delete
Chris Beall
parent
21e2be0ad6
commit
a46187ee67
197
base/DenseQR.cpp
197
base/DenseQR.cpp
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/*
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* DenseQR.cpp
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*
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* Created on: Oct 19, 2010
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* Author: nikai
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* Description: Dense QR, inspired by Tim Davis's dense solver
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*/
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#include <cassert>
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#include <math.h>
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#include <algorithm>
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#include "DenseQR.h"
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// all the lapack functions we need here
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extern "C" {
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void dlarft_ (char *direct, char *storev, int *n, int *k, double *V, int *ldv, double *Tau, double *T, int *ldt) ;
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void dlarfb_ (char *side, char *trans, char *direct, char *storev, int *m, int *n, int *k, double *V, int *ldv, double *T, int *ldt, double *C, int *ldc, double *Work, int *ldwork) ;
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void dlarfg_ (int *n, double *alpha, double *X, int *incx, double *tau) ;
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void dlarf_ (char *side, int *m, int *n, double *V, int *incv, double *tau, double *C, int *ldc, double *Work) ;
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}
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using namespace std;
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namespace gtsam {
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/* ************************************************************************* */
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/**
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* LARF applies a real elementary reflector H to a real m by n matrix
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* C, from either the left or the right. H is represented in the form
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*/
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void dlarf_wrap(long m, long n, long ldc, double *V, double tau, double *C, double *W)
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{
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static char left = 'L' ;
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double vsave ;
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if (m <= 0 || n <= 0) return ;
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vsave = V [0] ; // temporarily restore unit diagonal of V
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V [0] = 1 ;
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int m_ = m, n_ = n, ldc_ = ldc, one = 1 ;
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dlarf_ (&left, &m_, &n_, V, &one, &tau, C, &ldc_, W) ;
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V [0] = vsave ; // restore V [0]
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}
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/* ************************************************************************* */
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void dlarftb_wrap(long m, long n, long k, long ldc, long ldv, double *V, double *Tau, double *C, double *W)
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{
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static char direct = 'F';
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static char storev = 'C';
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static char side = 'L';
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static char trans = 'T';
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if (m <= 0 || n <= 0 || k <= 0) return ;
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double *T, *Work ;
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T = W ; // triangular k-by-k matrix for block reflector
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Work = W + k*k ; // workspace of size n*k or m*k for larfb
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// construct and apply the k-by-k upper triangular matrix T
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// larft and larfb are always used "Forward" and "Columnwise"
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assert (m >= k) ;
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int m_ = m, n_ = n, k_ = k, ldv_ = ldv, ldc_ = ldc;
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dlarft_(&direct, &storev, &m_, &k_, V, &ldv_, Tau, T, &k_) ;
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// Left, Transpose, Forward, Columwise:
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dlarfb_(&side, &trans, &direct, &storev, &m_, &n_, &k_, V, &ldv_,
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T, &k_, C, &ldc_, Work, &n_);
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}
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/* ************************************************************************* */
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long DenseQR(long m, long n, long npiv, double tol, long ntol, long fchunk,
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double *F, long *Stair, char *Rdead, double *Tau, double *W, double *wscale, double *wssq) {
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double tau, wk, *V;
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long k, t, g, g1, nv, k1, k2, i, t0, vzeros, mleft, nleft, vsize, minchunk, rank ;
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assert (F != NULL) ;
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assert (Stair != NULL) ;
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assert (Rdead != NULL) ;
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assert (Tau != NULL) ;
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assert (W != NULL) ;
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assert (m >= 0 && n >= 0) ;
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npiv = max (0l, npiv) ; // npiv must be between 0 and n
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npiv = min (n, npiv) ;
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g1 = 0 ; // row index of first queued-up Householder
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k1 = 0 ; // pending Householders are in F (g1:t, k1:k2-1)
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k2 = 0 ;
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V = F ; // Householder vectors start here
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g = 0 ; // number of good Householders found
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nv = 0 ; // number of Householder reflections queued up
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vzeros = 0 ; // number of explicit zeros in queued-up H's
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t = 0 ; // staircase of current column
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fchunk = max (fchunk, 1l) ;
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minchunk = max (4l, fchunk/4l) ;
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rank = min (m,npiv) ;
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ntol = min (ntol, npiv) ;
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for (k = 0; k < n; k++) {
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t0 = t; // t0 = staircase of column k-1
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t = Stair[k]; // t = staircase of this column k
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if (g >= m) {
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for (; k < npiv; k++) {
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Rdead[k] = 1;
