--- /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.
+ *****************************************************************/
+
+/* shuffle.c
+ *
+ * Routines for randomizing sequences.
+ *
+ * All routines are alphabet-independent (DNA, protein, RNA, whatever);
+ * they assume that input strings are purely alphabetical [a-zA-Z], and
+ * will return strings in all upper case [A-Z].
+ *
+ * All return 1 on success, and 0 on failure; 0 status invariably
+ * means the input string was not alphabetical.
+ *
+ * StrShuffle() - shuffled string, preserve mono-symbol composition.
+ * StrDPShuffle() - shuffled string, preserve mono- and di-symbol composition.
+ *
+ * StrMarkov0() - random string, same zeroth order Markov properties.
+ * StrMarkov1() - random string, same first order Markov properties.
+ *
+ * StrReverse() - simple reversal of string
+ * StrRegionalShuffle() - mono-symbol shuffled string in regional windows
+ *
+ * There are also similar routines for shuffling alignments:
+ *
+ * AlignmentShuffle() - alignment version of StrShuffle().
+ * AlignmentBootstrap() - sample with replacement; a bootstrap dataset.
+ * QRNAShuffle() - shuffle a pairwise alignment, preserving all gap positions.
+ *
+ * CVS $Id: shuffle.c,v 1.6 2002/10/09 14:26:09 eddy Exp)
+ */
+
+#include <string.h>
+#include <ctype.h>
+
+#include "squid.h"
+#include "sre_random.h"
+
+/* Function: StrShuffle()
+ *
+ * Purpose: Returns a shuffled version of s2, in s1.
+ * (s1 and s2 can be identical, to shuffle in place.)
+ *
+ * Args: s1 - allocated space for shuffled string.
+ * s2 - string to shuffle.
+ *
+ * Return: 1 on success.
+ */
+int
+StrShuffle(char *s1, char *s2)
+{
+ int len;
+ int pos;
+ char c;
+
+ if (s1 != s2) strcpy(s1, s2);
+ for (len = strlen(s1); len > 1; len--)
+ {
+ pos = CHOOSE(len);
+ c = s1[pos];
+ s1[pos] = s1[len-1];
+ s1[len-1] = c;
+ }
+ return 1;
+}
+
+/* Function: StrDPShuffle()
+ * Date: SRE, Fri Oct 29 09:15:17 1999 [St. Louis]
+ *
+ * Purpose: Returns a shuffled version of s2, in s1.
+ * (s1 and s2 may be identical; i.e. a string
+ * may be shuffled in place.) The shuffle is a
+ * "doublet-preserving" (DP) shuffle. Both
+ * mono- and di-symbol composition are preserved.
+ *
+ * Done by searching for a random Eulerian
+ * walk on a directed multigraph.
+ * Reference: S.F. Altschul and B.W. Erickson, Mol. Biol.
+ * Evol. 2:526-538, 1985. Quoted bits in my comments
+ * are from Altschul's outline of the algorithm.
+ *
+ * Args: s1 - RETURN: the string after it's been shuffled
+ * (space for s1 allocated by caller)
+ * s2 - the string to be shuffled
+ *
+ * Returns: 0 if string can't be shuffled (it's not all [a-zA-z]
+ * alphabetic.
+ * 1 on success.
+ */
+int
+StrDPShuffle(char *s1, char *s2)
+{
+ int len;
+ int pos; /* a position in s1 or s2 */
+ int x,y; /* indices of two characters */
+ char **E; /* edge lists: E[0] is the edge list from vertex A */
+ int *nE; /* lengths of edge lists */
+ int *iE; /* positions in edge lists */
+ int n; /* tmp: remaining length of an edge list to be shuffled */
+ char sf; /* last character in s2 */
+ char Z[26]; /* connectivity in last edge graph Z */
+ int keep_connecting; /* flag used in Z connectivity algorithm */
+ int is_eulerian; /* flag used for when we've got a good Z */
+
+ /* First, verify that the string is entirely alphabetic.
+ */
+ len = strlen(s2);
+ for (pos = 0; pos < len; pos++)
+ if (! isalpha(s2[pos])) return 0;
+
+ /* "(1) Construct the doublet graph G and edge ordering E
+ * corresponding to S."
+ *
+ * Note that these also imply the graph G; and note,
+ * for any list x with nE[x] = 0, vertex x is not part
+ * of G.
