scalation.mathstat

package scalation.mathstat

Members list

Type members

Classlikes

The `Bidiagonal` class is used to create a bidiagonal matrix from matrix a. It uses the Householder Bidiagonalization Algorithm to compute orthogonal matrices u and v such that u.t * a * v = b a = u * b * v.t where matrix b is bidiagonal, i.e., it will only have non-zero elements on its main diagonal and its super-diagonal (the diagonal above the main). u is an m-by-n matrix b is an n-by-n matrix (bidiagonal) v is an n-by-n matrix

Value parameters

a: the m-by-n matrix to bidiagonalize (requires m >= n)

Attributes

Supertypes: class Object

trait Matchable

class Any

The BoxcoxForm class applies a and scaled p = b_(0) BOX-COX-transformation. When l is zero, switch to a log-transformation. For power l (λ in textbooks),

 x -> (x^l - 1) / l

Value parameters

w: the transform argument vector (w -> b)

Attributes

Supertypes: trait Transform

class Object

trait Matchable

class Any

The Canvas class provides a canvas on which to draw the plot.

Value parameters

height: the frame height
lines: flag for generating a line plot
width: the frame width
x: the x vector of data values (horizontal)
y: the y vector of data values (primary vertical)
z: the z vector of data values (secondary vertical) to compare with y

Attributes

Supertypes: trait ZoomablePanel

trait MouseMotionListener

trait MouseListener

trait MouseWheelListener

trait EventListener

class JPanel

trait Accessible

class JComponent

class Container

class Component

trait Serializable

trait MenuContainer

trait ImageObserver

class Object

trait Matchable

class Any
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The CenterForm class applies the CENTER-transformation so the new mean will be zero (subtract original mean b(0)).

x -> x - μ

Value parameters

x_: the input vector or matrix to be transformed (needed to get w)

Attributes

Supertypes: trait Transform

class Object

trait Matchable

class Any

The Combinatorics object provides several common combinatorics functions, such as factorial permutations, combinations, gamma and beta functions.

Attributes

Supertypes: class Object

trait Matchable

class Any
Self type: Combinatorics.type

The Correlogram trait provides functions for computing the Auto-Correlation Function (ACF) and the Partial Auto-Correlation Function (PACF).

Value parameters

adjusted: whether to adjust to account for the number of elements in the sum Σ (or use dim-1)
y: the time series data (response vector)

Attributes

See also: VectorD.acov
Supertypes: class Object

trait Matchable

class Any
Known subtypes: class AR

The CosForm class applies a shifted b_(0) and scaled b_(1) COSINE-transformation. For phase shift b_(0) = φ = s and frequency b_(1) = f with scaling 2πf,

x -> cos (2πfx + φ)

Value parameters

w: the transform argument vector (w -> b)

Attributes

Supertypes: trait Transform

class Object

trait Matchable

class Any

The Eigenvalue class is used to find the eigenvalues of an n-by-n matrix a using an iterative technique that applies similarity transformations to convert a into an upper triangular matrix, so that the eigenvalues appear along the diagonal. To improve performance, the a matrix is first reduced to Hessenburg form. During the iterative steps, a shifted QR decomposition is performed.

Value parameters

a: the matrix whose eigenvalues are sought

Attributes

Supertypes: class Object

trait Matchable

class Any

The EigenvalueSym class is used to find the eigenvalues of an n-by-n symmetric matrix a using an iterative technique, the Symmetric QR Algorithm.

Value parameters

a: the symmetric matrix whose eigenvalues are sought

Attributes

See also: Algorithm 8.3.3 in Matrix Computations.
Supertypes: class Object

trait Matchable

class Any

The Eigenvector class is used to find the eigenvectors of an n-by-n matrix a by solving equations of the form (a - eI)v = 0 where e is the eigenvalue and v is the eigenvector. Place the eigenvectors in a matrix column-wise.

Value parameters

_e: the vector of eigenvalues of matrix a
a: the matrix whose eigenvectors are sought

Attributes

Supertypes: class Object

trait Matchable

class Any

The ExpForm class applies a shifted b_(0) and scaled b_(1) EXP-transformation. For shift s and scale a,

 x -> exp (ax + s)

Value parameters

w: the transform argument vector (w -> b)

Attributes

Supertypes: trait Transform

class Object

trait Matchable

class Any
Known subtypes: class NExpForm

The Fac_Cholesky class provides methods to factor an n-by-n symmetric, positive definite matrix a into the product of two matrices: l - an n-by-n left lower triangular matrix l.t - an n-by-n right upper triangular matrix - transpose of l such that a = l * l.t.

Value parameters

a: the symmetric, positive definite matrix to be factored

Attributes

Supertypes: trait Factorization

class Object

trait Matchable

class Any

The Fac_Inverse class provides methods to factor an n-by-n identity matrix I into the product of two matrices a and a^-1 a * a^-1 = I where a is the given matrix and a^-1 is its inverse.

Value parameters

a: the given n-by-n square matrix

Attributes

Companion: object
Supertypes: trait Factorization

class Object

trait Matchable

class Any

The Fac_Inverse companion object provides methods for matrix imversion.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: Fac_Inverse.type

The Fac_LQ class provides methods to factor an 'm-by-n' matrix 'aa' into the product of two matrices, when m < n. 'l' - an 'm-by-m' left lower triangular matrix 'q' - an 'm-by-n' orthogonal matrix and such that 'aa = l * q'. Note, orthogonal means that 'q.t * q = I'.

Value parameters

aa: the matrix to be factored into l and q

Attributes

See also: Fac-QR
Supertypes: trait Factorization

class Object

trait Matchable

class Any

The Fac_LU companion object provides functions related to LU Factorization.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: Fac_LU.type

The Fac_LU class provides methods to factor an m-by-n matrix into its lower and upper triangular products: A = LU when partial pivoting is not needed PA = LU where P is the permutation matrix A = QLU where Q = P.inverse where a is the given matrix, l is an m-by-n lower triangular matrix, and u is an n-by-n upper triangular matrix. The permutation matrix is represented by the piv vector. Once factored, can be used to solve a system of linear equations. Solve for x in Ax = b: Ax = QLUx = b => LUx = Pb using steps (1) and (2) (1) Solve Ly = Pb using forward substitution for y (2) Solve Ux = y using backward substitution for x

Value parameters

a: the given m-by-n rectangular matrix

Attributes

Companion: object
Supertypes: trait Factorization

class Object

trait Matchable

class Any

The Fac_QR companion object provides a factory method and example matrices to factor.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: Fac_QR.type

The Fac_QR class provides methods to factor an m-by-n matrix a into the product of two matrices: q - an m-by-n orthogonal matrix and r - an n-by-n right upper triangular matrix such that a = q * r. It uses uses Householder orthogonalization.

Value parameters

aa: the matrix to be factored into q and r
needQ: flag indicating whether a full q matrix is needed

Attributes

See also: 5.1 and 5.2 in Matrix Computations

QRDecomposition.java in Jama

www.stat.wisc.edu/~larget/math496/qr.html

This implementation improves performance by working with the transpose the original matrix and reorders operations to facilitate parallelism (see par directory).
Companion: object
Supertypes: trait Factorization

class Object

trait Matchable

class Any
Known subtypes: class Fac_QR_RR

The Fac_QR_RR class provides methods to factor an 'm-by-n' matrix 'a' into the product of two matrices: 'q' - an 'm-by-n' orthogonal matrix and 'r' - an 'n-by-n' right upper triangular matrix such that 'a = q * r'. It uses uses Householder orthogonalization.