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Stair[k] = 0;
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Tau[k] = 0;
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}
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for (; k < n; k++) {
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Stair[k] = m;
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Tau[k] = 0;
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}
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assert (nv == 0);
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return (rank);
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}
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t = max(g + 1, t);
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Stair[k] = t;
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vzeros += nv * (t - t0);
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if (nv >= minchunk) {
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vsize = (nv * (nv + 1)) / 2 + nv * (t - g1 - nv);
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if (vzeros > max(16l, vsize / 2)) {
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dlarftb_wrap(t0 - g1, n - k2, nv, m, m, V, // F (g1:t-1, k1:k1+nv-1)
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&Tau[k1], &F[g1+k2*m], W);
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nv = 0;
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vzeros = 0;
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}
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}
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// find a Householder reflection that reduces column k
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int n_ = t - g, one = 1;
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double *X = &F[g+k*m];
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dlarfg_(&n_, X, X + 1, &one, &tau);
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// check to see if the kth column is OK
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if (k < ntol && (wk = fabs(F[g+k*m])) <= tol) {
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if (wk != 0) {
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if ((*wscale) == 0) {
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(*wssq) = 1;
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}
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if ((*wscale) < wk) {
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double rr = (*wscale) / wk;
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(*wssq) = 1 + (*wssq) * rr * rr;
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(*wscale) = wk;
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} else {
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double rr = wk / (*wscale);
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(*wssq) += rr * rr;
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}
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}
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// zero out F (g:m-1,k) and flag it as dead
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for (i = g; i < m; i++)
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F[i+k*m] = 0;
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Stair[k] = 0;
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Tau[k] = 0;
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Rdead[k] = 1;
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// apply pending block of Householder reflections
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if (nv > 0) {
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dlarftb_wrap(t0 - g1, n - k2, nv, m, m, V, &Tau[k1], &F[g1+k2*m], W);
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nv = 0; // clear queued-up Householder reflections
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vzeros = 0;
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}
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} else {
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// one more good pivot column found
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Tau[k] = tau;
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if (nv == 0) {
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g1 = g;
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k1 = k;
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k2 = min(n, k + fchunk);
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V = &F[g1+k1*m];
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// check for switch to unblocked code
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mleft = m - g1; // number of rows left
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nleft = n - k1; // number of columns left
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if (mleft * (nleft - (fchunk + 4)) < 5000 || mleft <= fchunk / 2
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|| fchunk <= 1)
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k2 = n;
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}
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nv++; // one more pending update; V is F (g1:t-1, k1:k1+nv-1)
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// apply the kth Householder reflection to the current panel
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dlarf_wrap(t - g, k2 - k - 1, m, &F[g+k*m], tau, &F[g+(k+1)*m], W);
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g++; // one more pivot found
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if (k == k2 - 1 || g == m) {
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dlarftb_wrap(t - g1, n - k2, nv, m, m, V, &Tau[k1], &F[g1+(k2*m)], W);
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nv = 0; // clear queued-up Householder reflections
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vzeros = 0;
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}
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}
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if (k == npiv - 1) rank = g;
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}
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return rank;
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}
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}
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/*
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* DenseQR.h
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*
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* Created on: Oct 19, 2010
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* Author: nikai
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* Description: Dense QR, inspired by Tim Davis's dense solver
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*/
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#pragma once
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namespace gtsam {
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long DenseQR(
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long m, // F is m-by-n with leading dimension m
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long n,
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long npiv, // number of pivot columns
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double tol, // a column is flagged as dead if its norm is <= tol
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long ntol, // apply tol only to first ntol pivot columns
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long fchunk, // block size for compact WY Householder reflections,
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// treated as 1 if fchunk <= 1
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// input/output
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double *F, // frontal matrix F of size m-by-n
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long *Stair, // size n, entries F (Stair[k]:m-1, k) are all zero,
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// and remain zero on output.
