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scalation/scalation/scalation.mathstat

scalation.mathstat

package scalation.mathstat

Members list

Type members

Classlikes

class Bidiagonal(a: MatrixD)
class Canvas(x: VectorD, y: VectorD, z: VectorD, width: Int, height: Int, lines: Boolean) extends ZoomablePanel

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

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 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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object Combinatorics

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

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
case class Complex(re: Double, im: Double) extends Fractional[Complex], Ordered[Complex]

The Complex class is used to represent and operate on complex numbers. Internally, a complex number is represented as two double precision floating point numbers (Double). Externally, two forms are supported:

The Complex class is used to represent and operate on complex numbers. Internally, a complex number is represented as two double precision floating point numbers (Double). Externally, two forms are supported:

a+bi   = 2.1+3.2i       via: Complex ("2.1+3.2i"),  'toString'
(a, b) = (2.1, 3.2)     via: create ("(2.1, 3.2)"),  'toString2'

Note: 'i * i = -1'.

Value parameters

im

the imaginary part (e.g., 3.2)

re

the real part (e.g., 2.1)

Attributes

Companion
object
Supertypes
trait Product
trait Equals
trait Ordered[Complex]
trait Comparable[Complex]
trait Fractional[Complex]
trait Numeric[Complex]
trait Ordering[Complex]
trait PartialOrdering[Complex]
trait Equiv[Complex]
trait Serializable
trait Comparator[Complex]
class Object
trait Matchable
class Any
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object Complex

The Complex companion object defines the origin (zero) and the four roots of unity as well as some utility functions.

The Complex companion object defines the origin (zero) and the four roots of unity as well as some utility functions.

Attributes

Companion
class
Supertypes
trait Product
trait Mirror
class Object
trait Matchable
class Any
Self type
Complex.type
trait Correlogram(y: VectorD)

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

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

Value parameters

y

the time series data (response vector)

Attributes

Supertypes
class Object
trait Matchable
class Any
Known subtypes
class AR
class AR1MA
class ARMA
class ARIMA
class SARIMA
class SARIMAX
class NullModel
class QuadSpline
class RandomWalk
class TrendModel
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class Eigenvalue(a: MatrixD)

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. Caveats: (1) it will not handle eigenvalues that are complex numbers, (2) it uses a simple shifting strategy that may slow convergence.

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. Caveats: (1) it will not handle eigenvalues that are complex numbers, (2) it uses a simple shifting strategy that may slow convergence.

Value parameters

a

the matrix whose eigenvalues are sought

Attributes

Supertypes
class Object
trait Matchable
class Any
class EigenvalueSym(a: MatrixD)

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.

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. Caveats: (1) it will not handle eigenvalues that are complex numbers, (2) it uses a simple shifting strategy that may slow convergence.

Supertypes
class Object
trait Matchable
class Any
class Eigenvector(a: MatrixD, _e: VectorD)

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.

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
class Fac_Cholesky(a: MatrixD) extends Factorization

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.

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 factor

Attributes

Supertypes
class Object
trait Matchable
class Any
class Fac_Inverse(a: MatrixD) extends Factorization

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.

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
class Object
trait Matchable
class Any
object Fac_Inverse

The Fac_Inverse companion object provides methods for matrix imversion.

The Fac_Inverse companion object provides methods for matrix imversion.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
class Fac_LU(a: MatrixD) extends Factorization

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

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
class Object
trait Matchable
class Any
object Fac_LU

The Fac_LU companion object provides functions related to LU Factorization.

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
class Fac_QR(aa: MatrixD, needQ: Boolean) extends Factorization

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.

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 factor into q and r

needQ

flag indicating whether a full q matrix is needed

Attributes

See also
Companion
object
Supertypes
class Object
trait Matchable
class Any
Known subtypes
class Fac_QR_RR
object Fac_QR

The Fac_QR companion object provides example matrices to factor.

The Fac_QR companion object provides example matrices to factor.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
Fac_QR.type
class Fac_QR_RR(aa: MatrixD, needQ: Boolean) extends Fac_QR, Pivoting

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.