+ */
+ E = MallocOrDie(sizeof(char *) * 26);
+ nE = MallocOrDie(sizeof(int) * 26);
+ for (x = 0; x < 26; x++)
+ {
+ E[x] = MallocOrDie(sizeof(char) * (len-1));
+ nE[x] = 0;
+ }
+
+ x = toupper(s2[0]) - 'A';
+ for (pos = 1; pos < len; pos++)
+ {
+ y = toupper(s2[pos]) - 'A';
+ E[x][nE[x]] = y;
+ nE[x]++;
+ x = y;
+ }
+
+ /* Now we have to find a random Eulerian edge ordering.
+ */
+ sf = toupper(s2[len-1]) - 'A';
+ is_eulerian = 0;
+ while (! is_eulerian)
+ {
+ /* "(2) For each vertex s in G except s_f, randomly select
+ * one edge from the s edge list of E(S) to be the
+ * last edge of the s list in a new edge ordering."
+ *
+ * select random edges and move them to the end of each
+ * edge list.
+ */
+ for (x = 0; x < 26; x++)
+ {
+ if (nE[x] == 0 || x == sf) continue;
+
+ pos = CHOOSE(nE[x]);
+ y = E[x][pos];
+ E[x][pos] = E[x][nE[x]-1];
+ E[x][nE[x]-1] = y;
+ }
+
+ /* "(3) From this last set of edges, construct the last-edge
+ * graph Z and determine whether or not all of its
+ * vertices are connected to s_f."
+ *
+ * a probably stupid algorithm for looking at the
+ * connectivity in Z: iteratively sweep through the
+ * edges in Z, and build up an array (confusing called Z[x])
+ * whose elements are 1 if x is connected to sf, else 0.
+ */
+ for (x = 0; x < 26; x++) Z[x] = 0;
+ Z[(int) sf] = keep_connecting = 1;
+
+ while (keep_connecting) {
+ keep_connecting = 0;
+ for (x = 0; x < 26; x++)
+ {
+ y = E[x][nE[x]-1]; /* xy is an edge in Z */
+ if (Z[x] == 0 && Z[y] == 1) /* x is connected to sf in Z */
+ {
+ Z[x] = 1;
+ keep_connecting = 1;
+ }
+ }
+ }
+
+ /* if any vertex in Z is tagged with a 0, it's
+ * not connected to sf, and we won't have a Eulerian
+ * walk.
+ */
+ is_eulerian = 1;
+ for (x = 0; x < 26; x++)
+ {
+ if (nE[x] == 0 || x == sf) continue;
+ if (Z[x] == 0) {
+ is_eulerian = 0;
+ break;
+ }
+ }
+
+ /* "(4) If any vertex is not connected in Z to s_f, the
+ * new edge ordering will not be Eulerian, so return to
+ * (2). If all vertices are connected in Z to s_f,
+ * the new edge ordering will be Eulerian, so
+ * continue to (5)."
+ *
+ * e.g. note infinite loop while is_eulerian is FALSE.
+ */
+ }
+
+ /* "(5) For each vertex s in G, randomly permute the remaining
+ * edges of the s edge list of E(S) to generate the s
+ * edge list of the new edge ordering E(S')."
+ *
+ * Essentially a StrShuffle() on the remaining nE[x]-1 elements
+ * of each edge list; unfortunately our edge lists are arrays,
+ * not strings, so we can't just call out to StrShuffle().
+ */
+ for (x = 0; x < 26; x++)
+ for (n = nE[x] - 1; n > 1; n--)
+ {
+ pos = CHOOSE(n);
+ y = E[x][pos];
+ E[x][pos] = E[x][n-1];
+ E[x][n-1] = y;
+ }
+
+ /* "(6) Construct sequence S', a random DP permutation of
+ * S, from E(S') as follows. Start at the s_1 edge list.
+ * At each s_i edge list, add s_i to S', delete the
+ * first edge s_i,s_j of the edge list, and move to
+ * the s_j edge list. Continue this process until
+ * all edge lists are exhausted."
+ */
+ iE = MallocOrDie(sizeof(int) * 26);
+ for (x = 0; x < 26; x++) iE[x] = 0;
+
+ pos = 0;
+ x = toupper(s2[0]) - 'A';
+ while (1)
+ {
+ s1[pos++] = 'A' + x; /* add s_i to S' */
+
+ y = E[x][iE[x]];
+ iE[x]++; /* "delete" s_i,s_j from edge list */
+
+ x = y; /* move to s_j edge list. */
+
+ if (iE[x] == nE[x])
+ break; /* the edge list is exhausted. */
+ }
+ s1[pos++] = 'A' + sf;
+ s1[pos] = '\0';
+
+ /* Reality checks.
