Examples of QRDecomposition

• Jama.QRDecomposition
  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 so that A = Q*R.

  The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns false.

• org.apache.commons.math.linear.QRDecomposition
  nist.gov/javanumerics/jama/">JAMA library, with the following changes:

  • a {@link #getQT() getQT} method has been added,
  • the solve and isFullRank methods have been replaced by a {@link #getSolver() getSolver} method and the equivalent methods provided bythe returned {@link DecompositionSolver}.

  @see MathWorld @see Wikipedia @version $Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $ @since 1.2
• org.apache.commons.math3.linear.QRDecomposition
  nist.gov/javanumerics/jama/">JAMA library, with the following changes:

  • a {@link #getQT() getQT} method has been added,
  • the {@code solve} and {@code isFullRank} methods have been replacedby a {@link #getSolver() getSolver} method and the equivalent methodsprovided by the returned {@link DecompositionSolver}.

  @see MathWorld @see Wikipedia @since 1.2 (changed to concrete class in 3.0)
• org.apache.mahout.math.QRDecomposition
  partially deprecated until unit tests are in place. Until this time, this class/interface is unsupported.
• org.ejml.factory.QRDecomposition

  QR decompositions decompose a rectangular matrix 'A' such that 'A=QR'. Where A ∈ ℜ ^{n × m} , n ≥ m, Q ∈ ℜ ^{n × n} is an orthogonal matrix, and R ∈ ℜ ^{n × m} is an upper triangular matrix. Some implementations of QR decomposition require that A has full rank.

  Some features of QR decompositions:

  • Can decompose rectangular matrices.
  • Numerically stable solutions to least-squares problem, but not as stable as SVD
  • Can incrementally add and remove columns from the decomposed matrix. See {@link org.ejml.alg.dense.linsol.qr.AdjLinearSolverQr}

  Orthogonal matrices have the following properties:

  • QQ^T=I
  • Q^T=Q^-1

  @see org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholder @see org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholderColumn @author Peter Abeles
• org.encog.mathutil.matrices.decomposition.QRDecomposition
  nist.gov/javanumerics/jama/
• org.jquantlib.math.matrixutilities.QRDecomposition
  fpl.fs.fed.us/optimization.html">MINPACK/J

  This subroutine uses householder transformations with optional column pivoting to compute a QR factorization of the {@latex$ m} by {@latex$ n} matrix {@latex$ A}.

  That is, Minpack_f77#qrfac determines an orthogonal matrix {@latex$ Q}, a permutation matrix {@latex$ P}, and an upper trapezoidal matrix {@latex$ R} with diagonal elements of nonincreasing magnitude, such that {@latex$ A*P = Q*R}.

  Return value ipvt is an integer array of length {@latex$ n}, which defines the permutation matrix {@latex$ P}such that {@latex$ A*P = Q*R}.

  Column {@latex$ j} of {@latex$ P} is column ipvt[j] of the identity matrix.

  See lmdiff.cpp for further details. @see MathWorld @see Wikipedia @see MINPACK/J @see MINPACK @author Richard Gomes

Examples of org.jquantlib.math.matrixutilities.QRDecomposition