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|
/**
* Author: Mark Larkin
*
* Copyright (c) 2007 Des Higgins, Julie Thompson and Toby Gibson.
*/
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <math.h>
#include "NJTree.h"
namespace clustalw
{
/****************************************************************************
* [ Improvement ideas in fast_nj_tree() ] by DDBJ & FUJITSU Limited.
* written by Tadashi Koike
* (takoike@genes.nig.ac.jp)
*******************
* <IMPROVEMENT 1> : Store the value of sum of the score to temporary array,
* and use again and again.
*
* In the main cycle, these are calculated again and again :
* diq = sum of distMat[n][ii] (n:1 to lastSeq-firstSeq+1),
* djq = sum of distMat[n][jj] (n:1 to lastSeq-firstSeq+1),
* dio = sum of distMat[n][mini] (n:1 to lastSeq-firstSeq+1),
* djq = sum of distMat[n][minj] (n:1 to lastSeq-firstSeq+1)
* // 'lastSeq' and 'firstSeq' are both constant values //
* and the result of above calculations is always same until
* a best pair of neighbour nodes is joined.
*
* So, we change the logic to calculate the sum[i] (=sum of distMat[n][i]
* (n:1 to lastSeq-firstSeq+1)) and store it to array, before
* beginning to find a best pair of neighbour nodes, and after that
* we use them again and again.
*
* tmat[i][j]
* 1 2 3 4 5
* +---+---+---+---+---+
* 1 | | | | | |
* +---+---+---+---+---+
* 2 | | | | | | 1) calculate sum of distMat[n][i]
* +---+---+---+---+---+ (n: 1 to lastSeq-firstSeq+1)
* 3 | | | | | | 2) store that sum value to sum[i]
* +---+---+---+---+---+
* 4 | | | | | | 3) use sum[i] during finding a best
* +---+---+---+---+---+ pair of neibour nodes.
* 5 | | | | | |
* +---+---+---+---+---+
* | | | | |
* V V V V V Calculate sum , and store it to sum[i]
* +---+---+---+---+---+
* sum[i] | | | | | |
* +---+---+---+---+---+
*
* At this time, we thought that we use upper triangle of the matrix
* because distMat[i][j] is equal to distMat[j][i] and distMat[i][i] is equal
* to zero. Therefore, we prepared sum_rows[i] and sum_cols[i] instead
* of sum[i] for storing the sum value.
*
* distMat[i][j]
* 1 2 3 4 5 sum_cols[i]
* +---+---+---+---+---+ +---+
* 1 | # | # | # | # | --> | | ... sum of distMat[1][2..5]
* + - +---+---+---+---+ +---+
* 2 | # | # | # | --> | | ... sum of distMat[2][3..5]
* + - + - +---+---+---+ +---+
* 3 | # | # | --> | | ... sum of distMat[3][4..5]
* + - + - + - +---+---+ +---+
* 4 | # | --> | | ... sum of distMat[4][5]
* + - + - + - + - +---+ +---+
* 5 | --> | | ... zero
* + - + - + - + - + - + +---+
* | | | | |
* V V V V V Calculate sum , sotre to sum[i]
* +---+---+---+---+---+
* sum_rows[i] | | | | | |
* +---+---+---+---+---+
* | | | | |
* | | | | +----- sum of distMat[1..4][5]
* | | | +--------- sum of distMat[1..3][4]
* | | +------------- sum of distMat[1..2][3]
* | +----------------- sum of distMat[1][2]
* +--------------------- zero
*
* And we use (sum_rows[i] + sum_cols[i]) instead of sum[i].
*
*******************
* <IMPROVEMENT 2> : We manage valid nodes with chain list, instead of
* tkill[i] flag array.
*
* In original logic, invalid(killed?) nodes after nodes-joining
* are managed with tkill[i] flag array (set to 1 when killed).
* By this method, it is conspicuous to try next node but skip it
* at the latter of finding a best pair of neighbor nodes.
*
* So, we thought that we managed valid nodes by using a chain list
* as below:
*
* 1) declare the list structure.
* struct {
* sint n; // entry number of node.
