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/*************************************************************************
* *
* Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
* All rights reserved. Email: russ@q12.org Web: www.q12.org *
* *
* This library is free software; you can redistribute it and/or *
* modify it under the terms of EITHER: *
* (1) The GNU Lesser General Public License as published by the Free *
* Software Foundation; either version 2.1 of the License, or (at *
* your option) any later version. The text of the GNU Lesser *
* General Public License is included with this library in the *
* file LICENSE.TXT. *
* (2) The BSD-style license that is included with this library in *
* the file LICENSE-BSD.TXT. *
* *
* This library is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files *
* LICENSE.TXT and LICENSE-BSD.TXT for more details. *
* *
*************************************************************************/
/*
THE ALGORITHM
-------------
solve A*x = b+w, with x and w subject to certain LCP conditions.
each x(i),w(i) must lie on one of the three line segments in the following
diagram. each line segment corresponds to one index set :
w(i)
/|\ | :
| | :
| |i in N :
w>0 | |state[i]=0 :
| | :
| | : i in C
w=0 + +-----------------------+
| : |
| : |
w<0 | : |i in N
| : |state[i]=1
| : |
| : |
+-------|-----------|-----------|----------> x(i)
lo 0 hi
the Dantzig algorithm proceeds as follows:
for i=1:n
* if (x(i),w(i)) is not on the line, push x(i) and w(i) positive or
negative towards the line. as this is done, the other (x(j),w(j))
for j<i are constrained to be on the line. if any (x,w) reaches the
end of a line segment then it is switched between index sets.
* i is added to the appropriate index set depending on what line segment
it hits.
we restrict lo(i) <= 0 and hi(i) >= 0. this makes the algorithm a bit
simpler, because the starting point for x(i),w(i) is always on the dotted
line x=0 and x will only ever increase in one direction, so it can only hit
two out of the three line segments.
NOTES
-----
this is an implementation of "lcp_dantzig2_ldlt.m" and "lcp_dantzig_lohi.m".
the implementation is split into an LCP problem object (dLCP) and an LCP
driver function. most optimization occurs in the dLCP object.
a naive implementation of the algorithm requires either a lot of data motion
or a lot of permutation-array lookup, because we are constantly re-ordering
rows and columns. to avoid this and make a more optimized algorithm, a
non-trivial data structure is used to represent the matrix A (this is
implemented in the fast version of the dLCP object).
during execution of this algorithm, some indexes in A are clamped (set C),
some are non-clamped (set N), and some are "don't care" (where x=0).
A,x,b,w (and other problem vectors) are permuted such that the clamped
indexes are first, the unclamped indexes are next, and the don't-care
indexes are last. this permutation is recorded in the array `p'.
initially p = 0..n-1, and as the rows and columns of A,x,b,w are swapped,
the corresponding elements of p are swapped.
because the C and N elements are grouped together in the rows of A, we can do
lots of work with a fast dot product function. if A,x,etc were not permuted
and we only had a permutation array, then those dot products would be much
slower as we would have a permutation array lookup in some inner loops.
A is accessed through an array of row pointers, so that element (i,j) of the
permuted matrix is A[i][j]. this makes row swapping fast. for column swapping
we still have to actually move the data.
during execution of this algorithm we maintain an L*D*L' factorization of
the clamped submatrix of A (call it `AC') which is the top left nC*nC
submatrix of A. there are two ways we could arrange the rows/columns in AC.
(1) AC is always permuted such that L*D*L' = AC. this causes a problem
when a row/column is removed from C, because then all the rows/columns of A
between the deleted index and the end of C need to be rotated downward.
this results in a lot of data motion and slows things down.
(2) L*D*L' is actually a factorization of a *permutation* of AC (which is
itself a permutation of the underlying A). this is what we do - the
permutation is recorded in the vector C. call this permutation A[C,C].
when a row/column is removed from C, all we have to do is swap two
rows/columns and manipulate C.
*/
#include <ode/common.h>
#include "lcp.h"
#include <ode/matrix.h>
#include <ode/misc.h>
#include "mat.h" // for testing
#include <ode/timer.h> // for testing
//***************************************************************************
// code generation parameters
// LCP debugging (mosty for fast dLCP) - this slows things down a lot
//#define DEBUG_LCP
//#define dLCP_SLOW // use slow dLCP object
#define dLCP_FAST // use fast dLCP object
// option 1 : matrix row pointers (less data copying)
#define ROWPTRS
#define ATYPE dReal **
#define AROW(i) (A[i])
// option 2 : no matrix row pointers (slightly faster inner loops)
//#define NOROWPTRS
//#define ATYPE dReal *
//#define AROW(i) (A+(i)*nskip)
// use protected, non-stack memory allocation system
#ifdef dUSE_MALLOC_FOR_ALLOCA
extern unsigned int dMemoryFlag;
#define ALLOCA(t,v,s) t* v = (t*) malloc(s)
#define UNALLOCA(t) free(t)
#else
#define ALLOCA(t,v,s) t* v =(t*)dALLOCA16(s)
#define UNALLOCA(t) /* nothing */
#endif
#define NUB_OPTIMIZATIONS
//***************************************************************************
// swap row/column i1 with i2 in the n*n matrix A. the leading dimension of
// A is nskip. this only references and swaps the lower triangle.
// if `do_fast_row_swaps' is nonzero and row pointers are being used, then
// rows will be swapped by exchanging row pointers. otherwise the data will
// be copied.
static void swapRowsAndCols (ATYPE A, int n, int i1, int i2, int nskip,
int do_fast_row_swaps)
{
int i;
dAASSERT (A && n > 0 && i1 >= 0 && i2 >= 0 && i1 < n && i2 < n &&
nskip >= n && i1 < i2);
# ifdef ROWPTRS
for (i=i1+1; i<i2; i++) A[i1][i] = A[i][i1];
for (i=i1+1; i<i2; i++) A[i][i1] = A[i2][i];
A[i1][i2] = A[i1][i1];
A[i1][i1] = A[i2][i1];
A[i2][i1] = A[i2][i2];
// swap rows, by swapping row pointers
if (do_fast_row_swaps) {
dReal *tmpp;
tmpp = A[i1];
A[i1] = A[i2];
A[i2] = tmpp;
}
else {
ALLOCA (dReal,tmprow,n * sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (tmprow == NULL) {
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
memcpy (tmprow,A[i1],n * sizeof(dReal));
memcpy (A[i1],A[i2],n * sizeof(dReal));
memcpy (A[i2],tmprow,n * sizeof(dReal));
UNALLOCA(tmprow);
}
// swap columns the hard way
for (i=i2+1; i<n; i++) {
dReal tmp = A[i][i1];
A[i][i1] = A[i][i2];
A[i][i2] = tmp;
}
# else
dReal tmp;
ALLOCA (dReal,tmprow,n * sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (tmprow == NULL) {
return;
}
#endif
if (i1 > 0) {
memcpy (tmprow,A+i1*nskip,i1*sizeof(dReal));
memcpy (A+i1*nskip,A+i2*nskip,i1*sizeof(dReal));
memcpy (A+i2*nskip,tmprow,i1*sizeof(dReal));
}
for (i=i1+1; i<i2; i++) {
tmp = A[i2*nskip+i];
A[i2*nskip+i] = A[i*nskip+i1];
A[i*nskip+i1] = tmp;
}
tmp = A[i1*nskip+i1];
A[i1*nskip+i1] = A[i2*nskip+i2];
A[i2*nskip+i2] = tmp;
for (i=i2+1; i<n; i++) {
tmp = A[i*nskip+i1];
A[i*nskip+i1] = A[i*nskip+i2];
A[i*nskip+i2] = tmp;
}
UNALLOCA(tmprow);
# endif
}
// swap two indexes in the n*n LCP problem. i1 must be <= i2.
