Fac_QR
Related Doc:
package par
the matrix to be factor into q and r
Perform backward substitution to solve for 'x' in 'r*x = b'.
Perform backward substitution to solve for 'x' in 'r*x = b'.
the right upper triangular matrix
the constant vector
Factor matrix 'a' into the product of two matrices, 'a = q * r', returning both the orthogonal 'q' matrix and the right upper triangular 'r' matrix.
Factor matrix 'a' into the product of two matrices, 'a = q * r', returning both the orthogonal 'q' matrix and the right upper triangular 'r' matrix.
Return the first factor, i.e., orthogonal 'q' matrix.
Return the first factor, i.e., orthogonal 'q' matrix.
Return the second factor, i.e., the right upper triangular 'r' matrix.
Return the second factor, i.e., the right upper triangular 'r' matrix.
Show the flaw by printing the error message.
Show the flaw by printing the error message.
the method where the error occurred
the error message
Compute the nullspace of matrix 'a: { x | a*x = 0 }' using QR Factorization 'q*r*x = 0'.
Compute the nullspace of matrix 'a: { x | a*x = 0 }' using QR Factorization 'q*r*x = 0'. Gives a basis of dimension 'n' - rank for the nullspace
the rank of the matrix (number of linearly independent row vectors) FIX: should work, but it does not
Compute the nullspace of matrix 'a: { x | a*x = 0 }' using QR Factorization 'q*r*x = 0'.
Compute the nullspace of matrix 'a: { x | a*x = 0 }' using QR Factorization 'q*r*x = 0'. Gives only one vector in the nullspace.
Solve for 'x' in 'a*x = b' using the QR Factorization 'a = q*r' via 'r*x = q.t * b'.
Solve for 'x' in 'a*x = b' using the QR Factorization 'a = q*r' via 'r*x = q.t * b'.
the constant vector
The
Fac_QRclass 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 Gram-Schmidt orthogonalization. Note, orthogonal means that 'q.t * q = I'. This version uses parallel processing to speed up execution.
http://en.wikipedia.org/wiki/Gram–Schmidt_process (stabilized Gram–Schmidt orthonormalization)
http://www.stat.wisc.edu/~larget/math496/qr.html