package scipy

Get an attribute of this module as a Py.Object.t. This is useful to pass a Python function to another function.

Append values to the end of an array.

Parameters ---------- arr : array_like Values are appended to a copy of this array. values : array_like These values are appended to a copy of `arr`. It must be of the correct shape (the same shape as `arr`, excluding `axis`). If `axis` is not specified, `values` can be any shape and will be flattened before use. axis : int, optional The axis along which `values` are appended. If `axis` is not given, both `arr` and `values` are flattened before use.

Returns ------- append : ndarray A copy of `arr` with `values` appended to `axis`. Note that `append` does not occur in-place: a new array is allocated and filled. If `axis` is None, `out` is a flattened array.

See Also -------- insert : Insert elements into an array. delete : Delete elements from an array.

Examples -------- >>> np.append(1, 2, 3, [4, 5, 6], [7, 8, 9]) array(1, 2, 3, ..., 7, 8, 9)

When `axis` is specified, `values` must have the correct shape.

>>> np.append([1, 2, 3], [4, 5, 6], [7, 8, 9], axis=0) array([1, 2, 3], [4, 5, 6], [7, 8, 9]) >>> np.append([1, 2, 3], [4, 5, 6], 7, 8, 9, axis=0) Traceback (most recent call last): ... ValueError: all the input arrays must have same number of dimensions

Approximate the Jacobian matrix of a callable function.

Parameters ---------- x : array_like The state vector at which to compute the Jacobian matrix. func : callable f(x,*args) The vector-valued function. epsilon : float The perturbation used to determine the partial derivatives. args : sequence Additional arguments passed to func.

Returns ------- An array of dimensions ``(lenf, lenx)`` where ``lenf`` is the length of the outputs of `func`, and ``lenx`` is the number of elements in `x`.

Notes ----- The approximation is done using forward differences.

array(object, dtype=None, copy=True, order='K', subok=False, ndmin=0)

Create an array.

Parameters ---------- object : array_like An array, any object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence. dtype : data-type, optional The desired data-type for the array. If not given, then the type will be determined as the minimum type required to hold the objects in the sequence. copy : bool, optional If true (default), then the object is copied. Otherwise, a copy will only be made if __array__ returns a copy, if obj is a nested sequence, or if a copy is needed to satisfy any of the other requirements (`dtype`, `order`, etc.). order : 'K', 'A', 'C', 'F', optional Specify the memory layout of the array. If object is not an array, the newly created array will be in C order (row major) unless 'F' is specified, in which case it will be in Fortran order (column major). If object is an array the following holds.

===== ========= =================================================== order no copy copy=True ===== ========= =================================================== 'K' unchanged F & C order preserved, otherwise most similar order 'A' unchanged F order if input is F and not C, otherwise C order 'C' C order C order 'F' F order F order ===== ========= ===================================================

When ``copy=False`` and a copy is made for other reasons, the result is the same as if ``copy=True``, with some exceptions for `A`, see the Notes section. The default order is 'K'. subok : bool, optional If True, then sub-classes will be passed-through, otherwise the returned array will be forced to be a base-class array (default). ndmin : int, optional Specifies the minimum number of dimensions that the resulting array should have. Ones will be pre-pended to the shape as needed to meet this requirement.

Returns ------- out : ndarray An array object satisfying the specified requirements.

See Also -------- empty_like : Return an empty array with shape and type of input. ones_like : Return an array of ones with shape and type of input. zeros_like : Return an array of zeros with shape and type of input. full_like : Return a new array with shape of input filled with value. empty : Return a new uninitialized array. ones : Return a new array setting values to one. zeros : Return a new array setting values to zero. full : Return a new array of given shape filled with value.

Notes ----- When order is 'A' and `object` is an array in neither 'C' nor 'F' order, and a copy is forced by a change in dtype, then the order of the result is not necessarily 'C' as expected. This is likely a bug.

Examples -------- >>> np.array(1, 2, 3) array(1, 2, 3)

Upcasting:

>>> np.array(1, 2, 3.0) array( 1., 2., 3.)

More than one dimension:

>>> np.array([1, 2], [3, 4]) array([1, 2], [3, 4])

Minimum dimensions 2:

>>> np.array(1, 2, 3, ndmin=2) array([1, 2, 3])

Type provided:

>>> np.array(1, 2, 3, dtype=complex) array( 1.+0.j, 2.+0.j, 3.+0.j)

Data-type consisting of more than one element:

>>> x = np.array((1,2),(3,4),dtype=('a','<i4'),('b','<i4')) >>> x'a' array(1, 3)

Creating an array from sub-classes:

>>> np.array(np.mat('1 2; 3 4')) array([1, 2], [3, 4])

>>> np.array(np.mat('1 2; 3 4'), subok=True) matrix([1, 2], [3, 4])

Return an array converted to a float type.

