X-Git-Url: https://pintos-os.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=src%2Fmath%2Fcovariance-matrix.c;h=89660ba9c1e3f5fbc1f4168af2ef8af549a43c7d;hb=8829e1f148c279db0f19b9e3bd746ace07d2d7f1;hp=817f7ed3158c7a29772af63845c8a2575de4bd9a;hpb=ceb0823669b8cb6784fd4f793d28451e33dfd512;p=pspp-builds.git

diff --git a/src/math/covariance-matrix.c b/src/math/covariance-matrix.c
index 817f7ed3..89660ba9 100644
--- a/src/math/covariance-matrix.c
+++ b/src/math/covariance-matrix.c
@@ -1,5 +1,5 @@
 /* PSPP - a program for statistical analysis.
-   Copyright (C) 2008 Free Software Foundation, Inc.
+   Copyright (C) 2008, 2009 Free Software Foundation, Inc.
 
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
@@ -43,29 +43,228 @@ struct covariance_accumulator
 {
   const struct variable *v1;
   const struct variable *v2;
-  double product;
   const union value *val1;
   const union value *val2;
+  double dot_product;
+  double sum1;
+  double sum2;
+  double ssize;
 };
 
+
+
+struct covariance_matrix
+{
+  struct design_matrix *cov;
+  struct design_matrix *ssize;
+  struct hsh_table *ca;
+  struct moments1 **m1;
+  struct moments **m;
+  const struct variable **v_variables;
+  const struct interaction_variable **interactions;
+  size_t n_variables;
+  size_t n_intr;
+  int n_pass;
+  int missing_handling;
+  enum mv_class missing_value;
+  void (*accumulate) (struct covariance_matrix *, const struct ccase *,
+		      const struct interaction_variable **, size_t);
+  void (*update_moments) (struct covariance_matrix *, size_t, double);
+};
+
+
+
+static struct hsh_table *covariance_hsh_create (size_t *);
 static hsh_hash_func covariance_accumulator_hash;
-static unsigned int hash_numeric_alpha (const struct variable *, const struct variable *, 
+static unsigned int hash_numeric_alpha (const struct variable *,
+					const struct variable *,
 					const union value *, size_t);
 static hsh_compare_func covariance_accumulator_compare;
 static hsh_free_func covariance_accumulator_free;
+static void update_moments1 (struct covariance_matrix *, size_t, double);
+static void update_moments2 (struct covariance_matrix *, size_t, double);
+static struct covariance_accumulator *get_new_covariance_accumulator (const
+								      struct
+								      variable
+								      *,
+								      const
+								      struct
+								      variable
+								      *,
+								      const
+								      union
+								      value *,
+								      const
+								      union
+								      value
+								      *);
+static void covariance_accumulate_listwise (struct covariance_matrix *,
+					    const struct ccase *,
+					    const struct interaction_variable **,
+					    size_t);
+static void covariance_accumulate_pairwise (struct covariance_matrix *,
+					    const struct ccase *,
+					    const struct interaction_variable **,
+					    size_t);
+
+struct covariance_matrix *
+covariance_matrix_init (size_t n_variables,
+			const struct variable *v_variables[], int n_pass,
+			int missing_handling, enum mv_class missing_value)
+{
+  size_t i;
+  struct covariance_matrix *result = NULL;
 
+  result = xmalloc (sizeof (*result));
+  result->cov = NULL;
+  result->n_variables = n_variables;
+  result->ca = covariance_hsh_create (&result->n_variables);
+  result->m = NULL;
+  result->m1 = NULL;
+  result->n_intr = 0;
+  result->missing_handling = missing_handling;
+  result->missing_value = missing_value;
+  result->accumulate = (result->missing_handling == LISTWISE) ?
+    covariance_accumulate_listwise : covariance_accumulate_pairwise;
+  if (n_pass == ONE_PASS)
+    {
+      result->update_moments = update_moments1;
+      result->m1 = xnmalloc (n_variables, sizeof (*result->m1));
+      for (i = 0; i < n_variables; i++)
+	{
+	  result->m1[i] = moments1_create (MOMENT_MEAN);
+	}
+    }
+  else
+    {
+      result->update_moments = update_moments2;
+      result->m = xnmalloc (n_variables, sizeof (*result->m));
+      for (i = 0; i < n_variables; i++)
+	{
+	  result->m[i] = moments_create (MOMENT_MEAN);
+	}
+    }
+  result->v_variables = v_variables;
+
+  result->n_pass = n_pass;
+
+  return result;
+}
+void
+covariance_interaction_set (struct covariance_matrix *cov, 
+			    const struct interaction_variable **intr, size_t n_intr)
+{
+  cov->interactions = intr;
+  cov->n_intr = n_intr;
+}
+
+static size_t 
+get_n_rows (size_t n_variables, const struct variable *v_variables[])
+{
+  size_t i;
+  size_t result = 0;
+  for (i = 0; i < n_variables; i++)
+    {
+      if (var_is_numeric (v_variables[i]))
+	{
+	  result++;
+	}
+      else if (var_is_alpha (v_variables[i]))
+	{
+	  size_t n_categories = cat_get_n_categories (v_variables[i]);
+	  result += n_categories - 1;
+	}
+    }
+  return result;
+}
 /*
   The covariances are stored in a DESIGN_MATRIX structure.
  */
 struct design_matrix *
-covariance_matrix_create (size_t n_variables, const struct variable *v_variables[])
+covariance_matrix_create (size_t n_variables,
+			  const struct variable *v_variables[])
 {
-  return design_matrix_create (n_variables, v_variables, (size_t) n_variables);
+  size_t n_rows = get_n_rows (n_variables, v_variables);
+  return design_matrix_create (n_variables, v_variables, n_rows);
 }
 