* void *prev; // pointer to previous entry.
* void *next; // pointer to next entry.
* }
* 2) construct a valid node list.
*
* +-----+ +-----+ +-----+ +-----+ +-----+
* NULL<-|prev |<---|prev |<---|prev |<---|prev |<- - - -|prev |
* | 0 | | 1 | | 2 | | 3 | | n |
* | next|--->| next|--->| next|--->| next|- - - ->| next|->NULL
* +-----+ +-----+ +-----+ +-----+ +-----+
*
* 3) when finding a best pair of neighbor nodes, we use
* this chain list as loop counter.
*
* 4) If an entry was killed by node-joining, this chain list is
* modified to remove that entry.
*
* EX) remove the entry No 2.
* +-----+ +-----+ +-----+ +-----+
* NULL<-|prev |<---|prev |<--------------|prev |<- - - -|prev |
* | 0 | | 1 | | 3 | | n |
* | next|--->| next|-------------->| next|- - - ->| next|->NULL
* +-----+ +-----+ +-----+ +-----+
* +-----+
* NULL<-|prev |
* | 2 |
* | next|->NULL
* +-----+
*
* By this method, speed is up at the latter of finding a best pair of
* neighbor nodes.
*
*******************
* <IMPROVEMENT 3> : Cut the frequency of division.
*
* At comparison between 'total' and 'tmin' in the main cycle, total is
* divided by (2.0*fnseqs2) before comparison. If N nodes are available,
* that division happen (N*(N-1))/2 order.
*
* We thought that the comparison relation between tmin and total/(2.0*fnseqs2)
* is equal to the comparison relation between (tmin*2.0*fnseqs2) and total.
* Calculation of (tmin*2.0*fnseqs2) is only one time. so we stop dividing
* a total value and multiply tmin and (tmin*2.0*fnseqs2) instead.
*
*******************
* <IMPROVEMENT 4> : some transformation of the equation (to cut operations).
*
* We transform an equation of calculating 'total' in the main cycle.
*
*/
void NJTree::generateTree(clustalw::PhyloTree* phyTree,
clustalw::DistMatrix* distMat,
clustalw::SeqInfo* seqInfo,
ofstream* log)
{
if (log == NULL)
{
verbose = false;
}
register int i;
int l[4], nude, k;
int nc, mini, minj, j, ii, jj;
double fnseqs, fnseqs2 = 0, sumd;
double diq, djq, dij, dio, djo, da;
double tmin, total, dmin;
double bi, bj, b1, b2, b3, branch[4];
int typei, typej; /* 0 = node; 1 = OTU */
int firstSeq = seqInfo->firstSeq;
int lastSeq = seqInfo->lastSeq;
int numSeqs = seqInfo->numSeqs;
/* IMPROVEMENT 1, STEP 0 : declare variables */
double *sumCols, *sumRows, *join;
sumCols = new double[numSeqs + 1];
sumRows = new double[numSeqs + 1];
join = new double[numSeqs + 1];
/* IMPROVEMENT 2, STEP 0 : declare variables */
int loop_limit;
typedef struct _ValidNodeID
{
int n;
struct _ValidNodeID *prev;
struct _ValidNodeID *next;
} ValidNodeID;
ValidNodeID *tvalid, *lpi, *lpj, *lpii, *lpjj, *lp_prev, *lp_next;
/*
* correspondence of the loop counter variables.
* i .. lpi->n, ii .. lpii->n
* j .. lpj->n, jj .. lpjj->n
*/
fnseqs = (double)lastSeq - firstSeq + 1;
/*********************** First initialisation ***************************/
if (verbose)
{
(*log) << "\n\n\t\t\tNeighbor-joining Method\n"
<< "\n Saitou, N. and Nei, M. (1987)" << " The Neighbor-joining Method:"
<< "\n A New Method for Reconstructing Phylogenetic Trees."
