[Buildroot] [PATCH 1/1] package/dieharder: drop rgb_operm
Arnout Vandecappelle
arnout at mind.be
Mon Apr 4 19:44:57 UTC 2022
On 03/04/2022 22:56, Fabrice Fontaine wrote:
> Fix the following build failure:
>
> /home/autobuild/autobuild/instance-7/output-1/host/lib/gcc/m68k-buildroot-linux-uclibc/11.2.0/../../../../m68k-buildroot-linux-uclibc/bin/ld: dieharder-add_ui_rngs.o:(.data+0xd8): undefined reference to `rgb_operm'
>
> Fixes:
> - http://autobuild.buildroot.org/results/7be339674291b39f8eddb8ad065f0988128ecfe9
>
> Signed-off-by: Fabrice Fontaine <fontaine.fabrice at gmail.com>
> ---
> .../0005-Remove-defunct-rgb_operm.patch | 732 ++++++++++++++++++
> 1 file changed, 732 insertions(+)
> create mode 100644 package/dieharder/0005-Remove-defunct-rgb_operm.patch
>
> diff --git a/package/dieharder/0005-Remove-defunct-rgb_operm.patch b/package/dieharder/0005-Remove-defunct-rgb_operm.patch
> new file mode 100644
> index 0000000000..efc311dbaa
> --- /dev/null
> +++ b/package/dieharder/0005-Remove-defunct-rgb_operm.patch
> @@ -0,0 +1,732 @@
> +From 40d377b86c856f5a4510a6f5cd56be004873ad77 Mon Sep 17 00:00:00 2001
> +From: =?UTF-8?q?Marcus=20M=C3=BCller?= <mueller at kit.edu>
> +Date: Mon, 12 Oct 2020 21:30:12 +0200
> +Subject: [PATCH] Remove defunct rgb_operm
> +
> +[Retrieved from:
> +https://github.com/eddelbuettel/dieharder/pull/2/commits/40d377b86c856f5a4510a6f5cd56be004873ad77]
> +Signed-off-by: Fabrice Fontaine <fontaine.fabrice at gmail.com>
Applied to master, thanks.
Regards,
Arnout
> +---
> + include/Makefile.am | 1 -
> + include/dieharder/rgb_operm.h | 38 --
> + include/dieharder/tests.h | 2 -
> + libdieharder/rgb_operm.c | 633 ----------------------------------
> + 4 files changed, 674 deletions(-)
> + delete mode 100644 include/dieharder/rgb_operm.h
> + delete mode 100644 libdieharder/rgb_operm.c
> +
> +diff --git a/include/Makefile.am b/include/Makefile.am
> +index f80b4ff..e4659cd 100644
> +--- a/include/Makefile.am
> ++++ b/include/Makefile.am
> +@@ -33,7 +33,6 @@ nobase_include_HEADERS = dieharder/copyright.h \
> + dieharder/rgb_lagged_sums.h \
> + dieharder/rgb_lmn.h \
> + dieharder/rgb_minimum_distance.h \
> +- dieharder/rgb_operm.h \
> + dieharder/rgb_persist.h \
> + dieharder/rgb_permutations.h \
> + dieharder/rgb_timing.h \
> +diff --git a/include/dieharder/rgb_operm.h b/include/dieharder/rgb_operm.h
> +deleted file mode 100644
> +index c48fa37..0000000
> +--- a/include/dieharder/rgb_operm.h
> ++++ /dev/null
> +@@ -1,38 +0,0 @@
> +-/*
> +- * rgb_operm test header.
> +- */
> +-
> +-/*
> +- * function prototype
> +- */
> +-int rgb_operm(Test **test,int irun);
> +-
> +-static Dtest rgb_operm_dtest __attribute__((unused)) = {
> +- "RGB Overlapping Permuations Test",
> +- "rgb_operm",
> +- "\n\
> +-#========================================================================\n\
> +-# RGB Overlapping Permutations Test\n\
> +-# Forms both the exact (expected) covariance matrix for overlapping\n\
> +-# permutations of random integer and an empirical covariance matrix\n\
> +-# formed from a long string of samples. The difference is expected\n\
> +-# to have a chisq distribution and hence can be transformed into a\n\
> +-# sample p-value. Note that this is one possible functional replacement\n\
> +-# for the broken/defunct diehard operm5 test, but one that permits k (the\n\
> +-# number of numbers in the overlapping permutation window) to be varied\n\
> +-# from 2 to perhaps 8.\n\
> +-#\n",
> +- 100, /* Default psamples */
> +- 100000, /* Default tsamples */
> +- 1, /* We magically make all the bit tests return a single histogram */
> +- rgb_operm,
> +- 0
> +-};
> +-
> +-/*
> +- * Global variables.
