numeric¶
The numeric module provides methods that are lacking from the numpy module.
- nutils.numeric.overlapping(arr, axis=-1, n=2)¶
reinterpret data with overlaps
- nutils.numeric.full(shape, fill_value, dtype)¶
read-only equivalent to
numpy.full()
- nutils.numeric.normdim(ndim, n)¶
check bounds and make positive
- nutils.numeric.get(arr, axis, item)¶
take single item from array axis
- nutils.numeric.contract(A, B, axis=-1)¶
- nutils.numeric.dot(A, B, axis=-1)¶
Transform axis of A by contraction with first axis of B and inserting remaining axes. Note: with default axis=-1 this leads to multiplication of vectors and matrices following linear algebra conventions.
- nutils.numeric.meshgrid(*args, dtype=None)¶
Multi-dimensional meshgrid generalisation.
Meshgrid stacks
n
arbitry-dimensional arrays into an array that is one dimension higher than all dimensions combined, such thatretval[i]
equalsargs[i]
broadcasted to consecutive dimension slices. For two vector arguments this is almost equal tonumpy.meshgrid()
, with the main difference that dimensions are not swapped in the return values. The other difference is that the return value is a single array, but since the stacked axis is the first dimension the result can always be tuple unpacked.- Parameters:
args (sequence of
numpy.ndarray
objects or equivalent) – The arrays that are to be grid-stacked.dtype (
type
of output array) – If unspecified the dtype is determined automatically from the input arrays usingnumpy.result_type()
.
- Return type:
- nutils.numeric.simplex_grid(shape, spacing)¶
Multi-dimensional generator for equilateral simplex grids.
Simplex_grid generates a point cloud within an n-dimensional orthotope, which ranges from zero to a specified shape. The point coordinates are spaced in such a way that the nearest neighbours are at distance spacing, thus forming vertices of regular simplices. The returned array is two-dimensional, with the first axis being the spatial dimension (matching shape) and the second a stacking of the generated points.
- Parameters:
- Return type:
- nutils.numeric.normalize(A, axis=-1)¶
devide by normal
- nutils.numeric.diagonalize(arg, axis=-1, newaxis=-1)¶
insert newaxis, place axis on diagonal of axis and newaxis
- nutils.numeric.inv(A)¶
Matrix inverse.
Fully equivalent to
numpy.linalg.inv()
, with the exception that upon singular systemsinv()
does not raise aLinAlgError
, but rather issues aRuntimeWarning
and returns NaN (not a number) values. For arguments of dimension >2 the return array contains NaN values only for those entries that correspond to singular matrices.
- nutils.numeric.ix(args)¶
version of
numpy.ix_()
that allows for scalars
- nutils.numeric.ext(A)¶
Exterior For array of shape (n,n-1) return n-vector ex such that ex.array = 0 and det(arr;ex) = ex.ex
- nutils.numeric.unpack(n, atol, rtol)¶
Convert packed representation to floating point data.
The packed binary form is a floating point interpretation of signed integer data, such that any integer
n
maps onto floata
as follows:a = nan if n = -N-1 a = -inf if n = -N a = sinh(n*rtol)*atol/rtol if -N < n < N a = +inf if n = N,
where
N = 2**(nbits-1)-1
is the largest representable signed integer.Note that packing is both order and zero preserving. The transformation is designed such that the spacing around zero equals
atol
, while the relative spacing for most of the data range is approximately constant atrtol
. Precisely, the spacing between a valuea
and the adjacent value issqrt(atol**2 + (a*rtol)**2)
. Note that the truncation error equals half the spacing.The representable data range depends on the values of
atol
andrtol
and the bitsize ofn
. Useful values for different data types are:dtype
rtol
atol
range
int8
2e-1
2e-06
4e+05
int16
2e-3
2e-15
1e+16
int32
2e-7
2e-96
2e+97
- nutils.numeric.pack(a, atol, rtol, dtype)¶
Lossy compression of floating point data.
See
unpack()
for the definition of the packed binary form. The converse transformation uses rounding in packed domain to determine the closest matching value. In particular this may lead to values falling outside the representable data range to be clipped to infinity. Some examples of packed truncation:>>> def truncate(a, dtype, **tol): ... return unpack(pack(a, dtype=dtype, **tol), **tol) >>> truncate(0.5, dtype='int16', atol=2e-15, rtol=2e-3) 0.5004... >>> truncate(1, dtype='int16', atol=2e-15, rtol=2e-3) 0.9998... >>> truncate(2, dtype='int16', atol=2e-15, rtol=2e-3) 2.0013... >>> truncate(2, dtype='int16', atol=2e-15, rtol=2e-4) inf >>> truncate(2, dtype='int32', atol=2e-15, rtol=2e-4) 2.00013...
- nutils.numeric.accumulate(data, index, shape)¶
accumulate scattered data in dense array.
Accumulates values from
data
in an array of shapeshape
at positionsindex
, equivalent with:>>> def accumulate(data, index, shape): ... array = numpy.zeros(shape, data.dtype) ... for v, *ij in zip(data, *index): ... array[ij] += v ... return array
- nutils.numeric.asboolean(array, size, ordered=True)¶
convert index array to boolean.
A boolean array is returned as-is after confirming that the length is correct.
>>> asboolean([True, False], size=2) array([ True, False], dtype=bool)
A strictly increasing integer array is converted to the equivalent boolean array such that
asboolean(array, n).nonzero()[0] == array
.>>> asboolean([1,3], size=4) array([False, True, False, True], dtype=bool)
In case the order of integers is not important this must be explicitly specified using the
ordered
argument.>>> asboolean([3,1,1], size=4, ordered=False) array([False, True, False, True], dtype=bool)
- nutils.numeric.invmap(indices, length, missing=-1)¶
Create inverse index array.
Create the index array
inverse
with the givenlength
such thatinverse[indices[i]] == i
andinverse[j] == missing
for allj
not inindices
. It is an error to pass anindices
array with repeated indices, in which case the result is undefined.>>> m = invmap([3,1], length=5) >>> m[3] 0 >>> m[1] 1
- Parameters:
- Return type:
- nutils.numeric.levicivita(n, dtype=<class 'float'>)¶
n-dimensional Levi-Civita symbol.