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 factor into q and r

needQ

flag indicating whether a full q matrix is needed

Attributes

See also
Supertypes
trait Pivoting
class Fac_QR
class Object
trait Matchable
class Any
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class Fac_SVD(a: MatrixD) extends Factorization

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
class Object
trait Matchable
class Any
object Fac_SVD

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

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
trait Factorization

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

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_LU
class Fac_QR
class Fac_QR_RR
class Fac_SVD
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class FramelessHistogram(frameW: Int, frameH: Int, value: VectorD, numIntervals: Int)

The FramelessHistogram class should be used in embedded applications.

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
class FramelessPlot(x: VectorD, y: VectorD, z: VectorD, var width: Int, var height: Int)

The FramelessPlot class is used for embedded applications.

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
class HCanvas(frameW: Int, frameH: Int, value: VectorD, numIntervals: Int, counts: VectorD) extends JPanel

Create a canvas on which to draw the histogram.

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
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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class Hessenburg(a: MatrixD)

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.

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
class Histogram(value: VectorD, numIntervals: Int, _title: String, counts: VectorD) extends VizFrame

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.

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.

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

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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object Householder

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

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

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
class HouseholderT(a: MatrixD)

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

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
class MatrixD(val dim: Int, val dim2: Int, var v: Array[Array[Double]])

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

The MatrixD class stores and operates on Numeric Matrices of base type Double. the 'cfor' loop is used for innermost 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
object MatrixD

The `MatrixD companion object provides factory methods.

The `MatrixD companion object provides factory methods.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
MatrixD.type
class MatrixD2(val dim: Int, val dim2: Int, var v: Array[Array[Double]])

Attributes

Companion
object
Supertypes
class Object
trait Matchable
class Any
object MatrixD2

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
MatrixD2.type
object MatrixD2Example

The MatrixD2Example object provides example instances of theMatrixD2 class.

The MatrixD2Example object provides example instances of theMatrixD2 class.

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
object MatrixDExample

The MatrixDExample object provides example instances of theMatrixD class.

The MatrixDExample object provides example instances of theMatrixD class.

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
object MatrixI

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

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
trait Pivoting

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

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
object PivotingTest
object PivotingTest extends App, Pivoting

The PivotingTest object is used to test the Pivoting trait.

The PivotingTest object is used to test the Pivoting trait.

runMain scalation.mathstat.PivotingTest

Attributes

Supertypes
trait Pivoting
trait App
trait DelayedInit
class Object
trait Matchable
class Any
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Self type
class Plot(x: VectorD, y: VectorD, z: VectorD, _title: String, lines: Boolean) extends VizFrame

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

_title

the title of the plot

lines

flag for generating a line 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
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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object Plot

The Plot companion object provides factory methods for creating plots.

The Plot companion object provides factory methods for creating plots.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
Plot.type
class PlotC(f: FunctionV2S, lb: VectorD, ub: VectorD, path: ArrayBuffer[VectorD], opt: VectorD, var deltaF: Double, var lbF: Double, _title: String) extends VizFrame

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

_title

the title of the plot

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

path

the points on a path (e.g., a search path)

ub

the upper bounds on the plotting domain

Attributes

See also
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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class PlotM(x_: VectorD, y_: MatrixD, var label: Array[String], _title: String, lines: Boolean) extends VizFrame

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

_title

the title of the plot

label

the label/legend/key for each curve in the plot

lines

flag for generating a line 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
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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object PlotM

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

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
object Probability

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).

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
class RTensor4D(val dim: Int, val dim2: VectorI, val dim3: VectorI, val dim4: Int, var v: Array[Array[Array[Array[Double]]]]) extends Serializable

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).

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
object RTensor4D

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

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
class RTensorD(val dim: Int, val dim2: VectorI, val dim3: Int, var v: Array[Array[Array[Double]]]) extends Serializable

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).

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
object RTensorD

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

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
class StatTable(_title: String, stats: ArrayBuffer[Statistic]) extends Frame

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

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
Show all
class Statistic(val name: String, unbiased: Boolean)

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.

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

Attributes

Companion
object
Supertypes
class Object
trait Matchable
class Any
Known subtypes
object Statistic

The Statistic companion object provides additional values and functions.

The Statistic companion object provides additional values and functions.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
Statistic.type
case class Stats4TS(y: VectorD, lags_: Int)

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)

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

lags_

the maximum number of lags

y

the response vector (time-series data) for the training/full dataset

Attributes

Supertypes
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
Show all
class SymTriMatrixD(val d1: Int)

Attributes

Supertypes
class Object
trait Matchable
class Any
object SymmetricQRstep

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

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

Attributes

See also

Algorithm 8.3.2 in Matrix Computations.