> +- *
> +- * rgb_operm_k is the size of the overlapping window that is slid along
> +- * a data stream of rands from x_i to x_{i+k} to compute c[][].
> +- */
> +-unsigned int rgb_operm_k;
> +diff --git a/include/dieharder/tests.h b/include/dieharder/tests.h
> +index 1674aed..b50dbe3 100644
> +--- a/include/dieharder/tests.h
> ++++ b/include/dieharder/tests.h
> +@@ -11,7 +11,6 @@
> + #include <dieharder/rgb_kstest_test.h>
> + #include <dieharder/rgb_lagged_sums.h>
> + #include <dieharder/rgb_minimum_distance.h>
> +-#include <dieharder/rgb_operm.h>
> + #include <dieharder/rgb_permutations.h>
> + #include <dieharder/dab_bytedistrib.h>
> + #include <dieharder/dab_dct.h>
> +@@ -80,7 +79,6 @@
> + RGB_PERMUTATIONS,
> + RGB_LAGGED_SUMS,
> + RGB_LMN,
> +- RGB_OPERM,
> + DAB_BYTEDISTRIB,
> + DAB_DCT,
> + DAB_FILLTREE,
> +diff --git a/libdieharder/rgb_operm.c b/libdieharder/rgb_operm.c
> +deleted file mode 100644
> +index 15f8e9a..0000000
> +--- a/libdieharder/rgb_operm.c
> ++++ /dev/null
> +@@ -1,633 +0,0 @@
> +-/*
> +- * ========================================================================
> +- * $Id: rgb_operm.c 252 2006-10-10 13:17:36Z rgb $
> +- *
> +- * See copyright in copyright.h and the accompanying file COPYING
> +- * ========================================================================
> +- */
> +-
> +-/*
> +- * ========================================================================
> +- * This is the revised Overlapping Permutations test. It directly
> +- * simulates the covariance matrix of overlapping permutations. The way
> +- * this works below (tentatively) is:
> +- *
> +- * For a bit ntuple of length N, slide a window of length N to the
> +- * right one bit at a time. Compute the permutation index of the
> +- * original ntuple, the permutation index of the window ntuple, and
> +- * accumulate the covariance matrix of the two positions. This
> +- * can be directly and precisely computed as well. The simulated
> +- * result should be distributed according to the chisq distribution,
> +- * so we subtract the two and feed it into the chisq program as a
> +- * vector to compute p.
> +- *
> +- * This MAY NOT BE RIGHT. I'm working from both Marsaglia's limited
> +- * documentation (in a program that doesn't do ANYTHING like what the
> +- * documentation says it does) and from Nilpotent Markov Processes.
> +- * But I confess to not quite understand how to actually perform the
> +- * test in the latter -- it is very good at describing the construction
> +- * of the target matrix, not so good at describing how to transform
> +- * this into a chisq and p.
> +- *
> +- * FWIW, as I get something that actually works here, I'm going to
> +- * THOROUGHLY document it in the book that will accompany the test.
> +- *========================================================================
> +- */
> +-
> +-#include <dieharder/libdieharder.h>
> +-#define RGB_OPERM_KMAX 10
> +-
> +-/*
> +- * Some globals that will eventually go in the test include where they
> +- * arguably belong.