static void swapProblem (ATYPE A, dReal *x, dReal *b, dReal *w, dReal *lo,
dReal *hi, int *p, int *state, int *findex,
int n, int i1, int i2, int nskip,
int do_fast_row_swaps)
{
dReal tmp;
int tmpi;
dIASSERT (n>0 && i1 >=0 && i2 >= 0 && i1 < n && i2 < n && nskip >= n &&
i1 <= i2);
if (i1==i2) return;
swapRowsAndCols (A,n,i1,i2,nskip,do_fast_row_swaps);
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY)
return;
#endif
tmp = x[i1];
x[i1] = x[i2];
x[i2] = tmp;
tmp = b[i1];
b[i1] = b[i2];
b[i2] = tmp;
tmp = w[i1];
w[i1] = w[i2];
w[i2] = tmp;
tmp = lo[i1];
lo[i1] = lo[i2];
lo[i2] = tmp;
tmp = hi[i1];
hi[i1] = hi[i2];
hi[i2] = tmp;
tmpi = p[i1];
p[i1] = p[i2];
p[i2] = tmpi;
tmpi = state[i1];
state[i1] = state[i2];
state[i2] = tmpi;
if (findex) {
tmpi = findex[i1];
findex[i1] = findex[i2];
findex[i2] = tmpi;
}
}
// for debugging - check that L,d is the factorization of A[C,C].
// A[C,C] has size nC*nC and leading dimension nskip.
// L has size nC*nC and leading dimension nskip.
// d has size nC.
#ifdef DEBUG_LCP
static void checkFactorization (ATYPE A, dReal *_L, dReal *_d,
int nC, int *C, int nskip)
{
int i,j;
if (nC==0) return;
// get A1=A, copy the lower triangle to the upper triangle, get A2=A[C,C]
dMatrix A1 (nC,nC);
for (i=0; i<nC; i++) {
for (j=0; j<=i; j++) A1(i,j) = A1(j,i) = AROW(i)[j];
}
dMatrix A2 = A1.select (nC,C,nC,C);
// printf ("A1=\n"); A1.print(); printf ("\n");
// printf ("A2=\n"); A2.print(); printf ("\n");
// compute A3 = L*D*L'
dMatrix L (nC,nC,_L,nskip,1);
dMatrix D (nC,nC);
for (i=0; i<nC; i++) D(i,i) = 1/_d[i];
L.clearUpperTriangle();
for (i=0; i<nC; i++) L(i,i) = 1;
dMatrix A3 = L * D * L.transpose();
// printf ("L=\n"); L.print(); printf ("\n");
// printf ("D=\n"); D.print(); printf ("\n");
// printf ("A3=\n"); A2.print(); printf ("\n");
// compare A2 and A3
dReal diff = A2.maxDifference (A3);
if (diff > 1e-8)
dDebug (0,"L*D*L' check, maximum difference = %.6e\n",diff);
}
#endif
// for debugging
#ifdef DEBUG_LCP
static void checkPermutations (int i, int n, int nC, int nN, int *p, int *C)
{
int j,k;
dIASSERT (nC>=0 && nN>=0 && (nC+nN)==i && i < n);
for (k=0; k<i; k++) dIASSERT (p[k] >= 0 && p[k] < i);
for (k=i; k<n; k++) dIASSERT (p[k] == k);
for (j=0; j<nC; j++) {
int C_is_bad = 1;
for (k=0; k<nC; k++) if (C[k]==j) C_is_bad = 0;
dIASSERT (C_is_bad==0);
}
}
#endif
//***************************************************************************
// dLCP manipulator object. this represents an n*n LCP problem.
//
// two index sets C and N are kept. each set holds a subset of
// the variable indexes 0..n-1. an index can only be in one set.
// initially both sets are empty.
//
// the index set C is special: solutions to A(C,C)\A(C,i) can be generated.
#ifdef dLCP_SLOW
// simple but slow implementation of dLCP, for testing the LCP drivers.
#include "array.h"
struct dLCP {
int n,nub,nskip;
dReal *Adata,*x,*b,*w,*lo,*hi; // LCP problem data
ATYPE A; // A rows
dArray<int> C,N; // index sets
int last_i_for_solve1; // last i value given to solve1
dLCP (int _n, int _nub, dReal *_Adata, dReal *_x, dReal *_b, dReal *_w,
dReal *_lo, dReal *_hi, dReal *_L, dReal *_d,
dReal *_Dell, dReal *_ell, dReal *_tmp,
int *_state, int *_findex, int *_p, int *_C, dReal **Arows);
// the constructor is given an initial problem description (A,x,b,w) and
// space for other working data (which the caller may allocate on the stack).
// some of this data is specific to the fast dLCP implementation.
// the matrices A and L have size n*n, vectors have size n*1.
// A represents a symmetric matrix but only the lower triangle is valid.
// `nub' is the number of unbounded indexes at the start. all the indexes
// 0..nub-1 will be put into C.
~dLCP();
int getNub() { return nub; }
// return the value of `nub'. the constructor may want to change it,
// so the caller should find out its new value.
// transfer functions: transfer index i to the given set (C or N). indexes
// less than `nub' can never be given. A,x,b,w,etc may be permuted by these
// functions, the caller must be robust to this.
void transfer_i_to_C (int i);
// this assumes C and N span 1:i-1. this also assumes that solve1() has
// been recently called for the same i without any other transfer
// functions in between (thereby allowing some data reuse for the fast
// implementation).
void transfer_i_to_N (int i);
// this assumes C and N span 1:i-1.
void transfer_i_from_N_to_C (int i);
void transfer_i_from_C_to_N (int i);
int numC();
int numN();
// return the number of indexes in set C/N
int indexC (int i);
int indexN (int i);
// return index i in set C/N.
// accessor and arithmetic functions. Aij translates as A(i,j), etc.