Parameters ---------- a : array_like The input array. dtype : str or dtype object, optional Float type code to coerce input array `a`. If `dtype` is one of the 'int' dtypes, it is replaced with float64.

Returns ------- out : ndarray The input `a` as a float ndarray.

Examples -------- >>> np.asfarray(2, 3) array(2., 3.) >>> np.asfarray(2, 3, dtype='float') array(2., 3.) >>> np.asfarray(2, 3, dtype='int8') array(2., 3.)

Convert inputs to arrays with at least one dimension.

Scalar inputs are converted to 1-dimensional arrays, whilst higher-dimensional inputs are preserved.

Parameters ---------- arys1, arys2, ... : array_like One or more input arrays.

Returns ------- ret : ndarray An array, or list of arrays, each with ``a.ndim >= 1``. Copies are made only if necessary.

See Also -------- atleast_2d, atleast_3d

Examples -------- >>> np.atleast_1d(1.0) array(1.)

>>> x = np.arange(9.0).reshape(3,3) >>> np.atleast_1d(x) array([0., 1., 2.], [3., 4., 5.], [6., 7., 8.]) >>> np.atleast_1d(x) is x True

>>> np.atleast_1d(1, 3, 4) array([1]), array([3, 4])

concatenate((a1, a2, ...), axis=0, out=None)

Join a sequence of arrays along an existing axis.

Parameters ---------- a1, a2, ... : sequence of array_like The arrays must have the same shape, except in the dimension corresponding to `axis` (the first, by default). axis : int, optional The axis along which the arrays will be joined. If axis is None, arrays are flattened before use. Default is 0. out : ndarray, optional If provided, the destination to place the result. The shape must be correct, matching that of what concatenate would have returned if no out argument were specified.

Returns ------- res : ndarray The concatenated array.

See Also -------- ma.concatenate : Concatenate function that preserves input masks. array_split : Split an array into multiple sub-arrays of equal or near-equal size. split : Split array into a list of multiple sub-arrays of equal size. hsplit : Split array into multiple sub-arrays horizontally (column wise) vsplit : Split array into multiple sub-arrays vertically (row wise) dsplit : Split array into multiple sub-arrays along the 3rd axis (depth). stack : Stack a sequence of arrays along a new axis. hstack : Stack arrays in sequence horizontally (column wise) vstack : Stack arrays in sequence vertically (row wise) dstack : Stack arrays in sequence depth wise (along third dimension) block : Assemble arrays from blocks.

Notes ----- When one or more of the arrays to be concatenated is a MaskedArray, this function will return a MaskedArray object instead of an ndarray, but the input masks are *not* preserved. In cases where a MaskedArray is expected as input, use the ma.concatenate function from the masked array module instead.

Examples -------- >>> a = np.array([1, 2], [3, 4]) >>> b = np.array([5, 6]) >>> np.concatenate((a, b), axis=0) array([1, 2], [3, 4], [5, 6]) >>> np.concatenate((a, b.T), axis=1) array([1, 2, 5], [3, 4, 6]) >>> np.concatenate((a, b), axis=None) array(1, 2, 3, 4, 5, 6)

This function will not preserve masking of MaskedArray inputs.

>>> a = np.ma.arange(3) >>> a1 = np.ma.masked >>> b = np.arange(2, 5) >>> a masked_array(data=0, --, 2, mask=False, True, False, fill_value=999999) >>> b array(2, 3, 4) >>> np.concatenate(a, b) masked_array(data=0, 1, 2, 2, 3, 4, mask=False, fill_value=999999) >>> np.ma.concatenate(a, b) masked_array(data=0, --, 2, 2, 3, 4, mask=False, True, False, False, False, False, fill_value=999999)

exp(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True, signature, extobj)

Calculate the exponential of all elements in the input array.

Parameters ---------- x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`.

Returns ------- out : ndarray or scalar Output array, element-wise exponential of `x`. This is a scalar if `x` is a scalar.

See Also -------- expm1 : Calculate ``exp(x) - 1`` for all elements in the array. exp2 : Calculate ``2**x`` for all elements in the array.

Notes ----- The irrational number ``e`` is also known as Euler's number. It is approximately 2.718281, and is the base of the natural logarithm, ``ln`` (this means that, if :math:`x = \ln y = \log_e y`, then :math:`e^x = y`. For real input, ``exp(x)`` is always positive.