> +- */
> +-double fpipi(int pi1,int pi2,int nkp);
> +-uint piperm(size_t *data,int len);
> +-void make_cexact();
> +-void make_cexpt();
> +-int nperms,noperms;
> +-double **cexact,**ceinv,**cexpt,**idty;
> +-double *cvexact,*cvein,*cvexpt,*vidty;
> +-
> +-int rgb_operm(Test **test,int irun)
> +-{
> +-
> +- int i,j,n,nb,iv,s;
> +- uint csamples; /* rgb_operm_k^2 is vector size of cov matrix */
> +- uint *count,ctotal; /* counters */
> +- uint size;
> +- double pvalue,ntuple_prob,pbin; /* probabilities */
> +- Vtest *vtest; /* Chisq entry vector */
> +-
> +- gsl_matrix_view CEXACT,CEINV,CEXPT,IDTY;
> +-
> +- /*
> +- * For a given n = ntuple size in bits, there are n! bit orderings
> +- */
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("#==================================================================\n");
> +- printf("# rgb_operm: Running rgb_operm verbosely for k = %d.\n",rgb_operm_k);
> +- printf("# rgb_operm: Use -v = %d to focus.\n",D_RGB_OPERM);
> +- printf("# rgb_operm: ======================================================\n");
> +- }
> +-
> +- /*
> +- * Sanity check first
> +- */
> +- if((rgb_operm_k < 0) || (rgb_operm_k > RGB_OPERM_KMAX)){
> +- printf("\nError: rgb_operm_k must be a positive integer <= %u. Exiting.\n",RGB_OPERM_KMAX);
> +- exit(0);
> +- }
> +-
> +- nperms = gsl_sf_fact(rgb_operm_k);
> +- noperms = gsl_sf_fact(3*rgb_operm_k-2);
> +- csamples = rgb_operm_k*rgb_operm_k;
> +- gsl_permutation * p = gsl_permutation_alloc(nperms);
> +-
> +- /*
> +- * Allocate memory for value_max vector of Vtest structs and counts,
> +- * PER TEST. Note that we must free both of these when we are done
> +- * or leak.
> +- */
> +- vtest = (Vtest *)malloc(csamples*sizeof(Vtest));
> +- count = (uint *)malloc(csamples*sizeof(uint));
> +- Vtest_create(vtest,csamples+1);
> +-
> +- /*
> +- * We have to allocate and free the cexact and cexpt matrices here
> +- * or they'll be forgotten when these routines return.
> +- */
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("# rgb_operm: Creating and zeroing cexact[][] and cexpt[][].\n");
> +- }
> +- cexact = (double **)malloc(nperms*sizeof(double*));
> +- ceinv = (double **)malloc(nperms*sizeof(double*));
> +- cexpt = (double **)malloc(nperms*sizeof(double*));
> +- idty = (double **)malloc(nperms*sizeof(double*));
> +- cvexact = (double *)malloc(nperms*nperms*sizeof(double));
> +- cvein = (double *)malloc(nperms*nperms*sizeof(double));
> +- cvexpt = (double *)malloc(nperms*nperms*sizeof(double));
> +- vidty = (double *)malloc(nperms*nperms*sizeof(double));
> +- for(i=0;i<nperms;i++){
> +- /* Here we pack addresses to map the matrix addressing onto the vector */
> +- cexact[i] = &cvexact[i*nperms];
> +- ceinv[i] = &cvein[i*nperms];
> +- cexpt[i] = &cvexpt[i*nperms];
> +- idty[i] = &vidty[i*nperms];
> +- for(j = 0;j<nperms;j++){
> +- cexact[i][j] = 0.0;
> +- ceinv[i][j] = 0.0;
> +- cexpt[i][j] = 0.0;
> +- idty[i][j] = 0.0;
> +- }
> +- }
> +-
> +- make_cexact();
> +- make_cexpt();
> +-
> +- iv=0;
> +- for(i=0;i<nperms;i++){
> +- for(j=0;j<nperms;j++){
> +- cvexact[iv] = cexact[i][j];
> +- cvexpt[iv] = cexpt[i][j];
> +- vidty[iv] = 0.0;
> +- }
> +- }
> +-
> +- CEXACT = gsl_matrix_view_array(cvexact, nperms, nperms);
> +- CEINV = gsl_matrix_view_array(cvein , nperms, nperms);
> +- CEXPT = gsl_matrix_view_array(cvexpt , nperms, nperms);
> +- IDTY = gsl_matrix_view_array(vidty , nperms, nperms);
> +-
> +- /*
> +- * Hmmm, looks like cexact isn't invertible. Duh. So it has eigenvalues.
> +- * This seems to be important (how, I do not know) so let's find out.
> +- * Here is the gsl ritual for evaluating eigenvalues etc.