// make sure that only the lower triangle of A is ever referenced.
dReal Aii (int i);
dReal AiC_times_qC (int i, dReal *q);
dReal AiN_times_qN (int i, dReal *q); // for all Nj
void pN_equals_ANC_times_qC (dReal *p, dReal *q); // for all Nj
void pN_plusequals_ANi (dReal *p, int i, int sign=1);
// for all Nj. sign = +1,-1. assumes i > maximum index in N.
void pC_plusequals_s_times_qC (dReal *p, dReal s, dReal *q);
void pN_plusequals_s_times_qN (dReal *p, dReal s, dReal *q); // for all Nj
void solve1 (dReal *a, int i, int dir=1, int only_transfer=0);
// get a(C) = - dir * A(C,C) \ A(C,i). dir must be +/- 1.
// the fast version of this function computes some data that is needed by
// transfer_i_to_C(). if only_transfer is nonzero then this function
// *only* computes that data, it does not set a(C).
void unpermute();
// call this at the end of the LCP function. if the x/w values have been
// permuted then this will unscramble them.
};
dLCP::dLCP (int _n, int _nub, dReal *_Adata, dReal *_x, dReal *_b, dReal *_w,
dReal *_lo, dReal *_hi, dReal *_L, dReal *_d,
dReal *_Dell, dReal *_ell, dReal *_tmp,
int *_state, int *_findex, int *_p, int *_C, dReal **Arows)
{
dUASSERT (_findex==0,"slow dLCP object does not support findex array");
n = _n;
nub = _nub;
Adata = _Adata;
A = 0;
x = _x;
b = _b;
w = _w;
lo = _lo;
hi = _hi;
nskip = dPAD(n);
dSetZero (x,n);
last_i_for_solve1 = -1;
int i,j;
C.setSize (n);
N.setSize (n);
for (i=0; i<n; i++) {
C[i] = 0;
N[i] = 0;
}
# ifdef ROWPTRS
// make matrix row pointers
A = Arows;
for (i=0; i<n; i++) A[i] = Adata + i*nskip;
# else
A = Adata;
# endif
// lets make A symmetric
for (i=0; i<n; i++) {
for (j=i+1; j<n; j++) AROW(i)[j] = AROW(j)[i];
}
// if nub>0, put all indexes 0..nub-1 into C and solve for x
if (nub > 0) {
for (i=0; i<nub; i++) memcpy (_L+i*nskip,AROW(i),(i+1)*sizeof(dReal));
dFactorLDLT (_L,_d,nub,nskip);
memcpy (x,b,nub*sizeof(dReal));
dSolveLDLT (_L,_d,x,nub,nskip);
dSetZero (_w,nub);
for (i=0; i<nub; i++) C[i] = 1;
}
}
dLCP::~dLCP()
{
}
void dLCP::transfer_i_to_C (int i)
{
if (i < nub) dDebug (0,"bad i");
if (C[i]) dDebug (0,"i already in C");
if (N[i]) dDebug (0,"i already in N");
for (int k=0; k<i; k++) {
if (!(C[k] ^ N[k])) dDebug (0,"assumptions for C and N violated");
}
for (int k=i; k<n; k++)
if (C[k] || N[k]) dDebug (0,"assumptions for C and N violated");
if (i != last_i_for_solve1) dDebug (0,"assumptions for i violated");
last_i_for_solve1 = -1;
C[i] = 1;
}
void dLCP::transfer_i_to_N (int i)
{
if (i < nub) dDebug (0,"bad i");
if (C[i]) dDebug (0,"i already in C");
if (N[i]) dDebug (0,"i already in N");
for (int k=0; k<i; k++)
if (!C[k] && !N[k]) dDebug (0,"assumptions for C and N violated");
for (int k=i; k<n; k++)
if (C[k] || N[k]) dDebug (0,"assumptions for C and N violated");
last_i_for_solve1 = -1;
N[i] = 1;
}
void dLCP::transfer_i_from_N_to_C (int i)
{
if (i < nub) dDebug (0,"bad i");
if (C[i]) dDebug (0,"i already in C");
if (!N[i]) dDebug (0,"i not in N");
last_i_for_solve1 = -1;
N[i] = 0;
C[i] = 1;
}
void dLCP::transfer_i_from_C_to_N (int i)
{
if (i < nub) dDebug (0,"bad i");
if (N[i]) dDebug (0,"i already in N");
if (!C[i]) dDebug (0,"i not in C");
last_i_for_solve1 = -1;
C[i] = 0;
N[i] = 1;
}
int dLCP::numC()
{
int i,count=0;
for (i=0; i<n; i++) if (C[i]) count++;
return count;
}
int dLCP::numN()
{
int i,count=0;
for (i=0; i<n; i++) if (N[i]) count++;
return count;
}
int dLCP::indexC (int i)
{
int k,count=0;
for (k=0; k<n; k++) {
if (C[k]) {
if (count==i) return k;
count++;
}
}
dDebug (0,"bad index C (%d)",i);
return 0;
}
int dLCP::indexN (int i)
{
int k,count=0;
for (k=0; k<n; k++) {
if (N[k]) {
if (count==i) return k;
count++;
}
}
dDebug (0,"bad index into N");
return 0;
}
dReal dLCP::Aii (int i)
{
return AROW(i)[i];
}
dReal dLCP::AiC_times_qC (int i, dReal *q)
{
dReal sum = 0;
for (int k=0; k<n; k++) if (C[k]) sum += AROW(i)[k] * q[k];
return sum;
}
dReal dLCP::AiN_times_qN (int i, dReal *q)
{
dReal sum = 0;
for (int k=0; k<n; k++) if (N[k]) sum += AROW(i)[k] * q[k];
return sum;
}
void dLCP::pN_equals_ANC_times_qC (dReal *p, dReal *q)
{
dReal sum;
for (int ii=0; ii<n; ii++) if (N[ii]) {
sum = 0;
for (int jj=0; jj<n; jj++) if (C[jj]) sum += AROW(ii)[jj] * q[jj];
p[ii] = sum;
}
}
void dLCP::pN_plusequals_ANi (dReal *p, int i, int sign)
{
int k;
for (k=0; k<n; k++) if (N[k] && k >= i) dDebug (0,"N assumption violated");
if (sign > 0) {
for (k=0; k<n; k++) if (N[k]) p[k] += AROW(i)[k];
}
else {
for (k=0; k<n; k++) if (N[k]) p[k] -= AROW(i)[k];
}
}
void dLCP::pC_plusequals_s_times_qC (dReal *p, dReal s, dReal *q)
{
for (int k=0; k<n; k++) if (C[k]) p[k] += s*q[k];
}
void dLCP::pN_plusequals_s_times_qN (dReal *p, dReal s, dReal *q)
{
for (int k=0; k<n; k++) if (N[k]) p[k] += s*q[k];
}
void dLCP::solve1 (dReal *a, int i, int dir, int only_transfer)
{
ALLOCA (dReal,AA,n*nskip*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (AA == NULL) {
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,dd,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (dd == NULL) {
UNALLOCA(AA);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,bb,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (bb == NULL) {
UNALLOCA(AA);
UNALLOCA(dd);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
int ii,jj,AAi,AAj;
last_i_for_solve1 = i;
AAi = 0;
for (ii=0; ii<n; ii++) if (C[ii]) {
AAj = 0;
for (jj=0; jj<n; jj++) if (C[jj]) {
AA[AAi*nskip+AAj] = AROW(ii)[jj];
AAj++;
}
bb[AAi] = AROW(i)[ii];
AAi++;
}
if (AAi==0) {
UNALLOCA (AA);
UNALLOCA (dd);
UNALLOCA (bb);
return;
}
dFactorLDLT (AA,dd,AAi,nskip);
dSolveLDLT (AA,dd,bb,AAi,nskip);
AAi=0;
if (dir > 0) {
for (ii=0; ii<n; ii++) if (C[ii]) a[ii] = -bb[AAi++];
}
else {
for (ii=0; ii<n; ii++) if (C[ii]) a[ii] = bb[AAi++];
}
UNALLOCA (AA);
UNALLOCA (dd);
UNALLOCA (bb);
}
void dLCP::unpermute()
{
}
#endif // dLCP_SLOW
//***************************************************************************
// fast implementation of dLCP. see the above definition of dLCP for
// interface comments.
