Merge branch 'dev'

[culture.git] / grids.py

diff --git a/grids.py b/grids.py
index 47e5861..eea8c6c 100755 (executable)
--- a/grids.py
+++ b/grids.py
@@ -17,6 +17,92 @@ from torch.nn import functional as F
 import problem
 
 
 import problem
 
 

+def grow_islands(nb, height, width, nb_seeds, nb_iterations):
+    w = torch.empty(5, 1, 3, 3)
+
+    w[0, 0] = torch.tensor(
+        [
+            [1.0, 1.0, 1.0],
+            [1.0, 0.0, 1.0],
+            [1.0, 1.0, 1.0],
+        ]
+    )
+
+    w[1, 0] = torch.tensor(
+        [
+            [-1.0, 1.0, 0.0],
+            [1.0, 0.0, 0.0],
+            [0.0, 0.0, 0.0],
+        ]
+    )
+
+    w[2, 0] = torch.tensor(
+        [
+            [0.0, 1.0, -1.0],
+            [0.0, 0.0, 1.0],
+            [0.0, 0.0, 0.0],
+        ]
+    )
+
+    w[3, 0] = torch.tensor(
+        [
+            [0.0, 0.0, 0.0],
+            [0.0, 0.0, 1.0],
+            [0.0, 1.0, -1.0],
+        ]
+    )
+
+    w[4, 0] = torch.tensor(
+        [
+            [0.0, 0.0, 0.0],
+            [1.0, 0.0, 0.0],
+            [-1.0, 1.0, 0.0],
+        ]
+    )
+
+    Z = torch.zeros(nb, height, width)
+    U = Z.flatten(1)
+
+    for _ in range(nb_seeds):
+        M = F.conv2d(Z[:, None, :, :], w, padding=1)
+        M = torch.cat([M[:, :1], M[:, 1:].min(dim=1, keepdim=True).values], dim=1)
+        M = ((M[:, 0] == 0) & (Z == 0)).long()
+        Q = (M.flatten(1).max(dim=1).values > 0).long()[:, None]
+        M = M * torch.rand(M.size())
+        M = M.flatten(1)
+        M = F.one_hot(M.argmax(dim=1), num_classes=M.size(1))
+        U += M * Q
+
+    for _ in range(nb_iterations):
+        M = F.conv2d(Z[:, None, :, :], w, padding=1)
+        M = torch.cat([M[:, :1], M[:, 1:].min(dim=1, keepdim=True).values], dim=1)
+        M = ((M[:, 1] >= 0) & (Z == 0)).long()
+        Q = (M.flatten(1).max(dim=1).values > 0).long()[:, None]
+        M = M * torch.rand(M.size())
+        M = M.flatten(1)
+        M = F.one_hot(M.argmax(dim=1), num_classes=M.size(1))
+        U = Z.flatten(1)
+        U += M * Q
+
+    M = Z.clone()
+    Z = Z * (torch.arange(Z.size(1) * Z.size(2)) + 1).reshape(1, Z.size(1), Z.size(2))
+
+    while True:
+        W = Z.clone()
+        Z = F.max_pool2d(Z, 3, 1, 1) * M
+        if Z.equal(W):
+            break
+
+    Z = Z.long()
+    U = Z.flatten(1)
+    V = F.one_hot(U).max(dim=1).values
+    W = V.cumsum(dim=1) - V
+    N = torch.arange(Z.size(0))[:, None, None].expand_as(Z)
+    Z = W[N, Z]
+
+    return Z
+
+

 class Grids(problem.Problem):
     named_colors = [
         ("white", [255, 255, 255]),
 class Grids(problem.Problem):
     named_colors = [
         ("white", [255, 255, 255]),


@@ -32,11 +118,40 @@ class Grids(problem.Problem):
         ("gray", [128, 128, 128]),
     ]
 
         ("gray", [128, 128, 128]),
     ]
 

-    def __init__(self, device=torch.device("cpu")):
+    def __init__(
+        self,
+        max_nb_cached_chunks=None,
+        chunk_size=None,
+        nb_threads=-1,
+        tasks=None,
+    ):

         self.colors = torch.tensor([c for _, c in self.named_colors])
         self.height = 10
         self.width = 10
         self.colors = torch.tensor([c for _, c in self.named_colors])
         self.height = 10
         self.width = 10

