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// Copyright (c) 2019 by the SciSharp Team
// Code generated by CodeMinion: https://github.com/SciSharp/CodeMinion
using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.InteropServices;
using System.Text;
using Python.Runtime;
using Python.Included;
using Numpy.Models;
namespace Numpy
{
public partial class NumPy
{
/// <summary>
/// Dot product of two arrays. Specifically,
/// </summary>
/// <param name="a">
/// First argument.
/// </param>
/// <param name="b">
/// Second argument.
/// </param>
/// <param name="@out">
/// Output argument. This must have the exact kind that would be returned
/// if it was not used. In particular, it must have the right type, must be
/// C-contiguous, and its dtype must be the dtype that would be returned
/// for dot(a,b). This is a performance feature. Therefore, if these
/// conditions are not met, an exception is raised, instead of attempting
/// to be flexible.
/// </param>
/// <returns>
/// Returns the dot product of a and b. If a and b are both
/// scalars or both 1-D arrays then a scalar is returned; otherwise
/// an array is returned.
/// If out is given, then it is returned.
/// </returns>
public NDarray dot(NDarray a, NDarray b, NDarray @out = null)
{
//auto-generated code, do not change
var __self__=self;
var pyargs=ToTuple(new object[]
{
a,
b,
});
var kwargs=new PyDict();
if (@out!=null) kwargs["out"]=ToPython(@out);
dynamic py = __self__.InvokeMethod("dot", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Compute the dot product of two or more arrays in a single function call,
/// while automatically selecting the fastest evaluation order.
///
/// multi_dot chains numpy.dot and uses optimal parenthesization
/// of the matrices [1] [2]. Depending on the shapes of the matrices,
/// this can speed up the multiplication a lot.
///
/// If the first argument is 1-D it is treated as a row vector.
/// If the last argument is 1-D it is treated as a column vector.
/// The other arguments must be 2-D.
///
/// Think of multi_dot as:
///
/// Notes
///
/// The cost for a matrix multiplication can be calculated with the
/// following function:
///
/// Let’s assume we have three matrices
/// .
///
/// The costs for the two different parenthesizations are as follows:
///
/// References
/// </summary>
/// <param name="arrays">
/// If the first argument is 1-D it is treated as row vector.
/// If the last argument is 1-D it is treated as column vector.
/// The other arguments must be 2-D.
/// </param>
/// <returns>
/// Returns the dot product of the supplied arrays.
/// </returns>
public NDarray linalg_multi_dot(NDarray[] arrays)
{
//auto-generated code, do not change
var linalg = self.GetAttr("linalg");
var __self__=linalg;
var pyargs=ToTuple(new object[]
{
arrays,
});
var kwargs=new PyDict();
dynamic py = __self__.InvokeMethod("multi_dot", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Return the dot product of two vectors.
///
/// The vdot(a, b) function handles complex numbers differently than
/// dot(a, b). If the first argument is complex the complex conjugate
/// of the first argument is used for the calculation of the dot product.
///
/// Note that vdot handles multidimensional arrays differently than dot:
/// it does not perform a matrix product, but flattens input arguments
/// to 1-D vectors first. Consequently, it should only be used for vectors.
/// </summary>
/// <param name="a">
/// If a is complex the complex conjugate is taken before calculation
/// of the dot product.
/// </param>
/// <param name="b">
/// Second argument to the dot product.
/// </param>
/// <returns>
/// Dot product of a and b. Can be an int, float, or
/// complex depending on the types of a and b.
/// </returns>
public NDarray vdot(NDarray a, NDarray b)
{
//auto-generated code, do not change
var __self__=self;
var pyargs=ToTuple(new object[]
{
a,
b,
});
var kwargs=new PyDict();
dynamic py = __self__.InvokeMethod("vdot", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Inner product of two arrays.
///
/// Ordinary inner product of vectors for 1-D arrays (without complex
/// conjugation), in higher dimensions a sum product over the last axes.