Supertypes
class Object
trait Matchable
class Any
Self type
class TensorD(val dim: Int, val dim2: Int, val dim3: Int, var v: Array[Array[Array[Double]]]) extends Serializable

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

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

RTensorD for non-rectangular (ragged) tensors.

Companion
object
Supertypes
trait Serializable
class Object
trait Matchable
class Any
object TensorD

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

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
class TimeStatistic(val name: String, var _lastTime: Double, _startTime: Double) extends Statistic

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

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
object TimeStatistic

The TimeStatistic companion object provides additional functions.

The TimeStatistic companion object provides additional functions.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
object TnT_Split

The TnT_Split object provides methods for splitting datasets into testing-sets and training-sets.

The TnT_Split object provides methods for splitting datasets into testing-sets and training-sets.

Attributes

Supertypes
class Object
trait Matchable
class Any
Self type
TnT_Split.type
class VMatrixD(dim_: Int, dim2_: Int, val dim2v: Int, formulas: Array[Array[Int]], v_: Array[Array[Double]]) extends MatrixD

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.

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
object VMatrixD

The `VMatrixD companion object provides factory methods.

The `VMatrixD companion object provides factory methods.

Attributes

Companion
class
Supertypes
class Object
trait Matchable
class Any
Self type
VMatrixD.type
class VectorD(val dim: Int, var v: Array[Double]) extends IndexedSeq[Double], PartiallyOrdered[VectorD], DefaultSerializable

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

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 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
object VectorD

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

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
class VectorI(val dim: Int, var v: Array[Int]) extends IndexedSeq[Int], PartiallyOrdered[VectorI], DefaultSerializable

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

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 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
object VectorI

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

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
class VectorL(val dim: Int, var v: Array[Long]) extends IndexedSeq[Long], PartiallyOrdered[VectorL], DefaultSerializable

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

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 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
object VectorL

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

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
class VectorS(val dim: Int, var v: Array[String]) extends IndexedSeq[String], PartiallyOrdered[VectorS], DefaultSerializable

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

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 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
object VectorS

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

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
class VectorT(val dim: Int, var v: Array[TimeNum]) extends IndexedSeq[TimeNum], PartiallyOrdered[VectorT], DefaultSerializable

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

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 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
object VectorT

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

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
final class bidiagonalTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class combinatoricsTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class combinatoricsTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class complexTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class correlogramTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class eigenTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_CholeskyTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_CholeskyTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_CholeskyTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_InverseTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_LUTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_LUTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_LUTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_QRTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_QRTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_QR_RRTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_SVDTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_SVDTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_SVDTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class fac_SVDTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class histogramTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class householderTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class inverseTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixCalc

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixCalc2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixD2Test

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixD2Test2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixDTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixDTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixDTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixDTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixDTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class matrixDTest6

Attributes

Supertypes
class Object
trait Matchable
class Any
final class plotCTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class plotMTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class plotMTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class plotTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class probabilityTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class probabilityTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class probabilityTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class probabilityTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class probabilityTest5

Attributes

Supertypes
class Object
trait Matchable
class Any
final class probabilityTest6

Attributes

Supertypes
class Object
trait Matchable
class Any
final class rTensor4DTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class rTensorDTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class statTableTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class statisticTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class stats4TSTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tensorDTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tensorDTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tensorDTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class timeStatisticTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class tnT_SplitTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class vMatrixDTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class vectorDTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class vectorDTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class vectorDTest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class vectorDTest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class vectorITest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class vectorLTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class vectorSTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class vectorSTest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class vectorTTest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class vectorTTest2

Attributes

Supertypes
class Object
trait Matchable
class Any

Types

type FactorType = (MatrixD, VectorD, MatrixD)

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

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

type FunctionM2V = MatrixD => VectorD

Top-level type definition for functions mapping:

Top-level type definition for functions mapping:

Attributes

type FunctionS2V = Double => VectorD

Top-level type definition for functions mapping:

Top-level type definition for functions mapping:

Attributes

type FunctionV2S = VectorD => Double

Value members

Concrete methods

def bidiagonalTest(): Unit

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

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

def combinatoricsTest(): Unit

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

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

runMain scalation.mathstat.combinatoricsTest

Attributes

def combinatoricsTest2(): Unit

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

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

runMain scalation.mathstat.combinatoricsTest2

Attributes

def comple(idx: Array[Int], dim: Int): Array[Int]

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

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

def complexTest(): Unit

The complexTest main function is used to test the Complex class.

