The Fac_LU companion object provides functions related to LU Factorization.
Attributes
Members list
Value members
Concrete methods
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 Fac_SVD.
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 Fac_SVD.
Value parameters
- a
-
the matrix whose condition number is sought
- a_lu
-
LU Factorization of matrix A
Attributes
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 Fac_SVD.
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 Fac_SVD.
Value parameters
- a
-
the matrix whose condition number is sought
- a_lu
-
LU Factorization of matrix A
Attributes
Compute the determinant of matrix a. The value of the determinant indicates, among other things, whether there is a unique solution to a system of linear equations (a nonzero determinant).
Compute the determinant of matrix a. The value of the determinant indicates, among other things, whether there is a unique solution to a system of linear equations (a nonzero determinant).
Value parameters
- a
-
the matrix whose determinant is sought
- lu
-
an LU factorization (use existing or make a new one)
Attributes
Diagnose matrix a looking for high correlation, high condition number, lower than expected rank, zero variance columns (there should only be one).
Diagnose matrix a looking for high correlation, high condition number, lower than expected rank, zero variance columns (there should only be one).
Value parameters
- a
-
the matrix to diagnose
Attributes
Return the inverse of matrix a by calling the inverse method in Fac_LU. Note: Fac_LU.inverse is generally faster and more robust than Fac_Inv.inverse.
Return the inverse of matrix a by calling the inverse method in Fac_LU. Note: Fac_LU.inverse is generally faster and more robust than Fac_Inv.inverse.
Value parameters
- a
-
the matrix whose inverse is sought
- lu
-
an LU factorization (use existing or make a new one)
Attributes
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.
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.
Value parameters
- 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)
Attributes
- See also
-
Algorithm 4.1 in HIGHAM1998
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.
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.
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.
Value parameters
- a
-
the matrix A whose norm is sought
- inv
-
whether or not to compute for inverse (default true)
Attributes
Solve a system of linear equations a*x = b.
Solve a system of linear equations a*x = b.
Value parameters
- a
-
the matrix A holding the coefficients of the equations
- b
-
the constant vector
- lu
-
LU Factorization of matrix A
Attributes
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.
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.
Value parameters
- a
-
the matrix A holding the coefficients of the equations
- b
-
the constant vector
Attributes
- See also
-
people.csail.mit.edu/bkph/articles/Pseudo_Inverse.pdf
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.
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.
Value parameters
- a
-
the matrix A holding the coefficients of the equations
- b
-
the constant vector
Attributes
- See also
-
people.csail.mit.edu/bkph/articles/Pseudo_Inverse.pdf
Solve for x in the equation a*x = b using LU Factorization. Return the solution vector x.
Solve for x in the equation a*x = b using LU Factorization. Return the solution vector x.
Value parameters
- a
-
the matrix A holding the coefficients of the equations
- b
-
the constant vector
Attributes
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.
Value parameters
- a
-
the matrix A to be factored
- b
-
the constant vector in Ax = b