Value parameters

aa: the matrix to be factored into q and r
needQ: flag indicating whether a full q matrix is needed

Attributes

See also: 5.1 and 5.2 in Matrix Computations

QRDecomposition.java in Jama

www.stat.wisc.edu/~larget/math496/qr.html

This implementation extends Fac_QR and adds column pivoting for greater robustness and reasonably accurate rank determination (Rank Revealing QR).
Companion: object
Supertypes: trait Pivoting

class Fac_QR

trait Factorization

class Object

trait Matchable

class Any
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The Fac_QR_RR object provides a convenient way to determine the rank of matrix.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: Fac_QR_RR.type

The `Fac_SVD` class is used to compute the Singular Value Decomposition (SVD) of matrix a using the Golub-Kahan-Reinsch Algorithm. Factor/decompose matrix 'a' into the product of three matrices: a = u * q * v.t where u is an m-by-n matrix of orthogonal eigenvectors of a * a.t (LEFT SINGULAR VECTORS) q is an n-by-n diagonal matrix of square roots of eigenvalues of a.t * a & a * a.t (SINGULAR VALUES) v is an n-by-n matrix of orthogonal eigenvectors of a.t * a (RIGHT SINGULAR VECTORS) The SVD algorithm implemented is based on plane rotations. It involves transforming the input matrix to its Bidiagonal form using the Householder transformation procedure. The Bidiagonal matrix is then used to obtain singular values using the QR algorithm.

Value parameters

a: the m-by-n matrix to factor/decompose (requires m >= n)

Attributes

Companion: object
Supertypes: trait Factorization

class Object

trait Matchable

class Any

The Fac_SVD object provides several test matrices as well as methods for making full representations, reducing dimensionality, determining rank and testing SVD factorizations.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: Fac_SVD.type

The Factorization trait is the template for classes implementing various forms of matrix factorization.

Attributes

Supertypes: class Object

trait Matchable

class Any
Known subtypes: class Fac_Cholesky

class Fac_Inverse

class Fac_LQ

class Fac_LU

class Fac_QR

class Fac_QR_RR

class Fac_SVD
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The FramelessHeatMap class should be used in embedded applications.

Value parameters

frameH: the height
frameW: the width
heat: the matrix of values (to be color-coded for display)
name: the column names for the matrix

Attributes

Supertypes: class Object

trait Matchable

class Any

The FramelessHistogram class should be used in embedded applications.

Value parameters

frameH: the height
frameW: the width
numIntervals: the number of intervals (typically 5 to 100)
value: the vector of values (want several per interval)

Attributes

Supertypes: class Object

trait Matchable

class Any

The FramelessPlot class is used for embedded applications.

Value parameters

height: the height
width: the width
x: the x vector of data values (horizontal)
y: the y vector of data values (primary vertical)
z: the z vector of data values (secondary vertical) to compare with y

Attributes

Supertypes: class Object

trait Matchable

class Any

Create a canvas on which to draw the histogram.

Value parameters

counts: the counts per interval, if available
frameH: the height
frameW: the width
numIntervals: the number of intervals (typically 5 to 100)
value: the vector of values (want several per interval)

Attributes

Supertypes: trait ZoomablePanel

trait MouseMotionListener

trait MouseListener

trait MouseWheelListener

trait EventListener

class JPanel

trait Accessible

class JComponent

class Container

class Component

trait Serializable

trait MenuContainer

trait ImageObserver

class Object

trait Matchable

class Any
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Zoom functionality has two options: (1) mouse wheel controls the amount of zooming (in/out); (2) mouse dragging repositions the objects in the panel (drawing canvas).

The `HeatMap` class takes a matrix of values and displays them in color-coded cells where the color is based on the cell value (e.g., correlation). The value for the cell 'heat(i, j)' is also displayed.

Zoom functionality has two options: (1) mouse wheel controls the amount of zooming (in/out); (2) mouse dragging repositions the objects in the panel (drawing canvas).

Value parameters

_title: the title of the heat-map (defaults to "HeatMap")
heat: the matrix of values (to be color-coded for display)
name: the column names for the matrix (defaults to null)

Attributes

See also: ZoomablePanel
Supertypes: class VizFrame

class Frame

class JFrame

trait RootPaneContainer

trait WindowConstants

class Frame

class Window

trait Accessible

class Container

class Component

trait Serializable

trait MenuContainer

trait ImageObserver

class Object

trait Matchable

class Any
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The Hessenburg class is used to reduce, via similarity transformations, an n-by-n matrix a to Hessenburg form h, where all elements two below the main diagonal are zero (or close to zero). Note, similarity transformations do not changes the eigenvalues.

Value parameters

a: the matrix to reduce to Hessenburg form

Attributes

Supertypes: class Object

trait Matchable

class Any

Zoom functionality has two options: (1) mouse wheel controls the amount of zooming (in/out); (2) mouse dragging repositions the objects in the panel (drawing canvas).

The `Histogram` class takes a vector of values, counts the number of values in each of several intervals and displays the counts vertically in a histogram.

Zoom functionality has two options: (1) mouse wheel controls the amount of zooming (in/out); (2) mouse dragging repositions the objects in the panel (drawing canvas).

Value parameters

_title: title of the histogram
counts: the counts per interval, if available
numIntervals: the number of intervals (typically 5 to 100)
value: the vector of values (want several per interval)

Attributes

See also: ZoomablePanel
Supertypes: class VizFrame

class Frame

class JFrame

trait RootPaneContainer

trait WindowConstants

class Frame

class Window

trait Accessible

class Container

class Component

trait Serializable

trait MenuContainer

trait ImageObserver

class Object

trait Matchable

class Any
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Create a canvas on which to draw the heat-map.

Value parameters

frameH: the frame height
frameW: the frame width
heat: the matrix of values (to be color-coded to display)
name: the column names for the matrix

Attributes

Supertypes: trait ZoomablePanel

trait MouseMotionListener

trait MouseListener

trait MouseWheelListener

trait EventListener

class JPanel

trait Accessible

class JComponent

class Container

class Component

trait Serializable

trait MenuContainer

trait ImageObserver

class Object

trait Matchable

class Any
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The Householder object provides methods to compute Householder vectors and reflector matrices.

Attributes

Supertypes: class Object

trait Matchable

class Any
Self type: Householder.type

The HouseholderT class performs a Householder Tridiagonalization on a symmetric matrix.

Value parameters

a: the symmetric matrix to tridiagonalize

Attributes

See also: Algorithm 8.3.1 in Matrix Computations.
Supertypes: class Object

trait Matchable

class Any

The Log1pForm class applies a shifted b_(0) and scaled b_(1) LOG-transformation.

Value parameters

x_: the transform argument is null

Attributes

Supertypes: trait Transform

class Object

trait Matchable

class Any

The LogForm class applies a shifted b_(0) and scaled b_(1) LOG-transformation. Note: the default w = (1, 1) corresponds to log1p and its inverse to expm1. For shift s and scale a,

x -> log (ax + s)

Value parameters

w: the transform argument vector (w -> b)

Attributes

Supertypes: trait Transform

class Object

trait Matchable

class Any

The MattixCalc class supports simple simple calculations on elements in a matrix.

Value parameters

header: the column names
x: the matrix of data

Attributes

Supertypes: class Object

trait Matchable

class Any

The `MatrixD companion object provides factory methods.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: MatrixD.type

The MatrixD class stores and operates on Numeric Matrices of base type Double. the 'cfor' loop is used for most loops for faster execution.

Value parameters

dim: the first (row) dimension of the matrix
dim2: the second (column) dimension of the matrix
v: the 2D array used to store matrix elements

Attributes

Companion: object
Supertypes: class Object

trait Matchable

class Any
Known subtypes: class VMatrixD

Attributes

Companion: object
Supertypes: class Object

trait Matchable

class Any

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: MatrixD2.type

The MatrixD2Example object provides example instances of theMatrixD2 class.

Attributes

Supertypes: class Object

trait Matchable

class Any
Self type: MatrixD2Example.type

The MatrixDExample object provides example instances of theMatrixD class.

