Package edu.cmu.tetrad.util

Class MatrixUtils

java.lang.Object
edu.cmu.tetrad.util.MatrixUtils
public final class MatrixUtils extends Object
Class Matrix includes several public static functions performing matrix operations. These function include: determinant, GJinverse, inverse, multiple, difference, transpose, trace, duplicate, minor, identity, mprint, impliedCovar, SEMimpliedCovar.
Version:
$Id: $Id
Author:
Tianjiao Chu, josephramsey, Kevin V. Bui

  • Method Summary

    Modifier and Type
    Method
    Description
    static double[][]
    asRow(double[] v)
    asRow.
    static Matrix
    cholesky(Matrix covar)
    cholesky.
    static double[]
    concatenate(double[][] vectors)
    Concatenates the vectors rows[i], i = 0...rows.length, into a single vector.
    static Matrix
    convertCovToCorr(Matrix m)
    Converts a covariance matrix to a correlation matrix in place; the same matrix is returned for convenience, but m is modified in the process.
    static org.ejml.simple.SimpleMatrix
    convertCovToCorr(org.ejml.simple.SimpleMatrix covarianceMatrix)
    Converts a covariance matrix into a correlation matrix.
    static double[][]
    convertLowerTriangleToSymmetric(double[][] arr)
    Converts a matrix in lower triangular form to a symmetric matrix in square form.
    static double[][]
    copyOf(double[][] arr)
    copyOf.
    static int[]
    copyOf(int[] arr, int length)
    copyOf.
    static double
    determinant(double[][] m)
    determinant.
    static double[][]
    directProduct(double[][] ma, double[][] mb)
    Computes the direct (Kronecker) outerProduct.
    static boolean
    equals(double[][] ma, double[][] mb)
    Tests two matrices for equality.
    static boolean
    equals(double[][] ma, double[][] mb, double tolerance)
    Tests to see whether two matrices are equal within the given tolerance.
    static boolean
    equals(double[] va, double[] vb)
    Tests two vectors for equality.
    static boolean
    equals(double[] va, double[] vb, double tolerance)
    Tests to see whether two vectors are equal within the given tolerance.
    static boolean
    hasDimensions(double[][] m, int i, int j)
    hasDimensions.
    static org.ejml.simple.SimpleMatrix
    identity(int size)
    identity.
    static Matrix
    impliedCovar(Matrix edgeCoef, Matrix errCovar)
    Calculates the implied covariance matrix from the given edge coefficient matrix and error covariance matrix.
    static double
    innerProduct(double[] ma, double[] mb)
    innerProduct.
    static double[][]
    inverse(double[][] m)
    Calculates the inverse of a given matrix.
    static double[][]
    invVech(double[] vech)
    invVech.
    static boolean
    isPositiveDefinite(Matrix matrix)
    Return true if the given matrix is symmetric positive definite--that is, if it would make a valid covariance matrix.
    static boolean
    isSquare(double[][] m)
    isSquare.
    static boolean
    isSymmetric(double[][] m, double tolerance)
    isSymmetric.
    static double[]
    product(double[][] ma, double[] mb)
    product.
    static double[][]
    product(double[][] ma, double[][] mb)
    product.
    static double[]
    product(double[] ma, double[][] mb)
    product.
    static Vector
    product(Vector ma, Matrix mb)
    product.
    static double[]
    scalarProduct(double scalar, double[] m)
    scalarProduct.
    static double[][]
    scalarProduct(double scalar, double[][] m)
    Multiplies the given matrix through by the given scalar.
    static double[][]
    submatrix(double[][] m, int rem)
    A copy of the original (square) matrix with the stated index row/column removed
    static double[][]
    subtract(double[][] ma, double[][] mb)
    subtract.
    static double[]
    subtract(double[] ma, double[] mb)
    subtract.
    static double[][]
    sum(double[][] ma, double[][] mb)
    sum.
    static double[]
    sum(double[] ma, double[] mb)
    sum.
    static int
    sum0ToN(int n)
    sum0ToN.
    static Matrix
    symmetrize(Matrix sigma)
    Computes the symmetrized version of the given square matrix.
    static String
    toString(boolean[][] m)
    Copies the given array, starting each line with a tab character..
    static String
    toString(double[] m)
    toString.
    static String
    toString(double[][] m)
    Copies the given array, using a standard scientific notation number formatter and beginning each line with a tab character.
    static String
    toString(double[][] m, NumberFormat nf)
    Converts a 2D array of doubles into a String representation using the specified NumberFormat.
    static String
    toString(double[][] m, NumberFormat nf, List<String> variables)
    Converts a two-dimensional array representing a matrix into a string representation using the specified number format and variable names.
    static String
    toString(double[][] m, List<String> variables)
    toString.
    static String
    toString(double[] m, NumberFormat nf)
    toString.
    static String
    toString(int[] m)
    toString.
    static String
    toString(int[][] m)
    toString.
    static String
    toString(int[][] m, List<String> variables)
    toString.
    static String
    toStringSquare(double[][] m, NumberFormat nf, List<String> variables)
    toStringSquare.
    static String
    toStringSquare(double[][] m, List<String> variables)
    toStringSquare.
    static String
    toStringSquare(int[][] m, List<String> variables)
    toStringSquare.
    static double
    trace(double[][] m)
    trace.
    static double[][]
    transpose(double[][] m)
    transpose.
    static double[][]
    vec(double[][] m)
    vec.
    static double[][]
    vech(double[][] m)
    vech.
    static double[][]
    vechToVecLeft(int n)
    The matrix which, when postmultiplied by vech, return vec.
    static double[][]
    zeros(int rows, int cols)
    zeros.

