Package smile.math.matrix
Class Matrix.LU
java.lang.Object
smile.math.matrix.Matrix.LU
- All Implemented Interfaces:
Serializable
- Enclosing class:
Matrix
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.
- See Also:
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Field Summary
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Constructor Summary
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Method Summary
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Field Details
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lu
The LU decomposition. -
ipiv
public final int[] ipivThe pivot vector. -
info
public final int infoIfinfo = 0
, the LU decomposition was successful. Ifinfo = 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.
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Constructor Details
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LU
Constructor.- Parameters:
lu
- LU decomposition matrix.ipiv
- the pivot vector.info
-info > 0
if the matrix is singular.
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Method Details
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isSingular
public boolean isSingular()Returns true if the matrix is singular.- Returns:
- true if the matrix is singular.
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det
public double det()Returns the matrix determinant.- Returns:
- the matrix determinant.
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inverse
Returns the inverse of matrix. For pseudo inverse, use QRDecomposition.- Returns:
- the inverse of matrix.
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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.
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solve
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.
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