Fac_QR_RR
The Fac_QR_RR class provides methods to factor an 'm-by-n' matrix 'a' into the product of two matrices: 'q' - an 'm-by-n' orthogonal matrix and 'r' - an 'n-by-n' right upper triangular matrix such that 'a = q * r'. It uses uses Householder orthogonalization.
Value parameters
- aa
-
the matrix to be factor into q and r
- needQ
-
flag indicating whether a full q matrix is needed
Attributes
- See also
-
5.1 and 5.2 in Matrix Computations
QRDecomposition.java in Jama
- Graph
-
- Supertypes
Members list
Value members
Concrete methods
Perform QR Factorization and result in a single matrix which contains Householder vectors of each columns in lower triangular of 'aa' matrix. This Rank Revealing algorithm uses Householder orthogonalization and pivoting.
Perform QR Factorization and result in a single matrix which contains Householder vectors of each columns in lower triangular of 'aa' matrix. This Rank Revealing algorithm uses Householder orthogonalization and pivoting.
Attributes
- See also
-
5.1 and 5.2 in Matrix Computations
QRDecomposition.java in Jama
- Definition Classes
Return the rank (number of independent columns) in matrix 'aa'.
Return the rank (number of independent columns) in matrix 'aa'.
Attributes
Inherited methods
Compute the full q orthogonal matrix based on updated values in at.
Compute the full q orthogonal matrix based on updated values in at.
Attributes
- Inherited from:
- Fac_QR
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.
Attributes
- Inherited from:
- Factorization
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.
Attributes
- Inherited from:
- Factorization
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.
Attributes
- Inherited from:
- Factorization
Return both the orthogonal q matrix and the right upper triangular r matrix.
Return both the orthogonal q matrix and the right upper triangular r matrix.
Attributes
- Inherited from:
- Fac_QR
Efficient calculation of inverse matrix a^-1 from existing factorization. a * a^-1 = I
Efficient calculation of inverse matrix a^-1 from existing factorization. a * a^-1 = I
Attributes
- Inherited from:
- Fac_QR
Return whether the matrix has been factored has aleady been factored.
Return whether the matrix has been factored has aleady been factored.
Attributes
- Inherited from:
- Factorization
Compute the nullspace of matrix a: { x | ax = 0 } using QR Factorization qr*x = 0. Gives a basis of dimension n - rank for the nullspace Caveat: requires dim >= dim2
Compute the nullspace of matrix a: { x | ax = 0 } using QR Factorization qr*x = 0. Gives a basis of dimension n - rank for the nullspace Caveat: requires dim >= dim2
Value parameters
- rank
-
the rank of the matrix (number of linearly independent column vectors)
Attributes
- Inherited from:
- Fac_QR
Compute the nullspace of matrix a: { x | ax = 0 } using QR Factorization qr*x = 0. Gives only one vector in the nullspace.
Compute the nullspace of matrix a: { x | ax = 0 } using QR Factorization qr*x = 0. Gives only one vector in the nullspace.
Value parameters
- x
-
a vector with the correct dimension
Attributes
- Inherited from:
- Fac_QR
Reorder the columns of matrix a according to the pivot vector piv.
Reorder the columns of matrix a according to the pivot vector piv.
Value parameters
- a
-
the matrix to reorder
- piv
-
the vector indicating the column swaps that occurred during pivoting
Attributes
- Inherited from:
- Pivoting
Reorder the rows of matrix a according to the pivot vector piv.
Reorder the rows of matrix a according to the pivot vector piv.
Value parameters
- a
-
the matrix to reorder
- piv
-
the vector indicating the row swaps that occurred during pivoting
Attributes
- Inherited from:
- Pivoting
Reset by setting factored to false.
Solve for x in aax = b using the QR Factorization aa = qr via r*x = q.t * b without actually calculating the q matrix. Note /~ is the back substitution operator (\ in MatLab).
Solve for x in aax = b using the QR Factorization aa = qr via r*x = q.t * b without actually calculating the q matrix. Note /~ is the back substitution operator (\ in MatLab).
Value parameters
- b
-
the constant vector
Attributes
- Inherited from:
- Fac_QR
Inherited fields
Flag indicating whether the matrix has been factored