-void covariance_matrix_destroy (struct design_matrix *x)
+static size_t 
+get_n_rows_s (const struct variable *var)
 {
-  design_matrix_destroy (x);
+  size_t result = 0;
+  if (var_is_numeric (var))
+    {
+      result++;
+    }
+  else
+    {
+      result += cat_get_n_categories (var) - 1;
+    }
+  return result;
+}
+static struct design_matrix *
+covariance_matrix_create_s (struct covariance_matrix *cov)
+{
+  struct variable **v_variables;
+  size_t n_variables;
+  size_t n_rows = 0;
+  size_t i;
+  size_t j;
+
+  n_variables = cov->n_variables + cov->n_intr;
+  v_variables = xnmalloc (n_variables, sizeof (*v_variables));
+  for (i = 0; i < cov->n_variables; i++)
+    {
+      v_variables[i] = cov->v_variables[i];
+      n_rows += get_n_rows_s (v_variables[i]);
+    }
+  for (j = 0; j < cov->n_intr; j++)
+    {
+      v_variables[i + j] = interaction_get_variable (cov->interactions[j]);
+      n_rows += get_n_rows_s (v_variables[i]);
+    }
+  return design_matrix_create (n_variables, v_variables, n_rows);
+}
+
+static void
+update_moments1 (struct covariance_matrix *cov, size_t i, double x)
+{
+  assert (cov->m1 != NULL);
+  moments1_add (cov->m1[i], x, 1.0);
+}
+
+static void
+update_moments2 (struct covariance_matrix *cov, size_t i, double x)
+{
+  assert (cov->m != NULL);
+  moments_pass_one (cov->m[i], x, 1.0);
+}
+
+void
+covariance_matrix_destroy (struct covariance_matrix *cov)
+{
+  size_t i;
+
+  assert (cov != NULL);
+  design_matrix_destroy (cov->cov);
+  design_matrix_destroy (cov->ssize);
+  hsh_destroy (cov->ca);
+  if (cov->n_pass == ONE_PASS)
+    {
+      for (i = 0; i < cov->n_variables; i++)
+	{
+	  moments1_destroy (cov->m1[i]);
+	}
+      free (cov->m1);
+    }
+  else
+    {
+      for (i = 0; i < cov->n_variables; i++)
+	{
+	  moments_destroy (cov->m[i]);
+	}
+      free (cov->m);
+    }
 }
 
 /*
@@ -74,53 +273,58 @@ void covariance_matrix_destroy (struct design_matrix *x)
  */
 static void
 covariance_update_categorical_numeric (struct design_matrix *cov, double mean,
-			  size_t row, 
-			  const struct variable *v2, double x, const union value *val2)
+				       size_t row,
+				       const struct variable *v2, double x,
+				       const union value *val2)
 {
   size_t col;
   double tmp;
-  
+
   assert (var_is_numeric (v2));
 
   col = design_matrix_var_to_column (cov, v2);
   assert (val2 != NULL);
-  tmp = gsl_matrix_get (cov->m, row, col);
-  gsl_matrix_set (cov->m, row, col, (val2->f - mean) * x + tmp);
-  gsl_matrix_set (cov->m, col, row, (val2->f - mean) * x + tmp);
+  tmp = design_matrix_get_element (cov, row, col);
+  design_matrix_set_element (cov, row, col, (val2->f - mean) * x + tmp);
+  design_matrix_set_element (cov, col, row, (val2->f - mean) * x + tmp);
 }
 static void
 column_iterate (struct design_matrix *cov, const struct variable *v,
 		double ssize, double x, const union value *val1, size_t row)
 {
+  int width = var_get_width (v);
   size_t col;
   size_t i;
   double y;
   double tmp;
   const union value *tmp_val;
 