Attributes

Supertypes: class Object

trait Matchable

class Any
Self type: MatrixDExample.type

The MatrixDOps object provides extension methods to support scalar op matrix operations, so that one can write 2.0 + x as well as x + 2.0.

Attributes

Supertypes: class Object

trait Matchable

class Any
Self type: MatrixDOps.type

The MatrixI object provides factory methods for classMatrixDwith integer elements. Low cost approach not requiring aMatrixI` class.

Attributes

Supertypes: class Object

trait Matchable

class Any
Self type: MatrixI.type

The MinMaxForm class applies the MIN-MAX-transformation to move the data into the range [l .. u] (subtract min, multiply by bounds lu range over min-max range and add lower bound). Like ''MinMaxScaler'' in sk-learn.

Value parameters

centered: whether the normalization should CENTER the data (defaults to true)
x_: the input vector or matrix to be transformed (needed to get w)

Attributes

See also: www.geeksforgeeks.org/machine-learning/standardscaler-minmaxscaler-and-robustscaler-techniques-ml/ x -> l + (x-min)(u-l)/(max-min)
Supertypes: trait Transform

class Object

trait Matchable

class Any

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait PartiallyOrdered[MyPartialOrder]

class Object

trait Matchable

class Any
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Attributes

Supertypes: class ExpForm

trait Transform

class Object

trait Matchable

class Any

The NormForm class applies the Z-transformation/normalization/standardization (subtract mean b(0) and divide by standard deviation b(1)). Like ''StandardScalar'' in sk-learn.

Value parameters

robust: whether to add a small value (ε) to the standard deviation to avoid DBZ when a whole column has zero stdev (σ) it should be removed in pre-processing
x_: the input vector or matrix to be transformed (needed to get w)

Attributes

See also: www.geeksforgeeks.org/machine-learning/standardscaler-minmaxscaler-and-robustscaler-techniques-ml/ x -> (x - μ)/σ robust version: (x - μ)/(σ + ε) or (x - μ)/√(σ² + ε)
Supertypes: trait Transform

class Object

trait Matchable

class Any

Attributes

Supertypes: class Any
Known subtypes: class MyPartialOrder

class VectorC

class VectorD

class VectorI

class VectorL

class VectorS

class VectorT
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The Pivoting trait is used when row or column pivoting of a matrix is needed.

Attributes

Supertypes: class Object

trait Matchable

class Any
Known subtypes: class Fac_QR_RR

Zoom functionality has two options: (1) mouse wheel controls the amount of zooming (in/out); (2) mouse dragging repositions the objects in the panel (drawing canvas).

The `Plot` class takes x and y vectors of data values and plots the (x, y) data points. Optionally, a z vector may be plotted with y. Note, axes are determined by the x and y vectors only. For more vertical vectors use `PlotM`.

Zoom functionality has two options: (1) mouse wheel controls the amount of zooming (in/out); (2) mouse dragging repositions the objects in the panel (drawing canvas).

Value parameters

lines: flag for generating a line plot
title: the title of the plot
x: the x vector of data values (horizontal), use null to use y's index
y: the y vector of data values (primary vertical, black)
z: the z vector of data values (secondary vertical, red) to compare with y

Attributes

See also: ZoomablePanel
Companion: object
Supertypes: class VizFrame

class Frame

class JFrame

trait RootPaneContainer

trait WindowConstants

class Frame

class Window

trait Accessible

class Container

class Component

trait Serializable

trait MenuContainer

trait ImageObserver

class Object

trait Matchable

class Any
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The Plot companion object provides factory methods for creating plots.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: Plot.type

Zoom functionality has two options: (1) mouse wheel controls the amount of zooming (in/out); (2) mouse dragging repositions the objects in the panel (drawing canvas).

The `PlotC` class takes a function f and displays color-coded values for z = f(x, y) over a two dimensional grid defined the lower lb and upper ub bounds. An optional path is included that can be used to show, for example, the search path taken by an optimizer (e.g., a Conjugate Gradient NLP solver).

Zoom functionality has two options: (1) mouse wheel controls the amount of zooming (in/out); (2) mouse dragging repositions the objects in the panel (drawing canvas).

Value parameters

deltaF: estimate of the range of possible functional values (if < 0, will be computed)
f: the function whose color-coded contour plot is sought
lb: the lower bounds on the plotting domain
lbF: the lower bound on the functional value
opt: the optimal value if known (defaults to null)
path: the points on a path (e.g., a search path)
title: the title of the plot
ub: the upper bounds on the plotting domain

Attributes

See also: ZoomablePanel
Supertypes: class VizFrame

class Frame

class JFrame

trait RootPaneContainer

trait WindowConstants

class Frame

class Window

trait Accessible

class Container

class Component

trait Serializable

trait MenuContainer

trait ImageObserver

class Object

trait Matchable

class Any
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The PlotM companion object provides a builder method for plotting several y vectors versus an x vector.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: PlotM.type

Zoom functionality has two options: (1) mouse wheel controls the amount of zooming (in/out); (2) mouse dragging repositions the objects in the panel (drawing canvas).

The `PlotM` class takes an x vector and a y matrix of data values and plots the (x, y_i) data points for each row y_i of the matrix.

Zoom functionality has two options: (1) mouse wheel controls the amount of zooming (in/out); (2) mouse dragging repositions the objects in the panel (drawing canvas).

Value parameters

label: the label/legend/key for each curve in the plot
lines: flag for generating a line plot
title: the title of the plot
x_: the x vector of data values (horizontal)
y_: the y matrix of data values where y(i) is the i-th vector (vertical)

Attributes

See also: ZoomablePanel
Companion: object
Supertypes: class VizFrame

class Frame

class JFrame

trait RootPaneContainer

trait WindowConstants

class Frame

class Window

trait Accessible

class Container

class Component

trait Serializable

trait MenuContainer

trait ImageObserver

class Object

trait Matchable

class Any
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The PowForm class applies a shifted s = b_(0) and scaled p = b_(1) POWER-transformation. For shift s and power p,

 x -> (x + s)^p

Value parameters

w: the transform argument vector (w -> b)

Attributes

Supertypes: trait Transform

class Object

trait Matchable

class Any
Known subtypes: class RecipForm

class RootForm

The PowRForm class applies a shifted s = b_(0) and scaled q = b_(1) POWER-transformation. For shift s and power q where q is converted to r a nearby rational number with an odd denominator

 x -> (x + s)↑q

Value parameters

w: the transform argument vector (w -> b)

Attributes

Supertypes: trait Transform

class Object

trait Matchable

class Any

The Probability object provides methods for operating on univariate and bivariate probability distributions of discrete random variables X and Y. A probability distribution is specified by its probability mass functions (pmf) stored either as a "probability vector" for a univariate distribution or a "probability matrix" for a bivariate distribution. joint probability matrix: pxy(i, j) = P(X = x_i, Y = y_j) marginal probability vector: px(i) = P(X = x_i) conditional probability matrix: px_y(i, j) = P(X = x_i|Y = y_j) In addition to computing joint, marginal and conditional probabilities, methods for computing entropy and mutual information are also provided. Entropy provides a measure of disorder or randomness. If there is little randomness, entropy will close to 0, while when randomness is high, entropy will be close to, e.g., log2 (px.dim). Mutual information provides a robust measure of dependency between random variables (contrast with correlation).

Attributes

Supertypes: class Object

trait Matchable

class Any
Self type: Probability.type

The RTensor4D class is an implementation for 3-dimensional ragged tensors. The tensor may only be ragged in the middle dimension (dim2) and whose sizes may only be dependent of the first index, e.g., i in (i, j, k). The names of the dimensions corresponds to MATLAB (row, column, sheet).