+ */
+ if (x != sf) Die("hey, you didn't end on s_f.");
+ if (pos != len) Die("hey, pos (%d) != len (%d).", pos, len);
+
+ /* Free and return.
+ */
+ Free2DArray((void **) E, 26);
+ free(nE);
+ free(iE);
+ return 1;
+}
+
+
+/* Function: StrMarkov0()
+ * Date: SRE, Fri Oct 29 11:08:31 1999 [St. Louis]
+ *
+ * Purpose: Returns a random string s1 with the same
+ * length and zero-th order Markov properties
+ * as s2.
+ *
+ * s1 and s2 may be identical, to randomize s2
+ * in place.
+ *
+ * Args: s1 - allocated space for random string
+ * s2 - string to base s1's properties on.
+ *
+ * Returns: 1 on success; 0 if s2 doesn't look alphabetical.
+ */
+int
+StrMarkov0(char *s1, char *s2)
+{
+ int len;
+ int pos;
+ float p[26]; /* symbol probabilities */
+
+ /* First, verify that the string is entirely alphabetic.
+ */
+ len = strlen(s2);
+ for (pos = 0; pos < len; pos++)
+ if (! isalpha(s2[pos])) return 0;
+
+ /* Collect zeroth order counts and convert to frequencies.
+ */
+ FSet(p, 26, 0.);
+ for (pos = 0; pos < len; pos++)
+ p[(int)(toupper(s2[pos]) - 'A')] += 1.0;
+ FNorm(p, 26);
+
+ /* Generate a random string using those p's.
+ */
+ for (pos = 0; pos < len; pos++)
+ s1[pos] = FChoose(p, 26) + 'A';
+ s1[pos] = '\0';
+
+ return 1;
+}
+
+
+/* Function: StrMarkov1()
+ * Date: SRE, Fri Oct 29 11:22:20 1999 [St. Louis]
+ *
+ * Purpose: Returns a random string s1 with the same
+ * length and first order Markov properties
+ * as s2.
+ *
+ * s1 and s2 may be identical, to randomize s2
+ * in place.
+ *
+ * Args: s1 - allocated space for random string
+ * s2 - string to base s1's properties on.
+ *
+ * Returns: 1 on success; 0 if s2 doesn't look alphabetical.
+ */
+int
+StrMarkov1(char *s1, char *s2)
+{
+ int len;
+ int pos;
+ int x,y;
+ int i; /* initial symbol */
+ float p[26][26]; /* symbol probabilities */
+
+ /* First, verify that the string is entirely alphabetic.
+ */
+ len = strlen(s2);
+ for (pos = 0; pos < len; pos++)
+ if (! isalpha(s2[pos])) return 0;
+
+ /* Collect first order counts and convert to frequencies.
+ */
+ for (x = 0; x < 26; x++) FSet(p[x], 26, 0.);
+
+ i = x = toupper(s2[0]) - 'A';
+ for (pos = 1; pos < len; pos++)
+ {
+ y = toupper(s2[pos]) - 'A';
+ p[x][y] += 1.0;
+ x = y;
+ }
+ for (x = 0; x < 26; x++)
+ FNorm(p[x], 26);
+
+ /* Generate a random string using those p's.
+ */
+ x = i;
+ s1[0] = x + 'A';
+ for (pos = 1; pos < len; pos++)
+ {
+ y = FChoose(p[x], 26);
+ s1[pos] = y + 'A';
+ x = y;
+ }
+ s1[pos] = '\0';
+
+ return 1;
+}
+
+
+
+/* Function: StrReverse()
+ * Date: SRE, Thu Nov 20 10:54:52 1997 [St. Louis]
+ *
+ * Purpose: Returns a reversed version of s2, in s1.
+ * (s1 and s2 can be identical, to reverse in place)
+ *
+ * Args: s1 - allocated space for reversed string.
+ * s2 - string to reverse.
+ *
+ * Return: 1.
+ */
+int
+StrReverse(char *s1, char *s2)
+{
+ int len;
+ int pos;
+ char c;
+
+ len = strlen(s2);
+ for (pos = 0; pos < len/2; pos++)
+ { /* swap ends */
+ c = s2[len-pos-1];
+ s1[len-pos-1] = s2[pos];
+ s1[pos] = c;
+ }
+ if (len%2) { s1[pos] = s2[pos]; } /* copy middle residue in odd-len s2 */
+ s1[len] = '\0';
+ return 1;
+}
+
+/* Function: StrRegionalShuffle()
+ * Date: SRE, Thu Nov 20 11:02:34 1997 [St. Louis]
+ *
+ * Purpose: Returns a regionally shuffled version of s2, in s1.