-  col = design_matrix_var_to_column (cov, v);  
+  col = design_matrix_var_to_column (cov, v);
   for (i = 0; i < cat_get_n_categories (v) - 1; i++)
     {
       col += i;
       y = -1.0 * cat_get_category_count (i, v) / ssize;
       tmp_val = cat_subscript_to_value (i, v);
-      if (compare_values (tmp_val, val1, v))
+      if (!value_equal (tmp_val, val1, width))
 	{
 	  y += -1.0;
 	}
-      tmp = gsl_matrix_get (cov->m, row, col);
-      gsl_matrix_set (cov->m, row, col, x * y + tmp);
-      gsl_matrix_set (cov->m, col, row, x * y + tmp);
+      tmp = design_matrix_get_element (cov, row, col);
+      design_matrix_set_element (cov, row, col, x * y + tmp);
+      design_matrix_set_element (cov, col, row, x * y + tmp);
     }
 }
+
 /*
   Call this function in the second data pass. The central moments are
   MEAN1 and MEAN2. Any categorical variables should already have their
   values summarized in in its OBS_VALS element.
  */
-void covariance_pass_two (struct design_matrix *cov, double mean1, double mean2,
-			  double ssize, const struct variable *v1, 
-			  const struct variable *v2, const union value *val1, const union value *val2)
+void
+covariance_pass_two (struct design_matrix *cov, double mean1, double mean2,
+		     double ssize, const struct variable *v1,
+		     const struct variable *v2, const union value *val1,
+		     const union value *val2)
 {
   size_t row;
   size_t col;
@@ -136,13 +340,13 @@ void covariance_pass_two (struct design_matrix *cov, double mean1, double mean2,
 	  row += i;
 	  x = -1.0 * cat_get_category_count (i, v1) / ssize;
 	  tmp_val = cat_subscript_to_value (i, v1);
-	  if (compare_values (tmp_val, val1, v1))
+	  if (!value_equal (tmp_val, val1, var_get_width (v1)))
 	    {
 	      x += 1.0;
 	    }
 	  if (var_is_numeric (v2))
 	    {
-	      covariance_update_categorical_numeric (cov, mean2, row, 
+	      covariance_update_categorical_numeric (cov, mean2, row,
 						     v2, x, val2);
 	    }
 	  else
@@ -155,22 +359,22 @@ void covariance_pass_two (struct design_matrix *cov, double mean1, double mean2,
   else if (var_is_alpha (v2))
     {
       /*
-	Reverse the orders of V1, V2, etc. and put ourselves back
-	in the previous IF scope.
+         Reverse the orders of V1, V2, etc. and put ourselves back
+         in the previous IF scope.
        */
       covariance_pass_two (cov, mean2, mean1, ssize, v2, v1, val2, val1);
     }
   else
     {
       /*
-	Both variables are numeric.
-      */
-      row = design_matrix_var_to_column (cov, v1);  
+         Both variables are numeric.
+       */
+      row = design_matrix_var_to_column (cov, v1);
       col = design_matrix_var_to_column (cov, v2);
       x = (val1->f - mean1) * (val2->f - mean2);
-      x += gsl_matrix_get (cov->m, col, row);
-      gsl_matrix_set (cov->m, row, col, x);
-      gsl_matrix_set (cov->m, col, row, x);
+      x += design_matrix_get_element (cov, col, row);
+      design_matrix_set_element (cov, row, col, x);
+      design_matrix_set_element (cov, col, row, x);
     }
 }
 
@@ -187,11 +391,13 @@ covariance_accumulator_hash (const void *h, const void *aux)
   const union value *val_max;
 
   /*
-    Order everything by the variables' indices. This ensures we get the
-    same key regardless of the order in which the variables are stored
-    and passed around.
+     Order everything by the variables' indices. This ensures we get the
+     same key regardless of the order in which the variables are stored
+     and passed around.
    */
-  v_min = (var_get_dict_index (ca->v1) < var_get_dict_index (ca->v2)) ? ca->v1 : ca->v2;
+  v_min =
+    (var_get_dict_index (ca->v1) <
+     var_get_dict_index (ca->v2)) ? ca->v1 : ca->v2;
   v_max = (ca->v1 == v_min) ? ca->v2 : ca->v1;
 
   val_min = (v_min == ca->v1) ? ca->val1 : ca->val2;
@@ -214,15 +420,9 @@ covariance_accumulator_hash (const void *h, const void *aux)
     }
   if (var_is_alpha (v_max) && var_is_alpha (v_min))
     {
-      unsigned int tmp;
-      char *x = xnmalloc (1 + var_get_width (v_max) + var_get_width (v_min), sizeof (*x));
-      strncpy (x, val_max->s, var_get_width (v_max));
-      strncat (x, val_min->s, var_get_width (v_min));
-      tmp = *n_vars * (*n_vars + 1 + idx_max)
-	+ idx_min
-	+ hsh_hash_string (x);
-      free (x);
-      return tmp;
+      unsigned hash = value_hash (val_max, var_get_width (v_max), 0);
+      hash = value_hash (val_min, var_get_width (v_min), hash);
+      return hash_int (*n_vars * (*n_vars + 1 + idx_max) + idx_min, hash);
     }
   return -1u;
 }
@@ -233,62 +433,66 @@ covariance_accumulator_hash (const void *h, const void *aux)
   in a single data pass. Call covariance_accumulate () for each case 
   in the data.
  */
-struct hsh_table *
-covariance_hsh_create (size_t n_vars)
+static struct hsh_table *
+covariance_hsh_create (size_t *n_vars)
 {
-  return hsh_create (n_vars * (n_vars + 1) / 2, covariance_accumulator_compare, 
-		     covariance_accumulator_hash, covariance_accumulator_free, &n_vars);
+  return hsh_create (*n_vars * *n_vars, covariance_accumulator_compare,
+		     covariance_accumulator_hash, covariance_accumulator_free,
+		     n_vars);
 }
 