Value parameters

dim: size of the 1st level/dimension (row) of the tensor (height)
dim2: variable size of the 2nd level/dimension (column) of the tensor (width)
dim3: variable size of the 3rd level/dimension (sheet) of the tensor (depth)
dim4: size of the 4th level/dimension (channel) of the tensor (spectra)
v: the 4D array for holding the tensor elements

Attributes

Companion: object
Supertypes: trait Serializable

class Object

trait Matchable

class Any

The RTensor4D companion object provides factory methods for the RTensor4D class.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: RTensor4D.type

The RTensorD companion object provides factory methods for the RTensorD class.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: RTensorD.type

The RTensorD class is an implementation for 3-dimensional ragged tensors. The tensor may only be ragged in the middle dimension (dim2) and whose sizes may only be dependent of the first index, e.g., i in (i, j, k). The names of the dimensions corresponds to MATLAB (row, column, sheet).

Value parameters

dim: size of the 1st level/dimension (row) of the tensor (height)
dim2: variable size of the 2nd level/dimension (column) of the tensor (width)
dim3: size of the 3rd level/dimension (sheet) of the tensor (depth)
v: the 3D array for holding the tensor elements

Attributes

Companion: object
Supertypes: trait Serializable

class Object

trait Matchable

class Any

Attributes

Supertypes: class PowForm

trait Transform

class Object

trait Matchable

class Any

Attributes

Supertypes: class PowForm

trait Transform

class Object

trait Matchable

class Any

The `Scala2LaTeX object provides methods for converting ScalaTion Equations into LaTeX.

Attributes

Supertypes: class Object

trait Matchable

class Any
Self type: Scala2LaTeX.type

The SinForm class applies a shifted b_(0) and scaled b_(1) SINE-transformation. For phase shift b_(0) = φ = s and frequency b_(1) = f with scaling 2πf,

x -> sin (2πfx + φ)

Value parameters

w: the transform argument vector (w -> b)

Attributes

Supertypes: trait Transform

class Object

trait Matchable

class Any

The StatBootstrap class is used to create bootstrap samples and compute statistics based on these pseudo-samples. Given a sample y from a population (typically unknown), create several pseudo-samples (bootstrap samples). This allows confidence intervals to be created with requiring distribution assumptions, such as the data are Normally distributed.

Value parameters

stream: the random number stream to use
unbiased: whether the estimators are restricted to be unbiased
y: the original sample of data

Attributes

Supertypes: class Statistic

class Object

trait Matchable

class Any

The StatTable class display statistical results in a frame's table.

Value parameters

_title: the title of the frame
stats: the statistics to be displayed in the table.

Attributes

Supertypes: class Frame

class JFrame

trait RootPaneContainer

trait WindowConstants

class Frame

class Window

trait Accessible

class Container

class Component

trait Serializable

trait MenuContainer

trait ImageObserver

class Object

trait Matchable

class Any
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The Statistic companion object provides additional values and functions.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: Statistic.type

The Statistic class is used to collect values and compute sample statistics on them (e.g., waiting time). Contrast with TimeStatistic defined in TimeStatistic.scala.

Value parameters

name: the name for this statistic (e.g., 'waitingTime')
unbiased: whether the estimators are restricted to be unbiased set to false for population (or MLE) statistics

Attributes

Companion: object
Supertypes: class Object

trait Matchable

class Any
Known subtypes: class StatBootstrap

class TimeStatistic

The Stats case class is used to hold basic statistical information: mean, variance, auto-covariance, and auto-correlation. Note gamma0 (biased) does not equal the sample variance (unbiased)

Value parameters

adjusted: whether to adjust to account for the number of elements in the sum Σ (or use dim-1)
lags_: the maximum number of lags
y: the response vector (time-series data) for the training/full dataset

Attributes

See also: VectorD.acov
Supertypes: trait Serializable

trait Product

trait Equals

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: class Object

trait Matchable

class Any

The SymmetricQRstep object performs a symmetric QR step with a Wilkinson shift.

Attributes

See also: Algorithm 8.3.2 in Matrix Computations.

http://people.inf.ethz.ch/arbenz/ewp/Lnotes/chapter3.pdf (Algorithm 3.6)
Supertypes: class Object

trait Matchable

class Any
Self type: SymmetricQRstep.type

The TensorD class is a simple implementation for 3-dimensional tensors. The names of the dimensions corresponds to MATLAB (row, column, sheet).

Value parameters

dim: size of the 1st level/dimension (row) of the tensor (height)
dim2: size of the 2nd level/dimension (column) of the tensor (width)
dim3: size of the 3rd level/dimension (sheet) of the tensor (depth)
v: the 3D array for holding the tensor elements

Attributes

See also: www.kolda.net/publication/TensorReview.pdf for details on layout

RTensorD for non-rectangular (ragged) tensors.
Companion: object
Supertypes: trait Serializable

class Object

trait Matchable

class Any

The TensorD companion object provides factory methods for the TensorD class.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: TensorD.type

The TimeStatistic companion object provides additional functions.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: TimeStatistic.type

The TimeStatistic class is used to collect values and compute time-persistent statistics on them (e.g., Number in Queue).

Value parameters

_lastTime: the time of last observation
_startTime: the time observation began
name: the name for this statistic (e.g., 'numberInQueue' or 'tellerQ')

Attributes

See also: staff.unak.is/andy/Year%203%20Simulation/Laboratories/v4manual/internal.htm
Companion: object
Supertypes: class Statistic

class Object

trait Matchable

class Any

The TnT_Split object provides methods for splitting datasets into TESTING-sets (.) and TRAINING-sets (-). There are three options on how to split the full dataset: (1) select at RANDOM n_test indices for the test-set (@see tnT_SplitTest) | -.--.---.--.----.--.---.-----.| (2) select the FIRSTn_testindices for the test-set (@see tnT_SplitTest2) | test-set | training-set | (3) select the LAST n_test indices for the test-set (@see tnT_SplitTest3`) | training-set | test-set |

Attributes

Supertypes: class Object

trait Matchable

class Any
Self type: TnT_Split.type

The Transform object defines hyper-parameters for Transforms.

Attributes

Companion: trait
Supertypes: class Object

trait Matchable

class Any
Self type: Transform.type

The Transform trait supports the use of transformation functions and makes it is easy to take the inverse transform. When a transformation uses arguments, they are remembered for use by the inverse transformation.

Value parameters

centered: whether the normalization should CENTER the data (defaults to true)
w: the transform argument vector or matrix (in subclasses pass x_ for input or w for weights)

Attributes

See also: Rat, pow_ in CommonFunctions.scala, and ↑ in ValueType.scala
Companion: object
Supertypes: class Object

trait Matchable

class Any
Known subtypes: class BoxcoxForm

class CenterForm

class CosForm

class ExpForm

class NExpForm

class Log1pForm

class LogForm

class MinMaxForm

class NormForm

class PowForm

class RecipForm

class RootForm

class PowRForm

class SinForm
Show all

The TransformS class holds a transform specification that contains default values for the parameters w and their bounds, e.g., w in x -> f(w_0 + w_1 * x)

Value parameters

l: the vector containing the lower bounds of shift and scale parameters a* @param u the vector containing the upper bounds of shift and scale parameters
w: the vector of two nonlinear parameters: shift w_0 and scale w_1 parameters

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

class Object

trait Matchable

class Any
Show all

The TranformT enum defines the types of transforms.

Value parameters

form: a function to instantiate a Transform
name: the name of the transform
wlu: the default vectors of parameters (w) and their lower (l) and upper bounds (u)

Attributes

Supertypes: trait Enum

trait Serializable

trait Product

trait Equals

class Object

trait Matchable

class Any
Show all

The VMatrixD class maintains virtual-matrices where the first dim2 columns are stored, while the last dim2v are virtual, i.e., calculated as needed. Virtual-matrices offer memory reduction for Quadratic, Cubic, and Symbolic Regression, where augmented columns can be calculated rather than stored.