> +- */
> +-
> +- gsl_vector *eval = gsl_vector_alloc (nperms);
> +- gsl_matrix *evec = gsl_matrix_alloc (nperms,nperms);
> +- /*
> +- gsl_eigen_nonsymm_workspace* w = gsl_eigen_nonsymmv_alloc(nperms);
> +- gsl_eigen_nonsymm_params (1,0,w);
> +- gsl_eigen_nonsymmv(&CEXACT.matrix, eval, evec, w);
> +- gsl_eigen_nonsymmv_free (w);
> +- */
> +- gsl_eigen_symmv_workspace* w = gsl_eigen_symmv_alloc(nperms);
> +- gsl_eigen_symmv(&CEXACT.matrix, eval, evec, w);
> +- gsl_eigen_symmv_free (w);
> +- gsl_eigen_symmv_sort (eval, evec, GSL_EIGEN_SORT_ABS_ASC);
> +-
> +- {
> +- int i;
> +-
> +- printf("#==================================================================\n");
> +- for (i = 0; i < nperms; i++) {
> +- double eval_i = gsl_vector_get (eval, i);
> +- gsl_vector_view evec_i = gsl_matrix_column (evec, i);
> +- printf ("eigenvalue[%u] = %g\n", i, eval_i);
> +- printf ("eigenvector[%u] = \n",i);
> +- gsl_vector_fprintf (stdout,&evec_i.vector, "%10.5f");
> +- }
> +- printf("#==================================================================\n");
> +- }
> +-
> +- gsl_vector_free (eval);
> +- gsl_matrix_free (evec);
> +-
> +-/*
> +- gsl_linalg_LU_decomp(&CEXACT.matrix, p, &s);
> +- gsl_linalg_LU_invert(&CEXACT, p, &CEINV);
> +- gsl_permutation_free(p);
> +- gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, &CEINV.matrix, &CEXPT.matrix, 0.0, &IDTY.matrix);
> +- printf("#==================================================================\n");
> +- printf("# Should be inverse of C, assuming it is invertible:\n");
> +- for(i=0;i<nperms;i++){
> +- printf("# ");
> +- for(j = 0;j<nperms;j++){
> +- printf("%8.3f ",idty[i][j]);
> +- }
> +- printf("\n");
> +- }
> +- printf("#==================================================================\n");
> +- printf("#==================================================================\n");
> +- printf("# Should be normal on identity:\n");
> +- for(i=0;i<nperms;i++){
> +- printf("# ");
> +- for(j = 0;j<nperms;j++){
> +- printf("%8.3f ",idty[i][j]);
> +- }
> +- printf("\n");
> +- }
> +- printf("#==================================================================\n");
> +- */
> +-
> +-
> +-
> +- /*
> +- * OK, at this point we have two matrices: cexact[][] is filled with
> +- * the exact covariance matrix expected for the overlapping permutations.
> +- * cexpt[][] has been filled numerically by generating strings of random
> +- * uints or floats, generating sort index permutations, and
> +- * using them to IDENTICALLY generate an "experimental" version of c[][].
> +- * The two should correspond, in the limit of large tsamples. IF I
> +- * understand Alhakim, Kawczak and Molchanov, then the way to implement
> +- * the simplest possible chisq test is to evaluate:
> +- * cexact^-1 cexpt \approx I
> +- * where the diagonal terms should form a vector that is chisq distributed?
> +- * Let's try this...
> +- */
> +-
> +-
> +-
> +- /*
> +- * Free cexact[][] and cexpt[][]
> +- * Fix this when we're done so we don't leak; for now to much trouble.
> +- for(i=0;i<nperms;i++){
> +- free(cexact[i]);
> +- free(cexpt[i]);
> +- }
> +- free(cexact);
> +- free(cexpt);
> +- */
> +-
> +- return(0);
> +-
> +-}
> +-
> +-void make_cexact()
> +-{
> +-
> +- int i,j,k,ip,t,nop;
> +- double fi,fj;
> +- /*
> +- * This is the test vector.
> +- */
> +- double testv[RGB_OPERM_KMAX*2]; /* easier than malloc etc, but beware length */
> +- /*
> +- * pi[] is the permutation index of a sample. ps[] holds the
> +- * actual sample.
> +- */
> +- size_t pi[4096],ps[4096];
> +- /*
> +- * We seem to have made a mistake of sorts. We actually have to sum
> +- * BOTH the forward AND the backward directions. That means that the
> +- * permutation vector has to be of length 3k-1, with the pi=1 term
> +- * corresponding to the middle. So for k=2, instead of 0,1,2 we need
> +- * 0 1 2 3 4 and we'll have to do 23, 34 in the leading direction and
> +- * 21, 10 in the trailing direction.
