object Fac_LU extends Error
The Fac_LU companion object provides functions related to LU Factorization.
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def
conditionNum(a: MatriD, a_lu: Fac_LU[MatriD]): Double
Compute the condition number of matrix 'a', which equals
Compute the condition number of matrix 'a', which equals
||a|| ||b|| where b = a.inverse
Requires 'a' to be a square matrix. For rectangular matrices, @see
SVDecomp.- a
the matrix whose condition number is sought
- a_lu
LU Factorization of matrix A
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def
conditionNum2(a: MatriD, a_lu: Fac_LU[MatriD]): Double
Compute the condition number of matrix 'a', which equals
Compute the condition number of matrix 'a', which equals
||a|| ||b|| where b = a.inverse
Requires 'a' to be a square matrix. For rectangular matrices, @see
SVDecomp.- a
the matrix whose condition number is sought
- a_lu
LU Factorization of matrix A
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def
flaw(method: String, message: String): Unit
Show the flaw by printing the error message.
Show the flaw by printing the error message.
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the method where the error occurred
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the error message
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def
norm1est(a: MatriD, inv: Boolean): Double
Compute an estimate of the L1 norm of 'this' matrix, i.e., maximum absolute column sum.
Compute an estimate of the L1 norm of 'this' matrix, i.e., maximum absolute column sum. It uses an adapted version of Hager's algorithm.
- a
the matrix A whose norm is sought
- inv
whether or not to compute for inverse (default true)
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def
norm1est(a: MatriD, a_lu: Fac_LU[MatriD], inv: Boolean = true): Double
Compute an estimate of the L1 norm of 'this' matrix, i.e., maximum absolute column sum.
Compute an estimate of the L1 norm of 'this' matrix, i.e., maximum absolute column sum. It uses an adapted version of Hager's algorithm.
- a
the matrix A whose norm is sought
- a_lu
LU Factorization of matrix A
- inv
whether or not to compute for inverse (default true)
- See also
www.maths.manchester.ac.uk/~higham/narep/narep135.pdf
Higham, N.J. "Fortran Codes for Estimating the One-Norm of a Real or Complex Matrix, with Applications to Condition Estimation." ACM Trans. Math. Soft., 14, 1988, pp. 381-396.
Algorithm 4.1 in HIGHAM1998
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def
solve(a: MatriD, lu: Fac_LU[MatriD], b: VectoD): VectoD
Solve a system of linear equations 'a*x = b'.
Solve a system of linear equations 'a*x = b'.
- a
the matrix A holding the coefficients of the equations
- lu
LU Factorization of matrix A
- b
the constant vector
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def
solveOver(a: MatriD, b: VectoD): VectoD
Solve for 'x' in the equation 'a*x = b' in an over determined system of linear equation using least squares.
Solve for 'x' in the equation 'a*x = b' in an over determined system of linear equation using least squares. Return the solution vector 'x'.
- a
the matrix A holding the coefficients of the equations
- b
the constant vector
- See also
people.csail.mit.edu/bkph/articles/Pseudo_Inverse.pdf
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def
solveUnder(a: MatriD, b: VectoD): VectoD
Solve for 'x' in the equation 'a*x = b' in an under determined system of linear equation by finding the smallest solution.
Solve for 'x' in the equation 'a*x = b' in an under determined system of linear equation by finding the smallest solution. Return the solution vector 'x'.
- a
the matrix A holding the coefficients of the equations
- b
the constant vector
- See also
people.csail.mit.edu/bkph/articles/Pseudo_Inverse.pdf
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def
test(a: MatriD, b: VectoD): Unit
Test the LU Factorization of matrix 'a' into 'l' and 'u' and its usage in solving a system of linear equations.
Test the LU Factorization of matrix 'a' into 'l' and 'u' and its usage in solving a system of linear equations.
- a
the matrix A to be factored
- b
the constant vector in Ax = b
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