<< "\n Mol. Biol. Evol., 4(4), 406-425\n" << "\n\n This is an UNROOTED tree\n"
<< "\n Numbers in parentheses are branch lengths\n\n";
}
if (fnseqs == 2)
{
if (verbose)
{
(*log) << "Cycle 1 = SEQ: 1 (" << setw(9) << setprecision(5)
<< (*distMat)(firstSeq, firstSeq + 1)
<< ") joins SEQ: 2 ("
<< setw(9) << setprecision(5)
<< (*distMat)(firstSeq, firstSeq + 1) << ")";
}
return ;
}
mini = minj = 0;
/* IMPROVEMENT 1, STEP 1 : Allocate memory */
/* IMPROVEMENT 1, STEP 2 : Initialize arrays to 0 */
phyTree->leftBranch.resize(numSeqs + 2, 0.0);
phyTree->rightBranch.resize(numSeqs + 2, 0.0);
tkill.resize(numSeqs + 1, 0);
av.resize(numSeqs + 1, 0.0);
/* IMPROVEMENT 2, STEP 1 : Allocate memory */
tvalid = new ValidNodeID[numSeqs + 1];
/* tvalid[0] is special entry in array. it points a header of valid entry list */
tvalid[0].n = 0;
tvalid[0].prev = NULL;
tvalid[0].next = &tvalid[1];
/* IMPROVEMENT 2, STEP 2 : Construct and initialize the entry chain list */
for (i = 1, loop_limit = lastSeq - firstSeq + 1, lpi = &tvalid[1],
lp_prev = &tvalid[0], lp_next = &tvalid[2]; i <= loop_limit; ++i,
++lpi, ++lp_prev, ++lp_next)
{
(*distMat)(i, i) = av[i] = 0.0;
tkill[i] = 0;
lpi->n = i;
lpi->prev = lp_prev;
lpi->next = lp_next;
}
tvalid[loop_limit].next = NULL;
/*
* IMPROVEMENT 1, STEP 3 : Calculate the sum of score value that
* is sequence[i] to others.
*/
double matValue;
sumd = 0.0;
for (lpj = tvalid[0].next; lpj != NULL; lpj = lpj->next)
{
double tmp_sum = 0.0;
j = lpj->n;
/* calculate sumRows[j] */
for (lpi = tvalid[0].next; lpi->n < j; lpi = lpi->next)
{
i = lpi->n;
matValue = (*distMat)(i, j);
tmp_sum = tmp_sum + matValue;
}
sumRows[j] = tmp_sum;
tmp_sum = 0.0;
/* Set lpi to that lpi->n is greater than j */
if ((lpi != NULL) && (lpi->n == j))
{
lpi = lpi->next;
}
/* calculate sumCols[j] */
for (; lpi != NULL; lpi = lpi->next)
{
i = lpi->n;
tmp_sum += (*distMat)(j, i);
}
sumCols[j] = tmp_sum;
}
/*********************** Enter The Main Cycle ***************************/
for (nc = 1, loop_limit = (lastSeq - firstSeq + 1-3); nc <= loop_limit; ++nc)
{
sumd = 0.0;
/* IMPROVEMENT 1, STEP 4 : use sum value */
for (lpj = tvalid[0].next; lpj != NULL; lpj = lpj->next)
{
sumd += sumCols[lpj->n];
}
/* IMPROVEMENT 3, STEP 0 : multiply tmin and 2*fnseqs2 */
fnseqs2 = fnseqs - 2.0; /* Set fnseqs2 at this point. */
tmin = 99999.0 * 2.0 * fnseqs2;
/*.................compute SMATij values and find the smallest one ........*/
mini = minj = 0;
/* jj must starts at least 2 */
if ((tvalid[0].next != NULL) && (tvalid[0].next->n == 1))
{
lpjj = tvalid[0].next->next;
}
else
{
lpjj = tvalid[0].next;
}
for (; lpjj != NULL; lpjj = lpjj->next)
{
jj = lpjj->n;
for (lpii = tvalid[0].next; lpii->n < jj; lpii = lpii->next)
{
ii = lpii->n;
diq = djq = 0.0;
/* IMPROVEMENT 1, STEP 4 : use sum value */
diq = sumCols[ii] + sumRows[ii];
djq = sumCols[jj] + sumRows[jj];
/*
* always ii < jj in this point. Use upper
* triangle of score matrix.