//
// `p' records the permutation of A,x,b,w,etc. p is initially 1:n and is
// permuted as the other vectors/matrices are permuted.
//
// A,x,b,w,lo,hi,state,findex,p,c are permuted such that sets C,N have
// contiguous indexes. the don't-care indexes follow N.
//
// an L*D*L' factorization is maintained of A(C,C), and whenever indexes are
// added or removed from the set C the factorization is updated.
// thus L*D*L'=A[C,C], i.e. a permuted top left nC*nC submatrix of A.
// the leading dimension of the matrix L is always `nskip'.
//
// at the start there may be other indexes that are unbounded but are not
// included in `nub'. dLCP will permute the matrix so that absolutely all
// unbounded vectors are at the start. thus there may be some initial
// permutation.
//
// the algorithms here assume certain patterns, particularly with respect to
// index transfer.
#ifdef dLCP_FAST
struct dLCP {
int n,nskip,nub;
ATYPE A; // A rows
dReal *Adata,*x,*b,*w,*lo,*hi; // permuted LCP problem data
dReal *L,*d; // L*D*L' factorization of set C
dReal *Dell,*ell,*tmp;
int *state,*findex,*p,*C;
int nC,nN; // size of each index set
dLCP (int _n, int _nub, dReal *_Adata, dReal *_x, dReal *_b, dReal *_w,
dReal *_lo, dReal *_hi, dReal *_L, dReal *_d,
dReal *_Dell, dReal *_ell, dReal *_tmp,
int *_state, int *_findex, int *_p, int *_C, dReal **Arows);
int getNub() { return nub; }
void transfer_i_to_C (int i);
void transfer_i_to_N (int i)
{ nN++; } // because we can assume C and N span 1:i-1
void transfer_i_from_N_to_C (int i);
void transfer_i_from_C_to_N (int i);
int numC() { return nC; }
int numN() { return nN; }
int indexC (int i) { return i; }
int indexN (int i) { return i+nC; }
dReal Aii (int i) { return AROW(i)[i]; }
dReal AiC_times_qC (int i, dReal *q) { return dDot (AROW(i),q,nC); }
dReal AiN_times_qN (int i, dReal *q) { return dDot (AROW(i)+nC,q+nC,nN); }
void pN_equals_ANC_times_qC (dReal *p, dReal *q);
void pN_plusequals_ANi (dReal *p, int i, int sign=1);
void pC_plusequals_s_times_qC (dReal *p, dReal s, dReal *q)
{ for (int i=0; i<nC; i++) p[i] += s*q[i]; }
void pN_plusequals_s_times_qN (dReal *p, dReal s, dReal *q)
{ for (int i=0; i<nN; i++) p[i+nC] += s*q[i+nC]; }
void solve1 (dReal *a, int i, int dir=1, int only_transfer=0);
void unpermute();
};
dLCP::dLCP (int _n, int _nub, dReal *_Adata, dReal *_x, dReal *_b, dReal *_w,
dReal *_lo, dReal *_hi, dReal *_L, dReal *_d,
dReal *_Dell, dReal *_ell, dReal *_tmp,
int *_state, int *_findex, int *_p, int *_C, dReal **Arows)
{
n = _n;
nub = _nub;
Adata = _Adata;
A = 0;
x = _x;
b = _b;
w = _w;
lo = _lo;
hi = _hi;
L = _L;
d = _d;
Dell = _Dell;
ell = _ell;
tmp = _tmp;
state = _state;
findex = _findex;
p = _p;
C = _C;
nskip = dPAD(n);
dSetZero (x,n);
int k;
# ifdef ROWPTRS
// make matrix row pointers
A = Arows;
for (k=0; k<n; k++) A[k] = Adata + k*nskip;
# else
A = Adata;
# endif
nC = 0;
nN = 0;
for (k=0; k<n; k++) p[k]=k; // initially unpermuted
/*
// for testing, we can do some random swaps in the area i > nub
if (nub < n) {
for (k=0; k<100; k++) {
int i1,i2;
do {
i1 = dRandInt(n-nub)+nub;
i2 = dRandInt(n-nub)+nub;
}
while (i1 > i2);
//printf ("--> %d %d\n",i1,i2);
swapProblem (A,x,b,w,lo,hi,p,state,findex,n,i1,i2,nskip,0);
}
}
*/
// permute the problem so that *all* the unbounded variables are at the
// start, i.e. look for unbounded variables not included in `nub'. we can
// potentially push up `nub' this way and get a bigger initial factorization.
// note that when we swap rows/cols here we must not just swap row pointers,
// as the initial factorization relies on the data being all in one chunk.
// variables that have findex >= 0 are *not* considered to be unbounded even
// if lo=-inf and hi=inf - this is because these limits may change during the
// solution process.
for (k=nub; k<n; k++) {
if (findex && findex[k] >= 0) continue;
if (lo[k]==-dInfinity && hi[k]==dInfinity) {
swapProblem (A,x,b,w,lo,hi,p,state,findex,n,nub,k,nskip,0);
nub++;
}
}
// if there are unbounded variables at the start, factorize A up to that
// point and solve for x. this puts all indexes 0..nub-1 into C.