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • equals

      public static boolean equals(double[][] ma, double[][] mb)
      Tests two matrices for equality.
      Parameters:
      ma - The first 2D matrix to check.
      mb - The second 2D matrix to check.
      Returns:
      True iff the first and second matrices are equal.

    • equals

      public static boolean equals(double[] va, double[] vb)
      Tests two vectors for equality.
      Parameters:
      va - The first 1D matrix to check.
      vb - The second 1D matrix to check.
      Returns:
      True iff the first and second matrices are equal.

    • equals

      public static boolean equals(double[][] ma, double[][] mb, double tolerance)
      Tests to see whether two matrices are equal within the given tolerance. If any two corresponding elements differ by more than the given tolerance, false is returned.
      Parameters:
      ma - The first 2D matrix to check.
      mb - The second 2D matrix to check.
      tolerance - A double >= 0.
      Returns:
      Ibid.

    • equals

      public static boolean equals(double[] va, double[] vb, double tolerance)
      Tests to see whether two vectors are equal within the given tolerance. If any two corresponding elements differ by more than the given tolerance, false is returned.
      Parameters:
      va - The first matrix to check.
      vb - The second matrix to check.
      tolerance - A double >= 0.
      Returns:
      Ibid.

    • isSquare

      public static boolean isSquare(double[][] m)

      isSquare.

      Parameters:
      m - A 2D double matrix.
      Returns:
      Ibid.

    • isSymmetric

      public static boolean isSymmetric(double[][] m, double tolerance)

      isSymmetric.

      Parameters:
      m - The matrix to check.
      tolerance - A double >= 0.
      Returns:
      Ibid.

    • determinant

      public static double determinant(double[][] m)

      determinant.

      Parameters:
      m - The matrix whose determinant is sought. Must be square.
      Returns:
      Ibid.

    • submatrix

      public static double[][] submatrix(double[][] m, int rem)
      A copy of the original (square) matrix with the stated index row/column removed
      Parameters:
      m - an array of objects
      rem - a int
      Returns:
      an array of objects

    • inverse

      public static double[][] inverse(double[][] m)
      Calculates the inverse of a given matrix.
      Parameters:
      m - the input matrix to calculate the inverse of
      Returns:
      the inverse of the input matrix as a 2D array of doubles

    • product

      public static double[][] product(double[][] ma, double[][] mb)

      product.

      Parameters:
      ma - an array of objects
      mb - an array of objects
      Returns:
      the outerProduct of ma and mb. The dimensions of ma and mb must be compatible for multiplication.

    • product

      public static double[] product(double[] ma, double[][] mb)

      product.

      Parameters:
      ma - an array of objects
      mb - an array of objects
      Returns:
      an array of objects

    • product

      public static Vector product(Vector ma, Matrix mb)

      product.

      Parameters:
      ma - a Vector object
      mb - a Matrix object
      Returns:
      a Vector object

    • product

      public static double[] product(double[][] ma, double[] mb)

      product.

      Parameters:
      ma - an array of objects
      mb - an array of objects
      Returns:
      an array of objects

    • innerProduct

      public static double innerProduct(double[] ma, double[] mb)

      innerProduct.

      Parameters:
      ma - an array of objects
      mb - an array of objects
      Returns:
      a double

    • transpose

      public static double[][] transpose(double[][] m)

      transpose.

      Parameters:
      m - an array of objects
      Returns:
      the transpose of the given matrix.

    • trace

      public static double trace(double[][] m)

      trace.

      Parameters:
      m - an array of objects
      Returns:
      the trace of the given (square) m.

    • identity

      public static org.ejml.simple.SimpleMatrix identity(int size)

      identity.

      Parameters:
      size - a int
      Returns:
      the identity matrix of the given order.

    • sum

      public static double[][] sum(double[][] ma, double[][] mb)

      sum.

      Parameters:
      ma - an array of objects
      mb - an array of objects
      Returns:
      the sum of ma and mb.