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char *Rdead, // size npiv; all zero on input. If k is dead,
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// Rdead [k] is set to 1
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// output, not defined on input
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double *Tau, // size n, Householder coefficients
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// workspace, undefined on input and output
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double *W, // size b*(n+b), where b = min (fchunk,n,m)
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// input/output
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double *wscale,
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double *wssq
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);
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}
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/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010, Georgia Tech Research Corporation,
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* Atlanta, Georgia 30332-0415
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* All Rights Reserved
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* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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* See LICENSE for the license information
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* -------------------------------------------------------------------------- */
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/*
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* DenseQRUtil.cpp
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*
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* Created on: Jul 1, 2010
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* Author: nikai
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* Description: the utility functions for DenseQR
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*/
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#include <cstring>
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#include <gtsam/base/timing.h>
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#include <gtsam/base/DenseQRUtil.h>
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#include <boost/numeric/ublas/matrix.hpp>
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#include <boost/numeric/ublas/matrix_proxy.hpp>
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#include <boost/numeric/ublas/triangular.hpp>
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using namespace std;
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namespace ublas = boost::numeric::ublas;
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#ifdef GT_USE_LAPACK
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namespace gtsam {
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/* ************************************************************************* */
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long* MakeStairs(Matrix& A) {
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const long m = A.size1();
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const long n = A.size2();
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long* Stair = new long[n];
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// record the starting pointer of each row
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double* a[m];
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list<int> remained;
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a[0] = A.data().begin();
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for(int i=0; i<m-1; i++) {
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a[i+1] = a[i] + n;
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remained.push_back(i);
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}
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remained.push_back(m-1);
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// reorder the rows
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int j;
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vector<int> sorted;
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list<int>::iterator itRemained;
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for(j = 0; j < n; ) {
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// remove the non-zero rows in the current column
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for(itRemained = remained.begin(); itRemained!=remained.end(); ) {
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if (*(a[*itRemained]) != 0) {
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sorted.push_back(*itRemained);
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itRemained = remained.erase(itRemained);
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} else {
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a[*itRemained]++;
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itRemained ++;
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}
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}
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// record the stair number
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Stair[j++] = m - remained.size();
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if(remained.empty()) break;
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}
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// all the remained columns have maximum stair
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for (; j<n; j++)
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Stair[j] = m;
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// copy the new row
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Matrix A_new = zeros(m,n);
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int offset[m];
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offset[0] = 0;
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for(int i=1; i<m; i++)
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offset[i] = offset[i-1] +n;
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vector<int>::const_iterator itSorted;
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double* ptr1 = A.data().begin();
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double* ptr2 = A_new.data().begin();
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int row = 0, sizeOfRow = n * sizeof(double);
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for(itSorted=sorted.begin(); itSorted!=sorted.end(); itSorted++, row++)
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memcpy(ptr2+offset[row], ptr1+offset[*itSorted], sizeOfRow);
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A = A_new;
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return Stair;
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}
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void printColumnMajor(const double* a, const long m, const long n) {
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for(int i=0; i<m; i++) {
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for(int j=0; j<n; j++)
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cout << a[j*m+i] << "\t";
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cout << endl;
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}