if (nub > 0) {
for (k=0; k<nub; k++) memcpy (L+k*nskip,AROW(k),(k+1)*sizeof(dReal));
dFactorLDLT (L,d,nub,nskip);
memcpy (x,b,nub*sizeof(dReal));
dSolveLDLT (L,d,x,nub,nskip);
dSetZero (w,nub);
for (k=0; k<nub; k++) C[k] = k;
nC = nub;
}
// permute the indexes > nub such that all findex variables are at the end
if (findex) {
int num_at_end = 0;
for (k=n-1; k >= nub; k--) {
if (findex[k] >= 0) {
swapProblem (A,x,b,w,lo,hi,p,state,findex,n,k,n-1-num_at_end,nskip,1);
num_at_end++;
}
}
}
// print info about indexes
/*
for (k=0; k<n; k++) {
if (k<nub) printf ("C");
else if (lo[k]==-dInfinity && hi[k]==dInfinity) printf ("c");
else printf (".");
}
printf ("\n");
*/
}
void dLCP::transfer_i_to_C (int i)
{
int j;
if (nC > 0) {
// ell,Dell were computed by solve1(). note, ell = D \ L1solve (L,A(i,C))
for (j=0; j<nC; j++) L[nC*nskip+j] = ell[j];
d[nC] = dRecip (AROW(i)[i] - dDot(ell,Dell,nC));
}
else {
d[0] = dRecip (AROW(i)[i]);
}
swapProblem (A,x,b,w,lo,hi,p,state,findex,n,nC,i,nskip,1);
C[nC] = nC;
nC++;
# ifdef DEBUG_LCP
checkFactorization (A,L,d,nC,C,nskip);
if (i < (n-1)) checkPermutations (i+1,n,nC,nN,p,C);
# endif
}
void dLCP::transfer_i_from_N_to_C (int i)
{
int j;
if (nC > 0) {
dReal *aptr = AROW(i);
# ifdef NUB_OPTIMIZATIONS
// if nub>0, initial part of aptr unpermuted
for (j=0; j<nub; j++) Dell[j] = aptr[j];
for (j=nub; j<nC; j++) Dell[j] = aptr[C[j]];
# else
for (j=0; j<nC; j++) Dell[j] = aptr[C[j]];
# endif
dSolveL1 (L,Dell,nC,nskip);
for (j=0; j<nC; j++) ell[j] = Dell[j] * d[j];
for (j=0; j<nC; j++) L[nC*nskip+j] = ell[j];
d[nC] = dRecip (AROW(i)[i] - dDot(ell,Dell,nC));
}
else {
d[0] = dRecip (AROW(i)[i]);
}
swapProblem (A,x,b,w,lo,hi,p,state,findex,n,nC,i,nskip,1);
C[nC] = nC;
nN--;
nC++;
// @@@ TO DO LATER
// if we just finish here then we'll go back and re-solve for
// delta_x. but actually we can be more efficient and incrementally
// update delta_x here. but if we do this, we wont have ell and Dell
// to use in updating the factorization later.
# ifdef DEBUG_LCP
checkFactorization (A,L,d,nC,C,nskip);
# endif
}
void dLCP::transfer_i_from_C_to_N (int i)
{
// remove a row/column from the factorization, and adjust the
// indexes (black magic!)
int j,k;
for (j=0; j<nC; j++) if (C[j]==i) {
dLDLTRemove (A,C,L,d,n,nC,j,nskip);
for (k=0; k<nC; k++) if (C[k]==nC-1) {
C[k] = C[j];
if (j < (nC-1)) memmove (C+j,C+j+1,(nC-j-1)*sizeof(int));
break;
}
dIASSERT (k < nC);
break;
}
dIASSERT (j < nC);
swapProblem (A,x,b,w,lo,hi,p,state,findex,n,i,nC-1,nskip,1);
nC--;
nN++;
# ifdef DEBUG_LCP
checkFactorization (A,L,d,nC,C,nskip);
# endif
}
void dLCP::pN_equals_ANC_times_qC (dReal *p, dReal *q)
{
// we could try to make this matrix-vector multiplication faster using
// outer product matrix tricks, e.g. with the dMultidotX() functions.
// but i tried it and it actually made things slower on random 100x100
// problems because of the overhead involved. so we'll stick with the
// simple method for now.
for (int i=0; i<nN; i++) p[i+nC] = dDot (AROW(i+nC),q,nC);
}
void dLCP::pN_plusequals_ANi (dReal *p, int i, int sign)
{
dReal *aptr = AROW(i)+nC;
if (sign > 0) {
for (int i=0; i<nN; i++) p[i+nC] += aptr[i];
}
else {
for (int i=0; i<nN; i++) p[i+nC] -= aptr[i];
}
}
void dLCP::solve1 (dReal *a, int i, int dir, int only_transfer)
{
// the `Dell' and `ell' that are computed here are saved. if index i is
// later added to the factorization then they can be reused.
//
// @@@ question: do we need to solve for entire delta_x??? yes, but
// only if an x goes below 0 during the step.
int j;
if (nC > 0) {
dReal *aptr = AROW(i);
# ifdef NUB_OPTIMIZATIONS
// if nub>0, initial part of aptr[] is guaranteed unpermuted
for (j=0; j<nub; j++) Dell[j] = aptr[j];
for (j=nub; j<nC; j++) Dell[j] = aptr[C[j]];
# else
for (j=0; j<nC; j++) Dell[j] = aptr[C[j]];
# endif
dSolveL1 (L,Dell,nC,nskip);
for (j=0; j<nC; j++) ell[j] = Dell[j] * d[j];
if (!only_transfer) {
for (j=0; j<nC; j++) tmp[j] = ell[j];
dSolveL1T (L,tmp,nC,nskip);
if (dir > 0) {
for (j=0; j<nC; j++) a[C[j]] = -tmp[j];
}
else {
for (j=0; j<nC; j++) a[C[j]] = tmp[j];
}
}
}
}
void dLCP::unpermute()
{
// now we have to un-permute x and w
int j;
ALLOCA (dReal,tmp,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (tmp == NULL) {
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
memcpy (tmp,x,n*sizeof(dReal));
for (j=0; j<n; j++) x[p[j]] = tmp[j];
memcpy (tmp,w,n*sizeof(dReal));
for (j=0; j<n; j++) w[p[j]] = tmp[j];
UNALLOCA (tmp);
}
#endif // dLCP_FAST
//***************************************************************************
// an unoptimized Dantzig LCP driver routine for the basic LCP problem.
// must have lo=0, hi=dInfinity, and nub=0.