The complexTest main function is used to test the Complex class.

runMain scalation.mathstat.complexTest

Attributes

def correlogramTest(): Unit

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

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

runMain scalation.mathstat.correlogramTest

Attributes

def diagnoseMat(x: MatrixD): Unit

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

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

def dupDim(dim: Int, d: Int): VectorI

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

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

def eigenTest(): Unit

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

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

def fac_CholeskyTest(): Unit

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

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

def fac_CholeskyTest2(): Unit

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

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

runMain scalation.mathstat.fac_CholeskyTest2

Attributes

def fac_CholeskyTest3(): Unit

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

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

def fac_InverseTest(): Unit

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

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

runMain scalation.mathstat.fac_InverseTest

Attributes

def fac_LUTest(): Unit

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

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

runMain scalation.mathstat.fac_LUTest

Attributes

def fac_LUTest2(): Unit

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

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

runMain scalation.mathstat.fac_LUTest2

Attributes

def fac_LUTest3(): Unit

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

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

runMain scalation.mathstat.fac_LUTest3

Attributes

def fac_QRTest(): Unit

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

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

Attributes

See also

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

runMain scalation.mathstat.fac_QRTest

def fac_QRTest2(): Unit

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.

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

def fac_QR_RRTest(): Unit

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

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

Attributes

See also
def fac_SVDTest(): Unit

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

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

Attributes

See also
def fac_SVDTest2(): Unit

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

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

runMain scalation.mathstat.fac_SVDTest2

Attributes

def fac_SVDTest3(): Unit

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

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

runMain scalation.mathstat.fac_SVDTest3

Attributes

def fac_SVDTest4(): Unit

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.

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

def func2vector(f: FunctionS2S, ab: Interval, n: Int): VectorD

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

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

def histogramTest(): Unit

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

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

def householderTest(): Unit

The HouseholderTest main function is used to test Householder object.

The HouseholderTest main function is used to test Householder object.

Attributes

See also

www.math.siu.edu/matlab/tutorial4.pdf

runMain scalation.mathstat.householderTest

def inverseTest(): Unit

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

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

runMain scalation.mathstat.inverseTest

Attributes

def matrixCalc(): Unit

Read a matrix from a CSV file and perform calculations, e.g. grade calculations.

Read a matrix from a CSV file and perform calculations, e.g. grade calculations.

runMain scalation.mathstat.matrixCalc

Attributes

def matrixCalc2(): Unit

Custom calculation

Custom calculation

runMain scalation.mathstat.matrixCalc2

Attributes

def matrixD2Test(): Unit

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

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

runMain scalation.mathstat.matrixD2Test

Attributes

def matrixD2Test2(): Unit

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

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

runMain scalation.mathstat.matrixD2Test2

Attributes

def matrixDTest(): Unit

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

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

runMain scalation.mathstat.matrixDTest

Attributes

def matrixDTest2(): Unit

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

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

runMain scalation.mathstat.matrixDTest2

Attributes

def matrixDTest3(): Unit

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

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

def matrixDTest4(): Unit

The matrixDTest4 main function tests the MatrixD class. Test the split methods: split and split_

The matrixDTest4 main function tests the MatrixD class. Test the split methods: split and split_

runMain scalation.mathstat.matrixDTest4

Attributes

def matrixDTest5(): Unit

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

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

runMain scalation.mathstat.matrixDTest5

Attributes

def matrixDTest6(): Unit

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

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

runMain scalation.mathstat.matrixDTest6

Attributes

def matrixize(f: FunctionV2V): FunctionM2M

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

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

Value parameters

f

the vector function to matrixize

Attributes

def plotCTest(): Unit

The plotCTest main function is used to test the PlotC class.

The plotCTest main function is used to test the PlotC class.