    • sum

      public static double[] sum(double[] ma, double[] mb)

      sum.

      Parameters:
      ma - an array of objects
      mb - an array of objects
      Returns:
      an array of objects

    • subtract

      public static double[][] subtract(double[][] ma, double[][] mb)

      subtract.

      Parameters:
      ma - an array of objects
      mb - an array of objects
      Returns:
      an array of objects

    • subtract

      public static double[] subtract(double[] ma, double[] mb)

      subtract.

      Parameters:
      ma - an array of objects
      mb - an array of objects
      Returns:
      an array of objects

    • directProduct

      public static double[][] directProduct(double[][] ma, double[][] mb)
      Computes the direct (Kronecker) outerProduct.
      Parameters:
      ma - an array of objects
      mb - an array of objects
      Returns:
      an array of objects

    • scalarProduct

      public static double[][] scalarProduct(double scalar, double[][] m)
      Multiplies the given matrix through by the given scalar.
      Parameters:
      scalar - a double
      m - an array of objects
      Returns:
      an array of objects

    • scalarProduct

      public static double[] scalarProduct(double scalar, double[] m)

      scalarProduct.

      Parameters:
      scalar - a double
      m - an array of objects
      Returns:
      an array of objects

    • concatenate

      public static double[] concatenate(double[][] vectors)
      Concatenates the vectors rows[i], i = 0...rows.length, into a single vector.
      Parameters:
      vectors - an array of objects
      Returns:
      an array of objects

    • asRow

      public static double[][] asRow(double[] v)

      asRow.

      Parameters:
      v - an array of objects
      Returns:
      the vector as a 1 x n row matrix.

    • impliedCovar

      public static Matrix impliedCovar(Matrix edgeCoef, Matrix errCovar)
      Calculates the implied covariance matrix from the given edge coefficient matrix and error covariance matrix. This method assumes that the provided matrices satisfy the necessary mathematical properties for the computation.
      Parameters:
      edgeCoef - the edge coefficient matrix, representing direct effects among variables. Must not contain undefined (NaN) values.
      errCovar - the error covariance matrix, representing variances and covariances of errors. Must not contain undefined (NaN) values.
      Returns:
      the implied covariance matrix, computed as ((I - B)⁻¹) Cov(e) ((I - B)⁻¹)ᵀ, where B is the edge coefficient matrix and Cov(e) is the error covariance matrix.
      Throws:
      IllegalArgumentException - if either the edge coefficient matrix or the error covariance matrix contains undefined (NaN) values.

    • vech

      public static double[][] vech(double[][] m)

      vech.

      Parameters:
      m - an array of objects
      Returns:
      vech of the given array. (This is what you get when you stack all of the elements of m in the lower triangular of m to form a vector. The elements are stacked in columns left to right, top to bottom.)

    • invVech

      public static double[][] invVech(double[] vech)

      invVech.

      Parameters:
      vech - an array of objects
      Returns:
      the symmetric matrix for which the given array is the vech.

    • vec

      public static double[][] vec(double[][] m)

      vec.

      Parameters:
      m - an array of objects
      Returns:
      vech of the given array. (This is what you get when you stack all of the elements of m to form a vector. The elements are stacked in columns left to right, top to bottom.)

    • sum0ToN

      public static int sum0ToN(int n)

      sum0ToN.

      Parameters:
      n - a int
      Returns:
      the sum of integers from 0 up to n.

    • vechToVecLeft

      public static double[][] vechToVecLeft(int n)
      The matrix which, when postmultiplied by vech, return vec.
      Parameters:
      n - the size of the square matrix that vec and vech come from.
      Returns:
      an array of objects

    • hasDimensions

      public static boolean hasDimensions(double[][] m, int i, int j)

      hasDimensions.

      Parameters:
      m - an array of objects
      i - a int
      j - a int
      Returns:
      true just in case the given matrix has the given dimensions --that is, just in case m.length == i and m[0].length == j.

    • zeros

      public static double[][] zeros(int rows, int cols)

      zeros.

      Parameters:
      rows - a int
      cols - a int
      Returns:
      an array of objects

    • isPositiveDefinite

      public static boolean isPositiveDefinite(Matrix matrix)
      Return true if the given matrix is symmetric positive definite--that is, if it would make a valid covariance matrix.
      Parameters:
      matrix - a Matrix object
      Returns:
      a boolean

    • cholesky

      public static Matrix cholesky(Matrix covar)

      cholesky.