Value parameters

dim2_: the stored second (column) dimension of the matrix
dim2v: the virtual second (column) dimension of the matrix
dim_: the first (row) dimension of the matrix
formulas: the formulas used to calculate the last dim2v columns Array (1, 1) => x1 * x1; Array (1, 2) => x1 * x2
v_: the 2D array used to store matrix the first dim2_ columns

Attributes

See also: scalation.modeling.SymbolicRegression
Companion: object
Supertypes: class MatrixD

class Object

trait Matchable

class Any

The `VMatrixD companion object provides factory methods.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: VMatrixD.type

The VectorC class stores and operates on Numeric Vectors of base type Complex.

Value parameters

dim: the dimension/size of the vector
v: the 1D array used to store vector elements

Attributes

Companion: object
Supertypes: trait DefaultSerializable

trait Serializable

trait PartiallyOrdered[VectorC]

trait IndexedSeq[Complex]

trait IndexedSeqOps[Complex, IndexedSeq, IndexedSeq[Complex]]

trait IndexedSeq[Complex]

trait IndexedSeqOps[Complex, IndexedSeq, IndexedSeq[Complex]]

trait Seq[Complex]

trait SeqOps[Complex, IndexedSeq, IndexedSeq[Complex]]

trait Cloneable[IndexedSeq[Complex]]

trait Cloneable

trait Seq[Complex]

trait Pure

trait Equals

trait SeqOps[Complex, IndexedSeq, IndexedSeq[Complex]]

trait PartialFunction[Int, Complex]

trait Int => Complex

trait Iterable[Complex]

trait Iterable[Complex]

trait IterableFactoryDefaults[Complex, IndexedSeq]

trait IterableOps[Complex, IndexedSeq, IndexedSeq[Complex]]

trait IterableOnceOps[Complex, IndexedSeq, IndexedSeq[Complex]]

trait IterableOnce[Complex]

class Object

trait Matchable

class Any
Show all

The VectorC object is the companion object for the VectorC class.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: VectorC.type

The VectorD object is the companion object for the VectorD class.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: VectorD.type

The VectorD class stores and operates on Numeric Vectors of base type Double.

Value parameters

dim: the dimension/size of the vector
v: the 1D array used to store vector elements

Attributes

Companion: object
Supertypes: trait DefaultSerializable

trait Serializable

trait PartiallyOrdered[VectorD]

trait IndexedSeq[Double]

trait IndexedSeqOps[Double, IndexedSeq, IndexedSeq[Double]]

trait IndexedSeq[Double]

trait IndexedSeqOps[Double, IndexedSeq, IndexedSeq[Double]]

trait Seq[Double]

trait SeqOps[Double, IndexedSeq, IndexedSeq[Double]]

trait Cloneable[IndexedSeq[Double]]

trait Cloneable

trait Seq[Double]

trait Pure

trait Equals

trait SeqOps[Double, IndexedSeq, IndexedSeq[Double]]

trait PartialFunction[Int, Double]

trait Int => Double

trait Iterable[Double]

trait Iterable[Double]

trait IterableFactoryDefaults[Double, IndexedSeq]

trait IterableOps[Double, IndexedSeq, IndexedSeq[Double]]

trait IterableOnceOps[Double, IndexedSeq, IndexedSeq[Double]]

trait IterableOnce[Double]

class Object

trait Matchable

class Any
Show all

The VectorDOps object provides extension methods to support scalar op vector operations, so that one can write 2.0 + x as well as x + 2.0.

Attributes

Supertypes: class Object

trait Matchable

class Any
Self type: VectorDOps.type

The VectorI class stores and operates on Numeric Vectors of base type Int.

Value parameters

dim: the dimension/size of the vector
v: the 1D array used to store vector elements

Attributes

Companion: object
Supertypes: trait DefaultSerializable

trait Serializable

trait PartiallyOrdered[VectorI]

trait IndexedSeq[Int]

trait IndexedSeqOps[Int, IndexedSeq, IndexedSeq[Int]]

trait IndexedSeq[Int]

trait IndexedSeqOps[Int, IndexedSeq, IndexedSeq[Int]]

trait Seq[Int]

trait SeqOps[Int, IndexedSeq, IndexedSeq[Int]]

trait Cloneable[IndexedSeq[Int]]

trait Cloneable

trait Seq[Int]

trait Pure

trait Equals

trait SeqOps[Int, IndexedSeq, IndexedSeq[Int]]

trait PartialFunction[Int, Int]

trait Int => Int

trait Iterable[Int]

trait Iterable[Int]

trait IterableFactoryDefaults[Int, IndexedSeq]

trait IterableOps[Int, IndexedSeq, IndexedSeq[Int]]

trait IterableOnceOps[Int, IndexedSeq, IndexedSeq[Int]]

trait IterableOnce[Int]

class Object

trait Matchable

class Any
Show all

The VectorI object is the companion object for the VectorI class.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: VectorI.type

The VectorL class stores and operates on Numeric Vectors of base type Long.

Value parameters

dim: the dimension/size of the vector
v: the 1D array used to store vector elements

Attributes

Companion: object
Supertypes: trait DefaultSerializable

trait Serializable

trait PartiallyOrdered[VectorL]

trait IndexedSeq[Long]

trait IndexedSeqOps[Long, IndexedSeq, IndexedSeq[Long]]

trait IndexedSeq[Long]

trait IndexedSeqOps[Long, IndexedSeq, IndexedSeq[Long]]

trait Seq[Long]

trait SeqOps[Long, IndexedSeq, IndexedSeq[Long]]

trait Cloneable[IndexedSeq[Long]]

trait Cloneable

trait Seq[Long]

trait Pure

trait Equals

trait SeqOps[Long, IndexedSeq, IndexedSeq[Long]]

trait PartialFunction[Int, Long]

trait Int => Long

trait Iterable[Long]

trait Iterable[Long]

trait IterableFactoryDefaults[Long, IndexedSeq]

trait IterableOps[Long, IndexedSeq, IndexedSeq[Long]]

trait IterableOnceOps[Long, IndexedSeq, IndexedSeq[Long]]

trait IterableOnce[Long]

class Object

trait Matchable

class Any
Show all

The VectorL object is the companion object for the VectorL class.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: VectorL.type

The VectorS class stores and operates on Numeric Vectors of base type String.

Value parameters

dim: the dimension/size of the vector
v: the 1D array used to store vector elements

Attributes

Companion: object
Supertypes: trait DefaultSerializable

trait Serializable

trait PartiallyOrdered[VectorS]

trait IndexedSeq[String]

trait IndexedSeqOps[String, IndexedSeq, IndexedSeq[String]]

trait IndexedSeq[String]

trait IndexedSeqOps[String, IndexedSeq, IndexedSeq[String]]

trait Seq[String]

trait SeqOps[String, IndexedSeq, IndexedSeq[String]]

trait Cloneable[IndexedSeq[String]]

trait Cloneable

trait Seq[String]

trait Pure

trait Equals

trait SeqOps[String, IndexedSeq, IndexedSeq[String]]

trait PartialFunction[Int, String]

trait Int => String

trait Iterable[String]

trait Iterable[String]

trait IterableFactoryDefaults[String, IndexedSeq]

trait IterableOps[String, IndexedSeq, IndexedSeq[String]]

trait IterableOnceOps[String, IndexedSeq, IndexedSeq[String]]

trait IterableOnce[String]

class Object

trait Matchable

class Any
Show all

The VectorS object is the companion object for the VectorS class.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: VectorS.type

The VectorT object is the companion object for the VectorT class.

Attributes

Companion: class
Supertypes: class Object

trait Matchable

class Any
Self type: VectorT.type

The VectorT class stores and operates on Numeric Vectors of base type TimeNum.

