The Fac_QR 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
Members list
Value members
Concrete 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
Perform QR Factorization and store the result in a single matrix which contains Householder vectors of each column in the lower triangle of the aa matrix. This algorithm uses Householder orthogonalization.
Perform QR Factorization and store the result in a single matrix which contains Householder vectors of each column in the lower triangle of the aa matrix. This algorithm uses Householder orthogonalization.
Attributes
- See also
-
5.1 and 5.2 in Matrix Computations
QRDecomposition.java in Jama
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
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
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
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
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 methods
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 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
Reset by setting factored to false.
Inherited fields
Flag indicating whether the matrix has been factored