> +- */
> +- gsl_permutation **operms;
> +-
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("#==================================================================\n");
> +- printf("# rgb_operm: Running cexact()\n");
> +- }
> +-
> +- /*
> +- * Test fpipi(). This is probably cruft, actually.
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("# rgb_operm: Testing fpipi()\n");
> +- for(i=0;i<nperms;i++){
> +- for(j = 0;j<nperms;j++){
> +- printf("# rgb_operm: fpipi(%u,%u,%u) = %f\n",i,j,nperms,fpipi(i,j,nperms));
> +- }
> +- }
> +- }
> +- */
> +-
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("#==================================================================\n");
> +- printf("# rgb_operm: Forming set of %u overlapping permutations\n",noperms);
> +- printf("# rgb_operm: Permutations\n");
> +- printf("# rgb_operm:==============================\n");
> +- }
> +- operms = (gsl_permutation**) malloc(noperms*sizeof(gsl_permutation*));
> +- for(i=0;i<noperms;i++){
> +- operms[i] = gsl_permutation_alloc(3*rgb_operm_k - 2);
> +- /* Must quiet down
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("# rgb_operm: ");
> +- }
> +- */
> +- if(i == 0){
> +- gsl_permutation_init(operms[i]);
> +- } else {
> +- gsl_permutation_memcpy(operms[i],operms[i-1]);
> +- gsl_permutation_next(operms[i]);
> +- }
> +- /*
> +- MYDEBUG(D_RGB_OPERM){
> +- gsl_permutation_fprintf(stdout,operms[i]," %u");
> +- printf("\n");
> +- }
> +- */
> +- }
> +-
> +- /*
> +- * We now form c_exact PRECISELY the same way that we do c_expt[][]
> +- * below, except that instead of pulling random samples of integers
> +- * or floats and averaging over the permutations thus represented,
> +- * we iterate over the complete set of equally weighted permutations
> +- * to get an exact answer. Note that we have to center on 2k-1 and
> +- * go both forwards and backwards.
> +- */
> +- for(t=0;t<noperms;t++){
> +- /*
> +- * To sort into a perm, test vector needs to be double.
> +- */
> +- for(k=0;k<3*rgb_operm_k - 2;k++) testv[k] = (double) operms[t]->data[k];
> +-
> +- /* Not cruft, but quiet...
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("#------------------------------------------------------------------\n");
> +- printf("# Generating offset sample permutation pi's\n");
> +- }
> +- */
> +- for(k=0;k<2*rgb_operm_k - 1;k++){
> +- gsl_sort_index((size_t *) ps,&testv[k],1,rgb_operm_k);
> +- pi[k] = piperm((size_t *) ps,rgb_operm_k);
> +-
> +- /* Not cruft, but quiet...
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("# %u: ",k);
> +- for(ip=k;ip<rgb_operm_k+k;ip++){
> +- printf("%.1f ",testv[ip]);
> +- }
> +- printf("\n# ");
> +- for(ip=0;ip<rgb_operm_k;ip++){
> +- printf("%u ",ps[ip]);
> +- }
> +- printf(" = %u\n",pi[k]);
> +- }
> +- */
> +-
> +- }
> +-
> +- /*
> +- * This is the business end of things. The covariance matrix is the
> +- * the sum of a central function of the permutation indices that yields
> +- * nperms-1/nperms on diagonal, -1/nperms off diagonal, for all the
> +- * possible permutations, for the FIRST permutation in a sample (fi)
> +- * times the sum of the same function over all the overlapping permutations
> +- * drawn from the same sample. Quite simple, really.
> +- */
> +- for(i=0;i<nperms;i++){
> +- fi = fpipi(i,pi[rgb_operm_k-1],nperms);
> +- for(j=0;j<nperms;j++){
> +- fj = 0.0;
> +- for(k=0;k<rgb_operm_k;k++){
> +- fj += fpipi(j,pi[rgb_operm_k - 1 + k],nperms);
> +- if(k != 0){
> +- fj += fpipi(j,pi[rgb_operm_k - 1 - k],nperms);
> +- }
> +- }
> +- cexact[i][j] += fi*fj;
> +- }
> +- }
> +-
> +- }
> +-
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("# rgb_operm:==============================\n");
> +- printf("# rgb_operm: cexact[][] = \n");
> +- }
> +- for(i=0;i<nperms;i++){
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("# ");
> +- }
> +- for(j=0;j<nperms;j++){
> +- cexact[i][j] /= noperms;
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("%10.6f ",cexact[i][j]);
> +- }
> +- }
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("\n");
> +- }
> +- }
> +-
> +- /*
> +- * Free operms[]
> +- */
> +- for(i=0;i<noperms;i++){
> +- gsl_permutation_free(operms[i]);
> +- }
> +- free(operms);
> +-
> +-}
> +-
> +-void make_cexpt()
> +-{
> +-
> +- int i,j,k,ip,t;
> +- double fi,fj;
> +- /*
> +- * This is the test vector.