-static void 
+static void
 covariance_accumulator_free (void *c_, const void *aux UNUSED)
 {
   struct covariance_accumulator *c = c_;
   assert (c != NULL);
   free (c);
 }
-static int
-match_nodes (const struct covariance_accumulator *c, const struct variable *v1,
-	     const struct variable *v2, const union value *val1,
-	     const union value *val2)
+
+static int 
+ordered_match_nodes (const struct covariance_accumulator *c, const struct variable *v1,
+		     const struct variable *v2, const union value *val1, const union value *val2)
 {
-  if (var_get_dict_index (v1) == var_get_dict_index (c->v1) && 
-      var_get_dict_index (v2) == var_get_dict_index (c->v2))
+  size_t result;
+  size_t m;
+
+  result = var_get_dict_index (v1) ^ var_get_dict_index (c->v1);
+  m = var_get_dict_index (v2) ^ var_get_dict_index (c->v2);
+  result = result|m;
+  if (var_is_alpha (v1))
     {
-      if (var_is_numeric (v1) && var_is_numeric (v2))
-	{
-	  return 0;
-	}
-      if (var_is_numeric (v1) && var_is_alpha (v2))
-	{
-	  if (compare_values (val2, c->val2, v2))
-	    {
-	      return 0;
-	    }
-	}
-      if (var_is_alpha (v1) && var_is_numeric (v2))
+      result |= value_compare_3way (val1, c->val1, var_get_width (v1));
+      if (var_is_alpha (v2))
 	{
-	  if (compare_values (val1, c->val1, v1))
-	    {
-	      return 0;
-	    }
-	}
-      if (var_is_alpha (v1) && var_is_alpha (v2))
-	{
-	  if (compare_values (val1, c->val1, v1))
-	    {
-	      if (compare_values (val2, c->val2, v2))
-		{
-		  return 0;
-		}
-	    }
+	  result |= value_compare_3way (val2, c->val2, var_get_width (v2));
 	}
     }
-  else if (v2 == c->v1 && v1 == c->v2)
+  else if (var_is_alpha (v2))
     {
-      return -match_nodes (c, v2, v1, val2, val1);
+      result |= value_compare_3way (val2, c->val2, var_get_width (v2));
     }
-  return 1;
+  return result;
+}
+  
+/*
+  Hash comparison. Returns 0 for a match, or a non-zero int
+  otherwise. The sign of a non-zero return value *should* indicate the
+  position of C relative to the covariance_accumulator described by
+  the other arguments. But for now, it just returns 1 for any
+  non-match.  This should be changed when someone figures out how to
+  compute a sensible sign for the return value.
+ */
+static int
+match_nodes (const struct covariance_accumulator *c,
+	     const struct variable *v1, const struct variable *v2,
+	     const union value *val1, const union value *val2)
+{
+  size_t n;
+  size_t m;
+
+  n = ordered_match_nodes (c, v1, v2, val1, val2);
+  m = ordered_match_nodes (c, v2, v1, val2, val1);
+  return (n & m);
 }
 
 /*
@@ -296,29 +500,30 @@ match_nodes (const struct covariance_accumulator *c, const struct variable *v1,
   a struct hsh_table in src/libpspp/hash.c.
 */
 static int
-covariance_accumulator_compare (const void *a1_, const void *a2_, const void *aux UNUSED)
+covariance_accumulator_compare (const void *a1_, const void *a2_,
+				const void *aux UNUSED)
 {
-  const struct covariance_accumulator *a1 =  a1_;
-  const struct covariance_accumulator *a2 =  a2_;
+  const struct covariance_accumulator *a1 = a1_;
+  const struct covariance_accumulator *a2 = a2_;
 
   if (a1 == NULL && a2 == NULL)
     return 0;
 
   if (a1 == NULL || a2 == NULL)
     return 1;
-
+  
   return match_nodes (a1, a2->v1, a2->v2, a2->val1, a2->val2);
 }
 
 static unsigned int
-hash_numeric_alpha (const struct variable *v1, const struct variable *v2, 
+hash_numeric_alpha (const struct variable *v1, const struct variable *v2,
 		    const union value *val, size_t n_vars)
 {
   unsigned int result = -1u;
   if (var_is_numeric (v1) && var_is_alpha (v2))
     {
       result = n_vars * ((n_vars + 1) + var_get_dict_index (v1))
-	+ var_get_dict_index (v2) + hsh_hash_string (val->s);
+	+ var_get_dict_index (v2) + value_hash (val, var_get_width (v2), 0);
     }
   else if (var_is_alpha (v1) && var_is_numeric (v2))
     {
@@ -329,8 +534,8 @@ hash_numeric_alpha (const struct variable *v1, const struct variable *v2,
 
