Class SymmMatrix.BunchKaufman

java.lang.Object
smile.math.matrix.SymmMatrix.BunchKaufman
All Implemented Interfaces:
`Serializable`
Enclosing class:
`SymmMatrix`

public static class SymmMatrix.BunchKaufman extends Object implements Serializable
The LU decomposition. For an m-by-n matrix A with `m >= n`, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If `m < n`, then L is m-by-m and U is m-by-n.

The LU decomposition with pivoting always exists, even if the matrix is singular. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations if it is not singular. The decomposition can also be used to calculate the determinant.

• Field Summary

Fields
Modifier and Type
Field
Description
`final int`
`info`
If `info = 0`, the LU decomposition was successful.
`final int[]`
`ipiv`
The pivot vector.
`final SymmMatrix`
`lu`
The Bunchâ€“Kaufman decomposition.
• Constructor Summary

Constructors
Constructor
Description
```BunchKaufman(SymmMatrix lu, int[] ipiv, int info)```
Constructor.
• Method Summary

Modifier and Type
Method
Description
`double`
`det()`
Returns the matrix determinant.
`Matrix`
`inverse()`
Returns the inverse of matrix.
`boolean`
`isSingular()`
Returns true if the matrix is singular.
`double[]`
`solve(double[] b)`
Solve A * x = b.
`void`
`solve(Matrix B)`
Solve A * X = B.

Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• Field Details

• lu

public final SymmMatrix lu
The Bunchâ€“Kaufman decomposition.
• ipiv

public final int[] ipiv
The pivot vector.
• info

public final int info
If `info = 0`, the LU decomposition was successful. If `info = i > 0`, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.
• Constructor Details

• BunchKaufman

public BunchKaufman(SymmMatrix lu, int[] ipiv, int info)
Constructor.
Parameters:
`lu` - LU decomposition matrix.
`ipiv` - the pivot vector.
`info` - `info > 0` if the matrix is singular.
• Method Details

• isSingular

public boolean isSingular()
Returns true if the matrix is singular.
Returns:
true if the matrix is singular.
• det

public double det()
Returns the matrix determinant.
Returns:
the matrix determinant.
• inverse

public Matrix inverse()
Returns the inverse of matrix.
Returns:
the inverse of matrix.
• solve

public double[] solve(double[] b)
Solve A * x = b.
Parameters:
`b` - the right hand side of linear system.
Returns:
the solution vector.
Throws:
`RuntimeException` - when the matrix is singular.
• solve

public void solve(Matrix B)
Solve A * X = B. B will be overwritten with the solution matrix on output.
Parameters:
`B` - the right hand side of linear system. On output, B will be overwritten with the solution matrix.
Throws:
`RuntimeException` - when the matrix is singular.