double pearson
( const mclv* a
, const mclv* b
, dim n
)
{ double suma = mclvSum(a)
; double sumb = mclvSum(b)
; double sumasq = mclvPowSum(a, 2.0)
; double sumbsq = mclvPowSum(b, 2.0)
; double nom = sqrt( (n*sumasq - suma*suma) * (n*sumbsq - sumb*sumb) )
; double num = n * mclvIn(a, b) - suma * sumb
; return nom ? num / nom : 0.0
; }
mclMatrix* mclDiagOrdering
( const mclMatrix* M
, mclVector** vecp_attr
)
{ int n_cols = N_COLS(M)
; mclMatrix* diago = mclxAllocZero(NULL, NULL)
; long col
; if (*vecp_attr != NULL)
mclvFree(vecp_attr)
; *vecp_attr = mclvResize(NULL, n_cols)
; for (col=0;col<n_cols;col++)
{ ofs offset = -1
; double selfval = mclvIdxVal(M->cols+col, col, &offset)
; double center = mclvPowSum(M->cols+col, 2.0)
/* double maxval = mclvMaxValue(M->cols+col)
*/
; double bar = MCX_MAX(center, selfval) - dpsd_delta
; mclIvp* ivp = (*vecp_attr)->ivps+col
; ivp->idx = col
; ivp->val = center ? selfval / center : 0
; if (offset >= 0) /* take only higher valued entries */
mclvSelectGqBar(diago->cols+col, bar)
; }
; return diago
; }
double mclvNorm
( const mclVector* vec
, double power
)
{ if(power > 0.0)
mcxErr("mclvNorm", "pbd: negative power argument <%f>", (double) power)
, mcxExit(1)
; return pow((double) mclvPowSum(vec, power), 1.0 / power)
; }
mclv* reduce_v
( const mclv* u
)
{ mclv* v = mclvClone(u)
; dim n = v->n_ivps
; double s = mclvSum(v)
; double sq = mclvPowSum(v, 2.0)
; if (s)
mclvSelectGqBar(v, 0.25 * sq / s)
;fprintf(stderr, "from %d to %d entries\n", (int) n, (int) v->n_ivps)
; return v
; }
static void tf_ssq
( mclx* mx
, double val
)
{ dim i
; for (i=0;i<N_COLS(mx);i++)
{ mclv* v = mx->cols+i
; double ssq = mclvPowSum(v, 2.0)
; double sum = mclvSum(v)
; double self = mclvSelf(v)
; if (sum-self)
mclvSelectGtBar(v, val * (ssq - self*self) / (sum - self))
; }
; }
static void vary_threshold
( mcxIO* xf
, FILE* fp
, int vary_a
, int vary_z
, int vary_s
, int vary_n
, unsigned mode
)
{ dim cor_i = 0, j
; int step
; mclx* mx
; unsigned long noe
; pval* allvals
; dim n_allvals = 0
; double sum_vals = 0.0
; mx = mclxRead(xf, EXIT_ON_FAIL)
; mcxIOclose(xf)
; if (transform)
mclgTFexec(mx, transform)
; noe = mclxNrofEntries(mx)
; allvals = mcxAlloc(noe * sizeof allvals[0], EXIT_ON_FAIL)
; if (!weight_scale)
{ if (mode == 'c')
weight_scale = 1.0
; else
weight_scale = vary_n
; }
n_allvals = get_n_sort_allvals(mx, allvals, noe, &sum_vals, FALSE)
; if (mode == 'c')
{ double smallest = n_allvals ? allvals[n_allvals-1] : -DBL_MAX
; if (vary_a * 1.0 / vary_n < smallest)
{ while (vary_a * 1.0 / vary_n < smallest)
vary_a++
; vary_a--
; }
mcxTell
( me
, "smallest correlation is %.2f, using starting point %.2f"
, smallest
, vary_a * 1.0 / vary_n
)
; }
if (output_flags & OUTPUT_TABLE)
{
;fprintf(fp, "L\tD\tR\tS\tcce\tEWmean\tEWmed\tEWiqr\tNDmean\tNDmed\tNDiqr\tCCF\t%s\n", mode == 'k' ? "kNN" : mode == 'l' ? "N" : "Cutoff")
;} else
{ if (output_flags & OUTPUT_KEY)
{
