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.
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.
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)
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).