qr.c File Reference

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "include/hholder.h"
#include "include/qr.h"

Functions
int	qr (double **A, int m, int n, double *B, double *X, double *rnorm, double *tau, double *res, double **wws, double *ws)
int	qr_decomp (double **a, int M, int N, double *tau, double **cchain, double *chain)
int	qr_solve (double **QR, int M, int N, double *tau, double *b, double *x, double *residual, double *resNorm, double **cchain, double *chain)
int	qr_QTvec (double **QR, double *tau, double *v, double *help)
int	qr_Qvec (double **QR, double *tau, double *v, double *help)
int	qr_invRvec (double **A, double *X)
int	qr_weight (int N, int M, double **A, double *b, double *weight)
Variables
int	qr_M
int	qr_N
int	qr_MNmin

---

Function Documentation

int qr (  double **  A, int  m, int  n, double *  B, double *  X, double *  rnorm, double *  tau, double *  res, double **  wws, double *  ws )

Parameters: A  On entry, a[m][n] contains the m by n matrix A. On exit, a[][] contains the QR factorization m  Dimensions of matrix A are a[m][n] n  Dimensions of matrix A are a[m][n] B  B[] is an m-vector containing the right-hand side vector b. X  On exit, x[] will contain the solution vector x. rnorm  On exit, rnorm contains the Euclidean norm of the residual vector tau  On exit, tau[] will contain the householder coefficients. res  An m-array of working space, res[]. On output contains residual b - Ax wws  m*n array of working space ws  2m-array of working space

int qr_decomp (  double **  a, int  M, int  N, double *  tau, double **  cchain, double *  chain )

Factorise a general M x N matrix A into A = Q R where Q is orthogonal (M x M) and R is upper triangular (M x N). Q is stored as a packed set of Householder vectors in the strict lower triangular part of the input matrix A and a set of coefficients in vector tau. R is stored in the diagonal and upper triangle of the input matrix. The full matrix for Q can be obtained as the product Q = Q_1 Q_2 .. Q_k and it's transform as the product Q^T = Q_k .. Q_2 Q_1 where k = min(M,N) and Q_i = (I - tau_i * h_i * h_i^T) and where h_i is a Householder vector h_i = [1, A(i+1,i), A(i+2,i), ... , A(M,i)] This storage scheme is the same as in LAPACK. NOTICE! The calling program must take care that pointer tau is of size n. Returns: Function returns 0 if ok. Parameters: a  contains coefficient matrix A (m*n) as input and factorisation QR as output M  nr of rows in matrix A N  nr of columns in matrix A tau  n-vector for householder coefficients cchain  m*n array of working space chain  2m array of working space

int qr_invRvec (  double **  A, double *  X )

Form the product R^-1 v. (R is saved in the upper triangel of QR matrix.) Returns: Returns 0 if ok.

int qr_QTvec (  double **  QR, double *  tau, double *  v, double *  help )

Form the product Q^T v from householder vectors saved in the lower triangel of QR matrix and householder coefficients saved in vector tau. Returns: Returns 0 if ok.

int qr_Qvec (  double **  QR, double *  tau, double *  v, double *  help )

Form the product Q v from householder vectors saved in the lower triangel of QR matrix and householder coefficients saved in vector tau. Returns: Returns 0 if ok.

int qr_solve (  double **  QR, int  M, int  N, double *  tau, double *  b, double *  x, double *  residual, double *  resNorm, double **  cchain, double *  chain )

Find the least squares solution to the overdetermined system A x = b for m >= n using the QR factorisation A = Q R. qr_decomp() must be used prior to this function in order to form the QR factorisation of A. Solution is formed in the following order: QR x = b => R x = Q^T b => x = R^-1 (Q^T b) NOTICE! The calling program must take care that pointers b, x and residual are of the right size. Returns: Function returns 0 if ok. Parameters: QR  m*n matrix containing householder vectors of A M  nr of rows in matrix A N  nr of columns in matrix A tau  vector containing householder coefficients tau b  Contains m-vector b of A x = b x  solution vector x of length n residual  residual vector of length m resNorm  norm^2 of the residual vector cchain  m*n array of the working space chain  2m lenght array of the working space

int qr_weight (  int  N, int  M, double **  A, double *  b, double *  weight )

Algorithm for weighting the problem that is given to qr-algorithm. Square roots of weights are used because in qr the difference w*A-w*b is squared. Returns: Algorithm returns zero if successful, 1 if arguments are inappropriate.

---

Variable Documentation

int qr_M

Global variables for this routine

int qr_MNmin

int qr_N

---