;fprintf(fp, "-------------------------------------------------------------------------------\n")
;fprintf(fp, " L Percentage of nodes in the largest component\n")
;fprintf(fp, " D Percentage of nodes in components of size at most %d [-div option]\n", (int) divide_g)
;fprintf(fp, " R Percentage of nodes not in L or D: 100 - L -D\n")
;fprintf(fp, " S Percentage of nodes that are singletons\n")
;fprintf(fp, " cce Expected size of component, nodewise [ sum(sz^2) / sum^2(sz) ]\n")
;fprintf(fp, "*EW Edge weight traits (mean, median and IQR, all scaled!)\n")
;fprintf(fp, " Scaling is used to avoid printing of fractional parts throughout.\n")
;fprintf(fp, " The scaling factor is %.2f [-report-scale option]\n", weight_scale)
;fprintf(fp, " ND Node degree traits [mean, median and IQR]\n")
;fprintf(fp, " CCF Clustering coefficient %s\n", compute_flags & COMPUTE_CLCF ? "(not computed; use --clcf to include this)" : "")
;fprintf(fp, " eff Induced component efficiency %s\n", compute_flags & COMPUTE_EFF ? "(not computed; use --eff to include this)" : "")
;if (mode == 'c')
fprintf(fp, "Cutoff The threshold used.\n")
;else if (mode == 't')
fprintf(fp, "*Cutoff The threshold with scale factor %.2f and fractional parts removed\n", weight_scale)
;else if (mode == 'k')
fprintf(fp, "k-NN The knn parameter\n")
;else if (mode == 'l')
fprintf(fp, "N The knn parameter (merge mode)\n")
;else if (mode == 'n')
fprintf(fp, "ceil The ceil parameter\n")
;fprintf(fp, "Total number of nodes: %lu\n", (ulong) N_COLS(mx))
;}
fprintf(fp, "-------------------------------------------------------------------------------\n")
;fprintf(fp, " L D R S cce *EWmean *EWmed *EWiqr NDmean NDmed NDiqr CCF eff %6s \n", mode == 'k' ? "k-NN" : mode == 'l' ? "N" : mode == 'n' ? "Ceil" : "Cutoff")
;fprintf(fp, "-------------------------------------------------------------------------------\n")
; }
for (step = vary_a; step <= vary_z; step += vary_s)
{ double cutoff = step * 1.0 / vary_n
; double eff = -1.0
; mclv* nnodes = mclvCanonical(NULL, N_COLS(mx), 0.0)
; mclv* degree = mclvCanonical(NULL, N_COLS(mx), 0.0)
; dim i, n_sample = 0
; double cor, y_prev, iqr = 0.0
; mclx* cc = NULL, *res = NULL
; mclv* sz, *ccsz = NULL
; int step2 = vary_z + vary_a - step
; sum_vals = 0.0
; if (mode == 't' || mode == 'c')
mclxSelectValues(mx, &cutoff, NULL, MCLX_EQT_GQ)
, res = mx
; else if (mode == 'k')
{ res = rebase_g ? mclxCopy(mx) : mx
; mclxKNNdispatch(res, step2, n_thread_l, 1)
; }
else if (mode == 'l')
{ res = mx
; mclxKNNdispatch(res, step2, n_thread_l, 0)
; }
else if (mode == 'n')
{ res = rebase_g ? mclxCopy(mx) : mx
; mclv* cv = mclgCeilNB(res, step2, NULL, NULL, NULL)
; mclvFree(&cv)
; }
sz = mclxColSizes(res, MCL_VECTOR_COMPLETE)
; mclvSortDescVal(sz)
; cc = clmUGraphComponents(res, NULL) /* fixme: user has to specify -tf '#max()' if graph is directed */
; if (cc)
{ ccsz = mclxColSizes(cc, MCL_VECTOR_COMPLETE)
