Re: [Buildroot] [PATCH 1/1] package/dieharder: drop rgb_operm

[Arnout Vandecappelle <arnout@mind.be>]

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@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@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@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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