For complex arguments, ``x = a + ib``, we can write :math:`e^x = e^a e^b`. The first term, :math:`e^a`, is already known (it is the real argument, described above). The second term, :math:`e^b`, is :math:`\cos b + i \sin b`, a function with magnitude 1 and a periodic phase.

References ---------- .. 1 Wikipedia, 'Exponential function', https://en.wikipedia.org/wiki/Exponential_function .. 2 M. Abramovitz and I. A. Stegun, 'Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,' Dover, 1964, p. 69, http://www.math.sfu.ca/~cbm/aands/page_69.htm

Examples -------- Plot the magnitude and phase of ``exp(x)`` in the complex plane:

>>> import matplotlib.pyplot as plt

>>> x = np.linspace(-2*np.pi, 2*np.pi, 100) >>> xx = x + 1j * x:, np.newaxis # a + ib over complex plane >>> out = np.exp(xx)

>>> plt.subplot(121) >>> plt.imshow(np.abs(out), ... extent=-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi, cmap='gray') >>> plt.title('Magnitude of exp(x)')

>>> plt.subplot(122) >>> plt.imshow(np.angle(out), ... extent=-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi, cmap='hsv') >>> plt.title('Phase (angle) of exp(x)') >>> plt.show()

Minimize a function using Sequential Least SQuares Programming

Python interface function for the SLSQP Optimization subroutine originally implemented by Dieter Kraft.

Parameters ---------- func : callable f(x,*args) Objective function. Must return a scalar. x0 : 1-D ndarray of float Initial guess for the independent variable(s). eqcons : list, optional A list of functions of length n such that eqconsj(x,*args) == 0.0 in a successfully optimized problem. f_eqcons : callable f(x,*args), optional Returns a 1-D array in which each element must equal 0.0 in a successfully optimized problem. If f_eqcons is specified, eqcons is ignored. ieqcons : list, optional A list of functions of length n such that ieqconsj(x,*args) >= 0.0 in a successfully optimized problem. f_ieqcons : callable f(x,*args), optional Returns a 1-D ndarray in which each element must be greater or equal to 0.0 in a successfully optimized problem. If f_ieqcons is specified, ieqcons is ignored. bounds : list, optional A list of tuples specifying the lower and upper bound for each independent variable (xl0, xu0),(xl1, xu1),... Infinite values will be interpreted as large floating values. fprime : callable `f(x,*args)`, optional A function that evaluates the partial derivatives of func. fprime_eqcons : callable `f(x,*args)`, optional A function of the form `f(x, *args)` that returns the m by n array of equality constraint normals. If not provided, the normals will be approximated. The array returned by fprime_eqcons should be sized as ( len(eqcons), len(x0) ). fprime_ieqcons : callable `f(x,*args)`, optional A function of the form `f(x, *args)` that returns the m by n array of inequality constraint normals. If not provided, the normals will be approximated. The array returned by fprime_ieqcons should be sized as ( len(ieqcons), len(x0) ). args : sequence, optional Additional arguments passed to func and fprime. iter : int, optional The maximum number of iterations. acc : float, optional Requested accuracy. iprint : int, optional The verbosity of fmin_slsqp :

* iprint <= 0 : Silent operation * iprint == 1 : Print summary upon completion (default) * iprint >= 2 : Print status of each iterate and summary disp : int, optional Over-rides the iprint interface (preferred). full_output : bool, optional If False, return only the minimizer of func (default). Otherwise, output final objective function and summary information. epsilon : float, optional The step size for finite-difference derivative estimates. callback : callable, optional Called after each iteration, as ``callback(x)``, where ``x`` is the current parameter vector.

Returns ------- out : ndarray of float The final minimizer of func. fx : ndarray of float, if full_output is true The final value of the objective function. its : int, if full_output is true The number of iterations. imode : int, if full_output is true The exit mode from the optimizer (see below). smode : string, if full_output is true Message describing the exit mode from the optimizer.

See also -------- minimize: Interface to minimization algorithms for multivariate functions. See the 'SLSQP' `method` in particular.

Notes ----- Exit modes are defined as follows ::

-1 : Gradient evaluation required (g & a) 0 : Optimization terminated successfully. 1 : Function evaluation required (f & c) 2 : More equality constraints than independent variables 3 : More than 3*n iterations in LSQ subproblem 4 : Inequality constraints incompatible 5 : Singular matrix E in LSQ subproblem 6 : Singular matrix C in LSQ subproblem 7 : Rank-deficient equality constraint subproblem HFTI 8 : Positive directional derivative for linesearch 9 : Iteration limit exceeded

Examples -------- Examples are given :ref:`in the tutorial <tutorial-sqlsp>`.

isfinite(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True, signature, extobj)

Test element-wise for finiteness (not infinity or not Not a Number).