void dSolveLCPBasic (int n, dReal *A, dReal *x, dReal *b,
dReal *w, int nub, dReal *lo, dReal *hi)
{
dAASSERT (n>0 && A && x && b && w && nub == 0);
int i,k;
int nskip = dPAD(n);
ALLOCA (dReal,L,n*nskip*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (L == NULL) {
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,d,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (d == NULL) {
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,delta_x,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (delta_x == NULL) {
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,delta_w,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (delta_w == NULL) {
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,Dell,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (Dell == NULL) {
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,ell,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (ell == NULL) {
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,tmp,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (tmp == NULL) {
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal*,Arows,n*sizeof(dReal*));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (Arows == NULL) {
UNALLOCA(tmp);
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (int,p,n*sizeof(int));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (p == NULL) {
UNALLOCA(Arows);
UNALLOCA(tmp);
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (int,C,n*sizeof(int));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (C == NULL) {
UNALLOCA(p);
UNALLOCA(Arows);
UNALLOCA(tmp);
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (int,dummy,n*sizeof(int));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (dummy == NULL) {
UNALLOCA(C);
UNALLOCA(p);
UNALLOCA(Arows);
UNALLOCA(tmp);
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
dLCP lcp (n,0,A,x,b,w,tmp,tmp,L,d,Dell,ell,tmp,dummy,dummy,p,C,Arows);
nub = lcp.getNub();
for (i=0; i<n; i++) {
w[i] = lcp.AiC_times_qC (i,x) - b[i];
if (w[i] >= 0) {
lcp.transfer_i_to_N (i);
}
else {
for (;;) {
// compute: delta_x(C) = -A(C,C)\A(C,i)
dSetZero (delta_x,n);
lcp.solve1 (delta_x,i);
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY) {
UNALLOCA(dummy);
UNALLOCA(C);
UNALLOCA(p);
UNALLOCA(Arows);
UNALLOCA(tmp);
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
return;
}
#endif
delta_x[i] = 1;
// compute: delta_w = A*delta_x
dSetZero (delta_w,n);
lcp.pN_equals_ANC_times_qC (delta_w,delta_x);
lcp.pN_plusequals_ANi (delta_w,i);
delta_w[i] = lcp.AiC_times_qC (i,delta_x) + lcp.Aii(i);
// find index to switch
int si = i; // si = switch index
int si_in_N = 0; // set to 1 if si in N
dReal s = -w[i]/delta_w[i];
if (s <= 0) {
dMessage (d_ERR_LCP, "LCP internal error, s <= 0 (s=%.4e)",s);
if (i < (n-1)) {
dSetZero (x+i,n-i);
dSetZero (w+i,n-i);
}
goto done;
}
for (k=0; k < lcp.numN(); k++) {
if (delta_w[lcp.indexN(k)] < 0) {
dReal s2 = -w[lcp.indexN(k)] / delta_w[lcp.indexN(k)];
if (s2 < s) {
s = s2;
si = lcp.indexN(k);
si_in_N = 1;
}
}
}
for (k=0; k < lcp.numC(); k++) {
if (delta_x[lcp.indexC(k)] < 0) {
dReal s2 = -x[lcp.indexC(k)] / delta_x[lcp.indexC(k)];
if (s2 < s) {
s = s2;
si = lcp.indexC(k);
si_in_N = 0;
}
}
}
// apply x = x + s * delta_x
lcp.pC_plusequals_s_times_qC (x,s,delta_x);
x[i] += s;
lcp.pN_plusequals_s_times_qN (w,s,delta_w);
w[i] += s * delta_w[i];
// switch indexes between sets if necessary
if (si==i) {
w[i] = 0;
lcp.transfer_i_to_C (i);
break;
}
if (si_in_N) {
w[si] = 0;
lcp.transfer_i_from_N_to_C (si);
}
else {
x[si] = 0;
lcp.transfer_i_from_C_to_N (si);
}
}
}
}
done:
lcp.unpermute();
UNALLOCA (L);
UNALLOCA (d);
UNALLOCA (delta_x);
UNALLOCA (delta_w);
UNALLOCA (Dell);
UNALLOCA (ell);
UNALLOCA (tmp);
UNALLOCA (Arows);
UNALLOCA (p);
UNALLOCA (C);
UNALLOCA (dummy);
}
//***************************************************************************
// an optimized Dantzig LCP driver routine for the lo-hi LCP problem.
void dSolveLCP (int n, dReal *A, dReal *x, dReal *b,
dReal *w, int nub, dReal *lo, dReal *hi, int *findex)
{
dAASSERT (n>0 && A && x && b && w && lo && hi && nub >= 0 && nub <= n);
int i,k,hit_first_friction_index = 0;
int nskip = dPAD(n);
// if all the variables are unbounded then we can just factor, solve,
// and return
if (nub >= n) {
dFactorLDLT (A,w,n,nskip); // use w for d
dSolveLDLT (A,w,b,n,nskip);
memcpy (x,b,n*sizeof(dReal));
dSetZero (w,n);
return;
}
# ifndef dNODEBUG
// check restrictions on lo and hi
for (k=0; k<n; k++) dIASSERT (lo[k] <= 0 && hi[k] >= 0);
# endif
ALLOCA (dReal,L,n*nskip*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (L == NULL) {
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,d,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (d == NULL) {
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,delta_x,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (delta_x == NULL) {
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,delta_w,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (delta_w == NULL) {
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,Dell,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (Dell == NULL) {
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,ell,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (ell == NULL) {
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal*,Arows,n*sizeof(dReal*));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (Arows == NULL) {
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (int,p,n*sizeof(int));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (p == NULL) {
UNALLOCA(Arows);
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (int,C,n*sizeof(int));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (C == NULL) {
UNALLOCA(p);
UNALLOCA(Arows);
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
int dir;
dReal dirf;
// for i in N, state[i] is 0 if x(i)==lo(i) or 1 if x(i)==hi(i)
ALLOCA (int,state,n*sizeof(int));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (state == NULL) {
UNALLOCA(C);
UNALLOCA(p);
UNALLOCA(Arows);
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
// create LCP object. note that tmp is set to delta_w to save space, this
// optimization relies on knowledge of how tmp is used, so be careful!
dLCP *lcp=new dLCP(n,nub,A,x,b,w,lo,hi,L,d,Dell,ell,delta_w,state,findex,p,C,Arows);
nub = lcp->getNub();
// loop over all indexes nub..n-1. for index i, if x(i),w(i) satisfy the
// LCP conditions then i is added to the appropriate index set. otherwise
// x(i),w(i) is driven either +ve or -ve to force it to the valid region.
// as we drive x(i), x(C) is also adjusted to keep w(C) at zero.
// while driving x(i) we maintain the LCP conditions on the other variables
// 0..i-1. we do this by watching out for other x(i),w(i) values going
// outside the valid region, and then switching them between index sets
// when that happens.
for (i=nub; i<n; i++) {
// the index i is the driving index and indexes i+1..n-1 are "dont care",
// i.e. when we make changes to the system those x's will be zero and we
// don't care what happens to those w's. in other words, we only consider
// an (i+1)*(i+1) sub-problem of A*x=b+w.
// if we've hit the first friction index, we have to compute the lo and
// hi values based on the values of x already computed. we have been
// permuting the indexes, so the values stored in the findex vector are
// no longer valid. thus we have to temporarily unpermute the x vector.
// for the purposes of this computation, 0*infinity = 0 ... so if the
// contact constraint's normal force is 0, there should be no tangential
// force applied.
if (hit_first_friction_index == 0 && findex && findex[i] >= 0) {
// un-permute x into delta_w, which is not being used at the moment
for (k=0; k<n; k++) delta_w[p[k]] = x[k];
// set lo and hi values
for (k=i; k<n; k++) {
dReal wfk = delta_w[findex[k]];
if (wfk == 0) {
hi[k] = 0;
lo[k] = 0;
}
else {
hi[k] = dFabs (hi[k] * wfk);
lo[k] = -hi[k];
}
}
hit_first_friction_index = 1;
}
// thus far we have not even been computing the w values for indexes
// greater than i, so compute w[i] now.
w[i] = lcp->AiC_times_qC (i,x) + lcp->AiN_times_qN (i,x) - b[i];
// if lo=hi=0 (which can happen for tangential friction when normals are
// 0) then the index will be assigned to set N with some state. however,
// set C's line has zero size, so the index will always remain in set N.
