/***************************************************************** * SQUID - a library of functions for biological sequence analysis * Copyright (C) 1992-2002 Washington University School of Medicine * * This source code is freely distributed under the terms of the * GNU General Public License. See the files COPYRIGHT and LICENSE * for details. *****************************************************************/ /* cluster.c * SRE, Sun Jul 18 09:49:47 1993 * moved to squid Thu Mar 3 08:42:57 1994 * RCS $Id: cluster.c 217 2011-03-19 10:27:10Z andreas $ (Original squid RCS Id: cluster.c,v 1.3 1999/07/15 22:32:16 eddy Exp) * * almost identical to bord.c, from fd * also now contains routines for constructing difference matrices * from alignments * * "branch ordering": Input a symmetric or upper-right-diagonal * NxN difference matrix (usually constructed by pairwise alignment * and similarity calculations for N sequences). Use the simple * cluster analysis part of the Fitch/Margoliash tree-building algorithm * (as described by Fitch and Margoliash 1967 as well as Feng * and Doolittle 1987) to calculate the topology of an "evolutionary * tree" consistent with the difference matrix. Returns an array * which represents the tree. * * The input difference matrix is just an NxN matrix of floats. * A good match is a small difference score (the algorithm is going * to search for minima among the difference scores). The original difference * matrix remains unchanged by the calculations. * * The output requires some explanation. A phylogenetic * tree is a binary tree, with N "leaves" and N-1 "nodes". The * topology of the tree may be completely described by N-1 structures * containing two pointers; each pointer points to either a leaf * or another node. Here, this is implemented with integer indices * rather than pointers. An array of N-1 pairs of ints is returned. * If the index is in the range (0..N-1), it is a "leaf" -- the * number of one of the sequences. If the index is in the range * (N..2N-2), it is another "node" -- (index-N) is the index * of the node in the returned array. * * If both indices of a member of the returned array point to * nodes, the tree is "compound": composed of more than one * cluster of related sequences. * * The higher-numbered elements of the returned array were the * first constructed, and hence represent the distal tips * of the tree -- the most similar sequences. The root * is node 0. ****************************************************************** * * Algorithm * * INITIALIZATIONS: * - copy the difference matrix (otherwise the caller's copy would * get destroyed by the operations of this algorithm). If * it's asymmetric, make it symmetric. * - make a (0..N-1) array of ints to keep track of the indices in * the difference matrix as they get swapped around. Initialize * this matrix to 0..N-1. * - make a (0..N-2) array of int[2] to store the results (the tree * topology). Doesn't need to be initialized. * - keep track of a "N'", the current size of the difference * matrix being operated on. * * PROCESSING THE DIFFERENCE MATRIX: * - for N' = N down to N' = 2 (N-1 steps): * - in the half-diagonal N'xN' matrix, find the indices i,j at which * there's the minimum difference score * * Store the results: * - at position N'-2 of the result array, store coords[i] and * coords[j]. * * Move i,j rows, cols to the outside edges of the matrix: * - swap row i and row N'-2 * - swap row j and row N'-1 * - swap column i and column N'-2 * - swap column j and column N'-1 * - swap indices i, N'-2 in the index array * - swap indices j, N'-1 in the index array * * Build a average difference score for differences to i,j: * - for all columns, find avg difference between rows i and j and store in row i: * row[i][col] = (row[i][col] + row[j][col]) / 