*/
dij = (*distMat)(ii, jj);
/*
* IMPROVEMENT 3, STEP 1 : fnseqs2 is
* already calculated.
*/
/* fnseqs2 = fnseqs - 2.0 */
/* IMPROVEMENT 4 : transform the equation */
/*-------------------------------------------------------------------*
* OPTIMIZE of expression 'total = d2r + fnseqs2*dij + dr*2.0' *
* total = d2r + fnseq2*dij + 2.0*dr *
* = d2r + fnseq2*dij + 2(sumd - dij - d2r) *
* = d2r + fnseq2*dij + 2*sumd - 2*dij - 2*d2r *
* = fnseq2*dij + 2*sumd - 2*dij - 2*d2r + d2r *
* = fnseq2*dij + 2*sumd - 2*dij - d2r *
* = fnseq2*dij + 2*sumd - 2*dij - (diq + djq - 2*dij) *
* = fnseq2*dij + 2*sumd - 2*dij - diq - djq + 2*dij *
* = fnseq2*dij + 2*sumd - 2*dij + 2*dij - diq - djq *
* = fnseq2*dij + 2*sumd - diq - djq *
*-------------------------------------------------------------------*/
total = fnseqs2 * dij + 2.0 * sumd - diq - djq;
/*
* IMPROVEMENT 3, STEP 2 : abbrevlate
* the division on comparison between
* total and tmin.
*/
/* total = total / (2.0*fnseqs2); */
if (total < tmin)
{
tmin = total;
mini = ii;
minj = jj;
}
}
}
/* MEMO: always ii < jj in avobe loop, so mini < minj */
/*.................compute branch lengths and print the results ........*/
dio = djo = 0.0;
/* IMPROVEMENT 1, STEP 4 : use sum value */
dio = sumCols[mini] + sumRows[mini];
djo = sumCols[minj] + sumRows[minj];
dmin = (*distMat)(mini, minj);
dio = (dio - dmin) / fnseqs2;
djo = (djo - dmin) / fnseqs2;
bi = (dmin + dio - djo) *0.5;
bj = dmin - bi;
bi = bi - av[mini];
bj = bj - av[minj];
#if 0
(*log) << endl << "*** cycle " << nc << endl;
(*log) << "dmin = " << setw(9) << right << setprecision(9) << dmin << endl;
(*log) << "dio = " << setw(9) << right << setprecision(9) << dio << endl;
(*log) << "djo = " << setw(9) << right << setprecision(9) << djo << endl;
(*log) << "bi = " << setw(9) << right << setprecision(9) << bi << endl;
(*log) << "bj = " << setw(9) << right << setprecision(9) << bj << endl;
(*log) << "mini = " << setw(9) << mini << endl;
(*log) << "minj = " << setw(9) << minj << endl;
(*log) << "av[minj] = " << setw(9) << right << setprecision(9) << av[minj] << endl;
(*log) << "av[minj] = " << setw(9) << right << setprecision(9) << av[minj] << endl;
#endif
if (av[mini] > 0.0)
{
typei = 0;
}
else
{
typei = 1;
}
if (av[minj] > 0.0)
{
typej = 0;
}
else
{
typej = 1;
}
if (verbose)
{
(*log) << "\n Cycle" << setw(4) << nc << " = ";
}
/*
set (tiny? (AW&FS)) negative branch lengths to zero. Also set any tiny positive
branch lengths to zero.