-        self.device = device
+        self.cache_rec_coo = {}
+
+        all_tasks = [
+            self.task_replace_color,
+            self.task_translate,
+            self.task_grow,
+            self.task_half_fill,
+            self.task_frame,
+            self.task_detect,
+            self.task_count,
+            self.task_trajectory,
+            self.task_bounce,
+            self.task_scale,
+            self.task_symbols,
+            self.task_isometry,
+            #            self.task_islands,
+        ]
+
+        if tasks is None:
+            self.all_tasks = all_tasks
+        else:
+            self.all_tasks = [getattr(self, "task_" + t) for t in tasks.split(",")]
+
+        super().__init__(max_nb_cached_chunks, chunk_size, nb_threads)

 
     ######################################################################
 
 
     ######################################################################
 


@@ -110,10 +225,10 @@ class Grids(problem.Problem):
                 c = c.long()[:, None]
                 c = (
                     (1 - ((c == 1).long() + (c == 0).long() + (c == -1).long()))
                 c = c.long()[:, None]
                 c = (
                     (1 - ((c == 1).long() + (c == 0).long() + (c == -1).long()))

-                    * torch.tensor([64, 64, 64], device=c.device)
-                    + (c == 1).long() * torch.tensor([0, 255, 0], device=c.device)
-                    + (c == 0).long() * torch.tensor([255, 255, 255], device=c.device)
-                    + (c == -1).long() * torch.tensor([255, 0, 0], device=c.device)
+                    * torch.tensor([64, 64, 64])
+                    + (c == 1).long() * torch.tensor([0, 255, 0])
+                    + (c == 0).long() * torch.tensor([255, 255, 255])
+                    + (c == -1).long() * torch.tensor([255, 0, 0])

                 )
                 y[...] = c[:, :, None, None]
 
                 )
                 y[...] = c[:, :, None, None]
 


@@ -195,121 +310,133 @@ class Grids(problem.Problem):
         return len(self.colors)
 
     # @torch.compile
         return len(self.colors)
 
     # @torch.compile

-    def rec_coo_(self, nb_rec, min_height=3, min_width=3):
-        # @torch.compile
-        def overlap(ia, ja, ib, jb):
-            return (
-                ia[1] >= ib[0] and ia[0] <= ib[1] and ja[1] >= jb[0] and ja[0] <= jb[1]
-            )
+    def rec_coo(
+        self,
+        nb_rec,
+        min_height=3,
+        min_width=3,
+        surface_max=None,
+        prevent_overlap=False,
+    ):
+        if surface_max is None:
+            surface_max = self.height * self.width // 2

 
 

-        if nb_rec == 3:
-            while True:
-                i = torch.randint(self.height + 1, (nb_rec, 2)).sort(dim=1).values
-                j = torch.randint(self.width + 1, (nb_rec, 2)).sort(dim=1).values
-                if (
-                    not (
-                        overlap(i[0], j[0], i[1], j[1])
-                        or overlap(i[0], j[0], i[2], j[2])
-                        or overlap(i[1], j[1], i[2], j[2])
-                    )
-                    and (i[:, 1] - i[:, 0]).min() >= min_height
-                    and (j[:, 1] - j[:, 0]).min() >= min_width
-                ):
-                    break
-            return (
-                (i[0, 0], j[0, 0], i[0, 1], j[0, 1]),
-                (i[1, 0], j[1, 0], i[1, 1], j[1, 1]),
-                (i[2, 0], j[2, 0], i[2, 1], j[2, 1]),
-            )
+        signature = (nb_rec, min_height, min_width, surface_max)

 
 

-    # That's quite a tensorial spaghetti mess to sample
-    # non-overlapping rectangles quickly, but made the generation of
-    # 100k samples go from 1h50 with a lame pure python code to 3min30s
-    # with this one.
-    # @torch.compile
-    def rec_coo(self, nb_rec, min_height=3, min_width=3):
-        nb_trials = 200
+        try:
+            return self.cache_rec_coo[signature].pop()
+        except IndexError:
+            pass
+        except KeyError:
+            pass