// with the "normal" switching logic, if w changed sign then the index
// would have to switch to set C and then back to set N with an inverted
// state. this is pointless, and also computationally expensive. to
// prevent this from happening, we use the rule that indexes with lo=hi=0
// will never be checked for set changes. this means that the state for
// these indexes may be incorrect, but that doesn't matter.
// see if x(i),w(i) is in a valid region
if (lo[i]==0 && w[i] >= 0) {
lcp->transfer_i_to_N (i);
state[i] = 0;
}
else if (hi[i]==0 && w[i] <= 0) {
lcp->transfer_i_to_N (i);
state[i] = 1;
}
else if (w[i]==0) {
// this is a degenerate case. by the time we get to this test we know
// that lo != 0, which means that lo < 0 as lo is not allowed to be +ve,
// and similarly that hi > 0. this means that the line segment
// corresponding to set C is at least finite in extent, and we are on it.
// NOTE: we must call lcp->solve1() before lcp->transfer_i_to_C()
lcp->solve1 (delta_x,i,0,1);
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY) {
UNALLOCA(state);
UNALLOCA(C);
UNALLOCA(p);
UNALLOCA(Arows);
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
return;
}
#endif
lcp->transfer_i_to_C (i);
}
else {
// we must push x(i) and w(i)
for (;;) {
// find direction to push on x(i)
if (w[i] <= 0) {
dir = 1;
dirf = REAL(1.0);
}
else {
dir = -1;
dirf = REAL(-1.0);
}
// compute: delta_x(C) = -dir*A(C,C)\A(C,i)
lcp->solve1 (delta_x,i,dir);
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY) {
UNALLOCA(state);
UNALLOCA(C);
UNALLOCA(p);
UNALLOCA(Arows);
UNALLOCA(ell);
UNALLOCA(Dell);
UNALLOCA(delta_w);
UNALLOCA(delta_x);
UNALLOCA(d);
UNALLOCA(L);
return;
}
#endif
// note that delta_x[i] = dirf, but we wont bother to set it
// compute: delta_w = A*delta_x ... note we only care about
// delta_w(N) and delta_w(i), the rest is ignored
lcp->pN_equals_ANC_times_qC (delta_w,delta_x);
lcp->pN_plusequals_ANi (delta_w,i,dir);
delta_w[i] = lcp->AiC_times_qC (i,delta_x) + lcp->Aii(i)*dirf;
// find largest step we can take (size=s), either to drive x(i),w(i)
// to the valid LCP region or to drive an already-valid variable
// outside the valid region.
int cmd = 1; // index switching command
int si = 0; // si = index to switch if cmd>3
dReal s = -w[i]/delta_w[i];
if (dir > 0) {
if (hi[i] < dInfinity) {
dReal s2 = (hi[i]-x[i])/dirf; // step to x(i)=hi(i)
if (s2 < s) {
s = s2;
cmd = 3;
}
}
}
else {
if (lo[i] > -dInfinity) {
dReal s2 = (lo[i]-x[i])/dirf; // step to x(i)=lo(i)
if (s2 < s) {
s = s2;
cmd = 2;
}
}
}
for (k=0; k < lcp->numN(); k++) {
if ((state[lcp->indexN(k)]==0 && delta_w[lcp->indexN(k)] < 0) ||
(state[lcp->indexN(k)]!=0 && delta_w[lcp->indexN(k)] > 0)) {
// don't bother checking if lo=hi=0
if (lo[lcp->indexN(k)] == 0 && hi[lcp->indexN(k)] == 0) continue;
dReal s2 = -w[lcp->indexN(k)] / delta_w[lcp->indexN(k)];
if (s2 < s) {
s = s2;
cmd = 4;
si = lcp->indexN(k);
}
}
}
for (k=nub; k < lcp->numC(); k++) {
if (delta_x[lcp->indexC(k)] < 0 && lo[lcp->indexC(k)] > -dInfinity) {
dReal s2 = (lo[lcp->indexC(k)]-x[lcp->indexC(k)]) /
delta_x[lcp->indexC(k)];
if (s2 < s) {
s = s2;
cmd = 5;
si = lcp->indexC(k);
}
}
if (delta_x[lcp->indexC(k)] > 0 && hi[lcp->indexC(k)] < dInfinity) {
dReal s2 = (hi[lcp->indexC(k)]-x[lcp->indexC(k)]) /
delta_x[lcp->indexC(k)];
if (s2 < s) {
s = s2;
cmd = 6;
si = lcp->indexC(k);
}
}
}
//static char* cmdstring[8] = {0,"->C","->NL","->NH","N->C",
// "C->NL","C->NH"};
//printf ("cmd=%d (%s), si=%d\n",cmd,cmdstring[cmd],(cmd>3) ? si : i);
// if s <= 0 then we've got a problem. if we just keep going then
// we're going to get stuck in an infinite loop. instead, just cross
// our fingers and exit with the current solution.