The result is returned as a boolean array.

Parameters ---------- x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`.

Returns ------- y : ndarray, bool True where ``x`` is not positive infinity, negative infinity, or NaN; false otherwise. This is a scalar if `x` is a scalar.

See Also -------- isinf, isneginf, isposinf, isnan

Notes ----- Not a Number, positive infinity and negative infinity are considered to be non-finite.

NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Also that positive infinity is not equivalent to negative infinity. But infinity is equivalent to positive infinity. Errors result if the second argument is also supplied when `x` is a scalar input, or if first and second arguments have different shapes.

Examples -------- >>> np.isfinite(1) True >>> np.isfinite(0) True >>> np.isfinite(np.nan) False >>> np.isfinite(np.inf) False >>> np.isfinite(np.NINF) False >>> np.isfinite(np.log(-1.),1.,np.log(0)) array(False, True, False)

>>> x = np.array(-np.inf, 0., np.inf) >>> y = np.array(2, 2, 2) >>> np.isfinite(x, y) array(0, 1, 0) >>> y array(0, 1, 0)

sqrt(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True, signature, extobj)

Return the non-negative square-root of an array, element-wise.

Parameters ---------- x : array_like The values whose square-roots are required. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`.

Returns ------- y : ndarray An array of the same shape as `x`, containing the positive square-root of each element in `x`. If any element in `x` is complex, a complex array is returned (and the square-roots of negative reals are calculated). If all of the elements in `x` are real, so is `y`, with negative elements returning ``nan``. If `out` was provided, `y` is a reference to it. This is a scalar if `x` is a scalar.

See Also -------- lib.scimath.sqrt A version which returns complex numbers when given negative reals.

Notes ----- *sqrt* has--consistent with common convention--as its branch cut the real 'interval' `-inf`, 0), and is continuous from above on it. A branch cut is a curve in the complex plane across which a given complex function fails to be continuous. Examples -------- >>> np.sqrt([1,4,9]) array([ 1., 2., 3.]) >>> np.sqrt([4, -1, -3+4J]) array([ 2.+0.j, 0.+1.j, 1.+2.j]) >>> np.sqrt([4, -1, np.inf]) array([ 2., nan, inf])

Stack arrays in sequence vertically (row wise).

This is equivalent to concatenation along the first axis after 1-D arrays of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by `vsplit`.

This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions `concatenate`, `stack` and `block` provide more general stacking and concatenation operations.

Parameters ---------- tup : sequence of ndarrays The arrays must have the same shape along all but the first axis. 1-D arrays must have the same length.

Returns ------- stacked : ndarray The array formed by stacking the given arrays, will be at least 2-D.

See Also -------- stack : Join a sequence of arrays along a new axis. hstack : Stack arrays in sequence horizontally (column wise). dstack : Stack arrays in sequence depth wise (along third dimension). concatenate : Join a sequence of arrays along an existing axis. vsplit : Split array into a list of multiple sub-arrays vertically. block : Assemble arrays from blocks.

Examples -------- >>> a = np.array(1, 2, 3) >>> b = np.array(2, 3, 4) >>> np.vstack((a,b)) array([1, 2, 3], [2, 3, 4])

>>> a = np.array([1], [2], [3]) >>> b = np.array([2], [3], [4]) >>> np.vstack((a,b)) array([1], [2], [3], [2], [3], [4])

None

zeros(shape, dtype=float, order='C')

Return a new array of given shape and type, filled with zeros.

Parameters ---------- shape : int or tuple of ints Shape of the new array, e.g., ``(2, 3)`` or ``2``. dtype : data-type, optional The desired data-type for the array, e.g., `numpy.int8`. Default is `numpy.float64`. order : 'C', 'F', optional, default: 'C' Whether to store multi-dimensional data in row-major (C-style) or column-major (Fortran-style) order in memory.

Returns ------- out : ndarray Array of zeros with the given shape, dtype, and order.

See Also -------- zeros_like : Return an array of zeros with shape and type of input. empty : Return a new uninitialized array. ones : Return a new array setting values to one. full : Return a new array of given shape filled with value.

Examples -------- >>> np.zeros(5) array( 0., 0., 0., 0., 0.)

>>> np.zeros((5,), dtype=int) array(0, 0, 0, 0, 0)

>>> np.zeros((2, 1)) array([ 0.], [ 0.])

>>> s = (2,2) >>> np.zeros(s) array([ 0., 0.], [ 0., 0.])

>>> np.zeros((2,), dtype=('x', 'i4'), ('y', 'i4')) # custom dtype array((0, 0), (0, 0), dtype=('x', '<i4'), ('y', '<i4'))