2.0 * - copy the contents of row i to column i (it's a symmetric * matrix, no need to recalculate) * - store an index N'+N-2 at position N'-2 of the index array: means * that this row/column is now a node rather than a leaf, and * contains minimum values * * Continue: * - go to the next N' * * GARBAGE COLLECTION & RETURN. * ********************************************************************** * * References: * * Feng D-F and R.F. Doolittle. "Progressive sequence alignment as a * prerequisite to correct phylogenetic trees." J. Mol. Evol. * 25:351-360, 1987. * * Fitch W.M. and Margoliash E. "Construction of phylogenetic trees." * Science 155:279-284, 1967. * ********************************************************************** * * SRE, 18 March 1992 (bord.c) * SRE, Sun Jul 18 09:52:14 1993 (cluster.c) * added to squid Thu Mar 3 09:13:56 1994 ********************************************************************** * Mon May 4 09:47:02 1992: keep track of difference scores at each node */ #include #include #include #include "squid.h" #include "sqfuncs.h" #ifdef MEMDEBUG #include "dbmalloc.h" #endif /* Function: Cluster() * * Purpose: Cluster analysis on a distance matrix. Constructs a * phylogenetic tree which contains the topology * and info for each node: branch lengths, how many * sequences are included under the node, and which * sequences are included under the node. * * Args: dmx - the NxN distance matrix ( >= 0.0, larger means more diverged) * N - size of mx (number of sequences) * mode - CLUSTER_MEAN, CLUSTER_MAX, or CLUSTER_MIN * ret_tree- RETURN: the tree * * Return: 1 on success, 0 on failure. * The caller is responsible for freeing the tree's memory, * by calling FreePhylo(tree, N). */ int Cluster(float **dmx, int N, enum clust_strategy mode, struct phylo_s **ret_tree) { struct phylo_s *tree; /* (0..N-2) phylogenetic tree */ float **mx; /* copy of difference matrix */ int *coord; /* (0..N-1), indices for matrix coords */ int i, j; /* coords of minimum difference */ int idx; /* counter over seqs */ int Np; /* N', a working copy of N */ int row, col; /* loop variables */ float min; /* best minimum score found */ float *trow; /* tmp pointer for swapping rows */ float tcol; /* tmp storage for swapping cols */ float *diff; /* (0..N-2) difference scores at nodes */ int swapfoo; /* for SWAP() macro */ /************************** * Initializations. **************************/ /* We destroy the matrix we work on, so make a copy of dmx. */ mx = MallocOrDie (sizeof(float *) * N); for (i = 0; i < N; i++) { mx[i] = MallocOrDie (sizeof(float) * N); for (j = 0; j < N; j++) mx[i][j] = dmx[i][j]; } /* coord array alloc, (0..N-1) */ coord = MallocOrDie (N * sizeof(int)); diff = MallocOrDie ((N-1) * sizeof(float)); /* init the coord array to 0..N-1 */ for (col = 0; col < N; col++) coord[col] = col; for (i = 0; i < N-1; i++) diff[i] = 0.0; /* tree array alloc, (0..N-2) */ if ((tree = AllocPhylo(N)) == NULL) Die("AllocPhylo() failed"); /********************************* * Process the difference matrix *********************************/ /* N-prime, for an NxN down to a 2x2 diffmx */ j= 0; /* just to silence gcc uninit warnings */ for (Np = N; Np >= 2; Np--) { /* find a minimum on the N'xN' matrix*/ min = 999999.; for (row = 0; row < Np; row++) for (col = row+1; col < Np; col++) if (mx[row][col] < min) { min = mx[row][col]; i = row; j = col; } /* We're clustering row i with col j. write necessary * data into a node on the tree */ /* topology info */ tree[Np-2].left = coord[i]; tree[Np-2].right = coord[j]; if (coord[i] >= N) tree[coord[i]-N].parent = N + Np - 2; if (coord[j] >= N) tree[coord[j]-N].parent = N + Np - 2; /* keep score info */ diff[Np-2] = tree[Np-2].diff = min; /* way-simple branch length estimation */ tree[Np-2].lblen = tree[Np-2].rblen = min; if (coord[i] >= N) tree[Np-2].lblen -= diff[coord[i]-N]; if (coord[j] >= N) tree[Np-2].rblen -= diff[coord[j]-N]; /* number seqs included at node */ if (coord[i] < N) { tree[Np-2].incnum ++; tree[Np-2].is_in[coord[i]] = 1; } else { tree[Np-2].incnum += tree[coord[i]-N].incnum; for (idx = 0; idx < N; idx++) tree[Np-2].is_in[idx] |= tree[coord[i]-N].is_in[idx]; } if (coord[j] < N) { tree[Np-2].incnum ++; tree[Np-2].is_in[coord[j]] = 1; } else { tree[Np-2].incnum += tree[coord[j]-N].incnum; for (idx = 0; idx < N; idx++) tree[Np-2].is_in[idx] |= tree[coord[j]-N].is_in[idx]; } /* Now build a new matrix, by merging row i with row j and * column i with column j; see Fitch and Margoliash */ /* Row and column swapping. */ /* watch out for swapping i, j away: */ if (i == Np-1 || j == Np-2) SWAP(i,j); if (i != Np-2) { /* swap row i, row N'-2 */ trow = mx[Np-2]; mx[Np-2] = mx[i]; mx[i] = trow; /* swap col i, col N'-2 */ for (row = 0; row < Np; row++) { tcol = mx[row][Np-2]; mx[row][Np-2] = mx[row][i]; mx[row][i] = tcol; } /* swap coord i, coord N'-2 */ SWAP(coord[i], coord[Np-2]); } if (j != Np-1) { /* swap row j, row N'-1 */ trow = mx[Np-1]; mx[Np-1] = mx[j]; mx[j] = trow; /* swap col j, col N'-1 */ for (row = 0; row < Np; row++) { tcol = mx[row][Np-1]; mx[row][Np-1] = mx[row][j]; mx[row][j] = tcol; } /* swap coord j, coord N'-1 */ SWAP(coord[j], coord[Np-1]); } /* average i and j together; they're now at Np-2 and Np-1 though */ i = Np-2; j = Np-1; /* merge by saving avg of cols of row i and row j */ for (col = 0; col < Np; col++) { switch (mode) { case CLUSTER_MEAN: mx[i][col] =(mx[i][col]+ mx[j][col]) / 2.0; break; case CLUSTER_MIN: mx[i][col] = MIN(mx[i][col], mx[j][col]); break; case CLUSTER_MAX: mx[i][col] = MAX(mx[i][col], mx[j][col]); break; default: mx[i][col] =(mx[i][col]+ mx[j][col]) / 2.0; break; } } /* copy those rows to columns */ for (col = 0; col < Np; col++) mx[col][i] = mx[i][col]; /* store the node index in coords */ coord[Np-2] = Np+N-2; } /************************** * Garbage collection and return **************************/ Free2DArray((void **) mx, N); free(coord); free(diff); *ret_tree = tree; return 1; } /* Function: AllocPhylo() * * Purpose: Allocate space for a phylo_s array. N-1 structures * are allocated, one for each node; in each node, a 0..N * is_in flag array is also allocated and initialized to * all zeros. * * Args: N - size; number of sequences being clustered * * Return: pointer to the allocated array * */ struct phylo_s * AllocPhylo(int N) { struct phylo_s *tree; int i; if ((tree = (struct phylo_s *) malloc ((N-1) * sizeof(struct phylo_s))) == NULL) return NULL; for (i = 0; i < N-1; i++) { tree[i].diff = 0.0; tree[i].lblen = tree[i].rblen = 0.0; tree[i].left = tree[i].right = tree[i].parent = -1; tree[i].incnum = 0; if ((tree[i].is_in = (char *) calloc (N, sizeof(char))) == NULL) return NULL; } return tree; } /* Function: FreePhylo() * * Purpose: Free a clustree array that was built to cluster N sequences. * * Args: tree - phylogenetic tree to free * N - size of clustree; number of sequences it clustered * * Return: (void) */ void FreePhylo(struct phylo_s *tree, int N) { int idx; for (idx = 0; idx < N-1; idx++) free(tree[idx].is_in); free(tree); } /* Function: MakeDiffMx() * * Purpose: Given a set of aligned sequences, construct * an NxN fractional difference matrix. (i.e. 1.0 is * completely different, 0.0 is exactly identical). * * Args: aseqs - flushed, aligned sequences * num - number of aseqs * ret_dmx - RETURN: difference matrix * * Return: 1 on success, 0 on failure. * Caller must free diff matrix with FMX2Free(dmx) */ void MakeDiffMx(char **aseqs, int num, float ***ret_dmx) { float **dmx; /* RETURN: distance matrix */ int i,j; /* counters