 
 

+        N = 10000

         while True:
         while True:

-            v = (
-                (
-                    torch.rand(nb_trials * nb_rec, self.height + 1, device=self.device)
-                    .sort(dim=-1)
-                    .indices
-                    < 2
-                )
-                .long()
-                .cumsum(dim=1)
-                == 1
-            ).long()
+            while True:
+                i = torch.randint(self.height, (N * nb_rec, 2)).sort(dim=-1).values
+                j = torch.randint(self.width, (N * nb_rec, 2)).sort(dim=-1).values

 
 

-            h = (
-                (
-                    torch.rand(nb_trials * nb_rec, self.width + 1, device=self.device)
-                    .sort(dim=-1)
-                    .indices
-                    < 2
+                big_enough = (
+                    (i[:, 1] >= i[:, 0] + min_height)
+                    & (j[:, 1] >= j[:, 0] + min_height)
+                    & ((i[:, 1] - i[:, 0]) * (j[:, 1] - j[:, 0]) <= surface_max)

                 )
                 )

-                .long()
-                .cumsum(dim=1)
-                == 1
-            ).long()
-
-            i = torch.logical_and(
-                v.sum(dim=-1) >= min_height, h.sum(dim=-1) >= min_width
-            )

 
 

-            v, h = v[i], h[i]
-            v = v[: v.size(0) - v.size(0) % nb_rec]
-            h = h[: h.size(0) - h.size(0) % nb_rec]
-            v = v.reshape(v.size(0) // nb_rec, nb_rec, -1)
-            h = h.reshape(h.size(0) // nb_rec, nb_rec, -1)
+                i, j = i[big_enough], j[big_enough]

 
 

-            r = v[:, :, :, None] * h[:, :, None, :]
+                n = i.size(0) - i.size(0) % nb_rec

 
 

-            valid = r.sum(dim=1).flatten(1).max(dim=-1).values == 1
+                if n > 0:
+                    break

 
 

-            v = v[valid]
-            h = h[valid]
+            i = i[:n].reshape(n // nb_rec, nb_rec, -1)
+            j = j[:n].reshape(n // nb_rec, nb_rec, -1)
+
+            if prevent_overlap:
+                can_fit = ((i[:, :, 1] - i[:, :, 0]) * (j[:, :, 1] - j[:, :, 0])).sum(
+                    dim=-1
+                ) <= self.height * self.width
+                i, j = i[can_fit], j[can_fit]
+                if nb_rec == 2:
+                    A_i1, A_i2, A_j1, A_j2 = (
+                        i[:, 0, 0],
+                        i[:, 0, 1],
+                        j[:, 0, 0],
+                        j[:, 0, 1],
+                    )
+                    B_i1, B_i2, B_j1, B_j2 = (
+                        i[:, 1, 0],
+                        i[:, 1, 1],
+                        j[:, 1, 0],
+                        j[:, 1, 1],
+                    )
+                    no_overlap = torch.logical_not(
+                        (A_i1 >= B_i2)
+                        & (A_i2 <= B_i1)
+                        & (A_j1 >= B_j1)
+                        & (A_j2 <= B_j1)
+                    )
+                    i, j = i[no_overlap], j[no_overlap]
+                elif nb_rec == 3:
+                    A_i1, A_i2, A_j1, A_j2 = (
+                        i[:, 0, 0],
+                        i[:, 0, 1],
+                        j[:, 0, 0],
+                        j[:, 0, 1],
+                    )
+                    B_i1, B_i2, B_j1, B_j2 = (
+                        i[:, 1, 0],
+                        i[:, 1, 1],
+                        j[:, 1, 0],
+                        j[:, 1, 1],
+                    )
+                    C_i1, C_i2, C_j1, C_j2 = (
+                        i[:, 2, 0],
+                        i[:, 2, 1],
+                        j[:, 2, 0],
+                        j[:, 2, 1],
+                    )
+                    no_overlap = (
+                        (
+                            (A_i1 >= B_i2)
+                            | (A_i2 <= B_i1)
+                            | (A_j1 >= B_j2)
+                            | (A_j2 <= B_j1)
+                        )
+                        & (
+                            (A_i1 >= C_i2)
+                            | (A_i2 <= C_i1)
+                            | (A_j1 >= C_j2)
+                            | (A_j2 <= C_j1)
+                        )
+                        & (
+                            (B_i1 >= C_i2)
+                            | (B_i2 <= C_i1)
+                            | (B_j1 >= C_j2)
+                            | (B_j2 <= C_j1)
+                        )
+                    )
+                    i, j = (i[no_overlap], j[no_overlap])
+                else:
+                    assert nb_rec == 1