///
/// Notes
///
/// For vectors (1-D arrays) it computes the ordinary inner-product:
///
/// More generally, if ndim(a) = r > 0 and ndim(b) = s > 0:
///
/// or explicitly:
///
/// In addition a or b may be scalars, in which case:
/// </summary>
/// <param name="b">
/// If a and b are nonscalar, their last dimensions must match.
/// </param>
/// <param name="a">
/// If a and b are nonscalar, their last dimensions must match.
/// </param>
/// <returns>
/// out.shape = a.shape[:-1] + b.shape[:-1]
/// </returns>
public NDarray inner(NDarray b, NDarray a)
{
//auto-generated code, do not change
var __self__=self;
var pyargs=ToTuple(new object[]
{
b,
a,
});
var kwargs=new PyDict();
dynamic py = __self__.InvokeMethod("inner", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Compute the outer product of two vectors.
///
/// Given two vectors, a = [a0, a1, ..., aM] and
/// b = [b0, b1, ..., bN],
/// the outer product [1] is:
///
/// References
/// </summary>
/// <param name="a">
/// First input vector. Input is flattened if
/// not already 1-dimensional.
/// </param>
/// <param name="b">
/// Second input vector. Input is flattened if
/// not already 1-dimensional.
/// </param>
/// <param name="@out">
/// A location where the result is stored
/// </param>
/// <returns>
/// out[i, j] = a[i] * b[j]
/// </returns>
public NDarray outer(NDarray a, NDarray b, NDarray @out = null)
{
//auto-generated code, do not change
var __self__=self;
var pyargs=ToTuple(new object[]
{
a,
b,
});
var kwargs=new PyDict();
if (@out!=null) kwargs["out"]=ToPython(@out);
dynamic py = __self__.InvokeMethod("outer", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Matrix product of two arrays.
///
/// Notes
///
/// The behavior depends on the arguments in the following way.
///
/// matmul differs from dot in two important ways:
///
/// The matmul function implements the semantics of the @ operator introduced
/// in Python 3.5 following PEP465.
/// </summary>
/// <param name="x2">
/// Input arrays, scalars not allowed.
/// </param>
/// <param name="x1">
/// Input arrays, scalars not allowed.
/// </param>
/// <param name="@out">
/// A location into which the result is stored. If provided, it must have
/// a shape that matches the signature (n,k),(k,m)->(n,m). If not
/// provided or None, a freshly-allocated array is returned.
/// </param>
/// <returns>
/// The matrix product of the inputs.
/// This is a scalar only when both x1, x2 are 1-d vectors.
/// </returns>
public NDarray matmul(NDarray x2, NDarray x1, NDarray @out = null)
{
//auto-generated code, do not change
var __self__=self;
var pyargs=ToTuple(new object[]
{
x2,
x1,
});
var kwargs=new PyDict();
if (@out!=null) kwargs["out"]=ToPython(@out);
dynamic py = __self__.InvokeMethod("matmul", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Compute tensor dot product along specified axes for arrays >= 1-D.
///
/// Given two tensors (arrays of dimension greater than or equal to one),
/// a and b, and an array_like object containing two array_like
/// objects, (a_axes, b_axes), sum the products of a’s and b’s
/// elements (components) over the axes specified by a_axes and
/// b_axes. The third argument can be a single non-negative
/// integer_like scalar, N; if it is such, then the last N
/// dimensions of a and the first N dimensions of b are summed
/// over.
///
/// Notes
///
/// When axes is integer_like, the sequence for evaluation will be: first
/// the -Nth axis in a and 0th axis in b, and the -1th axis in a and
/// Nth axis in b last.
///
/// When there is more than one axis to sum over - and they are not the last
/// (first) axes of a (b) - the argument axes should consist of
/// two sequences of the same length, with the first axis to sum over given
/// first in both sequences, the second axis second, and so forth.
/// </summary>
/// <param name="b">
/// Tensors to “dot”.
/// </param>
/// <param name="a">
/// Tensors to “dot”.
/// </param>
public NDarray tensordot(NDarray b, NDarray a, int[] axes = null)
{
//auto-generated code, do not change
var __self__=self;
var pyargs=ToTuple(new object[]
{
b,
a,
axes,
});
var kwargs=new PyDict();
dynamic py = __self__.InvokeMethod("tensordot", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Evaluates the Einstein summation convention on the operands.