 
 static double
-update_product (const struct variable *v1, const struct variable *v2, const union value *val1,
-		const union value *val2)
+update_product (const struct variable *v1, const struct variable *v2,
+		const union value *val1, const union value *val2)
 {
   assert (v1 != NULL);
   assert (v2 != NULL);
@@ -346,191 +551,479 @@ update_product (const struct variable *v1, const struct variable *v2, const unio
     }
   if (var_is_numeric (v1) && var_is_alpha (v2))
     {
-      return (val1->f);
+      return val1->f;
     }
   if (var_is_numeric (v2) && var_is_alpha (v1))
     {
-      update_product (v2, v1, val2, val1);
+      return val2->f;
+    }
+  else
+    {
+      return 0.0;
+    }
+}
+static double
+update_sum (const struct variable *var, const union value *val, double weight)
+{
+  assert (var != NULL);
+  assert (val != NULL);
+  if (var_is_alpha (var))
+    {
+      return weight;
+    }
+  return val->f;
+}
+static struct covariance_accumulator *
+get_new_covariance_accumulator (const struct variable *v1,
+				const struct variable *v2,
+				const union value *val1,
+				const union value *val2)
+{
+  if ((v1 != NULL) && (v2 != NULL) && (val1 != NULL) && (val2 != NULL))
+    {
+      struct covariance_accumulator *ca;
+      ca = xmalloc (sizeof (*ca));
+      ca->v1 = v1;
+      ca->v2 = v2;
+      ca->val1 = val1;
+      ca->val2 = val2;
+      return ca;
+    }
+  return NULL;
+}
+
+static const struct variable **
+get_covariance_variables (const struct covariance_matrix *cov)
+{
+  return cov->v_variables;
+}
+
+static void
+update_hash_entry_intr (struct hsh_table *c,
+			const struct variable *v1,
+			const struct variable *v2,
+			const union value *val1, const union value *val2, 
+			const struct interaction_value *i_val1,
+			const struct interaction_value *i_val2)
+{
+  struct covariance_accumulator *ca;
+  struct covariance_accumulator *new_entry;
+  double iv_f1;
+  double iv_f2;
+
+  iv_f1 = interaction_value_get_nonzero_entry (i_val1);
+  iv_f2 = interaction_value_get_nonzero_entry (i_val2);
+  ca = get_new_covariance_accumulator (v1, v2, val1, val2);
+  ca->dot_product = update_product (ca->v1, ca->v2, ca->val1, ca->val2);
+  ca->dot_product *= iv_f1 * iv_f2;
+  ca->sum1 = update_sum (ca->v1, ca->val1, iv_f1);
+  ca->sum2 = update_sum (ca->v2, ca->val2, iv_f2);
+  ca->ssize = 1.0;
+  new_entry = hsh_insert (c, ca);
+
+  if (new_entry != NULL)
+    {
+      new_entry->dot_product += ca->dot_product;
+      new_entry->ssize += 1.0;
+      new_entry->sum1 += ca->sum1;
+      new_entry->sum2 += ca->sum2;
+      /*
+	If DOT_PRODUCT is null, CA was not already in the hash
+	hable, so we don't free it because it was just inserted.
+	If DOT_PRODUCT was not null, CA is already in the hash table.
+	Unnecessary now, it must be freed here.
+      */
+      free (ca);
     }
-  return 0.0;
 }
+
+static void
+update_hash_entry (struct hsh_table *c,
+		   const struct variable *v1,
+		   const struct variable *v2,
+		   const union value *val1, const union value *val2)
+{
+  struct covariance_accumulator *ca;
+  struct covariance_accumulator *new_entry;
+
+  ca = get_new_covariance_accumulator (v1, v2, val1, val2);
+  ca->dot_product = update_product (ca->v1, ca->v2, ca->val1, ca->val2);
+  ca->sum1 = update_sum (ca->v1, ca->val1, 1.0);
+  ca->sum2 = update_sum (ca->v2, ca->val2, 1.0);
+  ca->ssize = 1.0;
+  new_entry = hsh_insert (c, ca);
+
+  if (new_entry != NULL)
+    {
+      new_entry->dot_product += ca->dot_product;
+      new_entry->ssize += 1.0;
+      new_entry->sum1 += ca->sum1;
+      new_entry->sum2 += ca->sum2;
+      /*
+	If DOT_PRODUCT is null, CA was not already in the hash
+	hable, so we don't free it because it was just inserted.
+	If DOT_PRODUCT was not null, CA is already in the hash table.
+	Unnecessary now, it must be freed here.
+      */
+      free (ca);
+    }
+}
+
+static void
+inner_intr_loop (struct covariance_matrix *cov, const struct ccase  *ccase, const struct variable *var1,
+		 const union value *val1, const struct interaction_variable **i_var, 
+		 const struct interaction_value *i_val1, size_t j)
+{
+  struct variable *var2;
+  union value *val2;
+  struct interaction_value *i_val2;
+
+  var2 = interaction_get_variable (i_var[j]);
+  i_val2 = interaction_case_data (ccase, i_var[j]);
+  val2 = interaction_value_get (i_val2);
+  
+  if (!var_is_value_missing (var2, val2, cov->missing_value))
+    {
+      update_hash_entry_intr (cov->ca, var1, var2, val1, val2, i_val1, i_val2);
+    }
+}	 
 /*
-  Compute the covariance matrix in a single data-pass.
+  Compute the covariance matrix in a single data-pass. Cases with
+  missing values are dropped pairwise, in other words, only if one of
+  the two values necessary to accumulate the inner product is missing.
+
+  Do not call this function directly. Call it through the struct
+  covariance_matrix ACCUMULATE member function, for example,
+  cov->accumulate (cov, ccase).
  */
-void 
-covariance_accumulate (struct hsh_table *cov, struct moments1 **m,
-		       const struct ccase *ccase, const struct variable **vars,
-		       size_t n_vars)
+static void
+covariance_accumulate_pairwise (struct covariance_matrix *cov,
+				const struct ccase *ccase, 
+				const struct interaction_variable **i_var,
+				size_t n_intr)
 {
   size_t i;
   size_t j;
-  const union value *val;
-  struct covariance_accumulator *ca;
-  struct covariance_accumulator *entry;
+  const union value *val1;
+  const union value *val2;
+  const struct variable **v_variables;
+  const struct variable *var1;
+  const struct variable *var2;
+  struct interaction_value *i_val1 = NULL;
+  struct interaction_value *i_val2 = NULL;
+
+  assert (cov != NULL);
+  assert (ccase != NULL);
 