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}
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/* ************************************************************************* */
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void householder_denseqr(Matrix &A, long* Stair) {
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tic("householder_denseqr");
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long m = A.size1();
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long n = A.size2();
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bool allocedStair = false;
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if (Stair == NULL) {
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allocedStair = true;
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Stair = new long[n];
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for(int j=0; j<n; j++)
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Stair[j] = m;
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}
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tic("householder_denseqr: row->col");
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// convert from row major to column major
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ublas::matrix<double, ublas::column_major> Acolwise(A);
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double *a = Acolwise.data().begin();
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toc("householder_denseqr: row->col");
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tic("householder_denseqr: denseqr_front");
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long npiv = min(m,n);
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double tol = -1; long ntol = -1; // no tolerance is used
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long fchunk = m < 32 ? m : 32;
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char Rdead[npiv]; memset(Rdead, 0, sizeof(char)*npiv);
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double Tau[n];
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long b = min(fchunk, min(n, m));
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double W[b*(n+b)];
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double wscale = 0;
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double wssq = 0;
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||||||
// todo: do something with the rank
|
|
||||||
long rank = DenseQR(m, n, npiv, tol, ntol, fchunk,
|
|
||||||
a, Stair, Rdead, Tau, W, &wscale, &wssq);
|
|
||||||
toc("householder_denseqr: denseqr_front");
|
|
||||||
|
|
||||||
|
|
||||||
for(long j=0; j<npiv; ++j)
|
|
||||||
if(Rdead[j]) {
|
|
||||||
cout << "In householder_denseqr, aborting because some columns were found to be\n"
|
|
||||||
"numerically linearly-dependent and we cannot handle this case yet." << endl;
|
|
||||||
print(A, "The matrix being factored was\n");
|
|
||||||
ublas::matrix_range<ublas::matrix<double,ublas::column_major> > Acolsub(
|
|
||||||
ublas::project(Acolwise, ublas::range(0, min(m,n)), ublas::range(0,n)));
|
|
||||||
print(Matrix(ublas::triangular_adaptor<typeof(Acolsub), ublas::upper>(Acolsub)), "and the result was\n");
|
|
||||||
cout << "The following columns are \"dead\":";
|
|
||||||
for(long k=0; k<npiv; ++k)
|
|
||||||
if(Rdead[k]) cout << " " << k;
|
|
||||||
cout << endl;
|
|
||||||
exit(1);
|
|
||||||
}
|
|
||||||
|
|
||||||
tic("householder_denseqr: col->row");
|
|
||||||
long k0 = 0;
|
|
||||||
long j0;
|
|
||||||
int k;
|
|
||||||
memset(A.data().begin(), 0, m*n*sizeof(double));
|
|
||||||
for(long j=0; j<n; j++, k0+=m) {
|
|
||||||
k = k0;
|
|
||||||
j0 = min(j+1,m);
|
|
||||||
for(int i=0; i<j0; i++, k++)
|
|
||||||
A(i,j) = a[k];
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
toc("householder_denseqr: col->row");
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
if(allocedStair) delete[] Stair;
|
|
||||||
|
|
||||||
toc("householder_denseqr");
|
|
||||||
}
|
|
||||||
|
|
||||||
void householder_denseqr_colmajor(ublas::matrix<double, ublas::column_major>& A, long *Stair) {
|
|
||||||
tic("householder_denseqr");
|
|
||||||
|
|
||||||
long m = A.size1();
|
|
||||||
long n = A.size2();
|
|
||||||
|
|
||||||
assert(Stair != NULL);
|
|
||||||
|
|
||||||
tic("householder_denseqr: denseqr_front");
|
|
||||||
long npiv = min(m,n);
|
|
||||||
double tol = -1; long ntol = -1; // no tolerance is used
|
|
||||||
long fchunk = m < 32 ? m : 32;
|
|
||||||
char Rdead[npiv]; memset(Rdead, 0, sizeof(char)*npiv);
|
|
||||||
double Tau[n];
|
|
||||||
long b = min(fchunk, min(n, m));
|
|
||||||
double W[b*(n+b)];
|
|
||||||
double wscale = 0;
|
|
||||||
double wssq = 0;
|
|
||||||
|
|
||||||
|
|
||||||
// todo: do something with the rank
|
|
||||||
long rank = DenseQR(m, n, npiv, tol, ntol, fchunk,
|
|
||||||
A.data().begin(), Stair, Rdead, Tau, W, &wscale, &wssq);
|
|
||||||
toc("householder_denseqr: denseqr_front");
|
|
||||||
|
|
||||||
for(long j=0; j<npiv; ++j)
|
|
||||||
if(Rdead[j]) {
|
|
||||||
cout << "In householder_denseqr, aborting because some columns were found to be\n"
|
|
||||||
"numerically linearly-dependent and we cannot handle this case yet." << endl;
|
|
||||||
print(A, "The matrix being factored was\n");
|
|
||||||
ublas::matrix_range<ublas::matrix<double,ublas::column_major> > Acolsub(
|
|
||||||
ublas::project(A, ublas::range(0, min(m,n)), ublas::range(0,n)));
|
|
||||||
print(Matrix(ublas::triangular_adaptor<typeof(Acolsub), ublas::upper>(Acolsub)), "and the result was\n");
|
|
||||||
cout << "The following columns are \"dead\":";
|
|
||||||
for(long k=0; k<npiv; ++k)
|
|
||||||
if(Rdead[k]) cout << " " << k;
|
|
||||||
cout << endl;
|
|
||||||
exit(1);
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
toc("householder_denseqr");
|
|
||||||
|
|
||||||
}
|
|
||||||
|
|
||||||
} // namespace gtsam
|
|
||||||
#endif
|
|
||||||
|
|
@ -1,38 +0,0 @@
|
||||||
/* ----------------------------------------------------------------------------
|
|
||||||
|
|
||||||
* GTSAM Copyright 2010, Georgia Tech Research Corporation,
|
|
||||||
* Atlanta, Georgia 30332-0415
|
|
||||||
* All Rights Reserved
|
|
||||||
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
|
|
||||||
|
|
||||||
* See LICENSE for the license information
|
|
||||||
|
|
||||||
* -------------------------------------------------------------------------- */
|
|
||||||
|
|
||||||
/*
|
|
||||||
* DenseQRUtil.h
|
|
||||||
*
|
|
||||||
* Created on: Jul 1, 2010
|
|
||||||
* Author: nikai
|
|
||||||
* Description: the utility functions for DenseQR
|
|
||||||
*/
|
|
||||||
|
|
||||||
#pragma once
|
|
||||||
|
|
||||||
#include <gtsam/base/Matrix.h>
|
|
||||||
|
|
||||||
#ifdef GT_USE_LAPACK
|
|
||||||
#include <gtsam/base/DenseQR.h>
|
|
||||||
|
|
||||||
namespace gtsam {
|
|
||||||
|
|
||||||
/** make stairs and speed up householder_denseqr. Stair is defined as the row index of where zero entries start in each column */
|
|
||||||
long* MakeStairs(Matrix &A);
|
|
||||||
|
|
||||||
/** Householder tranformation, zeros below diagonal */
|
|
||||||
void householder_denseqr(Matrix &A, long* Stair = NULL);
|
|
||||||
|
|
||||||
/** Householder tranformation in column mafor form */
|
|
||||||
void householder_denseqr_colmajor(boost::numeric::ublas::matrix<double, boost::numeric::ublas::column_major>& A, long *Stair);
|
|
||||||
}
|
|
||||||
#endif
|
|
||||||
Loading…
Reference in New Issue