///
/// Using the Einstein summation convention, many common multi-dimensional,
/// linear algebraic array operations can be represented in a simple fashion.
/// In implicit mode einsum computes these values.
///
/// In explicit mode, einsum provides further flexibility to compute
/// other array operations that might not be considered classical Einstein
/// summation operations, by disabling, or forcing summation over specified
/// subscript labels.
///
/// See the notes and examples for clarification.
///
/// Notes
///
/// The Einstein summation convention can be used to compute
/// many multi-dimensional, linear algebraic array operations. einsum
/// provides a succinct way of representing these.
///
/// A non-exhaustive list of these operations,
/// which can be computed by einsum, is shown below along with examples:
///
/// The subscripts string is a comma-separated list of subscript labels,
/// where each label refers to a dimension of the corresponding operand.
/// Whenever a label is repeated it is summed, so np.einsum('i,i', a, b)
/// is equivalent to np.inner(a,b). If a label
/// appears only once, it is not summed, so np.einsum('i', a) produces a
/// view of a with no changes. A further example np.einsum('ij,jk', a, b)
/// describes traditional matrix multiplication and is equivalent to
/// np.matmul(a,b). Repeated subscript labels in one
/// operand take the diagonal. For example, np.einsum('ii', a) is equivalent
/// to np.trace(a).
///
/// In implicit mode, the chosen subscripts are important
/// since the axes of the output are reordered alphabetically. This
/// means that np.einsum('ij', a) doesn’t affect a 2D array, while
/// np.einsum('ji', a) takes its transpose. Additionally,
/// np.einsum('ij,jk', a, b) returns a matrix multiplication, while,
/// np.einsum('ij,jh', a, b) returns the transpose of the
/// multiplication since subscript ‘h’ precedes subscript ‘i’.
///
/// In explicit mode the output can be directly controlled by
/// specifying output subscript labels. This requires the
/// identifier ‘->’ as well as the list of output subscript labels.
/// This feature increases the flexibility of the function since
/// summing can be disabled or forced when required. The call
/// np.einsum('i->', a) is like np.sum(a, axis=-1),
/// and np.einsum('ii->i', a) is like np.diag(a).
/// The difference is that einsum does not allow broadcasting by default.
/// Additionally np.einsum('ij,jh->ih', a, b) directly specifies the
/// order of the output subscript labels and therefore returns matrix
/// multiplication, unlike the example above in implicit mode.
///
/// To enable and control broadcasting, use an ellipsis. Default
/// NumPy-style broadcasting is done by adding an ellipsis
/// to the left of each term, like np.einsum('...ii->...i', a).
/// To take the trace along the first and last axes,
/// you can do np.einsum('i...i', a), or to do a matrix-matrix
/// product with the left-most indices instead of rightmost, one can do
/// np.einsum('ij...,jk...->ik...', a, b).
///
/// When there is only one operand, no axes are summed, and no output
/// parameter is provided, a view into the operand is returned instead
/// of a new array. Thus, taking the diagonal as np.einsum('ii->i', a)
/// produces a view (changed in version 1.10.0).
///
/// einsum also provides an alternative way to provide the subscripts
/// and operands as einsum(op0, sublist0, op1, sublist1, ..., [sublistout]).
/// If the output shape is not provided in this format einsum will be
/// calculated in implicit mode, otherwise it will be performed explicitly.
/// The examples below have corresponding einsum calls with the two
/// parameter methods.
///
/// Views returned from einsum are now writeable whenever the input array
/// is writeable. For example, np.einsum('ijk...->kji...', a) will now
/// have the same effect as np.swapaxes(a, 0, 2)
/// and np.einsum('ii->i', a) will return a writeable view of the diagonal
/// of a 2D array.
///
/// Added the optimize argument which will optimize the contraction order
/// of an einsum expression. For a contraction with three or more operands this
/// can greatly increase the computational efficiency at the cost of a larger
/// memory footprint during computation.