over sequences */ /* Allocate 2D float matrix */ dmx = FMX2Alloc(num, num); /* Calculate distances; symmetric matrix * record difference, not identity (1 - identity) */ for (i = 0; i < num; i++) for (j = i; j < num; j++) dmx[i][j] = dmx[j][i] = 1.0 - PairwiseIdentity(aseqs[i], aseqs[j]); *ret_dmx = dmx; return; } /* Function: MakeIdentityMx() * * Purpose: Given a set of aligned sequences, construct * an NxN fractional identity matrix. (i.e. 1.0 is * completely identical, 0.0 is completely different). * Virtually identical to MakeDiffMx(). It's * less confusing to have two distinct functions, I find. * * Args: aseqs - flushed, aligned sequences * num - number of aseqs * ret_imx - RETURN: identity matrix (caller must free) * * Return: 1 on success, 0 on failure. * Caller must free imx using FMX2Free(imx) */ void MakeIdentityMx(char **aseqs, int num, float ***ret_imx) { float **imx; /* RETURN: identity matrix */ int i,j; /* counters over sequences */ /* Allocate 2D float matrix */ imx = FMX2Alloc(num, num); /* Calculate distances, symmetric matrix */ for (i = 0; i < num; i++) for (j = i; j < num; j++) imx[i][j] = imx[j][i] = PairwiseIdentity(aseqs[i], aseqs[j]); *ret_imx = imx; return; } /* Function: PrintNewHampshireTree() * * Purpose: Print out a tree in the "New Hampshire" standard * format. See PHYLIP's draw.doc for a definition of * the New Hampshire format. * * Like a CFG, we generate the format string left to * right by a preorder tree traversal. * * Args: fp - file to print to * ainfo- alignment info, including sequence names * tree - tree to print * N - number of leaves * */ void PrintNewHampshireTree(FILE *fp, AINFO *ainfo, struct phylo_s *tree, int N) { struct intstack_s *stack; int code; float *blen; int docomma; blen = (float *) MallocOrDie (sizeof(float) * (2*N-1)); stack = InitIntStack(); PushIntStack(stack, N); /* push root on stack */ docomma = FALSE; /* node index code: * 0..N-1 = leaves; indexes of sequences. * N..2N-2 = interior nodes; node-N = index of node in tree structure. * code N is the root. * 2N..3N-2 = special flags for closing interior nodes; node-2N = index in tree */ while (PopIntStack(stack, &code)) { if (code < N) /* we're a leaf. */ { /* 1) print name:branchlength */ if (docomma) fputs(",", fp); fprintf(fp, "%s:%.5f", ainfo->sqinfo[code].name, blen[code]); docomma = TRUE; } else if (code < 2*N) /* we're an interior node */ { /* 1) print a '(' */ if (docomma) fputs(",\n", fp); fputs("(", fp); /* 2) push on stack: ), rchild, lchild */ PushIntStack(stack, code+N); PushIntStack(stack, tree[code-N].right); PushIntStack(stack, tree[code-N].left); /* 3) record branch lengths */ blen[tree[code-N].right] = tree[code-N].rblen; blen[tree[code-N].left] = tree[code-N].lblen; docomma = FALSE; } else /* we're closing an interior node */ { /* print a ):branchlength */ if (code == 2*N) fprintf(fp, ");\n"); else fprintf(fp, "):%.5f", blen[code-N]); docomma = TRUE; } } FreeIntStack(stack); free(blen); return; } /* Function: PrintPhylo() * * Purpose: Debugging output of a phylogenetic tree structure. */ void PrintPhylo(FILE *fp, AINFO *ainfo, struct phylo_s *tree, int N) { int idx; for (idx = 0; idx < N-1; idx++) { fprintf(fp, "Interior node %d (code %d)\n", idx, idx+N); fprintf(fp, "\tParent: %d (code %d)\n", tree[idx].parent-N, tree[idx].parent); fprintf(fp, "\tLeft: %d (%s) %f\n", tree[idx].left < N ? tree[idx].left-N : tree[idx].left, tree[idx].left < N ? ainfo->sqinfo[tree[idx].left].name : "interior", tree[idx].lblen); fprintf(fp, "\tRight: %d (%s) %f\n", tree[idx].right < N ? tree[idx].right-N : tree[idx].right, tree[idx].right < N ? ainfo->sqinfo[tree[idx].right].name : "interior", tree[idx].rblen); fprintf(fp, "\tHeight: %f\n", tree[idx].diff); fprintf(fp, "\tIncludes:%d seqs\n", tree[idx].incnum); } }