-  assert (m != NULL);
+  v_variables = get_covariance_variables (cov);
+  assert (v_variables != NULL);
 
-  for (i = 0; i < n_vars; ++i)
+  for (i = 0; i < cov->n_variables; ++i)
     {
-      val = case_data (ccase, vars[i]);
-      if (var_is_alpha (vars[i]))
+      var1 = v_variables[i];
+      val1 = case_data (ccase, var1);
+      if (!var_is_value_missing (var1, val1, cov->missing_value))
 	{
-	  cat_value_update (vars[i], val);
-	}
-      else
-	{
-	  moments1_add (m[i], val->f, 1.0);
+	  cat_value_update (var1, val1);
+	  if (var_is_numeric (var1))
+	    cov->update_moments (cov, i, val1->f);
+
+	  for (j = i; j < cov->n_variables; j++)
+	    {
+	      var2 = v_variables[j];
+	      val2 = case_data (ccase, var2);
+	      if (!var_is_value_missing
+		  (var2, val2, cov->missing_value))
+		{
+		  update_hash_entry (cov->ca, var1, var2, val1, val2);
+		}
+	    }
+	  for (j = 0; j < cov->n_intr; j++)
+	    {
+	      inner_intr_loop (cov, ccase, var1, val1, i_var, i_val1, j);
+	    }
 	}
-      for (j = i; j < n_vars; j++)
+    }
+  for (i = 0; i < cov->n_intr; i++)
+    {
+      var1 = interaction_get_variable (i_var[i]);
+      i_val1 = interaction_case_data (ccase, i_var[i]);
+      val1 = interaction_value_get (i_val1);
+      cat_value_update (var1, val1);
+      if (!var_is_value_missing (var1, val1, cov->missing_value))
 	{
-	  ca = xmalloc (sizeof (*ca));
-	  ca->v1 = vars[i];
-	  ca->v2 = vars[j];
-	  ca->val1 = val;
-	  ca->val2 = case_data (ccase, ca->v2);
-	  ca->product = update_product (ca->v1, ca->v2, ca->val1, ca->val2);
-	  entry = hsh_insert (cov, ca);
-	  if (entry != NULL)
+	  for (j = i; j < cov->n_intr; j++)
 	    {
-	      entry->product += ca->product;
-	      /*
-		If ENTRY is null, CA was not already in the hash
-		hable, so we don't free it because it was just inserted.
-		If ENTRY was not null, CA is already in the hash table.
-		Unnecessary now, it must be freed here.
-	      */
-	      free (ca);
+	      inner_intr_loop (cov, ccase, var1, val1, i_var, i_val1, j);
 	    }
 	}
     }
 }
 
-static void 
-covariance_matrix_insert (struct design_matrix *cov, const struct variable *v1,
-			  const struct variable *v2, const union value *val1, 
-			  const union value *val2, double product)
+/*
+  Compute the covariance matrix in a single data-pass. Cases with
+  missing values are dropped listwise. In other words, if one of the
+  values for any variable in a case is missing, the entire case is
+  skipped. 
+
+  The caller must use a casefilter to remove the cases with missing
+  values before calling covariance_accumulate_listwise. This function
+  assumes that CCASE has already passed through this filter, and
+  contains no missing values.
+
+  Do not call this function directly. Call it through the struct
+  covariance_matrix ACCUMULATE member function, for example,
+  cov->accumulate (cov, ccase).
+ */
+static void
+covariance_accumulate_listwise (struct covariance_matrix *cov,
+				const struct ccase *ccase,
+				const struct interaction_variable **i_var,
+				size_t n_intr)
 {
-  size_t row;
-  size_t col;
   size_t i;
-  const union value *tmp_val;
+  size_t j;
+  const union value *val1;
+  const union value *val2;
+  const struct variable **v_variables;
+  struct interaction_value *i_val1 = NULL;
+  struct interaction_value *i_val2 = NULL;
 
   assert (cov != NULL);
+  assert (ccase != NULL);
 