///
/// Typically a ‘greedy’ algorithm is applied which empirical tests have shown
/// returns the optimal path in the majority of cases. In some cases ‘optimal’
/// will return the superlative path through a more expensive, exhaustive search.
/// For iterative calculations it may be advisable to calculate the optimal path
/// once and reuse that path by supplying it as an argument. An example is given
/// below.
///
/// See numpy.einsum_path for more details.
/// </summary>
/// <param name="subscripts">
/// Specifies the subscripts for summation as comma separated list of
/// subscript labels. An implicit (classical Einstein summation)
/// calculation is performed unless the explicit indicator ‘->’ is
/// included as well as subscript labels of the precise output form.
/// </param>
/// <param name="operands">
/// These are the arrays for the operation.
/// </param>
/// <param name="@out">
/// If provided, the calculation is done into this array.
/// </param>
/// <param name="dtype">
/// If provided, forces the calculation to use the data type specified.
/// Note that you may have to also give a more liberal casting
/// parameter to allow the conversions. Default is None.
/// </param>
/// <param name="order">
/// Controls the memory layout of the output. ‘C’ means it should
/// be C contiguous. ‘F’ means it should be Fortran contiguous,
/// ‘A’ means it should be ‘F’ if the inputs are all ‘F’, ‘C’ otherwise.
/// ‘K’ means it should be as close to the layout as the inputs as
/// is possible, including arbitrarily permuted axes.
/// Default is ‘K’.
/// </param>
/// <param name="casting">
/// Controls what kind of data casting may occur. Setting this to
/// ‘unsafe’ is not recommended, as it can adversely affect accumulations.
///
/// Default is ‘safe’.
/// </param>
/// <param name="optimize">
/// Controls if intermediate optimization should occur. No optimization
/// will occur if False and True will default to the ‘greedy’ algorithm.
/// Also accepts an explicit contraction list from the np.einsum_path
/// function. See np.einsum_path for more details. Defaults to False.
/// </param>
/// <returns>
/// The calculation based on the Einstein summation convention.
/// </returns>
public NDarray einsum(string subscripts, NDarray[] operands, NDarray @out = null, Dtype dtype = null, string order = null, string casting = "safe", object optimize = null)
{
//auto-generated code, do not change
var __self__=self;
var pyargs=ToTuple(new object[]
{
subscripts,
operands,
});
var kwargs=new PyDict();
if (@out!=null) kwargs["out"]=ToPython(@out);
if (dtype!=null) kwargs["dtype"]=ToPython(dtype);
if (order!=null) kwargs["order"]=ToPython(order);
if (casting!="safe") kwargs["casting"]=ToPython(casting);
if (optimize!=null) kwargs["optimize"]=ToPython(optimize);
dynamic py = __self__.InvokeMethod("einsum", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/*
/// <summary>
/// Evaluates the lowest cost contraction order for an einsum expression by
/// considering the creation of intermediate arrays.
///
/// Notes
///
/// The resulting path indicates which terms of the input contraction should be
/// contracted first, the result of this contraction is then appended to the
/// end of the contraction list. This list can then be iterated over until all
/// intermediate contractions are complete.
/// </summary>
/// <param name="subscripts">
/// Specifies the subscripts for summation.
/// </param>
/// <param name="operands">
/// These are the arrays for the operation.
/// </param>
/// <param name="optimize">
/// Choose the type of path. If a tuple is provided, the second argument is
/// assumed to be the maximum intermediate size created. If only a single
/// argument is provided the largest input or output array size is used
/// as a maximum intermediate size.
///
/// Default is ‘greedy’.
/// </param>
/// <returns>
/// A tuple of:
/// path
/// A list representation of the einsum path.
/// string_repr
/// A printable representation of the einsum path.
/// </returns>
public (list of tuples, string) einsum_path(string subscripts, NDarray[] operands, {bool optimize = "greedy")
{
//auto-generated code, do not change
var __self__=self;
var pyargs=ToTuple(new object[]
{
subscripts,
operands,
optimize,
});
var kwargs=new PyDict();
dynamic py = __self__.InvokeMethod("einsum_path", pyargs, kwargs);
var t = py as PyTuple;
return (ToCsharp<list of tuples>(t[0]), ToCsharp<string>(t[1]));
}
*/
/// <summary>
/// Raise a square matrix to the (integer) power n.
