Package com.imsl.math

Class SparseMatrix

java.lang.Object
com.imsl.math.SparseMatrix
All Implemented Interfaces:
Serializable
public class SparseMatrix extends Object implements Serializable
Sparse matrix of type double. The class represents a general real sparse matrix. It is intended to be efficiently and easily updated.

A SparseMatrix can be constructed from a set of arrays, or it can be abstractly created as an empty array and then incrementally built into final form. It is usually easier to create an empty SparseMatrix of set size and then use the set method to set the elements of the array. When setting the elements of the sparse array, their positions should be thought of as their positions in the dense array. Elements can be set in any order, but only the elements actually set are stored.

This class includes methods to update the sparse matrix. There are also methods to multiply a sparse matrix and a vector or to multiply two sparse matrices. To solve a sparse linear system use SparseCholesky or SuperLU.

See Also:

  • Constructor Details

    • SparseMatrix

      public SparseMatrix(int nRows, int nColumns)
      Creates a new instance of SparseMatrix. Initially this is the zero matrix.
      Parameters:
      nRows - an int containing the number of rows in the sparse matrix.
      nColumns - an int containing the number of columns in the sparse matrix.

    • SparseMatrix

      public SparseMatrix(SparseMatrix A)
      Creates a new instance of SparseMatrix which is a copy of another SparseMatrix.
      Parameters:
      A - the SparseMatrix object containing the sparse matrix to be copied.

    • SparseMatrix

      public SparseMatrix(SparseMatrix.SparseArray jsa)
      Constructs a sparse matrix from a SparseArray object.
      Parameters:
      jsa - is a SparseArray used to initialize the sparse matrix. The field numberOfNonZeros in jsa is not used for initialization, so it does not have to be set.

    • SparseMatrix

      public SparseMatrix(int nRows, int nColumns, int[][] index, double[][] values)
      Constructs a sparse matrix from SparseArray (Java Sparse Array) data.
      Parameters:
      nRows - an int containing the number of rows in the sparse matrix.
      nColumns - an int containing the number of columns in the sparse matrix.
      index - an int jagged array containing the column indices of all nonzero elements corresponding to the compressed representation of the sparse matrix in values. The size of index must be identical to the size of values. The i-th row contains the column indices of all nonzero elements of row i of the sparse matrix. The j-th element of row i is the column index of the value located at the same position in values.
      values - a double jagged array containing the compressed representation of a real sparse matrix of size nRows by nColumns. The number of rows in values must be nRows. The i-th row contains all nonzero elements of row i of the full sparse matrix.

  • Method Details

    • getNumberOfRows

      public int getNumberOfRows()
      Returns the number of rows in the matrix.
      Returns:
      an int containing the number of rows in the matrix.

    • getNumberOfColumns

      public int getNumberOfColumns()
      Returns the number of columns in the matrix.
      Returns:
      an int containing the number of columns in the matrix.

    • getNumberOfNonZeros

      public long getNumberOfNonZeros()
      Returns the number of nonzeros in the matrix.
      Returns:
      a long containing the number of nonzeros in the matrix.

    • get

      public double get(int iRow, int jColumn)
      Returns the value of an element in the matrix.
      Parameters:
      iRow - an int containing the row index of the element.
      jColumn - an int containing the column index of the element.
      Returns:
      a double containing the value of the iRow-th and jColumn-th element. If the element was never set, its value is zero.

    • set

      public void set(int iRow, int jColumn, double x)
      Sets the value of an element in the matrix.
      Parameters:
      iRow - an int containing the row index of the element.
      jColumn - an int containing the column index of the element.
      x - a double containing the value of the iRow-th and jColumn-th element.

    • plusEquals

      public double plusEquals(int iRow, int jColumn, double x)
      Adds a value to an element in the matrix.
      Parameters:
      iRow - an int containing the row index of the element.
      jColumn - an int containing the column index of the element.
      x - a double containing the value to be added to the iRow-th and jColumn-th element.
      Returns:
      a double containing the updated value of the element, which equals its old value plus x.