if (s <= 0) {
dMessage (d_ERR_LCP, "LCP internal error, s <= 0 (s=%.4e)",s);
if (i < (n-1)) {
dSetZero (x+i,n-i);
dSetZero (w+i,n-i);
}
goto done;
}
// apply x = x + s * delta_x
lcp->pC_plusequals_s_times_qC (x,s,delta_x);
x[i] += s * dirf;
// apply w = w + s * delta_w
lcp->pN_plusequals_s_times_qN (w,s,delta_w);
w[i] += s * delta_w[i];
// switch indexes between sets if necessary
switch (cmd) {
case 1: // done
w[i] = 0;
lcp->transfer_i_to_C (i);
break;
case 2: // done
x[i] = lo[i];
state[i] = 0;
lcp->transfer_i_to_N (i);
break;
case 3: // done
x[i] = hi[i];
state[i] = 1;
lcp->transfer_i_to_N (i);
break;
case 4: // keep going
w[si] = 0;
lcp->transfer_i_from_N_to_C (si);
break;
case 5: // keep going
x[si] = lo[si];
state[si] = 0;
lcp->transfer_i_from_C_to_N (si);
break;
case 6: // keep going
x[si] = hi[si];
state[si] = 1;
lcp->transfer_i_from_C_to_N (si);
break;
}
if (cmd <= 3) break;
}
}
}
done:
lcp->unpermute();
delete lcp;
UNALLOCA (L);
UNALLOCA (d);
UNALLOCA (delta_x);
UNALLOCA (delta_w);
UNALLOCA (Dell);
UNALLOCA (ell);
UNALLOCA (Arows);
UNALLOCA (p);
UNALLOCA (C);
UNALLOCA (state);
}
//***************************************************************************
// accuracy and timing test
extern "C" ODE_API void dTestSolveLCP()
{
int n = 100;
int i,nskip = dPAD(n);
#ifdef dDOUBLE
const dReal tol = REAL(1e-9);
#endif
#ifdef dSINGLE
const dReal tol = REAL(1e-4);
#endif
printf ("dTestSolveLCP()\n");
ALLOCA (dReal,A,n*nskip*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (A == NULL) {
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,x,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (x == NULL) {
UNALLOCA (A);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,b,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (b == NULL) {
UNALLOCA (x);
UNALLOCA (A);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,w,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (w == NULL) {
UNALLOCA (b);
UNALLOCA (x);
UNALLOCA (A);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,lo,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (lo == NULL) {
UNALLOCA (w);
UNALLOCA (b);
UNALLOCA (x);
UNALLOCA (A);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,hi,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (hi == NULL) {
UNALLOCA (lo);
UNALLOCA (w);
UNALLOCA (b);
UNALLOCA (x);
UNALLOCA (A);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,A2,n*nskip*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (A2 == NULL) {
UNALLOCA (hi);
UNALLOCA (lo);
UNALLOCA (w);
UNALLOCA (b);
UNALLOCA (x);
UNALLOCA (A);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,b2,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (b2 == NULL) {
UNALLOCA (A2);
UNALLOCA (hi);
UNALLOCA (lo);
UNALLOCA (w);
UNALLOCA (b);
UNALLOCA (x);
UNALLOCA (A);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,lo2,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (lo2 == NULL) {
UNALLOCA (b2);
UNALLOCA (A2);
UNALLOCA (hi);
UNALLOCA (lo);
UNALLOCA (w);
UNALLOCA (b);
UNALLOCA (x);
UNALLOCA (A);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,hi2,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (hi2 == NULL) {
UNALLOCA (lo2);
UNALLOCA (b2);
UNALLOCA (A2);
UNALLOCA (hi);
UNALLOCA (lo);
UNALLOCA (w);
UNALLOCA (b);
UNALLOCA (x);
UNALLOCA (A);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,tmp1,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (tmp1 == NULL) {
UNALLOCA (hi2);
UNALLOCA (lo2);
UNALLOCA (b2);
UNALLOCA (A2);
UNALLOCA (hi);
UNALLOCA (lo);
UNALLOCA (w);
UNALLOCA (b);
UNALLOCA (x);
UNALLOCA (A);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
ALLOCA (dReal,tmp2,n*sizeof(dReal));
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (tmp2 == NULL) {
UNALLOCA (tmp1);
UNALLOCA (hi2);
UNALLOCA (lo2);
UNALLOCA (b2);
UNALLOCA (A2);
UNALLOCA (hi);
UNALLOCA (lo);
UNALLOCA (w);
UNALLOCA (b);
UNALLOCA (x);
UNALLOCA (A);
dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
return;
}
#endif
double total_time = 0;
for (int count=0; count < 1000; count++) {
// form (A,b) = a random positive definite LCP problem
dMakeRandomMatrix (A2,n,n,1.0);
dMultiply2 (A,A2,A2,n,n,n);
dMakeRandomMatrix (x,n,1,1.0);
dMultiply0 (b,A,x,n,n,1);
for (i=0; i<n; i++) b[i] += (dRandReal()*REAL(0.2))-REAL(0.1);
// choose `nub' in the range 0..n-1
int nub = 50; //dRandInt (n);
// make limits
for (i=0; i<nub; i++) lo[i] = -dInfinity;
for (i=0; i<nub; i++) hi[i] = dInfinity;
//for (i=nub; i<n; i++) lo[i] = 0;
//for (i=nub; i<n; i++) hi[i] = dInfinity;
//for (i=nub; i<n; i++) lo[i] = -dInfinity;
//for (i=nub; i<n; i++) hi[i] = 0;
for (i=nub; i<n; i++) lo[i] = -(dRandReal()*REAL(1.0))-REAL(0.01);
for (i=nub; i<n; i++) hi[i] = (dRandReal()*REAL(1.0))+REAL(0.01);
// set a few limits to lo=hi=0
/*
for (i=0; i<10; i++) {
int j = dRandInt (n-nub) + nub;
lo[j] = 0;
hi[j] = 0;
}
*/
// solve the LCP. we must make copy of A,b,lo,hi (A2,b2,lo2,hi2) for
// SolveLCP() to permute. also, we'll clear the upper triangle of A2 to
// ensure that it doesn't get referenced (if it does, the answer will be
// wrong).
memcpy (A2,A,n*nskip*sizeof(dReal));
dClearUpperTriangle (A2,n);
memcpy (b2,b,n*sizeof(dReal));
memcpy (lo2,lo,n*sizeof(dReal));
memcpy (hi2,hi,n*sizeof(dReal));
dSetZero (x,n);
dSetZero (w,n);
dStopwatch sw;
dStopwatchReset (&sw);
dStopwatchStart (&sw);
dSolveLCP (n,A2,x,b2,w,nub,lo2,hi2,0);
#ifdef dUSE_MALLOC_FOR_ALLOCA
if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY) {
UNALLOCA (tmp2);
UNALLOCA (tmp1);
UNALLOCA (hi2);
UNALLOCA (lo2);
UNALLOCA (b2);
UNALLOCA (A2);
UNALLOCA (hi);
UNALLOCA (lo);
UNALLOCA (w);
UNALLOCA (b);
UNALLOCA (x);
UNALLOCA (A);
return;
}
#endif
dStopwatchStop (&sw);
double time = dStopwatchTime(&sw);
total_time += time;
double average = total_time / double(count+1) * 1000.0;
// check the solution
dMultiply0 (tmp1,A,x,n,n,1);
for (i=0; i<n; i++) tmp2[i] = b[i] + w[i];
dReal diff = dMaxDifference (tmp1,tmp2,n,1);
// printf ("\tA*x = b+w, maximum difference = %.6e - %s (1)\n",diff,
// diff > tol ? "FAILED" : "passed");
if (diff > tol) dDebug (0,"A*x = b+w, maximum difference = %.6e",diff);
int n1=0,n2=0,n3=0;
for (i=0; i<n; i++) {
if (x[i]==lo[i] && w[i] >= 0) {
n1++; // ok
}
else if (x[i]==hi[i] && w[i] <= 0) {
n2++; // ok
}
else if (x[i] >= lo[i] && x[i] <= hi[i] && w[i] == 0) {
n3++; // ok
}
else {
dDebug (0,"FAILED: i=%d x=%.4e w=%.4e lo=%.4e hi=%.4e",i,
x[i],w[i],lo[i],hi[i]);
}
}
// pacifier
printf ("passed: NL=%3d NH=%3d C=%3d ",n1,n2,n3);
printf ("time=%10.3f ms avg=%10.4f\n",time * 1000.0,average);
}
UNALLOCA (A);
UNALLOCA (x);
UNALLOCA (b);
UNALLOCA (w);
UNALLOCA (lo);
UNALLOCA (hi);
UNALLOCA (A2);
UNALLOCA (b2);
UNALLOCA (lo2);
UNALLOCA (hi2);
UNALLOCA (tmp1);
UNALLOCA (tmp2);
}
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