; if (compute_flags & COMPUTE_EFF)
{ clmPerformanceTable pftable
; clmPerformance(mx, cc, &pftable)
; eff = pftable.efficiency
; }
}
if (mode == 't' || mode == 'c')
{ for
(
; n_allvals > 0 && allvals[n_allvals-1] < cutoff
; n_allvals--
)
; sum_vals = 0.0
; for (i=0;i<n_allvals;i++)
sum_vals += allvals[i]
; }
else if (mode == 'k' || mode == 'n' || mode == 'l')
{ n_allvals = get_n_sort_allvals(res, allvals, noe, &sum_vals, FALSE)
; }
levels[cor_i].sim_median= mcxMedian(allvals, n_allvals, sizeof allvals[0], pval_get_double, &iqr)
; levels[cor_i].sim_iqr = iqr
; levels[cor_i].sim_mean = n_allvals ? sum_vals / n_allvals : 0.0
; levels[cor_i].nb_median = mcxMedian(sz->ivps, sz->n_ivps, sizeof sz->ivps[0], ivp_get_double, &iqr)
; levels[cor_i].nb_iqr = iqr
; levels[cor_i].nb_mean = mclvSum(sz) / N_COLS(res)
; levels[cor_i].cc_exp = cc ? mclvPowSum(ccsz, 2.0) / N_COLS(res) : 0
; levels[cor_i].nb_sum = mclxNrofEntries(res)
; if (compute_flags & COMPUTE_CLCF)
{ mclv* clcf = mclgCLCFdispatch(res, n_thread_l)
; levels[cor_i].clcf = mclvSum(clcf) / N_COLS(mx)
; mclvFree(&clcf)
; }
else
levels[cor_i].clcf = 0.0
; levels[cor_i].threshold = mode == 'k' || mode == 'l' || mode == 'n' ? step2 : cutoff
; levels[cor_i].bigsize = cc ? cc->cols[0].n_ivps : 0
; levels[cor_i].n_single = 0
; levels[cor_i].n_edge = n_allvals
; levels[cor_i].n_lq = 0
; if (cc)
for (i=0;i<N_COLS(cc);i++)
{ dim n = cc->cols[N_COLS(cc)-1-i].n_ivps
; if (n == 1)
levels[cor_i].n_single++
; if (n <= divide_g)
levels[cor_i].n_lq += n
; else
break
; }
if (levels[cor_i].bigsize <= divide_g)
levels[cor_i].bigsize = 0
; y_prev = sz->ivps[0].val
/* wiki says:
A scale-free network is a network whose degree distribution follows a power
law, at least asymptotically. That is, the fraction P(k) of nodes in the
network having k connections to other nodes goes for large values of k as P(k)
~ k^−g where g is a constant whose value is typically in the range 2<g<3,
although occasionally it may lie outside these bounds.
*/
; for (i=1;i<sz->n_ivps;i++)
{ double y = sz->ivps[i].val
; if (y > y_prev - 0.5)
continue /* same as node degree seen last */
; nnodes->ivps[n_sample].val = log( (i*1.0) / (1.0*N_COLS(res))) /* x = #nodes >= k, as fraction */
; degree->ivps[n_sample].val = log(y_prev ? y_prev : 1) /* y = k = degree of node */
; n_sample++
;if(0)fprintf(stderr, "k=%.0f\tn=%d\t%.3f\t%.3f\n", (double) y_prev, (int) i, (double) nnodes->ivps[n_sample-1].val, (double) degree->ivps[n_sample-1].val)
; y_prev = y
; }
nnodes->ivps[n_sample].val = 0
; nnodes->ivps[n_sample++].val = log(y_prev ? y_prev : 1)
;if(0){fprintf(stderr, "k=%.0f\tn=%d\t%.3f\t%.3f\n", (double) sz->ivps[sz->n_ivps-1].val, (int) N_COLS(res), (double) nnodes->ivps[n_sample-1].val, (double) degree->ivps[n_sample-1].val)
;}
; mclvResize(nnodes, n_sample)
; mclvResize(degree, n_sample)
; cor = pearson(nnodes, degree, n_sample)
; levels[cor_i].degree_cor = cor * cor
