cPython 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):
- _ctypes.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]
.Note that unlike
data_as
, a reference will not be kept to the array: code likectypes.c_void_p((a + b).ctypes.data)
will result in a pointer to a deallocated array, and should be spelt(a + b).ctypes.data_as(ctypes.c_void_p)
- _ctypes.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 (seec_intp
). This base-type could bectypes.c_int
,ctypes.c_long
, orctypes.c_longlong
depending on the platform. The ctypes array contains the shape of the underlying array.
- _ctypes.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.
- _ctypes.data_as(obj)
Return the data pointer cast to a particular c-types object. For example, calling
self._as_parameter_
is equivalent toself.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))
.The returned pointer will keep a reference to the array.
- _ctypes.shape_as(obj)
Return the shape tuple as an array of some other c-types type. For example:
self.shape_as(ctypes.c_short)
.
- _ctypes.strides_as(obj)
Return the strides tuple as an array of some other c-types type. For example:
self.strides_as(ctypes.c_longlong)
.
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 = np.array([[0, 1], [2, 3]], dtype=np.int32) >>> x array([[0, 1], [2, 3]], dtype=int32) >>> x.ctypes.data 31962608 # may vary >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)) <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents c_uint(0) >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents c_ulong(4294967296) >>> x.ctypes.shape <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary >>> x.ctypes.strides <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary
- 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.
- 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()¶
- dtype¶
Data-type of the array’s elements.
Warning
Setting
arr.dtype
is discouraged and may be deprecated in the future. Setting will replace thedtype
without modifying the memory (see alsondarray.view
andndarray.astype
).None
d : numpy dtype object
ndarray.astype : Cast the values contained in the array to a new data-type. ndarray.view : Create a view of the same data but a different data-type. 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.
- filestr or Path
A string naming the dump file.
Changed in version 1.17.0:
pathlib.Path
objects are now accepted.
- dumps()¶
Returns the pickle of the array as a string. pickle.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.
- valuescalar
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.])
Fill expects a scalar value and always behaves the same as assigning to a single array element. The following is a rare example where this distinction is important:
>>> a = np.array([None, None], dtype=object) >>> a[0] = np.array(3) >>> a array([array(3), None], dtype=object) >>> a.fill(np.array(3)) >>> a array([array(3), array(3)], dtype=object)
Where other forms of assignments will unpack the array being assigned:
>>> a[...] = np.array(3) >>> a array([3, 3], dtype=object)
- 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.
- 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, 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:
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) <class '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’.
- yndarray
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.
- Parameters
values (list[float]) – numbers to place at indices
indices – array-like collection of 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
- 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.
- dtypestr or dtype
The data type of the view. The dtype size of the view can not be larger than that of the array itself.
- offsetint
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')
- 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_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.
- zStandard 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.>>> np.random.seed(123) >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[2, 2, 6], [1, 3, 6], [1, 0, 1]]) >>> x.item(3) 1 >>> x.item(7) 0 >>> x.item((0, 1)) 2 >>> x.item((2, 2)) 1
- 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
.- *argsArguments
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.>>> np.random.seed(123) >>> x = np.random.randint(9, size=(3, 3)) >>> x array([[2, 2, 6], [1, 3, 6], [1, 0, 1]]) >>> x.itemset(4, 0) >>> x.itemset((2, 2), 9) >>> x array([[2, 2, 6], [1, 0, 6], [1, 0, 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, initial=<no value>, where=True)¶
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, *, where=True)¶
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, initial=<no value>, where=True)¶
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_orderstring, 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
{‘<’, ‘little’} - little endian
{‘>’, ‘big’} - big endian
{‘=’, ‘native’} - native order, equivalent to
sys.byteorder
{‘|’, ‘I’} - ignore (no change to byte order)
The default value (‘S’) results in swapping the current byte order.
- new_arrarray
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.
- kthint 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.
Deprecated since version 1.22.0: Passing booleans as index is deprecated.
- axisint, optional
Axis along which to sort. Default is -1, which means sort along the last axis.
- kind{‘introselect’}, optional
Selection algorithm. Default is ‘introselect’.
- orderstr 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 partitioned 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)) >>> a array([1, 2, 3, 4])
- prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)¶
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
- 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_shapetuple of ints, or
n
ints Shape of resized array.
- refcheckbool, 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 references or is referenced ...
Unless
refcheck
is False:>>> a.resize((1, 1), refcheck=False) >>> a array([[0]]) >>> c array([[0]])
- new_shapetuple 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.- valobject
Value to be placed in field.
