Package smile.math.matrix

Class Matrix.QR

java.lang.Object
smile.math.matrix.Matrix.QR
All Implemented Interfaces:
Serializable
Enclosing class:
Matrix
public static class Matrix.QR extends Object implements Serializable
The QR decomposition. For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R such that A = Q*R.

The QR decomposition always exists, even if the matrix does not have full rank. The primary use of the QR decomposition is in the least squares solution of non-square systems of simultaneous linear equations.

See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    final Matrix
    qr
    The QR decomposition.
    final double[]
    tau
    The scalar factors of the elementary reflectors

  • Constructor Summary

    Constructors
    Constructor
    Description
    QR(Matrix qr, double[] tau)
    Constructor.

  • Method Summary

    Modifier and Type
    Method
    Description
    Matrix.Cholesky
    CholeskyOfAtA()
    Returns the Cholesky decomposition of A'A.
    Matrix
    Q()
    Returns the orthogonal factor.
    Matrix
    R()
    Returns the upper triangular factor.
    double[]
    solve(double[] b)
    Solves the least squares min || B - A*X ||.
    void
    solve(Matrix B)
    Solves the least squares min || B - A*X ||.

    Methods inherited from class java.lang.Object

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

  • Field Details

    • qr

      public final Matrix qr
      The QR decomposition.

    • tau

      public final double[] tau
      The scalar factors of the elementary reflectors

  • Constructor Details

    • QR

      public QR(Matrix qr, double[] tau)
      Constructor.
      Parameters:
      qr - the QR decomposition.
      tau - the scalar factors of the elementary reflectors

  • Method Details

    • CholeskyOfAtA

      public Matrix.Cholesky CholeskyOfAtA()
      Returns the Cholesky decomposition of A'A.
      Returns:
      the Cholesky decomposition of A'A.

    • R

      public Matrix R()
      Returns the upper triangular factor.
      Returns:
      the upper triangular factor.

    • Q

      public Matrix Q()
      Returns the orthogonal factor.
      Returns:
      the orthogonal factor.

    • solve

      public double[] solve(double[] b)
      Solves the least squares min || B - A*X ||.
      Parameters:
      b - the right hand side of overdetermined linear system.
      Returns:
      the solution vector beta that minimizes ||Y - X*beta||.
      Throws:
      RuntimeException - when the matrix is rank deficient.

    • solve

      public void solve(Matrix B)
      Solves the least squares min || B - A*X ||.
      Parameters:
      B - the right hand side of overdetermined linear system. B will be overwritten with the solution matrix on output.
      Throws:
      RuntimeException - when the matrix is rank deficient.