///
/// For positive integers n, the power is computed by repeated matrix
/// squarings and matrix multiplications. If n == 0, the identity matrix
/// of the same shape as M is returned. If n < 0, the inverse
/// is computed and then raised to the abs(n).
/// </summary>
/// <param name="a">
/// Matrix to be “powered.”
/// </param>
/// <param name="n">
/// The exponent can be any integer or long integer, positive,
/// negative, or zero.
/// </param>
/// <returns>
/// The return value is the same shape and type as M;
/// if the exponent is positive or zero then the type of the
/// elements is the same as those of M. If the exponent is
/// negative the elements are floating-point.
/// </returns>
public NDarray linalg_matrix_power(NDarray a, int n)
{
//auto-generated code, do not change
var linalg = self.GetAttr("linalg");
var __self__=linalg;
var pyargs=ToTuple(new object[]
{
a,
n,
});
var kwargs=new PyDict();
dynamic py = __self__.InvokeMethod("matrix_power", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Kronecker product of two arrays.
///
/// Computes the Kronecker product, a composite array made of blocks of the
/// second array scaled by the first.
///
/// Notes
///
/// The function assumes that the number of dimensions of a and b
/// are the same, if necessary prepending the smallest with ones.
/// If a.shape = (r0,r1,..,rN) and b.shape = (s0,s1,…,sN),
/// the Kronecker product has shape (r0*s0, r1*s1, …, rN*SN).
/// The elements are products of elements from a and b, organized
/// explicitly by:
///
/// where:
///
/// In the common 2-D case (N=1), the block structure can be visualized:
/// </summary>
public NDarray kron(NDarray b, NDarray a)
{
//auto-generated code, do not change
var __self__=self;
var pyargs=ToTuple(new object[]
{
b,
a,
});
var kwargs=new PyDict();
dynamic py = __self__.InvokeMethod("kron", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Compute the qr factorization of a matrix.
///
/// Factor the matrix a as qr, where q is orthonormal and r is
/// upper-triangular.
///
/// Notes
///
/// This is an interface to the LAPACK routines dgeqrf, zgeqrf,
/// dorgqr, and zungqr.
///
/// For more information on the qr factorization, see for example:
/// https://en.wikipedia.org/wiki/QR_factorization
///
/// Subclasses of ndarray are preserved except for the ‘raw’ mode. So if
/// a is of type matrix, all the return values will be matrices too.
///
/// New ‘reduced’, ‘complete’, and ‘raw’ options for mode were added in
/// NumPy 1.8.0 and the old option ‘full’ was made an alias of ‘reduced’. In
/// addition the options ‘full’ and ‘economic’ were deprecated. Because
/// ‘full’ was the previous default and ‘reduced’ is the new default,
/// backward compatibility can be maintained by letting mode default.
/// The ‘raw’ option was added so that LAPACK routines that can multiply
/// arrays by q using the Householder reflectors can be used. Note that in
/// this case the returned arrays are of type np.double or np.cdouble and
/// the h array is transposed to be FORTRAN compatible. No routines using
/// the ‘raw’ return are currently exposed by numpy, but some are available
/// in lapack_lite and just await the necessary work.
/// </summary>
/// <param name="a">
/// Matrix to be factored.
/// </param>
/// <param name="mode">
/// If K = min(M, N), then
///
/// The options ‘reduced’, ‘complete, and ‘raw’ are new in numpy 1.8,
/// see the notes for more information. The default is ‘reduced’, and to
/// maintain backward compatibility with earlier versions of numpy both
/// it and the old default ‘full’ can be omitted. Note that array h
/// returned in ‘raw’ mode is transposed for calling Fortran. The
/// ‘economic’ mode is deprecated. The modes ‘full’ and ‘economic’ may
/// be passed using only the first letter for backwards compatibility,
/// but all others must be spelled out. See the Notes for more
/// explanation.