      Parameters:
      covar - a Matrix object
      Returns:
      a Matrix object

    • convertCovToCorr

      public static Matrix convertCovToCorr(Matrix m)
      Converts a covariance matrix to a correlation matrix in place; the same matrix is returned for convenience, but m is modified in the process.
      Parameters:
      m - a Matrix object
      Returns:
      a Matrix object

    • convertCovToCorr

      public static org.ejml.simple.SimpleMatrix convertCovToCorr(org.ejml.simple.SimpleMatrix covarianceMatrix)
      Converts a covariance matrix into a correlation matrix. The correlation matrix is computed by normalizing the covariance matrix using the standard deviations derived from the diagonal elements of the covariance matrix.
      Parameters:
      covarianceMatrix - the input covariance matrix to be converted. It is assumed to be square and symmetric.
      Returns:
      the resulting correlation matrix where each element is scaled by the product of the standard deviations of the corresponding variables.

    • convertLowerTriangleToSymmetric

      public static double[][] convertLowerTriangleToSymmetric(double[][] arr)
      Converts a matrix in lower triangular form to a symmetric matrix in square form. The lower triangular matrix need not contain matrix elements to represent elements in the upper triangle.
      Parameters:
      arr - an array of objects
      Returns:
      an array of objects

    • toString

      public static String toString(double[][] m)
      Copies the given array, using a standard scientific notation number formatter and beginning each line with a tab character. The number format is DecimalFormat(" 0.0000;-0.0000").
      Parameters:
      m - an array of objects
      Returns:
      a String object

    • toString

      public static String toString(double[][] m, List<String> variables)

      toString.

      Parameters:
      m - an array of objects
      variables - a List object
      Returns:
      a String object

    • toString

      public static String toString(double[][] m, NumberFormat nf)
      Converts a 2D array of doubles into a String representation using the specified NumberFormat. This method delegates the formatting process to MatrixUtils.toString.
      Parameters:
      m - the 2D double array to be converted to a string
      nf - the NumberFormat to use for formatting the numbers in the array
      Returns:
      a String representation of the 2D array formatted using the specified NumberFormat

    • toString

      public static String toString(double[][] m, NumberFormat nf, List<String> variables)
      Converts a two-dimensional array representing a matrix into a string representation using the specified number format and variable names.
      Parameters:
      m - the matrix to convert, represented as a two-dimensional array of double values. Can be null.
      nf - the number format to use for formatting the individual matrix elements. Must not be null.
      variables - a list of variable names corresponding to the columns of the matrix. If null, default variable names will be generated.
      Returns:
      a string representation of the matrix. If the matrix is null or empty, a default message is returned.
      Throws:
      NullPointerException - if the provided number format is null.

    • toStringSquare

      public static String toStringSquare(double[][] m, List<String> variables)

      toStringSquare.

      Parameters:
      m - an array of objects
      variables - a List object
      Returns:
      a String object

    • toStringSquare

      public static String toStringSquare(double[][] m, NumberFormat nf, List<String> variables)

      toStringSquare.

      Parameters:
      m - an array of objects
      nf - a NumberFormat object
      variables - a List object
      Returns:
      a String object

    • toString

      public static String toString(int[] m)

      toString.

      Parameters:
      m - an array of objects
      Returns:
      a String object

    • toString

      public static String toString(int[][] m, List<String> variables)

      toString.

      Parameters:
      m - an array of objects
      variables - a List object
      Returns:
      a String object

    • toStringSquare

      public static String toStringSquare(int[][] m, List<String> variables)

      toStringSquare.

      Parameters:
      m - an array of objects
      variables - a List object
      Returns:
      a String object

    • toString

      public static String toString(double[] m)

      toString.

      Parameters:
      m - an array of objects
      Returns:
      a String object

    • toString

      public static String toString(double[] m, NumberFormat nf)

      toString.

      Parameters:
      m - an array of objects
      nf - a NumberFormat object
      Returns:
      a String object

    • toString

      public static String toString(int[][] m)

      toString.

      Parameters:
      m - an array of objects
      Returns:
      a String object

    • toString

      public static String toString(boolean[][] m)
      Copies the given array, starting each line with a tab character..
      Parameters:
      m - an array of objects
      Returns:
      a String object

    • copyOf

      public static int[] copyOf(int[] arr, int length)

      copyOf.

      Parameters:
      arr - an array of objects
      length - a int
      Returns:
      an array of objects

    • copyOf

      public static double[][] copyOf(double[][] arr)

      copyOf.

      Parameters:
      arr - an array of objects
      Returns:
      an array of objects

    • symmetrize

      public static Matrix symmetrize(Matrix sigma)
      Computes the symmetrized version of the given square matrix. The symmetrized matrix is calculated as (A + A^T) / 2, where A is the input matrix and A^T is its transpose. The method does not modify the original matrix.
      Parameters:
      sigma - the input square matrix to be symmetrized; must not be null. The matrix must have the same number of rows and columns.
      Returns:
      the symmetrized matrix computed as (A + A^T) / 2.
      Throws:
      NullPointerException - if the input matrix is null.
      IllegalArgumentException - if the input matrix is not square.