> +- */
> +- double testv[RGB_OPERM_KMAX*2]; /* easier than malloc etc, but beware length */
> +- /*
> +- * pi[] is the permutation index of a sample. ps[] holds the
> +- * actual sample.
> +- */
> +- int pi[4096],ps[4096];
> +-
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("#==================================================================\n");
> +- printf("# rgb_operm: Running cexpt()\n");
> +- }
> +-
> +- /*
> +- * We evaluate cexpt[][] by sampling. In a nutshell, this involves
> +- * a) Filling testv[] with 2*rgb_operm_k - 1 random uints or doubles
> +- * It clearly cannot matter which we use, as long as the probability of
> +- * exact duplicates in a sample is very low.
> +- * b) Using gsl_sort_index the exact same way it was used in make_cexact()
> +- * to generate the pi[] index, using ps[] as scratch space for the sort
> +- * indices.
> +- * c) Evaluating fi and fj from the SAMPLED result, tsamples times.
> +- * d) Normalizing.
> +- * Note that this is pretty much identical to the way we formed c_exact[][]
> +- * except that we are determining the relative frequency of each sort order
> +- * permutation 2*rgb_operm_k-1 long.
> +- *
> +- * NOTE WELL! I honestly think that it is borderline silly to view
> +- * this as a matrix and to go through all of this nonsense. The theoretical
> +- * c_exact[][] is computed from the observation that all the permutations
> +- * of n objects have equal weight = 1/n!. Consequently, they should
> +- * individually be binomially distributed, tending to normal with many
> +- * samples. Collectively they should be distributed like a vector of
> +- * equal binomial probabilities and a p-value should follow either from
> +- * chisq on n!-1 DoF or for that matter a KS test. I see no way that
> +- * making it into a matrix can increase the sensitivity of the test -- if
> +- * the p-values are well defined in the two cases they can only be equal
> +- * by their very definition.
> +- *
> +- * If you are a statistician reading these words and disagree, please
> +- * communicate with me and explain why I'm wrong. I'm still very much
> +- * learning statistics and would cherish gentle correction.
> +- */
> +- for(t=0;t<tsamples;t++){
> +- /*
> +- * To sort into a perm, test vector needs to be double.
> +- */
> +- for(k=0;k<3*rgb_operm_k - 2;k++) testv[k] = (double) gsl_rng_get(rng);
> +-
> +- /* Not cruft, but quiet...
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("#------------------------------------------------------------------\n");
> +- printf("# Generating offset sample permutation pi's\n");
> +- }
> +- */
> +- for(k=0;k<2*rgb_operm_k-1;k++){
> +- gsl_sort_index(ps,&testv[k],1,rgb_operm_k);
> +- pi[k] = piperm(ps,rgb_operm_k);
> +-
> +- /* Not cruft, but quiet...
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("# %u: ",k);
> +- for(ip=k;ip<rgb_operm_k+k;ip++){
> +- printf("%.1f ",testv[ip]);
> +- }
> +- printf("\n# ");
> +- for(ip=0;ip<rgb_operm_k;ip++){
> +- printf("%u ",permsample->data[ip]);
> +- }
> +- printf(" = %u\n",pi[k]);
> +- }
> +- */
> +- }
> +-
> +- /*
> +- * This is the business end of things. The covariance matrix is the
> +- * the sum of a central function of the permutation indices that yields
> +- * nperms-1/nperms on diagonal, -1/nperms off diagonal, for all the
> +- * possible permutations, for the FIRST permutation in a sample (fi)
> +- * times the sum of the same function over all the overlapping permutations
> +- * drawn from the same sample. Quite simple, really.