/// </param>
/// <returns>
/// A tuple of:
/// q
/// A matrix with orthonormal columns. When mode = ‘complete’ the
/// result is an orthogonal/unitary matrix depending on whether or not
/// a is real/complex. The determinant may be either +/- 1 in that
/// case.
/// r
/// The upper-triangular matrix.
/// (h, tau)
/// The array h contains the Householder reflectors that generate q
/// along with r. The tau array contains scaling factors for the
/// reflectors. In the deprecated ‘economic’ mode only h is returned.
/// </returns>
public (NDarray, NDarray, NDarray) linalg_qr(NDarray a, string mode = "reduced")
{
//auto-generated code, do not change
var linalg = self.GetAttr("linalg");
var __self__=linalg;
var pyargs=ToTuple(new object[]
{
a,
});
var kwargs=new PyDict();
if (mode!="reduced") kwargs["mode"]=ToPython(mode);
dynamic py = __self__.InvokeMethod("qr", pyargs, kwargs);
var t = py as PyTuple;
return (ToCsharp<NDarray>(t[0]), ToCsharp<NDarray>(t[1]), ToCsharp<NDarray>(t[2]));
}
/*
/// <summary>
/// Compute the condition number of a matrix.
///
/// This function is capable of returning the condition number using
/// one of seven different norms, depending on the value of p (see
/// Parameters below).
///
/// Notes
///
/// The condition number of x is defined as the norm of x times the
/// norm of the inverse of x [1]; the norm can be the usual L2-norm
/// (root-of-sum-of-squares) or one of a number of other matrix norms.
///
/// References
/// </summary>
/// <param name="x">
/// The matrix whose condition number is sought.
/// </param>
/// <param name="p">
/// Order of the norm:
///
/// inf means the numpy.inf object, and the Frobenius norm is
/// the root-of-sum-of-squares norm.
/// </param>
/// <returns>
/// The condition number of the matrix. May be infinite.
/// </returns>
public {float linalg_cond(NDarray x, {None p = null)
{
//auto-generated code, do not change
var linalg = self.GetAttr("linalg");
var __self__=linalg;
var pyargs=ToTuple(new object[]
{
x,
});
var kwargs=new PyDict();
if (p!=null) kwargs["p"]=ToPython(p);
dynamic py = __self__.InvokeMethod("cond", pyargs, kwargs);
return ToCsharp<{float>(py);
}
*/
/// <summary>
/// Return matrix rank of array using SVD method
///
/// Rank of the array is the number of singular values of the array that are
/// greater than tol.
///
/// Notes
///
/// The default threshold to detect rank deficiency is a test on the magnitude
/// of the singular values of M. By default, we identify singular values less
/// than S.max() * max(M.shape) * eps as indicating rank deficiency (with
/// the symbols defined above). This is the algorithm MATLAB uses [1]. It also
/// appears in Numerical recipes in the discussion of SVD solutions for linear
/// least squares [2].
///
/// This default threshold is designed to detect rank deficiency accounting for
/// the numerical errors of the SVD computation. Imagine that there is a column
/// in M that is an exact (in floating point) linear combination of other
/// columns in M. Computing the SVD on M will not produce a singular value
/// exactly equal to 0 in general: any difference of the smallest SVD value from
/// 0 will be caused by numerical imprecision in the calculation of the SVD.
/// Our threshold for small SVD values takes this numerical imprecision into
/// account, and the default threshold will detect such numerical rank
/// deficiency. The threshold may declare a matrix M rank deficient even if
/// the linear combination of some columns of M is not exactly equal to
/// another column of M but only numerically very close to another column of
/// M.
///
/// We chose our default threshold because it is in wide use. Other thresholds
/// are possible. For example, elsewhere in the 2007 edition of Numerical
/// recipes there is an alternative threshold of S.max() *
/// np.finfo(M.dtype).eps / 2. * np.sqrt(m + n + 1.). The authors describe
/// this threshold as being based on “expected roundoff error” (p 71).