-  row = design_matrix_var_to_column (cov, v1);
-  if (var_is_alpha (v1))
+  v_variables = get_covariance_variables (cov);
+  assert (v_variables != NULL);
+
+  for (i = 0; i < cov->n_variables; ++i)
     {
-      i = 0;
-      tmp_val = cat_subscript_to_value (i, v1);
-      while (!compare_values (tmp_val, val1, v1))
+      val1 = case_data (ccase, v_variables[i]);
+      cat_value_update (v_variables[i], val1);
+      if (var_is_numeric (v_variables[i]))
+	cov->update_moments (cov, i, val1->f);
+
+      for (j = i; j < cov->n_variables; j++)
 	{
-	  i++;
-	  tmp_val = cat_subscript_to_value (i, v1);
+	  update_hash_entry (cov->ca, v_variables[i], v_variables[j],
+			     val1, val2);
 	}
-      row += i;
-      if (var_is_numeric (v2))
+    }
+}
+
+/*
+  Call this function during the data pass. Each case will be added to
+  a hash containing all values of the covariance matrix. After the
+  data have been passed, call covariance_matrix_compute to put the
+  values in the struct covariance_matrix. 
+ */
+void
+covariance_matrix_accumulate (struct covariance_matrix *cov,
+			      const struct ccase *ccase, void **aux, size_t n_intr)
+{
+  cov->accumulate (cov, ccase, (const struct interaction_variable **) aux, n_intr);
+}
+
+/*
+  Return the value corresponding to subscript TARGET. If that value corresponds
+  to the origin, return NULL.
+ */
+static const union value *
+get_value_from_subscript (const struct design_matrix *dm, size_t target)
+{
+  const union value *result = NULL;
+  const struct variable *var;
+  size_t i;
+  
+  var = design_matrix_col_to_var (dm, target);
+  if (var_is_numeric (var))
+    {
+      return NULL;
+    }
+  for (i = 0; i < cat_get_n_categories (var); i++)
+    {
+      result = cat_subscript_to_value (i, var);
+      if (dm_get_exact_subscript (dm, var, result) == target)
 	{
-	  col = design_matrix_var_to_column (cov, v2);
+	  return result;
 	}
-      else
+    }
+  return NULL;
+}
+
+static bool
+is_covariance_contributor (const struct covariance_accumulator *ca, const struct design_matrix *dm,
+			   size_t i, size_t j)
+{
+  size_t k;
+  const struct variable *v1;
+  const struct variable *v2;
+  
+  assert (dm != NULL);
+  v1 = design_matrix_col_to_var (dm, i);
+  v2 = design_matrix_col_to_var (dm, j);
+  if (var_get_dict_index (v1) == var_get_dict_index(ca->v1))
+    {
+      if (var_get_dict_index (v2) == var_get_dict_index (ca->v2))
 	{
-	  col = design_matrix_var_to_column (cov, v2);
-	  i = 0;
-	  tmp_val = cat_subscript_to_value (i, v1);
-	  while (!compare_values (tmp_val, val1, v1))
+	  k = dm_get_exact_subscript (dm, v1, ca->val1);
+	  if (k == i)
 	    {
-	      i++;
-	      tmp_val = cat_subscript_to_value (i, v1);
-	    } 
-	  col += i;
+	      k = dm_get_exact_subscript (dm, v2, ca->val2);
+	      if (k == j)
+		{
+		  return true;
+		}
+	    }
 	}
-    }    
-  else
+    }
+  else if (var_get_dict_index (v1) == var_get_dict_index (ca->v2))
+    {
+      if (var_get_dict_index (v2) == var_get_dict_index (ca->v1))
+	{
+	  k = dm_get_exact_subscript (dm, v1, ca->val2);
+	  if (k == i)
+	    {
+	      k = dm_get_exact_subscript (dm, v2, ca->val1);
+	      if (k == j)
+		{
+		  return true;
+		}
+	    }
+	}
+    }
+  
+  return false;
+}
+static double
+get_sum (const struct covariance_matrix *cov, size_t i)
+{
+  size_t k;
+  double mean;
+  double n;
+  const struct variable *var;
+  const union value *val = NULL;
+
+  assert ( cov != NULL);
+  var = design_matrix_col_to_var (cov->cov, i);
+  if (var != NULL)
     {
-      if (var_is_numeric (v2))
+      if (var_is_alpha (var))
 	{
-	  col = design_matrix_var_to_column (cov, v2);
+	  val = get_value_from_subscript (cov->cov, i);
+	  k = cat_value_find (var, val);
+	  return cat_get_category_count (k, var);
 	}
       else
 	{
-	  covariance_matrix_insert (cov, v2, v1, val2, val1, product);
+	  k = 0;
+	  while (cov->v_variables[k] != var && k  < cov->n_variables)
+	    {
+	      k++;
+	    }
+	  if (k < cov->n_variables)
+	    {
+	      moments1_calculate (cov->m1[k], &n, &mean, NULL, NULL, NULL);
+	      return mean * n;
+	    }
 	}
     }
-  gsl_matrix_set (cov->m, row, col, product);
-  gsl_matrix_set (cov->m, col, row, product);
+      
+  return 0.0;
 }
-
-static double
-get_center (const struct variable *v, const union value *val, 
-	    const struct variable **vars, const struct moments1 **m, size_t n_vars,
-	    size_t ssize)
+static void
+update_ssize (struct design_matrix *dm, size_t i, size_t j, struct covariance_accumulator *ca)
 {
-  size_t i = 0;
-
-  while ((var_get_dict_index (vars[i]) != var_get_dict_index(v)) && (i < n_vars))
+  const struct variable *var;
+  double tmp;
+  var = design_matrix_col_to_var (dm, i);
+  if (var_get_dict_index (ca->v1) == var_get_dict_index (var))
     {
-      i++;
-    }  
-  if (var_is_numeric (v))
+      var = design_matrix_col_to_var (dm, j);
+      if (var_get_dict_index (ca->v2) == var_get_dict_index (var))
+	{
+	  tmp = design_matrix_get_element (dm, i, j);
+	  tmp += ca->ssize;
+	  design_matrix_set_element (dm, i, j, tmp);
+	}
+    }
+}
+static void
+covariance_accumulator_to_matrix (struct covariance_matrix *cov)
+{
+  size_t i;
+  size_t j;
+  double sum_i = 0.0;
+  double sum_j = 0.0;
+  double tmp = 0.0;
+  struct covariance_accumulator *entry;
+  struct hsh_iterator iter;
+
+  cov->cov = covariance_matrix_create_s (cov);
+  cov->ssize = covariance_matrix_create_s (cov);
+  entry = hsh_first (cov->ca, &iter);
+  while (entry != NULL)
     {
-      double mean;
-      moments1_calculate (m[i], NULL, &mean, NULL, NULL, NULL);
-      return mean;
+      entry = hsh_next (cov->ca, &iter);
     }
-  else 
+
+  for (i = 0; i < design_matrix_get_n_cols (cov->cov); i++)
     {
-      i = cat_value_find (v, val);
-      return (cat_get_category_count (i, v) / ssize);
+      sum_i = get_sum (cov, i);
+      for (j = i; j < design_matrix_get_n_cols (cov->cov); j++)
+	{
+	  sum_j = get_sum (cov, j);
+	  entry = hsh_first (cov->ca, &iter);
+	  while (entry != NULL)
+	    {
+	      update_ssize (cov->ssize, i, j, entry);
+	      /*
+		We compute the centered, un-normalized covariance matrix.
+	      */
+	      if (is_covariance_contributor (entry, cov->cov, i, j))
+		{
+		  design_matrix_set_element (cov->cov, i, j, entry->dot_product);
+		}
+	      entry = hsh_next (cov->ca, &iter);
+	    }
+	  tmp = design_matrix_get_element (cov->cov, i, j);
+	  tmp -= sum_i * sum_j / design_matrix_get_element (cov->ssize, i, j);
+	  design_matrix_set_element (cov->cov, i, j, tmp);
+	  design_matrix_set_element (cov->cov, j, i, tmp);
+	} 
     }
-  return 0.0;
 }
 