+ * (s1 and s2 can be identical to regionally
+ * shuffle in place.) See [Pearson88].
+ *
+ * Args: s1 - allocated space for regionally shuffled string.
+ * s2 - string to regionally shuffle
+ * w - window size (typically 10 or 20)
+ *
+ * Return: 1.
+ */
+int
+StrRegionalShuffle(char *s1, char *s2, int w)
+{
+ int len;
+ char c;
+ int pos;
+ int i, j;
+
+ if (s1 != s2) strcpy(s1, s2);
+ len = strlen(s1);
+
+ for (i = 0; i < len; i += w)
+ for (j = MIN(len-1, i+w-1); j > i; j--)
+ {
+ pos = i + CHOOSE(j-i);
+ c = s1[pos];
+ s1[pos] = s1[j];
+ s1[j] = c;
+ }
+ return 1;
+}
+
+
+/* Function: AlignmentShuffle()
+ * Date: SRE, Sun Apr 22 18:37:15 2001 [St. Louis]
+ *
+ * Purpose: Returns a shuffled version of ali2, in ali1.
+ * (ali1 and ali2 can be identical, to shuffle
+ * in place.) The alignment columns are shuffled,
+ * preserving % identity within the columns.
+ *
+ * Args: ali1 - allocated space for shuffled alignment
+ * [0..nseq-1][0..alen-1]
+ * ali2 - alignment to be shuffled
+ * nseq - number of sequences in the alignment
+ * alen - length of alignment, in columns.
+ *
+ * Returns: int
+ */
+int
+AlignmentShuffle(char **ali1, char **ali2, int nseq, int alen)
+{
+ int i;
+ int pos;
+ char c;
+
+ if (ali1 != ali2)
+ {
+ for (i = 0; i < nseq; i++) strcpy(ali1[i], ali2[i]);
+ }
+
+ for (i = 0; i < nseq; i++)
+ ali1[i][alen] = '\0';
+
+ for (; alen > 1; alen--)
+ {
+ pos = CHOOSE(alen);
+ for (i = 0; i < nseq; i++)
+ {
+ c = ali1[i][pos];
+ ali1[i][pos] = ali1[i][alen-1];
+ ali1[i][alen-1] = c;
+ }
+ }
+
+ return 1;
+}
+
+/* Function: AlignmentBootstrap()
+ * Date: SRE, Sun Apr 22 18:49:14 2001 [St. Louis]
+ *
+ * Purpose: Returns a bootstrapped alignment sample in ali1,
+ * constructed from ali2 by sampling columns with
+ * replacement.
+ *
+ * Unlike the other shuffling routines, ali1 and
+ * ali2 cannot be the same. ali2 is left unchanged.
+ * ali1 must be a properly allocated space for an
+ * alignment the same size as ali2.
+ *
+ * Args: ali1 - allocated space for bootstrapped alignment
+ * [0..nseq-1][0..alen-1]
+ * ali2 - alignment to be bootstrapped
+ * nseq - number of sequences in the alignment
+ * alen - length of alignment, in columns.
+ *
+ * Returns: 1 on success.
+ */
+int
+AlignmentBootstrap(char **ali1, char **ali2, int nseq, int alen)
+{
+ int pos;
+ int col;
+ int i;
+
+ for (pos = 0; pos < alen; pos++)
+ {
+ col = CHOOSE(alen);
+ for (i = 0; i < nseq; i++)
+ ali1[i][pos] = ali2[i][col];
+ }
+ for (i = 0; i < nseq; i++)
+ ali1[i][alen] = '\0';
+
+ return 1;
+}
+
+
+/* Function: QRNAShuffle()
+ * Date: SRE, Mon Dec 10 10:14:12 2001 [St. Louis]
+ *
+ * Purpose: Shuffle a pairwise alignment x,y while preserving the
+ * position of gaps; return the shuffled alignment in xs,
+ * ys.
+ *
+ * Works by doing three separate
+ * shuffles, of (1) columns with residues in both
+ * x and y, (2) columns with residue in x and gap in y,
+ * and (3) columns with gap in x and residue in y.