///
/// The thresholds above deal with floating point roundoff error in the
/// calculation of the SVD. However, you may have more information about the
/// sources of error in M that would make you consider other tolerance values
/// to detect effective rank deficiency. The most useful measure of the
/// tolerance depends on the operations you intend to use on your matrix. For
/// example, if your data come from uncertain measurements with uncertainties
/// greater than floating point epsilon, choosing a tolerance near that
/// uncertainty may be preferable. The tolerance may be absolute if the
/// uncertainties are absolute rather than relative.
///
/// References
/// </summary>
/// <param name="M">
/// input vector or stack of matrices
/// </param>
/// <param name="tol">
/// threshold below which SVD values are considered zero. If tol is
/// None, and S is an array with singular values for M, and
/// eps is the epsilon value for datatype of S, then tol is
/// set to S.max() * max(M.shape) * eps.
/// </param>
/// <param name="hermitian">
/// If True, M is assumed to be Hermitian (symmetric if real-valued),
/// enabling a more efficient method for finding singular values.
/// Defaults to False.
/// </param>
public int linalg_matrix_rank(NDarray M, NDarray tol = null, bool? hermitian = false)
{
//auto-generated code, do not change
var linalg = self.GetAttr("linalg");
var __self__=linalg;
var pyargs=ToTuple(new object[]
{
M,
});
var kwargs=new PyDict();
if (tol!=null) kwargs["tol"]=ToPython(tol);
if (hermitian!=false) kwargs["hermitian"]=ToPython(hermitian);
dynamic py = __self__.InvokeMethod("matrix_rank", pyargs, kwargs);
return ToCsharp<int>(py);
}
/// <summary>
/// Compute the sign and (natural) logarithm of the determinant of an array.
///
/// If an array has a very small or very large determinant, then a call to
/// det may overflow or underflow. This routine is more robust against such
/// issues, because it computes the logarithm of the determinant rather than
/// the determinant itself.
///
/// Notes
///
/// Broadcasting rules apply, see the numpy.linalg documentation for
/// details.
///
/// The determinant is computed via LU factorization using the LAPACK
/// routine z/dgetrf.
/// </summary>
/// <param name="a">
/// Input array, has to be a square 2-D array.
/// </param>
/// <returns>
/// A tuple of:
/// sign
/// A number representing the sign of the determinant. For a real matrix,
/// this is 1, 0, or -1. For a complex matrix, this is a complex number
/// with absolute value 1 (i.e., it is on the unit circle), or else 0.
/// logdet
/// The natural log of the absolute value of the determinant.
/// </returns>
public (NDarray, NDarray) linalg_slogdet(NDarray a)
{
//auto-generated code, do not change
var linalg = self.GetAttr("linalg");
var __self__=linalg;
var pyargs=ToTuple(new object[]
{
a,
});
var kwargs=new PyDict();
dynamic py = __self__.InvokeMethod("slogdet", pyargs, kwargs);
var t = py as PyTuple;
return (ToCsharp<NDarray>(t[0]), ToCsharp<NDarray>(t[1]));
}
/// <summary>
/// Return the sum along diagonals of the array.
///
/// If a is 2-D, the sum along its diagonal with the given offset
/// is returned, i.e., the sum of elements a[i,i+offset] for all i.
///
/// If a has more than two dimensions, then the axes specified by axis1 and
/// axis2 are used to determine the 2-D sub-arrays whose traces are returned.
/// The shape of the resulting array is the same as that of a with axis1
/// and axis2 removed.
/// </summary>
/// <param name="a">
/// Input array, from which the diagonals are taken.
/// </param>
/// <param name="offset">
/// Offset of the diagonal from the main diagonal. Can be both positive
/// and negative. Defaults to 0.
/// </param>
/// <param name="axis2">
/// Axes to be used as the first and second axis of the 2-D sub-arrays
/// from which the diagonals should be taken. Defaults are the first two
/// axes of a.
/// </param>
/// <param name="axis1">
/// Axes to be used as the first and second axis of the 2-D sub-arrays
/// from which the diagonals should be taken. Defaults are the first two
/// axes of a.
/// </param>
/// <param name="dtype">
/// Determines the data-type of the returned array and of the accumulator
/// where the elements are summed. If dtype has the value None and a is
/// of integer type of precision less than the default integer
/// precision, then the default integer precision is used. Otherwise,
/// the precision is the same as that of a.