- dtypedtype object
Data-type of the field in which to place
val
.- offsetint, 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]], dtype=int32) >>> x array([[1.0e+000, 1.5e-323, 1.5e-323], [1.5e-323, 1.0e+000, 1.5e-323], [1.5e-323, 1.5e-323, 1.0e+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, 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 flag 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.)- writebool, optional
Describes whether or not
a
can be written to.- alignbool, optional
Describes whether or not
a
is aligned properly for its type.- uicbool, 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, 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);
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 = np.array([[3, 1, 7], ... [2, 0, 0], ... [8, 5, 9]]) >>> 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 >>> y.setflags(write=0, align=0) >>> y.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : True WRITEABLE : False ALIGNED : False WRITEBACKIFCOPY : 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.Warning
Setting
arr.shape
is discouraged and may be deprecated in the future. Usingndarray.reshape
is the preferred approach.>>> 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 in-place modification. Use `.reshape()` to make a copy with the desired shape.
numpy.shape : Equivalent getter function. numpy.reshape : Function similar to setting
shape
. ndarray.reshape : Method similar to settingshape
.
- 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=None, order=None)¶
Sort an array in-place. Refer to
numpy.sort
for full documentation.- axisint, optional
Axis along which to sort. Default is -1, which means sort along the last axis.
- kind{‘quicksort’, ‘mergesort’, ‘heapsort’, ‘stable’}, optional
Sorting algorithm. The default is ‘quicksort’. Note that both ‘stable’ and ‘mergesort’ use timsort under the covers and, in general, the actual implementation will vary with datatype. The ‘mergesort’ option is retained for backwards compatibility.
Changed in version 1.15.0: The ‘stable’ option was added.
- orderstr 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. numpy.argsort : Indirect sort. numpy.lexsort : Indirect stable sort on multiple keys. numpy.searchsorted : Find elements in sorted array. numpy.partition: Partial sort.
See
numpy.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([(b'c', 1), (b'a', 2)], dtype=[('x', 'S1'), ('y', '<i8')])
- squeeze(axis=None)¶
Remove axes of length one from
a
.Refer to
numpy.squeeze
for full documentation.numpy.squeeze : equivalent function
- std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)¶
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.
Warning
Setting
arr.strides
is discouraged and may be deprecated in the future.numpy.lib.stride_tricks.as_strided
should be preferred to create a new view of the same data in a safer way.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, initial=0, where=True)¶
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
- property 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 is produced in C-order by default. This behavior is controlled by the
order
parameter.New in version 1.9.0.
- order{‘C’, ‘F’, ‘A’}, optional
Controls the memory layout of the bytes object. ‘C’ means C-order, ‘F’ means F-order, ‘A’ (short for Any) means ‘F’ if
a
is Fortran contiguous, ‘C’ otherwise. Default is ‘C’.
- sbytes
Python bytes exhibiting a copy of
a
’s raw data.
- frombuffer
Inverse of this operation, construct a 1-dimensional array from Python bytes.
>>> x = np.array([[0, 1], [2, 3]], dtype='<u2') >>> x.tobytes() b'\x00\x00\x01\x00\x02\x00\x03\x00' >>> x.tobytes('C') == x.tobytes() True >>> x.tobytes('F') b'\x00\x00\x02\x00\x01\x00\x03\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().- fidfile or str or Path
An open file object, or a string containing a filename.
Changed in version 1.17.0:
pathlib.Path
objects are now accepted.- sepstr
Separator between array items for text output. If “” (empty), a binary file is written, equivalent to
file.write(a.tobytes())
.- formatstr
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 an
a.ndim
-levels deep nested list of Python scalars.Return a copy of the array data as a (nested) Python list. Data items are converted to the nearest compatible builtin Python type, via the
item
function.If
a.ndim
is 0, then since the depth of the nested list is 0, it will not be a list at all, but a simple Python scalar.none
- yobject, or list of object, or list of list of object, or …
The possibly nested list of array elements.