 
 

-            if v.size(0) > 0:
+            if i.size(0) > 1:

                 break
 
                 break
 

-        av = torch.arange(v.size(2), device=self.device)[None, :]
-        ah = torch.arange(h.size(2), device=self.device)[None, :]
-
-        return [
-            (i1.item(), j1.item(), i2.item() + 1, j2.item() + 1)
-            for i1, j1, i2, j2 in zip(
-                v.size(2) - (v[0] * (v.size(2) - av)).max(dim=-1).values,
-                h.size(2) - (h[0] * (h.size(2) - ah)).max(dim=-1).values,
-                (v[0] * av).max(dim=-1).values,
-                (h[0] * ah).max(dim=-1).values,
-            )
+        self.cache_rec_coo[signature] = [
+            [
+                (
+                    i[n, k, 0].item(),
+                    j[n, k, 0].item(),
+                    i[n, k, 1].item(),
+                    j[n, k, 1].item(),
+                )
+                for k in range(nb_rec)
+            ]
+            for n in range(i.size(0))

         ]
 
         ]
 

-    # @torch.compile
-    def rec_coo_(self, x, n, min_height=3, min_width=3):
-        collision = x.new(x.size())
-        while True:
-            collision[...] = 0
-            result = []
-            for _ in range(n):
-                while True:
-                    i1, i2 = torch.randint(x.size(0), (2,))
-                    if i1 + min_height <= i2:
-                        break
-                while True:
-                    j1, j2 = torch.randint(x.size(1), (2,))
-                    if j1 + min_width <= j2:
-                        break
-                collision[i1:i2, j1:j2] += 1
-                if collision.max() > 1:
-                    break
-                result.append((i1, j1, i2, j2))
-            if collision.max() == 1:
-                break
-        return result
+        return self.cache_rec_coo[signature].pop()

 
     ######################################################################
 
 
     ######################################################################
 


@@ -318,7 +445,7 @@ class Grids(problem.Problem):
         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[: nb_rec + 1] + 1
         for X, f_X in [(A, f_A), (B, f_B)]:
         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[: nb_rec + 1] + 1
         for X, f_X in [(A, f_A), (B, f_B)]:

-            r = self.rec_coo(nb_rec)
+            r = self.rec_coo(nb_rec, prevent_overlap=True)

             for n in range(nb_rec):
                 i1, j1, i2, j2 = r[n]
                 X[i1:i2, j1:j2] = c[n]
             for n in range(nb_rec):
                 i1, j1, i2, j2 = r[n]
                 X[i1:i2, j1:j2] = c[n]


@@ -326,12 +453,16 @@ class Grids(problem.Problem):
 
     # @torch.compile
     def task_translate(self, A, f_A, B, f_B):
 
     # @torch.compile
     def task_translate(self, A, f_A, B, f_B):

-        di, dj = torch.randint(3, (2,)) - 1
+        while True:
+            di, dj = torch.randint(3, (2,)) - 1
+            if di.abs() + dj.abs() > 0:
+                break
+

         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[:nb_rec] + 1
         for X, f_X in [(A, f_A), (B, f_B)]:
             while True:
         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[:nb_rec] + 1
         for X, f_X in [(A, f_A), (B, f_B)]:
             while True:

