class Fac_LQ extends Factorization with Error
The Fac_LQ class provides methods to factor an 'm-by-n' matrix 'aa' into the
product of two matrices, when m < n.
'l' - an 'm-by-m' left lower triangular matrix 'q' - an 'm-by-n' orthogonal matrix and
such that 'aa = l * q'. Note, orthogonal means that 'q.t * q = I'.
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def
factor(): Fac_LQ
Factor matrix 'art' into the product of two matrices, 'art = qt * rt'.
Factor matrix 'art' into the product of two matrices, 'art = qt * rt'. Then compute 'r' and 'q'.
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- See also
http://math.stackexchange.com/questions/1640695/rq-decomposition
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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 the two factored matrices.
Return the two factored matrices.
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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
Solve for 'x' in 'aa*x = b' using the 'QR' Factorization 'aa = l*q' via 'x = q.t * l.inv * b'.
Solve for 'x' in 'aa*x = b' using the 'QR' Factorization 'aa = l*q' via 'x = q.t * l.inv * b'. FIX: need method that does not require calling 'inverse'
- b
the constant vector
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