+
 /*
-  Subtract the product of the means.
+  Call this function after passing the data.
  */
-static double
-center_entry (const struct covariance_accumulator *ca, const struct variable **vars,
-	      const struct moments1 **m, size_t n_vars, size_t ssize)
+void
+covariance_matrix_compute (struct covariance_matrix *cov)
 {
-  double m1;
-  double m2;
-  double result = 0.0;
-  
-  m1 = get_center (ca->v1, ca->val1, vars, m, n_vars, ssize);
-  m2 = get_center (ca->v2, ca->val2, vars, m, n_vars, ssize);
-  result = ca->product - ssize * m1 * m2;
-  return result;
+  if (cov->n_pass == ONE_PASS)
+    {
+      covariance_accumulator_to_matrix (cov);
+    }
 }
 
-/*
-  The first moments in M should be stored in the order corresponding
-  to the order of VARS. So, for example, VARS[0] has its moments in
-  M[0], VARS[1] has its moments in M[1], etc.
- */
 struct design_matrix *
-covariance_accumulator_to_matrix (struct hsh_table *cov, const struct moments1 **m,
-				  const struct variable **vars, size_t n_vars, size_t ssize)
+covariance_to_design (const struct covariance_matrix *c)
 {
-  double tmp;
-  struct covariance_accumulator *entry;
-  struct design_matrix *result = NULL;
-  struct hsh_iterator iter;
-  
-  result = covariance_matrix_create (n_vars, vars);
-
-  entry = hsh_first (cov, &iter);
-  
-  while (entry != NULL)
+  if (c != NULL)
     {
-      /*
-	We compute the centered, un-normalized covariance matrix.
-       */
-      tmp = center_entry (entry, vars, m, n_vars, ssize);
-      covariance_matrix_insert (result, entry->v1, entry->v2, entry->val1,
-				entry->val2, tmp);
-      entry = hsh_next (cov, &iter);
+      return c->cov;
     }
+  return NULL;
+}
+size_t
+covariance_matrix_get_n_rows (const struct covariance_matrix *c)
+{
+  return design_matrix_get_n_rows (c->cov);
+}
 
-  return result;
+double 
+covariance_matrix_get_element (const struct covariance_matrix *c, size_t row, size_t col)
+{
+  return (design_matrix_get_element (c->cov, row, col));
 }