*/
if (fabs(bi) < 0.0001)
{
bi = 0.0;
}
if (fabs(bj) < 0.0001)
{
bj = 0.0;
}
if (verbose)
{
if (typei == 0)
{
(*log) << "Node:" << setw(4) << mini << " (" << setw(9) << setprecision(5)
<< bi << ") joins ";
}
else
{
(*log) << " SEQ:" << setw(4) << mini << " (" << setw(9) << setprecision(5)
<< bi << ") joins ";
}
if (typej == 0)
{
(*log) << "Node:" << setw(4) << minj << " (" << setw(9) << setprecision(5)
<< bj << ")";
}
else
{
(*log) << " SEQ:" << setw(4) << minj << " (" << setw(9) << setprecision(5)
<< bj << ")";
}
(*log) << "\n";
}
phyTree->leftBranch[nc] = bi;
phyTree->rightBranch[nc] = bj;
for (i = 1; i <= lastSeq - firstSeq + 1; i++)
{
phyTree->treeDesc[nc][i] = 0;
}
if (typei == 0)
{
for (i = nc - 1; i >= 1; i--)
if (phyTree->treeDesc[i][mini] == 1)
{
for (j = 1; j <= lastSeq - firstSeq + 1; j++)
if (phyTree->treeDesc[i][j] == 1)
{
phyTree->treeDesc[nc][j] = 1;
}
break;
}
}
else
{
phyTree->treeDesc[nc][mini] = 1;
}
if (typej == 0)
{
for (i = nc - 1; i >= 1; i--)
if (phyTree->treeDesc[i][minj] == 1)
{
for (j = 1; j <= lastSeq - firstSeq + 1; j++)
if (phyTree->treeDesc[i][j] == 1)
{
phyTree->treeDesc[nc][j] = 1;
}
break;
}
}
else
{
phyTree->treeDesc[nc][minj] = 1;
}
/*
Here is where the -0.00005 branch lengths come from for 3 or more
identical seqs.
*/
/* if(dmin <= 0.0) dmin = 0.0001; */
if (dmin <= 0.0)
{
dmin = 0.000001;
}
av[mini] = dmin * 0.5;
/*........................Re-initialisation................................*/
fnseqs = fnseqs - 1.0;
tkill[minj] = 1;
/* IMPROVEMENT 2, STEP 3 : Remove tvalid[minj] from chain list. */
/* [ Before ]
* +---------+ +---------+ +---------+
* |prev |<-------|prev |<-------|prev |<---
* | n | | n(=minj)| | n |
* | next|------->| next|------->| next|----
* +---------+ +---------+ +---------+
*
* [ After ]
* +---------+ +---------+
* |prev |<--------------------------|prev |<---
* | n | | n |
* | next|-------------------------->| next|----
* +---------+ +---------+
* +---------+
* NULL---|prev |
* | n(=minj)|
* | next|---NULL
* +---------+
*/
(tvalid[minj].prev)->next = tvalid[minj].next;
if (tvalid[minj].next != NULL)
{
(tvalid[minj].next)->prev = tvalid[minj].prev;
}
tvalid[minj].prev = tvalid[minj].next = NULL;
/* IMPROVEMENT 1, STEP 5 : re-calculate sum values. */
for (lpj = tvalid[0].next; lpj != NULL; lpj = lpj->next)
{
double tmp_di = 0.0;
double tmp_dj = 0.0;
j = lpj->n;
/*
* subtrace a score value related with 'minj' from
* sum arrays .
*/
if (j < minj)
{
tmp_dj = (*distMat)(j, minj);
sumCols[j] -= tmp_dj;
}
else if (j > minj)
{
tmp_dj = (*distMat)(minj, j);
sumRows[j] -= tmp_dj;
} /* nothing to do when j is equal to minj. */
/*
* subtrace a score value related with 'mini' from
* sum arrays .
*/
if (j < mini)
{
tmp_di = (*distMat)(j, mini);
sumCols[j] -= tmp_di;
}
else if (j > mini)
{
tmp_di = (*distMat)(mini, j);
sumRows[j] -= tmp_di;
} /* nothing to do when j is equal to mini. */
/*
* calculate a score value of the new inner node.
* then, store it temporary to join[] array.
*/
join[j] = (tmp_dj + tmp_di) *0.5;
}
/*
* 1)
* Set the score values (stored in join[]) into the matrix,
* row/column position is 'mini'.
* 2)
* Add a score value of the new inner node to sum arrays.
