class Fac_Cholesky[MatT <: MatriD] extends Factorization with Error
The Fac_Cholesky class provides methods to factor an 'n-by-n' symmetric,
positive definite matrix 'a' into the product of two matrices:
'l' - an 'n-by-n' left lower triangular matrix 'l.t' - an 'n-by-n' right upper triangular matrix - transpose of 'l'
such that 'a = l * l.t'.
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new
Fac_Cholesky(a: MatT)
- a
the symmetric, positive definite matrix to be factor
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def
factor(): Fac_Cholesky[MatT]
Factor matrix 'a' into the product of 'l' and 'l.t' using Cholesky Factorization 'a = l * l.t', where 'l.t' is 'l's transpose.
Factor matrix 'a' into the product of 'l' and 'l.t' using Cholesky Factorization 'a = l * l.t', where 'l.t' is 'l's transpose. It uses the Cholesky–Banachiewicz algorithm.
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- See also
introcs.cs.princeton.edu/java/95linear
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def
factor1(): MatriD
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the first matrix.
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the first matrix.
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def
factor12(): (MatriD, MatriD)
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t' or a = q * r, returning both the first and second matrices.
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t' or a = q * r, returning both the first and second matrices.
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def
factor2(): MatriD
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the second matrix.
Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the second matrix.
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val
factored: Boolean
Flag indicating whether the matrix has been factored
Flag indicating whether the matrix has been factored
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def
factors: (MatriD, MatriD)
Return both the lower triangular matrix 'l' and its transpose 'l.t'.
Return both the lower triangular matrix 'l' and its transpose 'l.t'.
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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
solve(b: VectoD): VectoD
Use the lower triangular matrix 'l' from the Cholesky Factorization to solve a system of equations 'a * x = b'.
Use the lower triangular matrix 'l' from the Cholesky Factorization to solve a system of equations 'a * x = b'. Return the solution x using forward and backward substitution.
- b
the constant vector
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