Value parameters

dim: the dimension/size of the vector
v: the 1D array used to store vector elements

Attributes

Companion: object
Supertypes: trait DefaultSerializable

trait Serializable

trait PartiallyOrdered[VectorT]

trait IndexedSeq[TimeNum]

trait IndexedSeqOps[TimeNum, IndexedSeq, IndexedSeq[TimeNum]]

trait IndexedSeq[TimeNum]

trait IndexedSeqOps[TimeNum, IndexedSeq, IndexedSeq[TimeNum]]

trait Seq[TimeNum]

trait SeqOps[TimeNum, IndexedSeq, IndexedSeq[TimeNum]]

trait Cloneable[IndexedSeq[TimeNum]]

trait Cloneable

trait Seq[TimeNum]

trait Pure

trait Equals

trait SeqOps[TimeNum, IndexedSeq, IndexedSeq[TimeNum]]

trait PartialFunction[Int, TimeNum]

trait Int => TimeNum

trait Iterable[TimeNum]

trait Iterable[TimeNum]

trait IterableFactoryDefaults[TimeNum, IndexedSeq]

trait IterableOps[TimeNum, IndexedSeq, IndexedSeq[TimeNum]]

trait IterableOnceOps[TimeNum, IndexedSeq, IndexedSeq[TimeNum]]

trait IterableOnce[TimeNum]

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: class Object

trait Matchable

class Any

Attributes

Supertypes: class Object

trait Matchable

class Any

Attributes

Supertypes: class Object

trait Matchable

class Any

Attributes

Supertypes: class Object

trait Matchable

class Any

Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

Supertypes: class Object

trait Matchable

class Any

Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

Supertypes: class Object

trait Matchable

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Attributes

Supertypes: class Object

trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

Supertypes: class Object

trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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trait Matchable

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Attributes

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trait Matchable

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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Attributes

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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trait Matchable

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Attributes

Supertypes: class Object

trait Matchable

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Attributes

Supertypes: class Object

trait Matchable

class Any

Types

Factor type contains 'u, s, v' which are the left orthogonal matrix, the diagonal matrix/vector containing singular values and the right orthogonal matrix.

Attributes

Top-level type definition for functions mapping from MatrixD:

Attributes

Top-level type definition for functions mapping:

Attributes

Top-level type definition for functions mapping from VectorD:

Attributes

Value members

Concrete methods

The bidiagonalTest main function is used to test the Bidiagonal class. bidiagonalization answer = [ (21.8, -.613), (12.8, 2.24, 0.) ]

Attributes

See also: books.google.com/books?isbn=0801854148 (p. 252)

runMain scalation.mathstat.bidiagonalTest

The combinatoricsTest main function tests the methods in the Combinatorics object.

runMain scalation.mathstat.combinatoricsTest

Attributes

The combinatoricsTest2 main function tests the Gamma and Factorial functions in the Combinatorics object.

runMain scalation.mathstat.combinatoricsTest2

Attributes

Return the complement of index positions idx, e.g., comple (Array (1, 3), 5) = Array (0, 2, 4). param idx the index positions to be complemented param dim the exclusive upper bound

Attributes

The correlogramTest main function tests the Correlogram trait on a simple dataset.

runMain scalation.mathstat.correlogramTest

Attributes

Diagnose matrix x looking for high correlation, high condition number, lower than expected rank, zero variance columns (there should only be one).

Value parameters

x: the data matrix to diagnose

Attributes

Duplicate a fixed second.third dimension d into a vector with d repeated.

Value parameters

d: fixed size of the 2nd/3rd level/dimension (column/sheet) of the tensor
dim: size of the 1st level/dimension (row) of the tensor (height)

Attributes

The EigenTest main function is used to test the all the classes used in computing Eigenvalues and Eigenvectors for the non-symmetric/general case.

runMain scalation.mathstat.EigenTest

Attributes

The fac_CholeskyTest main function tests the Fac_Cholesky class. It compare the Cholesky and LU Factorization algorithms.

Attributes

See also: ece.uwaterloo.ca/~dwharder/NumericalAnalysis/04LinearAlgebra/cholesky

runMain scalation.mathstat.fac_CholeskyTest

The fac_CholeskyTest2 main function tests the Fac_Cholesky class. It compares the three Cholesky Factorization algorithms.

runMain scalation.mathstat.fac_CholeskyTest2

Attributes

The fac_CholeskyTest3 main function tests the Fac_Cholesky class. It compares the three Cholesky Factorization algorithms on challenging problems.

Attributes

See also: apps.dtic.mil/sti/pdfs/ADA205174.pdf

www.applied-mathematics.net/identification/papersLARS/_cholesky_shnabell.pdf

runMain scalation.mathstat.fac_CholeskyTest3

The fac_InverseTest main function is used to test the Fac_Inverse class.

runMain scalation.mathstat.fac_InverseTest

Attributes

The fac_LQTest main function is used to test the Fac_LQ class.

runMain scalation.mathstat.fac_LQTest

Attributes

The fac_LUTest main function is used to test the Fac_LU class. Test a Square Matrix.

runMain scalation.mathstat.fac_LUTest

Attributes

The fac_LUTest2 main function is used to test the Fac_LU class. Test a Rectangular Matrix.

runMain scalation.mathstat.fac_LUTest2

Attributes

The fac_LUTest3 main function is used to test the Fac_LU class.

runMain scalation.mathstat.fac_LUTest3

Attributes

The fac_QRTest main function is used to test the Fac_QR classes.

Attributes

See also: www.ee.ucla.edu/~vandenbe/103/lectures/qr.pdf

www.math.usm.edu/lambers/mat610/sum10/lecture9.pdf FIX: the nullspaceV function needs to be fixed.

runMain scalation.mathstat.fac_QRTest

The fac_QRTest2 main function is used to test the correctness of the solve method in the Fac_QR class as it would be used in Regression.

runMain scalation.mathstat.fac_QRTest2

Attributes

The fac_QR_RRTest main function is used to test the Fac_QR_RR classes.

Attributes

See also: www.ee.ucla.edu/~vandenbe/103/lectures/qr.pdf

www.math.usm.edu/lambers/mat610/sum10/lecture9.pdf

runMain scalation.mathstat.fac_QR_RRTest

The fac_SVDTest main function is used to test the Fac_SVD class.

Attributes

See also: www.ling.ohio-state.edu/~kbaker/pubs/Singular_Value_Decomposition_Tutorial.pdf

runMain scalation.mathstat.fac_SVDTest

The fac_SVDTest2 main function is used to test the Fac_SVD class.

runMain scalation.mathstat.fac_SVDTest2

Attributes

The fac_SVDTest3 main function is used to test the Fac_SVD class.

runMain scalation.mathstat.fac_SVDTest3

Attributes

The fac_SVDTest4 main function is used to test the Fac_SVD class. Test case a8 currently fails as ScalaTion does not consider 9.18964e-09 to be approximately zero.

runMain scalation.mathstat.fac_SVDTest4

Attributes

Sample a function at n+1 equally spaced points in the domain and return their functional values in a vector. Ex: sample f(x) on x in [0, 10] at 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Value parameters

ab: the interval of the domain [a, b]
f: the function to be sampled
n: the number of points to be evaluated

Attributes

The heatMapTest main function is used to test the HeatMap class. It tests creating a heat-map for a matrix

runMain scalation.mathstat.heatMapTest

Attributes

The heatMapTest2 main function is used to test the HeatMap class. It tests creating a heat-map for a CORRELATION matrix using a COVID-19 dataset.

runMain scalation.mathstat.heatMapTest2

Attributes

The heatMapTest3 main function is used to test the HeatMap class. It tests creating a heat-map for a LAGGED CROSS CORRELATION matrix for name(0) using a COVID-19 dataset.

runMain scalation.mathstat.heatMapTest3

Attributes

The histogramTest main function is used to test the Histogram class. As 'k' increases, the sum of Uniform approaches Normal.

runMain scalation.mathstat.histogramTest

Attributes

The HouseholderTest main function is used to test Householder object.