/// </param>
/// <param name="@out">
/// Array into which the output is placed. Its type is preserved and
/// it must be of the right shape to hold the output.
/// </param>
/// <returns>
/// If a is 2-D, the sum along the diagonal is returned. If a has
/// larger dimensions, then an array of sums along diagonals is returned.
/// </returns>
public NDarray trace(NDarray a, int? offset = 0, int? axis2 = null, int? axis1 = null, Dtype dtype = null, NDarray @out = null)
{
//auto-generated code, do not change
var __self__=self;
var pyargs=ToTuple(new object[]
{
a,
});
var kwargs=new PyDict();
if (offset!=0) kwargs["offset"]=ToPython(offset);
if (axis2!=null) kwargs["axis2"]=ToPython(axis2);
if (axis1!=null) kwargs["axis1"]=ToPython(axis1);
if (dtype!=null) kwargs["dtype"]=ToPython(dtype);
if (@out!=null) kwargs["out"]=ToPython(@out);
dynamic py = __self__.InvokeMethod("trace", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Solve the tensor equation a x = b for x.
///
/// It is assumed that all indices of x are summed over in the product,
/// together with the rightmost indices of a, as is done in, for example,
/// tensordot(a, x, axes=b.ndim).
/// </summary>
/// <param name="a">
/// Coefficient tensor, of shape b.shape + Q. Q, a tuple, equals
/// the shape of that sub-tensor of a consisting of the appropriate
/// number of its rightmost indices, and must be such that
/// prod(Q) == prod(b.shape) (in which sense a is said to be
/// ‘square’).
/// </param>
/// <param name="b">
/// Right-hand tensor, which can be of any shape.
/// </param>
/// <param name="axes">
/// Axes in a to reorder to the right, before inversion.
/// If None (default), no reordering is done.
/// </param>
public NDarray linalg_tensorsolve(NDarray a, NDarray b, int[] axes = null)
{
//auto-generated code, do not change
var linalg = self.GetAttr("linalg");
var __self__=linalg;
var pyargs=ToTuple(new object[]
{
a,
b,
});
var kwargs=new PyDict();
if (axes!=null) kwargs["axes"]=ToPython(axes);
dynamic py = __self__.InvokeMethod("tensorsolve", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Compute the ‘inverse’ of an N-dimensional array.
///
/// The result is an inverse for a relative to the tensordot operation
/// tensordot(a, b, ind), i. e., up to floating-point accuracy,
/// tensordot(tensorinv(a), a, ind) is the “identity” tensor for the
/// tensordot operation.
/// </summary>
/// <param name="a">
/// Tensor to ‘invert’. Its shape must be ‘square’, i. e.,
/// prod(a.shape[:ind]) == prod(a.shape[ind:]).
/// </param>
/// <param name="ind">
/// Number of first indices that are involved in the inverse sum.
/// Must be a positive integer, default is 2.
/// </param>
/// <returns>
/// a’s tensordot inverse, shape a.shape[ind:] + a.shape[:ind].
/// </returns>
public NDarray linalg_tensorinv(NDarray a, int? ind = 2)
{
//auto-generated code, do not change
var linalg = self.GetAttr("linalg");
var __self__=linalg;
var pyargs=ToTuple(new object[]
{
a,
});
var kwargs=new PyDict();
if (ind!=2) kwargs["ind"]=ToPython(ind);
dynamic py = __self__.InvokeMethod("tensorinv", pyargs, kwargs);
return ToCsharp<NDarray>(py);
}
/// <summary>
/// Generic Python-exception-derived object raised by linalg functions.
///
/// General purpose exception class, derived from Python’s exception.Exception
/// class, programmatically raised in linalg functions when a Linear
/// Algebra-related condition would prevent further correct execution of the
/// function.
/// </summary>
public void linalg_LinAlgError()
{
//auto-generated code, do not change
var linalg = self.GetAttr("linalg");
var __self__=linalg;
dynamic py = __self__.InvokeMethod("LinAlgError");
}
}
}