-                r = self.rec_coo(nb_rec)
+                r = self.rec_coo(nb_rec, prevent_overlap=True)

                 i1, j1, i2, j2 = r[nb_rec - 1]
                 if (
                     i1 + di >= 0
                 i1, j1, i2, j2 = r[nb_rec - 1]
                 if (
                     i1 + di >= 0


@@ -354,10 +485,10 @@ class Grids(problem.Problem):
         di, dj = torch.randint(2, (2,)) * 2 - 1
         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[:nb_rec] + 1
         di, dj = torch.randint(2, (2,)) * 2 - 1
         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[:nb_rec] + 1

-        direction = torch.randint(2, (1,))
+        direction = torch.randint(2, (1,)).item()

         for X, f_X in [(A, f_A), (B, f_B)]:
             while True:
         for X, f_X in [(A, f_A), (B, f_B)]:
             while True:

-                r = self.rec_coo(nb_rec)
+                r = self.rec_coo(nb_rec, prevent_overlap=True)

                 i1, j1, i2, j2 = r[nb_rec - 1]
                 if i1 + 3 < i2 and j1 + 3 < j2:
                     break
                 i1, j1, i2, j2 = r[nb_rec - 1]
                 if i1 + 3 < i2 and j1 + 3 < j2:
                     break


@@ -376,13 +507,13 @@ class Grids(problem.Problem):
                     f_X[i1:i2, j1:j2] = c[n]
 
     # @torch.compile
                     f_X[i1:i2, j1:j2] = c[n]
 
     # @torch.compile

-    def task_color_grow(self, A, f_A, B, f_B):
+    def task_half_fill(self, A, f_A, B, f_B):

         di, dj = torch.randint(2, (2,)) * 2 - 1
         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[: 2 * nb_rec] + 1
         di, dj = torch.randint(2, (2,)) * 2 - 1
         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[: 2 * nb_rec] + 1

-        direction = torch.randint(4, (1,))
+        direction = torch.randint(4, (1,)).item()

         for X, f_X in [(A, f_A), (B, f_B)]:
         for X, f_X in [(A, f_A), (B, f_B)]:

-            r = self.rec_coo(nb_rec)
+            r = self.rec_coo(nb_rec, prevent_overlap=True)

             for n in range(nb_rec):
                 i1, j1, i2, j2 = r[n]
                 X[i1:i2, j1:j2] = c[2 * n]
             for n in range(nb_rec):
                 i1, j1, i2, j2 = r[n]
                 X[i1:i2, j1:j2] = c[2 * n]


@@ -422,20 +553,24 @@ class Grids(problem.Problem):
         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[: nb_rec + 1] + 1
         for X, f_X in [(A, f_A), (B, f_B)]:
         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[: nb_rec + 1] + 1
         for X, f_X in [(A, f_A), (B, f_B)]:

-            r = self.rec_coo(nb_rec)
+            r = self.rec_coo(nb_rec, prevent_overlap=True)

             for n in range(nb_rec):
                 i1, j1, i2, j2 = r[n]
                 X[i1:i2, j1:j2] = c[n]
             for n in range(nb_rec):
                 i1, j1, i2, j2 = r[n]
                 X[i1:i2, j1:j2] = c[n]

-                f_X[i1:i2, j1:j2] = c[n]

                 if n == nb_rec - 1:
                 if n == nb_rec - 1:

-                    f_X[i1 + 1 : i2 - 1, j1 + 1 : j2 - 1] = 0
+                    f_X[i1:i2, j1] = c[n]
+                    f_X[i1:i2, j2 - 1] = c[n]
+                    f_X[i1, j1:j2] = c[n]
+                    f_X[i2 - 1, j1:j2] = c[n]
+                else:
+                    f_X[i1:i2, j1:j2] = c[n]

 
     # @torch.compile
     def task_detect(self, A, f_A, B, f_B):
         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[: nb_rec + 1] + 1
         for X, f_X in [(A, f_A), (B, f_B)]:
 
     # @torch.compile
     def task_detect(self, A, f_A, B, f_B):
         nb_rec = 3
         c = torch.randperm(len(self.colors) - 1)[: nb_rec + 1] + 1
         for X, f_X in [(A, f_A), (B, f_B)]:

-            r = self.rec_coo(nb_rec)
+            r = self.rec_coo(nb_rec, prevent_overlap=True)

             for n in range(nb_rec):
                 i1, j1, i2, j2 = r[n]
                 X[i1:i2, j1:j2] = c[n]
             for n in range(nb_rec):
                 i1, j1, i2, j2 = r[n]
                 X[i1:i2, j1:j2] = c[n]


@@ -478,29 +613,51 @@ class Grids(problem.Problem):
 
         return no, nq, nq_diag
 
 
         return no, nq, nq_diag
 

-    # @torch.compile

     def task_count(self, A, f_A, B, f_B):
     def task_count(self, A, f_A, B, f_B):

-        N = (torch.randint(4, (1,)) + 2).item()
-        c = torch.randperm(len(self.colors) - 1)[:N] + 1
+        while True:
+            error = False
+
+            N = torch.randint(5, (1,)).item() + 1
+            c = torch.zeros(N + 1)
+            c[1:] = torch.randperm(len(self.colors) - 1)[:N] + 1
+
+            for X, f_X in [(A, f_A), (B, f_B)]:
+                if not hasattr(self, "cache_count") or len(self.cache_count) == 0:
+                    self.cache_count = list(
+                        grow_islands(
+                            1000,
+                            self.height,
+                            self.width,
+                            nb_seeds=self.height * self.width // 8,
+                            nb_iterations=self.height * self.width // 10,
+                        )
+                    )

 
 

-        for X, f_X in [(A, f_A), (B, f_B)]:
-            nb = torch.zeros(N, dtype=torch.int64)
-            q = torch.randint(N, (self.height * self.width,))
-            k = torch.randperm(self.height * self.width)
-            for p in range(self.height * self.width):
-                i, j = k[p] % self.height, k[p] // self.height
-                no, nq, nq_diag = self.contact(X, i, j, c[q[p]])
-                if no == 0 and nq_diag == 0:
-                    if nq == 0:
-                        if nb[q[p]] < self.width:
-                            X[i, j] = c[q[p]]
-                            nb[q[p]] += 1
-                    if nq == 1:
-                        X[i, j] = c[q[p]]
-
-            for n in range(N):
-                for j in range(nb[n]):
-                    f_X[n, j] = c[n]
+                X[...] = self.cache_count.pop()
+
+                k = (X.max() + 1 + (c.size(0) - 1)).item()
+                V = torch.arange(k) // (c.size(0) - 1)
+                V = (V + torch.rand(V.size())).sort().indices[: X.max() + 1] % (
+                    c.size(0) - 1
+                ) + 1
+                V[0] = 0
+                X[...] = c[V[X]]
+
+                if F.one_hot(X.flatten()).max(dim=0).values.sum().item() == N + 1:
+                    f_X[...] = 0
+                    for e in range(1, N + 1):
+                        for j in range((X == c[e]).sum() + 1):
+                            if j < self.width:
+                                f_X[e - 1, j] = c[e]
+                            else:
+                                error = True
+                                break
+                else:
+                    error = True
+                    break
+
+            if not error:
+                break

 
     # @torch.compile
     def task_trajectory(self, A, f_A, B, f_B):
 
     # @torch.compile
     def task_trajectory(self, A, f_A, B, f_B):


@@ -508,7 +665,10 @@ class Grids(problem.Problem):
         for X, f_X in [(A, f_A), (B, f_B)]:
             while True:
                 di, dj = torch.randint(7, (2,)) - 3
         for X, f_X in [(A, f_A), (B, f_B)]:
             while True:
                 di, dj = torch.randint(7, (2,)) - 3

-                i, j = torch.randint(self.height, (1,)), torch.randint(self.width, (1,))
+                i, j = (
+                    torch.randint(self.height, (1,)).item(),
+                    torch.randint(self.width, (1,)).item(),
+                )

                 if (
                     abs(di) + abs(dj) > 0
                     and i + 2 * di >= 0
                 if (
                     abs(di) + abs(dj) > 0
                     and i + 2 * di >= 0