Attributes

See also: www.math.siu.edu/matlab/tutorial4.pdf

runMain scalation.mathstat.householderTest

The inverseTest main function checks the correctness of inverse matrices produced by several matrix factorization algorithms.

runMain scalation.mathstat.inverseTest

Attributes

Matricize a vector function (V2V) by applying it to each row of a matrix. MatrixD (for i <- x.indices yield f(x(i)))

Value parameters

f: the vector function to matricize
x: the matrix to apply the function to

Attributes

The matrixCalc0 main function is used to test the MatrixCalc class. It performs the RW and AR(1) time series model calculations.

runMain scalation.mathstat.matrixCalc0

Attributes

The matrixCalc2 main function read a matrix from a CSV file and perform calculations, e.g. grade calculations.

runMain scalation.mathstat.matrixCalc2

Attributes

The matrixCals3 main function allows for Custom calculations.

runMain scalation.mathstat.matrixCalc3

Attributes

The matrixD2Test main function tests the MatrixD2 class. Compares the performance of matrix addition implementations

runMain scalation.mathstat.matrixD2Test

Attributes

The matrixD2Test2 main function tests the MatrixD2 class. Compares the performance of matrix multiplication implementations.

runMain scalation.mathstat.matrixD2Test2

Attributes

The matrixDTest main function tests the MatrixD class. Compares the performance of matrix addition implementations

runMain scalation.mathstat.matrixDTest

Attributes

The matrixDTest2 main function tests the MatrixD class. Compares the performance of matrix multiplication implementations.

runMain scalation.mathstat.matrixDTest2

Attributes

The matrixDTest3 main function tests the MatrixD class. Test the back substitution (/~) operator for solving for x in u * x = y. It also computes an outer product

runMain scalation.mathstat.matrixDTest3

Attributes

The matrixDTest4 main function tests the MatrixD class. Test the split methods: split and split_ as well as shiftDiag and unshiftDiag

runMain scalation.mathstat.matrixDTest4

Attributes

The matrixDTest5 main function tests the MatrixD class. Test the covariance and correlation.

runMain scalation.mathstat.matrixDTest5

Attributes

The matrixDTest6 main function tests the MatrixD class. Test the insert method.

runMain scalation.mathstat.matrixDTest6

Attributes

The matrixDTest7 main function tests the MatrixD class. Test the convolution operators.

runMain scalation.mathstat.matrixDTest7

Attributes

Matrixize a vector function (V2V) to create a matrix function (M2M).

Value parameters

f: the vector function to matrixize

Attributes

The pivotingTest main function is used to test the Pivoting trait.

runMain scalation.mathstat.pivotingTest

Attributes

The plotCTest main function is used to test the PlotC class. For additional examples,

Attributes

See also: RidgeRegression, LassoRegression, BridgeRegression in modeling.

scalation.scala2d.writeImage

runMain scalation.mathstat.plotCTest

The plotMTest main functionb is used to test the PlotM class.

runMain scalation.mathstat.plotMTest

Attributes

The plotMTest2 main function is used to test the PlotM class. This version also plots lines connecting the points. ^ @see scalation.scala2d.writeImage

runMain scalation.mathstat.plotMTest2

Attributes

The plotTest main function is used to test the Plot class.

Attributes

See also: scalation.scala2d.writeImage

runMain scalation.mathstat.plotTest

The probabilityTest main function is used to test the Probability object.

runMain scalation.mathstat.probabilityTest

Attributes

The probabilityTest2 main function provides upper bounds for entropy and nentropy and plots entropy.

runMain scalation.mathstat.probabilityTest2

Attributes

The probabilityTest3 main function is used to test the Probability class. Plot probability and log-probability entropy and normalized entropy for binomial distributions.

runMain scalation.mathstat.probabilityTest3

Attributes

The probabilityTest4 main function is used to test the Probability class. It computes entropy, relative entropy and cross entropy and verifies that cross entropy == entropy + relative entropy

Attributes

See also: arxiv.org/pdf/0808.4111.pdf

runMain scalation.mathstat.probabilityTest4

The probabilityTest5 main function is used to test the Probability class. It computes joint, marginal and conditional probabilities as well as measures of independence.

Attributes

See also: ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and -statistics-spring-2014/readings/MIT18_05S14_Reading7a.pdf

runMain scalation.mathstat.probabilityTest5

The probabilityTest6 main function is used to test the Probability class. It computes joint, marginal and conditional probabilities.

runMain scalation.mathstat.probabilityTest6

Attributes

The rTensor4DTest main function is used to test the RTensor4D class.

runMain scalation.mathstat.rTensor4DTest

Attributes

The rTensorDTest main function is used to test the RTensorD class.

runMain scalation.mathstat.rTensorDTest

Attributes

The scala2LaTeXTest main method tests the Scala2LaTeX object by making a LaTeX equation from a ScalaTion model specification.

runMain scalation.mathstat.scala2LaTeXTest

Attributes

The scala2LaTeXTest2 main method tests the Scala2LaTeX object by making a LaTeX table from a matrix.

Attributes

See also: scalation.modeling.Regression

runMain scalation.mathstat.scala2LaTeXTest2

The scala2LaTeXTest3 main method tests the Scala2LaTeX object by making a LaTeX table from matrix of QoF metric vs. model. This test does In-Sample testing.

Attributes

See also: scalation.modeling.Regression

runMain scalation.mathstat.scala2LaTeXTest3

Return the sizes of all the second level arrays in u.

Value parameters

u: the 3D array

Attributes

Return the sizes of all the third level arrays in u.

Value parameters

u: the 4D array

Attributes

Return the sizes of all the third level arrays in u.

Value parameters

u: the 4D array

Attributes

The statBootstrapTest main function is used to test the StatBootstrap class. Test population, sample, and bootstrap statistics.

runMain scalation.mathstat.statBootstrapTest

Attributes

The statTableTest main function is used to test the StatTable class.

runMain scalation.mathstat.statTableTest

Attributes

The statisticTest main function is used to test the Statistic class. Test the collection of sample statistics.

runMain scalation.mathstat.statisticTest

Attributes

The statisticTest2 main function is used to test the Statistic class. Show critical values for z- and t-distributions.

Attributes

See also: www.brockport.edu/live/files/6864-standardnormaldistributiontablepdf

www.stat.purdue.edu/~lfindsen/stat503/t-Dist.pdf

runMain scalation.mathstat.statisticTest

The stats4TSTest main function tests the Stats4TS class on two simple datasets.

runMain scalation.mathstat.stats4TSTest

Attributes

Return the critical value for the t-distribution with a confidence level of p_ and error degrees of freedom of df. Uses inverse CDF (iCDF) Quantile.studentTInv.

Value parameters

df: the error degrees of freedom
p_: the confidence level (two tails)

Attributes

Compute the confidence interval half-width (ihw) for the given confidence level using the t-distribution.

Value parameters

n: the length of the vector/sample
p_: the confidence level
sig: the standard deviation of the vector/sample

Attributes

Test (2-tail) to see if two means (one given and one estimated) are significantly different, using the t-distribution.

Value parameters

mu: the estimated mean of the vector/sample
mu0: the given mean
n: the length of the vector/sample
p_: the confidence level
show: whether to show details of the test
sig: the standard deviation of the vector/sample

Attributes

Compute the product of the critical value from the t-distribution and the standard deviation of the vector.