Attributes

See also

scalation.scala2d.writeImage

runMain scalation.mathstat.plotCTest

def plotMTest(): Unit

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

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

runMain scalation.mathstat.plotMTest

Attributes

def plotMTest2(): Unit

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

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

def plotTest(): Unit

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

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

Attributes

See also

scalation.scala2d.writeImage

runMain scalation.mathstat.plotTest

def probabilityTest(): Unit

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

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

runMain scalation.mathstat.probabilityTest

Attributes

def probabilityTest2(): Unit

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

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

runMain scalation.mathstat.probabilityTest2

Attributes

def probabilityTest3(): Unit

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

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

def probabilityTest4(): Unit

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

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

def probabilityTest5(): Unit

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

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

def probabilityTest6(): Unit

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

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

runMain scalation.mathstat.probabilityTest6

Attributes

def rTensor4DTest(): Unit

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

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

runMain scalation.mathstat.rTensor4DTest

Attributes

def rTensorDTest(): Unit

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

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

runMain scalation.mathstat.rTensorDTest

Attributes

def sizes2(u: Array[Array[Array[Double]]]): VectorI

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

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

Value parameters

u

the 3D array

Attributes

def sizes2_(u: Array[Array[Array[Array[Double]]]]): VectorI

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

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

Value parameters

u

the 4D array

Attributes

def sizes3(u: Array[Array[Array[Array[Double]]]]): VectorI

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

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

Value parameters

u

the 4D array

Attributes

def statTableTest(): Unit

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

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

runMain scalation.mathstat.statTableTest

Attributes

def statisticTest(): Unit

The statisticTest main function is used to test the Statistic class.

The statisticTest main function is used to test the Statistic class.

runMain scalation.mathstat.statisticTest

Attributes

def stats4TSTest(): Unit

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

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

runMain scalation.mathstat.stats4TSTest

Attributes

def t_interval(sig: Double, n: Int, p: Double): Double

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

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

def t_meanTest(mu0: Double, mu: Double, sig: Double, n: Int, p: Double, show: Boolean): Boolean

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

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 significance/confidence level

show

whether to show details of the test

sig

the standard deviation of the vector/sample

Attributes

def t_sigma(sig: Double, df: Int, p: Double): Double

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

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

Value parameters

df

the degrees of freedom

p

the confidence level

sig

the standard deviation of the vector/sample

Attributes

def tensorDTest(): Unit

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

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

runMain scalation.mathstat.tensorDTest

Attributes

def tensorDTest2(): Unit

The TensorDTest2 main function is used to test the TensorD class. It tests pulling matrices and vectors from the tensor.

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

def tensorDTest3(): Unit

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.

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

def timeStatisticTest(): Unit

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

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

runMain scalation.mathstat.timeStatisticTest

Attributes

def tnT_SplitTest(): Unit

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.

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.

runMain scalation.mathstat.tnT_SplitTest

Attributes

def vMatrixDTest(): Unit

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.

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

def vectorDTest(): Unit

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

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

def vectorDTest2(): Unit

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

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

runMain scalation.mathstat.vectorDTest2

Attributes

def vectorDTest3(): Unit

The vectorDTest3 main function tests covariance and correlation methods provided by the VectorD class.

The vectorDTest3 main function tests covariance and correlation methods provided by the VectorD class.

runMain scalation.mathstat.vectorDTest3

Attributes

def vectorDTest4(): Unit

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

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

runMain scalation.mathstat.vectorDTest4

Attributes

def vectorITest(): Unit

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

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

def vectorLTest(): Unit

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

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

def vectorSTest(): Unit

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

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

def vectorSTest2(): Unit

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

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

def vectorTTest(): Unit

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

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

def vectorTTest2(): Unit

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

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

def vectorize(f: FunctionS2S): FunctionV2V

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

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

Value parameters

f

the scalar function to vectorize

Attributes

def z_interval(sig: Double, n: Int, p: Double): Double

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

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

def z_meanTest(mu0: Double, mu: Double, sig: Double, n: Int, p: Double, show: Boolean): Boolean

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

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 significance/confidence level

show

whether to show details of the test

sig

the standard deviation of the vector/sample

Attributes

def z_sigma(sig: Double, p: Double): Double

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

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

sig

the standard deviation of the vector/sample

Attributes

Concrete fields

val MAX_LAGS: Int
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