;if(0)fprintf(stdout, "cor at cutoff %.2f %.3f\n\n", cutoff, levels[cor_i-1].degree_cor)
; mclvFree(&nnodes)
; mclvFree(°ree)
; mclvFree(&sz)
; mclvFree(&ccsz)
; mclxFree(&cc)
; if(output_flags & OUTPUT_TABLE)
{ fprintf
( fp
, "%lu\t%lu\t%lu\t%lu\t%lu"
"\t%6g\t%6g\t%6g"
"\t%6g\t%lu\t%6g"
, (ulong) levels[cor_i].bigsize
, (ulong) levels[cor_i].n_lq
, (ulong) N_COLS(mx) - levels[cor_i].bigsize - levels[cor_i].n_lq
, (ulong) levels[cor_i].n_single
, (ulong) levels[cor_i].cc_exp
, (double) levels[cor_i].sim_mean
, (double) levels[cor_i].sim_median
, (double) levels[cor_i].sim_iqr
, (double) levels[cor_i].nb_mean
, (ulong) levels[cor_i].nb_median
, (double) levels[cor_i].nb_iqr
)
; if (compute_flags & COMPUTE_CLCF) fprintf(fp, "\t%6g", levels[cor_i].clcf) ; else fputs("\tNA", fp)
; if (eff >= 0.0) fprintf(fp, "\t%4g", eff) ; else fputs("\tNA", fp)
; fprintf(fp, "\t%6g", (double) levels[cor_i].threshold)
; fputc('\n', fp)
; }
else
{ fprintf
( fp
, "%3d %3d %3d %3d %7d "
"%7.0f %7.0f %6.0f"
"%6.1f %6.0f %6.0f"
, 0 ? 1 : (int) (0.5 + (100.0 * levels[cor_i].bigsize) / N_COLS(mx))
, 0 ? 1 : (int) (0.5 + (100.0 * levels[cor_i].n_lq) / N_COLS(mx))
, 0 ? 1 : (int) (0.5 + (100.0 * (N_COLS(mx) - levels[cor_i].bigsize - levels[cor_i].n_lq)) / N_COLS(mx))
, 0 ? 1 : (int) (0.5 + (100.0 * levels[cor_i].n_single) / N_COLS(mx))
, 0 ? 1 : (int) (0.5 + levels[cor_i].cc_exp)
, 0 ? 1.0 : (double) (levels[cor_i].sim_mean * weight_scale)
, 0 ? 1.0 : (double) (levels[cor_i].sim_median * weight_scale)
, 0 ? 1.0 : (double) (levels[cor_i].sim_iqr * weight_scale)
, 0 ? 1.0 : (double) (levels[cor_i].nb_mean )
, 0 ? 1.0 : (double) (levels[cor_i].nb_median + 0.5 )
, 0 ? 1.0 : (double) (levels[cor_i].nb_iqr + 0.5 )
)
; if (compute_flags & COMPUTE_CLCF)
fprintf(fp, " %3d", 0 ? 1 : (int) (0.5 + (100.0 * levels[cor_i].clcf)))
; else
fputs(" -", fp)
; if (eff >= 0.0)
fprintf(fp, " %3d", (int) (0.5 + 1000 * eff))
; else
fputs(" -", fp)
; if (mode == 'c')
fprintf(fp, "%8.2f\n", (double) levels[cor_i].threshold)
; else if (mode == 't')
fprintf(fp, "%8.0f\n", (double) levels[cor_i].threshold * weight_scale)
; else if (mode == 'k' || mode == 'n' || mode == 'l')
fprintf(fp, "%8.0f\n", (double) levels[cor_i].threshold)
; }
; cor_i++
; if (res != mx)
mclxFree(&res)
; }
if (!(output_flags & OUTPUT_TABLE))
{ if (weefreemen)
{
fprintf(fp, "-------------------------------------------------------------------------------\n")
;fprintf(fp, "The graph below plots the R^2 squared value for the fit of a log-log plot of\n")
;fprintf(fp, "<node degree k> versus <#nodes with degree >= k>, for the network resulting\n")
;fprintf(fp, "from applying a particular %s cutoff.\n", mode == 'c' ? "correlation" : "similarity")
;fprintf(fp, "-------------------------------------------------------------------------------\n")
; for (j=0;j<cor_i;j++)
{ dim jj
; for (jj=30;jj<=100;jj++)
{ char c = ' '
; if (jj * 0.01 < levels[j].degree_cor && (jj+1.0) * 0.01 > levels[j].degree_cor)