The array may be recreated via
a = np.array(a.tolist())
, although this may sometimes lose precision.For a 1D array,
a.tolist()
is almost the same aslist(a)
, except thattolist
changes numpy scalars to Python scalars:>>> a = np.uint32([1, 2]) >>> a_list = list(a) >>> a_list [1, 2] >>> type(a_list[0]) <class 'numpy.uint32'> >>> a_tolist = a.tolist() >>> a_tolist [1, 2] >>> type(a_tolist[0]) <class 'int'>
Additionally, for a 2D array,
tolist
applies recursively:>>> a = np.array([[1, 2], [3, 4]]) >>> list(a) [array([1, 2]), array([3, 4])] >>> a.tolist() [[1, 2], [3, 4]]
The base case for this recursion is a 0D array:
>>> a = np.array(1) >>> list(a) Traceback (most recent call last): ... TypeError: iteration over a 0-d array >>> a.tolist() 1
- tostring(order='C')¶
A compatibility alias for
tobytes
, with exactly the same behavior.Despite its name, it returns
bytes
notstr
s.Deprecated since version 1.19.0.
- 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
- 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.
Refer to
numpy.transpose
for full documentation.axes : None, tuple of ints, or
n
intsNone or no argument: reverses the order of the axes.
tuple of ints:
i
in thej
-th place in the tuple means that the array’si
-th axis becomes the transposed array’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).
- pndarray
View of the array with its axes suitably permuted.
transpose : Equivalent function. ndarray.T : Array property returning the array transposed. ndarray.reshape : Give a new shape to an array without changing its data.
>>> 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]])
>>> a = np.array([1, 2, 3, 4]) >>> a array([1, 2, 3, 4]) >>> a.transpose() array([1, 2, 3, 4])
- var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)¶
Returns the variance of the array elements, along given axis.
Refer to
numpy.var
for full documentation.numpy.var : equivalent function
- view([dtype][, type])¶
New view of array with the same data.
Note
Passing None for
dtype
is different from omitting the parameter, since the former invokesdtype(None)
which is an alias fordtype('float_')
.- dtypedata-type or ndarray sub-class, optional
Data-type descriptor of the returned view, e.g., float32 or int16. Omitting it 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).- typePython type, optional
Type of the returned view, e.g., ndarray or matrix. Again, omission of the parameter 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 last axis ofa
must be contiguous. This axis will be resized in the result.Changed in version 1.23.0: Only the last axis needs to be contiguous. Previously, the entire array had to be C-contiguous.
>>> 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.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 >>> x array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])
Using a view to convert an array to a recarray:
>>> z = x.view(np.recarray) >>> z.a array([1, 3], 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[:, ::2] >>> y array([[1, 3], [4, 6]], dtype=int16) >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) Traceback (most recent call last): ... ValueError: To change to a dtype of a different size, the last axis must be contiguous >>> z = y.copy() >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) array([[(1, 3)], [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])
However, views that change dtype are totally fine for arrays with a contiguous last axis, even if the rest of the axes are not C-contiguous:
>>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4) >>> x.transpose(1, 0, 2).view(np.int16) array([[[ 256, 770], [3340, 3854]], [[1284, 1798], [4368, 4882]], [[2312, 2826], [5396, 5910]]], dtype=int16)
- property voigt¶
Returns the tensor in Voigt notation
- property 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
- schrodinger.application.matsci.elasticity.tensors.get_uvec(vec)¶
Gets a unit vector parallel to input vector
- schrodinger.application.matsci.elasticity.tensors.get_spglib_symmops(spg_cell, symprec=0.01, cartesian=False)¶
- schrodinger.application.matsci.elasticity.tensors.symmetry_reduce(tensors, struct, tol=1e-08, **kwargs)¶
Function that converts a list of tensors corresponding to a structure and returns a dictionary consisting of unique tensor keys with symmop values corresponding to transformations that will result in derivative tensors from the original list
- Parameters
- Returns
dictionary consisting of unique tensors with symmetry operations corresponding to those which will reconstruct the remaining tensors as values
- schrodinger.application.matsci.elasticity.tensors.get_tkd_value(tensor_keyed_dict, tensor, allclose_kwargs=None)¶
Helper function to find a value in a tensor-keyed- dictionary using an approximation to the key. This is useful if rounding errors in construction occur or hashing issues arise in tensor-keyed-dictionaries (e. g. from symmetry_reduce). Resolves most hashing issues, and is preferable to redefining eq methods in the base tensor class.
- Parameters
tensor_keyed_dict (dict) – dict with Tensor keys
tensor – tensor to find value of in the dict
allclose_kwargs (dict) – dict of keyword-args to pass to allclose.
- schrodinger.application.matsci.elasticity.tensors.get_symmetric(array)¶
Return a symmetric matrix from a square matrix.
- Parameters
array (numpy.array) – Input array
- Return numpy.array
Symmetrized array