*/
for (lpj = tvalid[0].next; lpj != NULL; lpj = lpj->next)
{
j = lpj->n;
if (j < mini)
{
distMat->SetAt(j, mini, join[j]);
sumCols[j] += join[j];
}
else if (j > mini)
{
distMat->SetAt(mini, j, join[j]);
sumRows[j] += join[j];
} /* nothing to do when j is equal to mini. */
}
/* Re-calculate sumRows[mini],sumCols[mini]. */
sumCols[mini] = sumRows[mini] = 0.0;
/* calculate sumRows[mini] */
da = 0.0;
for (lpj = tvalid[0].next; lpj->n < mini; lpj = lpj->next)
{
da = da + join[lpj->n];
}
sumRows[mini] = da;
/* skip if 'lpj->n' is equal to 'mini' */
if ((lpj != NULL) && (lpj->n == mini))
{
lpj = lpj->next;
}
/* calculate sumCols[mini] */
da = 0.0;
for (; lpj != NULL; lpj = lpj->next)
{
da = da + join[lpj->n];
}
sumCols[mini] = da;
/*
* Clean up sumRows[minj], sumCols[minj] and score matrix
* related with 'minj'.
*/
sumCols[minj] = sumRows[minj] = 0.0;
for (j = 1; j <= lastSeq - firstSeq + 1; ++j)
{
distMat->SetAt(minj, j, 0.0);
distMat->SetAt(j, minj, 0.0);
join[j] = 0.0;
}
} /** end main cycle **/
/******************************Last Cycle (3 Seqs. left)********************/
nude = 1;
for (lpi = tvalid[0].next; lpi != NULL; lpi = lpi->next)
{
l[nude] = lpi->n;
++nude;
}
b1 = ((*distMat)(l[1], l[2]) + (*distMat)(l[1], l[3]) - (*distMat)(l[2], l[3])) *0.5;
b2 = (*distMat)(l[1], l[2]) - b1;
b3 = (*distMat)(l[1], l[3]) - b1;
branch[1] = b1 - av[l[1]];
branch[2] = b2 - av[l[2]];
branch[3] = b3 - av[l[3]];
/* Reset tiny negative and positive branch lengths to zero */
if (fabs(branch[1]) < 0.0001)
{
branch[1] = 0.0;
}
if (fabs(branch[2]) < 0.0001)
{
branch[2] = 0.0;
}
if (fabs(branch[3]) < 0.0001)
{
branch[3] = 0.0;
}
phyTree->leftBranch[lastSeq - firstSeq + 1-2] = branch[1];
phyTree->leftBranch[lastSeq - firstSeq + 1-1] = branch[2];
phyTree->leftBranch[lastSeq - firstSeq + 1] = branch[3];
for (i = 1; i <= lastSeq - firstSeq + 1; i++)
{
phyTree->treeDesc[lastSeq - firstSeq + 1-2][i] = 0;
}
if (verbose)
{
(*log) << "\n Cycle" << setw(4) << nc << " (Last cycle, trichotomy):\n";
}
for (i = 1; i <= 3; ++i)
{
if (av[l[i]] > 0.0)
{
if (verbose)
{
(*log) << "\n\t\t Node:" << setw(4) << l[i] <<" (" << setw(9)
<< setprecision(5) << branch[i] << ") ";
}
for (k = lastSeq - firstSeq + 1-3; k >= 1; k--)
if (phyTree->treeDesc[k][l[i]] == 1)
{
for (j = 1; j <= lastSeq - firstSeq + 1; j++)
if (phyTree->treeDesc[k][j] == 1)
{
phyTree->treeDesc[lastSeq - firstSeq + 1-2][j] = i;
}
break;
}
}
else
{
if (verbose)
{
(*log) << "\n\t\t SEQ:" << setw(4) << l[i] << " (" << setw(9)
<< setprecision(5) << branch[i] << ") ";
}
phyTree->treeDesc[lastSeq - firstSeq + 1-2][l[i]] = i;
}
if (i < 3)
{
if (verbose)
{
(*log) << "joins";
}
}
}
if (verbose)
{
(*log) << "\n";
}
/* IMPROVEMENT 2, STEP 4 : release memory area */
delete [] tvalid;
delete [] sumCols;
delete [] sumRows;
delete [] join;
}
}
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