@@ -549,8 +709,9 @@ class Grids(problem.Problem):
                 X[...] = 0
 
                 for _ in range((self.height * self.width) // 10):
                 X[...] = 0
 
                 for _ in range((self.height * self.width) // 10):

-                    i, j = torch.randint(self.height, (1,)), torch.randint(
-                        self.width, (1,)
+                    i, j = (
+                        torch.randint(self.height, (1,)).item(),
+                        torch.randint(self.width, (1,)).item(),

                     )
                     X[i, j] = c[0]
                     f_X[i, j] = c[0]
                     )
                     X[i, j] = c[0]
                     f_X[i, j] = c[0]


@@ -560,7 +721,10 @@ class Grids(problem.Problem):
                     if abs(di) + abs(dj) == 1:
                         break
 
                     if abs(di) + abs(dj) == 1:
                         break
 

-                i, j = torch.randint(self.height, (1,)), torch.randint(self.width, (1,))
+                i, j = (
+                    torch.randint(self.height, (1,)).item(),
+                    torch.randint(self.width, (1,)).item(),
+                )

 
                 X[i, j] = c[1]
                 f_X[i, j] = c[1]
 
                 X[i, j] = c[1]
                 f_X[i, j] = c[1]


@@ -598,18 +762,21 @@ class Grids(problem.Problem):
     def task_scale(self, A, f_A, B, f_B):
         c = torch.randperm(len(self.colors) - 1)[:2] + 1
 
     def task_scale(self, A, f_A, B, f_B):
         c = torch.randperm(len(self.colors) - 1)[:2] + 1
 

-        i, j = torch.randint(self.height // 2, (1,)), torch.randint(
-            self.width // 2, (1,)
+        i, j = (
+            torch.randint(self.height // 2, (1,)).item(),
+            torch.randint(self.width // 2, (1,)).item(),

         )
 
         for X, f_X in [(A, f_A), (B, f_B)]:
             for _ in range(3):
                 while True:
         )
 
         for X, f_X in [(A, f_A), (B, f_B)]:
             for _ in range(3):
                 while True:

-                    i1, j1 = torch.randint(self.height // 2 + 1, (1,)), torch.randint(
-                        self.width // 2 + 1, (1,)
+                    i1, j1 = (
+                        torch.randint(self.height // 2 + 1, (1,)).item(),
+                        torch.randint(self.width // 2 + 1, (1,)).item(),

                     )
                     )

-                    i2, j2 = torch.randint(self.height // 2 + 1, (1,)), torch.randint(
-                        self.width // 2 + 1, (1,)
+                    i2, j2 = (
+                        torch.randint(self.height // 2 + 1, (1,)).item(),
+                        torch.randint(self.width // 2 + 1, (1,)).item(),

                     )
                     if i1 < i2 and j1 < j2 and min(i2 - i1, j2 - j1) <= 3:
                         break
                     )
                     if i1 < i2 and j1 < j2 and min(i2 - i1, j2 - j1) <= 3:
                         break


@@ -639,7 +806,7 @@ class Grids(problem.Problem):
 
             ai, aj = i.float().mean(), j.float().mean()
 
 
             ai, aj = i.float().mean(), j.float().mean()
 

-            q = torch.randint(3, (1,)) + 1
+            q = torch.randint(3, (1,)).item() + 1

 
             X[i[0] + delta // 2 - 1, j[0] + delta // 2 - 1] = c[0]
             X[i[0] + delta // 2 - 1, j[0] + delta // 2 + 1] = c[0]
 
             X[i[0] + delta // 2 - 1, j[0] + delta // 2 - 1] = c[0]
             X[i[0] + delta // 2 - 1, j[0] + delta // 2 + 1] = c[0]


@@ -656,12 +823,12 @@ class Grids(problem.Problem):
             f_X[i[0] : i[0] + delta, j[0] : j[0] + delta] = c[q]
 