Value parameters

df: the error degrees of freedom
p_: the confidence level (two tails)
sig: the standard deviation of the vector/sample

Attributes

The tensorDTest main function is used to test the TensorD class.

runMain scalation.mathstat.tensorDTest

Attributes

The tensorDTest2 main function is used to test the TensorD class. It tests pulling matrices and vectors from the tensor.

runMain scalation.mathstat.tensorDTest2

Attributes

The tensorDTest3 main function is used to test the TensorD class. It tests the use of tensors and matrices for convolutional operation needed in Convolutional Nets.

runMain scalation.mathstat.tensorDTest3

Attributes

The tensorDTest4 main function is used to test the TensorD class. It tests all element-wise operations with TensorD, MatrixD, VectorD, and scalars that can actually broadcast properly.

runMain scalation.mathstat.tensorDTest4

Attributes

The tensorDTest5 main function is used to test the TensorD class. It tests other operations with TensorD, MatrixD, and VectorD.

runMain scalation.mathstat.tensorDTest5

Attributes

The tensorDTest6 main function is used to test the TensorD class. It tests operations with with and without broadcasting.

runMain scalation.mathstat.tensorDTest6

Attributes

The tensorDTest7 main function is used to test the TensorD class. It tests permuting tensors.

runMain scalation.mathstat.tensorDTest7

Attributes

The tensorDTest8 main function is used to test the TensorD class. It tests concatenating tensors.

runMain scalation.mathstat.tensorDTest8

Attributes

Tensorize a vector function (V2V) by applying it to each (row, column) of a tensor.

Value parameters

f: the vector function to tensorize
x: the tensor to apply the function to

Attributes

The timeStatisticTest main function is used to test the TimeStatistic class.

runMain scalation.mathstat.timeStatisticTest

Attributes

The tnT_SplitTest main function tests the TnT_Split object using the Texas Temperatures dataset. It is split into a testing-set and a training-set. Tests when rando = true and RANDOMLY picks the indices for the testing-set.

runMain scalation.mathstat.tnT_SplitTest

Attributes

The tnT_SplitTest2 main function tests the TnT_Split object using the Texas Temperatures dataset. It is split into a testing-set and a training-set. Tests when rando = false and picks the FIRST indices for the testing-set.

runMain scalation.mathstat.tnT_SplitTest2

Attributes

The tnT_SplitTest3 main function tests the TnT_Split object using the Texas Temperatures dataset. It is split into a testing-set and a training-set. Tests when rando = false and picks the LAST indices for the testing-set.

runMain scalation.mathstat.tnT_SplitTest3

Attributes

The transformTest tests the classes extending the Transform trait at the vector level.

runMain scalation.mathstat.transformTest

Attributes

The transformTest2 tests the classes extending the Transform trait at the matrix level.

runMain scalation.mathstat.transformTest2

Attributes

The transformTest3 tests the Transform class' ability to compose transformations.

runMain scalation.mathstat.transformTest3

Attributes

The transformTest4 tests the Transform class by plotting the transformations.

runMain scalation.mathstat.transformTest4

Attributes

The vMatrixDTest main function is used to test the VMatrixD class. It tests the calculation of X^T X, X^T y, and Cholesky Factorization for Regression and Quadratic (no-cross) Regression for the Texas Temperatures dataset.

Attributes

See also: scalation.modeling.regressionTest7

runMain scalation.mathstat.vMatrixDTest

The vectorCTest main function tests the operations provided by the VectorC class. Only the most commonly used inherited operations are shown.

Attributes

See also: mutable.IndexedSeq for a complete list

runMain scalation.mathstat.vectorCTest

The vectorCTest2 main function tests the indirect sorting operations provided by the VectorC class.

runMain scalation.mathstat.vectorCTest2

Attributes

The vectorCTest3 main function tests auto-covariance and auto-correlation methods provided by the VectorC class.

runMain scalation.mathstat.vectorCTest3

Attributes

The vectorDTest main function tests the operations provided by the VectorD class. Only the most commonly used inherited operations are shown.

Attributes

See also: mutable.IndexedSeq for a complete list

runMain scalation.mathstat.vectorDTest

The vectorDTest2 main function tests the indirect sorting operations provided by the VectorD class.

runMain scalation.mathstat.vectorDTest2

Attributes

The vectorDTest3 main function tests covariance and correlation methods provided by the VectorD class. Okay to use MatrixD in VectorD test code only.

runMain scalation.mathstat.vectorDTest3

Attributes

The vectorDTest4 main function tests auto-covariance and auto-correlation methods provided by the VectorD class.

runMain scalation.mathstat.vectorDTest4

Attributes

The vectorDTest5 main function tests convolution operators defined in the VectorD class: conv (*+), conv_, convs and convs_.

Attributes

See also: https://gregorygundersen.com/blog/2017/02/24/cnns/

runMain scalation.mathstat.vectorDTest5

The vectorDTest6 test the dot product implementations. Run this code for performance results. Note, due to JIT, reordering the code may change the relative performance. Generally, case 0 "x dot x (VectorD dot VectorD)" is the fastest.

Attributes

See also: Timer.scala

runMain scalation.mathstat.vectorDTest6

The vectorDTest7 test the dot product implementations. Run this code for performance results. Note, due to JIT, reordering the code may change the relative performance.

Attributes

See also: Timer.scala

runMain scalation.mathstat.vectorDTest7

The vectorITest main function tests the operations provided by the VectorI class. Only the most commonly used inherited operations are shown.

Attributes

See also: mutable.IndexedSeq for a complete list

runMain scalation.mathstat.vectorITest

The vectorLTest main function tests the operations provided by the VectorL class. Only the most commonly used inherited operations are shown.

Attributes

See also: mutable.IndexedSeq for a complete list

runMain scalation.mathstat.vectorLTest

The vectorSTest main function tests the operations provided by the VectorS class. Only the most commonly used inherited operations are shown.

Attributes

See also: mutable.IndexedSeq for a complete list

runMain scalation.mathstat.vectorSTest

The vectorSTest2 main function tests the operations provided by the VectorS class. It tests the map2Int method (String vector to Int vector).

runMain scalation.mathstat.vectorSTest2

Attributes

The vectorTTest main function tests the operations provided by the VectorT class. Only the most commonly used inherited operations are shown.

Attributes

See also: mutable.IndexedSeq for a complete list

runMain scalation.mathstat.vectorTTest

The vectorTTest2 main function tests the operations provided by the VectorT class. It tests the map2Long method (TimeNum vector to Long vector).

runMain scalation.mathstat.vectorTTest2

Attributes

Vectorize a scalar function (S2S) to create a vector function (V2V).

Value parameters

f: the scalar function to vectorize

Attributes

Return the critical value for the z-distribution with a confidence level of p_. Uses inverse CDF (iCDF) Quantile.normalInv.

Value parameters

p_: the confidence level (two tails)

Attributes

Compute the confidence interval half-width (ihw) for the given confidence level using the z-distribution.

Value parameters

n: the length of the vector/sample
p_: the confidence level
sig: the standard deviation of the vector/sample

Attributes

Test (2-tail) to see if two means (one given and one estimated) are significantly different, using the z-distribution.

Value parameters

mu: the estimated mean of the vector/sample
mu0: the given mean
n: the length of the vector/sample
p_: the confidence level
show: whether to show details of the test
sig: the standard deviation of the vector/sample

Attributes

Compute the product of the critical value from the z-distribution (Standard Normal) and the standard deviation of the vector.

Value parameters

p_: the confidence level (two tails)
sig: the standard deviation of the vector/sample

Attributes

Concrete fields

Extensions

extension [A, B, R](f: B => R)

The ⚬ extension method performs function composition f ⚬ g. The composition f ⚬ g = f (g (.)) maps A -g-> B -f-> R.

Type parameters

A: the type to which function g can be applied
B: the type to which function f can be applied
R: the return type for f ⚬ g

Value parameters

f: the function from domain B to range R

Attributes

See also: www.scala-lang.org/api/current/scala/Function1.html

extension (x: VecMat)

The mu_sig and min_max extend the methods defined for vectors and matrices to work for types that are either VectorD or MatrixD.

Value parameters

x: the argument that is either a VectorD or MatrixD.

Attributes

The mu_sig and min_max extend the methods defined for vectors and matrices to work for types that are either VectorD or MatrixD.

Value parameters

x: the argument that is either a VectorD or MatrixD.

Attributes

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