+ *
+ * xs,x and ys,y may be identical: that is, to shuffle
+ * an alignment "in place", destroying the original
+ * alignment, just call:
+ * QRNAShuffle(x,y,x,y);
+ *
+ * Args: xs, ys: allocated space for shuffled pairwise ali of x,y [L+1]
+ * x, y: pairwise alignment to be shuffled [0..L-1]
+ *
+ * Returns: 1 on success, 0 on failure.
+ * The shuffled alignment is returned in xs, ys.
+ */
+int
+QRNAShuffle(char *xs, char *ys, char *x, char *y)
+{
+ int L;
+ int *xycol, *xcol, *ycol;
+ int nxy, nx, ny;
+ int i;
+ int pos, c;
+ char xsym, ysym;
+
+ if (xs != x) strcpy(xs, x);
+ if (ys != y) strcpy(ys, y);
+
+ /* First, construct three arrays containing lists of the column positions
+ * of the three types of columns. (If a column contains gaps in both x and y,
+ * we've already simply copied it to the shuffled sequence.)
+ */
+ L = strlen(x);
+ xycol = MallocOrDie(sizeof(int) * L);
+ xcol = MallocOrDie(sizeof(int) * L);
+ ycol = MallocOrDie(sizeof(int) * L);
+ nxy = nx = ny = 0;
+
+ for (i = 0; i < L; i++)
+ {
+ if (isgap(x[i]) && isgap(y[i])) { continue; }
+ else if (! isgap(x[i]) && ! isgap(y[i])) { xycol[nxy] = i; nxy++; }
+ else if (isgap(x[i])) { ycol[ny] = i; ny++; }
+ else if (isgap(y[i])) { xcol[nx] = i; nx++; }
+ }
+
+ /* Second, shuffle the sequences indirectly, via shuffling these arrays.
+ * Yow, careful with those indices, and with order of the statements...
+ */
+ for (; nxy > 1; nxy--) {
+ pos = CHOOSE(nxy);
+ xsym = xs[xycol[pos]]; ysym = ys[xycol[pos]]; c = xycol[pos];
+ xs[xycol[pos]] = xs[xycol[nxy-1]]; ys[xycol[pos]] = ys[xycol[nxy-1]]; xycol[pos] = xycol[nxy-1];
+ xs[xycol[nxy-1]] = xsym; ys[xycol[nxy-1]] = ysym; xycol[pos] = xycol[nxy-1];
+ }
+ for (; nx > 1; nx--) {
+ pos = CHOOSE(nx);
+ xsym = xs[xcol[pos]]; ysym = ys[xcol[pos]]; c = xcol[pos];
+ xs[xcol[pos]] = xs[xcol[nx-1]]; ys[xcol[pos]] = ys[xcol[nx-1]]; xcol[pos] = xcol[nx-1];
+ xs[xcol[nx-1]] = xsym; ys[xcol[nx-1]] = ysym; xcol[nx-1] = c;
+ }
+ for (; ny > 1; ny--) {
+ pos = CHOOSE(ny);
+ xsym = xs[ycol[pos]]; ysym = ys[ycol[pos]]; c = ycol[pos];
+ xs[ycol[pos]] = xs[ycol[ny-1]]; ys[ycol[pos]] = ys[ycol[ny-1]]; ycol[pos] = ycol[ny-1];
+ xs[ycol[ny-1]] = xsym; ys[ycol[ny-1]] = ysym; ycol[ny-1] = c;
+ }
+
+ free(xycol); free(xcol); free(ycol);
+ return 1;
+}
+
+
+#ifdef TESTDRIVER
+/*
+ * cc -g -o testdriver -DTESTDRIVER -L. shuffle.c -lsquid -lm
+ */
+int
+main(int argc, char **argv)
+{
+ char s1[100];
+ char s2[100];
+
+ sre_srandom(42);
+ strcpy(s2, "GGGGGGGGGGCCCCCCCCCC");
+ /* strcpy(s2, "AGACATAAAGTTCCGTACTGCCGGGAT");
+ */
+ StrDPShuffle(s1, s2);
+ printf("DPshuffle: %s\n", s1);
+ StrMarkov0(s1,s2);
+ printf("Markov 0 : %s\n", s1);
+ StrMarkov1(s1,s2);
+ printf("Markov 1 : %s\n", s1);
+
+ strcpy(s1, "ACGTACGT--------ACGTACGT----ACGTACGT");
+ strcpy(s2, "ACGTACGTACGTACGT------------ACGTACGT");
+ QRNAShuffle(s1,s2,s1,s2);
+ printf("QRNA : %s\n", s1);
+ printf(" : %s\n", s2);
+
+ return 0;
+}
+#endif
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