c = 'X'
; else if (jj % 5 == 0)
c = '|'
; fputc(c, fp)
; }
if (mode == 'c')
fprintf(fp, "%8.2f\n", (double) levels[j].threshold)
; else
fprintf(fp, "%8.0f\n", (double) levels[j].threshold * weight_scale)
; }
fprintf(fp, "|----+----|----+----|----+----|----+----|----+----|----+----|----+----|--------\n")
;fprintf(fp, "| R^2 0.4 0.5 0.6 0.7 0.8 0.9 | 1.0 -o)\n")
;fprintf(fp, "+----+----+----+----+----+---------+----+----+----+----+----+----+----+ /\\\\\n")
;fprintf(fp, "| 2 4 6 8 2 4 6 8 | 2 4 6 8 | 2 4 6 8 | 2 4 6 8 | 2 4 6 8 | 2 4 6 8 | _\\_/\n")
;fprintf(fp, "+----+----|----+----|----+----|----+----|----+----|----+----|----+----+--------\n")
; }
else
fprintf(fp, "-------------------------------------------------------------------------------\n")
; }
mclxFree(&mx)
; mcxFree(allvals)
; }
double get_score
( const mclv* c
, const mclv* d
, const mclv* c_start
, const mclv* d_start
, const mclv* c_end
, const mclv* d_end
)
{ mclv* vecc = mclvClone(c)
; mclv* vecd = mclvClone(d)
; mclv* meet_c = mcldMeet(vecc, vecd, NULL)
; mclv* meet_d = mcldMeet(vecd, meet_c, NULL)
; mclv* cwid = mclvBinary(c_end, c_start, NULL, fltSubtract)
; mclv* dwid = mclvBinary(d_end, d_start, NULL, fltSubtract)
; mclv* rmin = mclvBinary(c_end, d_end, NULL, fltMin)
; mclv* lmax = mclvBinary(c_start, d_start, NULL, fltMax)
; mclv* delta = mclvBinary(rmin, lmax, NULL, fltSubtract)
; mclv* weightc, *weightd
; double ip, cd, csn, meanc, meand, mean, euclid, meet_fraction, score, sum_meet_c, sum_meet_d, reduction_c, reduction_d
; int nmeet = meet_c->n_ivps
; int nldif = vecc->n_ivps - nmeet
; int nrdif = vecd->n_ivps - nmeet
; mclvSelectGqBar(delta, 0.0)
; weightc= mclvBinary(delta, cwid, NULL, mydiv)
; weightd= mclvBinary(delta, dwid, NULL, mydiv)
#if 0
;if (c != d)mclvaDump
( cwid
, stdout
, 5
, "\n"
, 0)
,mclvaDump
( dwid
, stdout
, 5
, "\n"
, 0)
#endif
; sum_meet_c = 0.01 + mclvSum(meet_c)
; sum_meet_d = 0.01 + mclvSum(meet_d)
; mclvBinary(meet_c, weightc, meet_c, fltMultiply)
; mclvBinary(meet_d, weightd, meet_d, fltMultiply)
; reduction_c = mclvSum(meet_c) / sum_meet_c
; reduction_d = mclvSum(meet_d) / sum_meet_d
; ip = mclvIn(meet_c, meet_d)
; cd = sqrt(mclvPowSum(meet_c, 2.0) * mclvPowSum(meet_d, 2.0))
; csn = cd ? ip / cd : 0.0
; meanc = meet_c->n_ivps ? mclvSum(meet_c) / meet_c->n_ivps : 0.0
; meand = meet_d->n_ivps ? mclvSum(meet_d) / meet_d->n_ivps : 0.0
; mean = MCX_MIN(meanc, meand)
; euclid = 0
? 1.0
: ( mean
? sqrt(mclvPowSum(meet_c, 2.0) / mclvPowSum(vecc, 2.0))
: 0.0
)
; meet_fraction = pow((meet_c->n_ivps * 1.0 / vecc->n_ivps), 1.0)
; score = mean * csn * euclid * meet_fraction * 1.0
; mclvFree(&meet_c)
; mclvFree(&meet_d)
; fprintf
( stdout
, "%10d%10d%10d%10d%10d%10g%10g%10g%10g%10g%10g%10g\n"
, (int) c->vid
, (int) d->vid
, (int) nldif
, (int) nrdif
, (int) nmeet
, score
, mean
, csn
, euclid
, meet_fraction
, reduction_c
, reduction_d
)
; return score
; }