> +- */
> +- for(i=0;i<nperms;i++){
> +- fi = fpipi(i,pi[rgb_operm_k-1],nperms);
> +- for(j=0;j<nperms;j++){
> +- fj = 0.0;
> +- for(k=0;k<rgb_operm_k;k++){
> +- fj += fpipi(j,pi[rgb_operm_k - 1 + k],nperms);
> +- if(k != 0){
> +- fj += fpipi(j,pi[rgb_operm_k - 1 - k],nperms);
> +- }
> +- }
> +- cexpt[i][j] += fi*fj;
> +- }
> +- }
> +-
> +- }
> +-
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("# rgb_operm:==============================\n");
> +- printf("# rgb_operm: cexpt[][] = \n");
> +- }
> +- for(i=0;i<nperms;i++){
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("# ");
> +- }
> +- for(j=0;j<nperms;j++){
> +- cexpt[i][j] /= tsamples;
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("%10.6f ",cexpt[i][j]);
> +- }
> +- }
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("\n");
> +- }
> +- }
> +-
> +-}
> +-
> +-uint piperm(size_t *data,int len)
> +-{
> +-
> +- uint i,j,k,max,min;
> +- uint pindex,uret,tmp;
> +- static gsl_permutation** lookup = 0;
> +-
> +- /*
> +- * Allocate space for lookup table and fill it.
> +- */
> +- if(lookup == 0){
> +- lookup = (gsl_permutation**) malloc(nperms*sizeof(gsl_permutation*));
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("# rgb_operm: Allocating piperm lookup table of perms.\n");
> +- }
> +- for(i=0;i<nperms;i++){
> +- lookup[i] = gsl_permutation_alloc(rgb_operm_k);
> +- }
> +- for(i=0;i<nperms;i++){
> +- if(i == 0){
> +- gsl_permutation_init(lookup[i]);
> +- } else {
> +- gsl_permutation_memcpy(lookup[i],lookup[i-1]);
> +- gsl_permutation_next(lookup[i]);
> +- }
> +- }
> +-
> +- /*
> +- * This method yields a mirror symmetry in the permutations top to
> +- * bottom.
> +- for(i=0;i<nperms/2;i++){
> +- if(i == 0){
> +- gsl_permutation_init(lookup[i]);
> +- for(j=0;j<rgb_operm_k;j++){
> +- lookup[nperms-i-1]->data[rgb_operm_k-j-1] = lookup[i]->data[j];
> +- }
> +- } else {
> +- gsl_permutation_memcpy(lookup[i],lookup[i-1]);
> +- gsl_permutation_next(lookup[i]);
> +- for(j=0;j<rgb_operm_k;j++){
> +- lookup[nperms-i-1]->data[rgb_operm_k-j-1] = lookup[i]->data[j];
> +- }
> +- }
> +- }
> +- */
> +- MYDEBUG(D_RGB_OPERM){
> +- for(i=0;i<nperms;i++){
> +- printf("# rgb_operm: %u => ",i);
> +- gsl_permutation_fprintf(stdout,lookup[i]," %u");
> +- printf("\n");
> +- }
> +- }
> +-
> +- }
> +-
> +- for(i=0;i<nperms;i++){
> +- if(memcmp(data,lookup[i]->data,len*sizeof(uint))==0){
> +- /* Not cruft, but off:
> +- MYDEBUG(D_RGB_OPERM){
> +- printf("# piperm(): ");
> +- gsl_permutation_fprintf(stdout,lookup[i]," %u");
> +- printf(" = %u\n",i);
> +- }
> +- */
> +- return(i);
> +- }
> +- }
> +- printf("We'd better not get here...\n");
> +-
> +- return(0);
> +-
> +-}
> +-
> +-double fpipi(int pi1,int pi2,int nkp)
> +-{
> +-
> +- int i;
> +- double fret;
> +-
> +- /*
> +- * compute the k-permutation index from iperm for the window
> +- * at data[offset] of length len. If it matches pind, return
> +- * the first quantity, otherwise return the second.
> +- */
> +- if(pi1 == pi2){
> +-
> +- fret = (double) (nkp - 1.0)/nkp;
> +- if(verbose < 0){
> +- printf(" f(%d,%d) = %10.6f\n",pi1,pi2,fret);
> +- }
> +- return(fret);
> +-
> +- } else {
> +-
> +- fret = (double) (-1.0/nkp);
> +- if(verbose < 0){
> +- printf(" f(%d,%d) = %10.6f\n",pi1,pi2,fret);
> +- }
> +- return(fret);
> +-
> +- }
> +-
> +-
> +-}
> +-
> +-
> +-
> +-
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