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https://docs.kotharcomputing.comDocumentation for the Kothar platform, featuring the Forge automation environment, the Workshop for numerical experiments, and the Aleph language. Includes comprehensive library references for the standard library, tensor operations (RealTensor, ComplexTensor), and the AlephExpectation testing framework, as well as details on the Python SDK and REST API.
The Cauchy distribution represents the ratio of two normal distributions. It is defined by a location parameter a (default 0.0) and a half-width half-maximum parameter b (default 1.0).
The probability density function is defined as: f(x | a, b) = (bπ(1 + ((x-a)/b)²))⁻¹
The PiecewiseLinear distribution (inheriting from Distribution) returns random real numbers distributed linearly within specified intervals and densities.
[0.0, 1.0][1.0]The probability density function $f(x | I, w)$ for a value $x$ where $I_k \leq x < I_{k+1}$ is defined by the linear interpolation of densities $w$ over the intervals $I$.
Slice object (inheriting from Object) represents a range specification for indexing operations. It defines a start index, stop index, and step size, allowing for flexible data access patterns such as reverse iteration, skipping elements, and extracting subsequences from arrays, strings, and other indexable containers.The PauliString class represents a Pauli string and its complex coefficient using a numerically efficient bitstring representation. It uses bit logic to perform operations faster than OperatorProducts or OperatorSums.
Internally, each Pauli string is represented by a complex coefficient and two integers, xbits and zbits. The mapping for Pauli operators is:
00: Identity (I)10: X01: Z11: YThe class automatically handles the phase accrued during the multiplication of different terms.
NumpyFile class represents a handle to a NumPy file. It supports two formats: .npy files, which are used for a single direct array value, and .npz files, which are used for archives containing multiple named arrays.# Write a single array to a .npy file
NumpyFile("values.npy", "w").write([1.0, 2.0, 3.0])
# Read a .npy file as a list of reals
var values = NumpyFile("values.npy").read(as_real | as_list)
# Write a named array to a .npz archive
NumpyFile("archive.npz", "w").write("samples", [1, 2, 3])The PiecewiseConstant distribution returns random real numbers uniformly distributed within specified intervals (default: [0.0, 1.0]) and densities (default: [1.0]).
The probability density function is defined as:
$f(x | I, w) = \frac{w_k}{(I_{k+1} - I_k)\sum_k w_k}$ for $I_k \leq x < I_{k+1}$
Where $I_k$ are the elements of the intervals parameter and $w_k$ are the elements of the densities parameter.
ChiSquared distribution models the distribution of the sum of squares of n independent standard normal variables (with a default value of 1.0). Its probability density function is defined as: f(x | n) = x^((n/2)-1) * e^(-x/2) / (Gamma(n/2) * 2^(n/2)). It inherits from the Distribution base class.The real type represents floating-point numbers with fractional parts, adhering to IEEE 754 double-precision semantics.
Key characteristics:
Infinity or -Infinity.The Lattice class represents a crystal lattice consisting of a Bravais lattice and an atomic basis. When using predefined geometries, parameters typically follow the convention where a, b, and c represent side lengths, and theta and phi represent angles.
| Geometry | Parameters |
|---|---|
| square | a (intercell spacing) |
| rectangular | a (intercell spacing dim 11), b (intercell spacing dim 22) |
| triangular | a (intercell spacing) |
| oblique | a (intercell spacing dim 11), b (side length dim 22), theta (angle between primitive vectors) |
| honeycomb | a (intersite spacing) |
| chain | (Supported geometry) |
BasisState type represents a quantum product state of the form $|s_1s_2...s_n\rangle$. It is derived from the State base class. Specialized derived types include Fbit, HeterogenousQdit, HomogenousQdit, and Qbit.