--- /dev/null
+/*****************************************************************
+ * 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 <stdio.h>
+#include <string.h>
+#include <math.h>
+
+#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);
+ }
+}
+
+
+
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