    • checkSquareMatrix

      public void checkSquareMatrix()
      Check that the matrix is square.
      Throws:
      IllegalArgumentException - is thrown if the matrix is not square.

    • add

      public static SparseMatrix add(double alpha, double beta, SparseMatrix A, SparseMatrix B)
      Performs element-wise addition of two real sparse matrices A, B of type SparseMatrix, \(C \leftarrow \alpha A + \beta B.\)
      Parameters:
      alpha - a double scalar.
      beta - a double scalar.
      A - a SparseMatrix matrix.
      B - a SparseMatrix matrix.
      Returns:
      a SparseMatrix matrix representing the computed sum.
      Throws:
      IllegalArgumentException - This exception is thrown when the matrices are not of the same size.

    • multiply

      public double[] multiply(double[] x)
      Multiply the matrix by a vector.
      Parameters:
      x - a double column vector.
      Returns:
      a double vector representing the product of this matrix times x.
      Throws:
      IllegalArgumentException - This exception is thrown if the number of columns in the SparseMatrix object is not equal to the number of elements in the input column vector.

    • multiply

      public static double[] multiply(SparseMatrix A, double[] x)
      Multiply sparse matrix A and column array x, \(A x\).
      Parameters:
      A - a SparseMatrix matrix.
      x - a double column array.
      Returns:
      a double vector representing the product of the arguments, \(A x\).
      Throws:
      IllegalArgumentException - This exception is thrown when the number of columns in the input matrix is not equal to the number of elements in the input column vector.

    • multiply

      public static double[] multiply(double[] x, SparseMatrix A)
      Multiply row array x and sparse matrix A, \(x^TA \).
      Parameters:
      x - a double row array.
      A - a SparseMatrix matrix.
      Returns:
      a double vector representing the product of the arguments, \( x^T A \).
      Throws:
      IllegalArgumentException - This exception is thrown when the number of elements in the input vector is not equal to the number of rows of the matrix.

    • multiplySymmetric

      public static double[] multiplySymmetric(SparseMatrix A, double[] x)
      Multiply sparse symmetric matrix A and column vector x.
      Parameters:
      A - a SparseMatrix sparse symmetric matrix, where only the lower triangular part of the matrix is to be used.
      x - a double vector.
      Returns:
      a double vector representing the product of the arguments, \(Ax\).
      Throws:
      IllegalArgumentException - This exception is thrown when the input matrix is not square or the number of columns in the input matrix is not equal to the number of elements in the input column vector.

    • multiply

      public static SparseMatrix multiply(SparseMatrix A, SparseMatrix B)
      Multiply two sparse matrices A and B, \( C \leftarrow AB\).
      Parameters:
      A - a SparseMatrix sparse matrix.
      B - a SparseMatrix sparse matrix.
      Returns:
      the SparseMatrix product AB of A and B.
      Throws:
      IllegalArgumentException - This exception is thrown when the number of columns of matrix A is not equal to the number of rows of matrix B.

    • transpose

      public SparseMatrix transpose()
      Returns the transpose of the matrix.
      Returns:
      a SparseMatrix object which is the transpose of the constructed SparseMatrix object.

    • oneNorm

      public double oneNorm()
      Returns the matrix one norm of the sparse matrix.
      Returns:
      a double value equal to the maximum of the column sums of the absolute values of the array elements.

    • infinityNorm

      public double infinityNorm()
      Returns the infinity norm of the matrix.
      Returns:
      a double scalar value equal to the maximum of the row sums of the absolute values of the array elements of the sparse matrix.

    • frobeniusNorm

      public double frobeniusNorm()
      Returns the Frobenius norm of the matrix.
      Returns:
      a double scalar value equal to the Frobenius norm of the matrix.

    • toDenseMatrix

      public double[][] toDenseMatrix()
      Returns the sparse matrix as a dense matrix.
      Returns:
      a rectangular Java array of type double containing this matrix with all of the zeros explicitly present. The number of rows and columns in the returned matrix is the same as in the sparse matrix.

    • toSparseArray

      public SparseMatrix.SparseArray toSparseArray()
      Returns the sparse matrix in the SparseArray form.