     # @torch.compile
             f_X[i[0] : i[0] + delta, j[0] : j[0] + delta] = c[q]
 
     # @torch.compile

-    def task_ortho(self, A, f_A, B, f_B):
+    def task_isometry(self, A, f_A, B, f_B):

         nb_rec = 3
         di, dj = torch.randint(3, (2,)) - 1
         o = torch.tensor([[0.0, 1.0], [-1.0, 0.0]])
         m = torch.eye(2)
         nb_rec = 3
         di, dj = torch.randint(3, (2,)) - 1
         o = torch.tensor([[0.0, 1.0], [-1.0, 0.0]])
         m = torch.eye(2)

-        for _ in range(torch.randint(4, (1,))):
+        for _ in range(torch.randint(4, (1,)).item()):

             m = m @ o
         if torch.rand(1) < 0.5:
             m[0, :] = -m[0, :]
             m = m @ o
         if torch.rand(1) < 0.5:
             m[0, :] = -m[0, :]


@@ -710,9 +877,88 @@ class Grids(problem.Problem):
                 ):
                     break
 
                 ):
                     break
 

+    def compute_distance(self, walls, goal_i, goal_j):
+        max_length = walls.numel()
+        dist = torch.full_like(walls, max_length)
+
+        dist[goal_i, goal_j] = 0
+        pred_dist = torch.empty_like(dist)
+
+        while True:
+            pred_dist.copy_(dist)
+            dist[1:-1, 1:-1] = (
+                torch.cat(
+                    (
+                        dist[None, 1:-1, 1:-1],
+                        dist[None, 1:-1, 0:-2],
+                        dist[None, 2:, 1:-1],
+                        dist[None, 1:-1, 2:],
+                        dist[None, 0:-2, 1:-1],
+                    ),
+                    0,
+                ).min(dim=0)[0]
+                + 1
+            )
+
+            dist = walls * max_length + (1 - walls) * dist
+
+            if dist.equal(pred_dist):
+                return dist * (1 - walls)
+

     # @torch.compile
     # @torch.compile

-    def task_islands(self, A, f_A, B, f_B):
-        pass
+    def task_distance(self, A, f_A, B, f_B):
+        c = torch.randperm(len(self.colors) - 1)[:3] + 1
+        dist0 = torch.empty(self.height + 2, self.width + 2)
+        dist1 = torch.empty(self.height + 2, self.width + 2)
+        for X, f_X in [(A, f_A), (B, f_B)]:
+            nb_rec = torch.randint(3, (1,)).item() + 1
+            while True:
+                r = self.rec_coo(nb_rec, prevent_overlap=True)
+                X[...] = 0
+                f_X[...] = 0
+                for n in range(nb_rec):
+                    i1, j1, i2, j2 = r[n]
+                    X[i1:i2, j1:j2] = c[0]
+                    f_X[i1:i2, j1:j2] = c[0]
+                while True:
+                    i0, j0 = (
+                        torch.randint(self.height, (1,)).item(),
+                        torch.randint(self.width, (1,)).item(),
+                    )
+                    if X[i0, j0] == 0:
+                        break
+                while True:
+                    i1, j1 = (
+                        torch.randint(self.height, (1,)).item(),
+                        torch.randint(self.width, (1,)).item(),
+                    )
+                    if X[i1, j1] == 0:
+                        break
+                dist1[...] = 1
+                dist1[1:-1, 1:-1] = (X != 0).long()
+                dist1[...] = self.compute_distance(dist1, i1 + 1, j1 + 1)
+                if (
+                    dist1[i0 + 1, j0 + 1] >= 1
+                    and dist1[i0 + 1, j0 + 1] < self.height * 4
+                ):
+                    break
+
+            dist0[...] = 1
+            dist0[1:-1, 1:-1] = (X != 0).long()
+            dist0[...] = self.compute_distance(dist0, i0 + 1, j0 + 1)
+
+            dist0 = dist0[1:-1, 1:-1]
+            dist1 = dist1[1:-1, 1:-1]
+
+            D = dist1[i0, j0]
+            for d in range(1, D):
+                M = (dist0 == d) & (dist1 == D - d)
+                f_X[...] = (1 - M) * f_X + M * c[1]
+
+            X[i0, j0] = c[2]
+            f_X[i0, j0] = c[2]
+            X[i1, j1] = c[2]
+            f_X[i1, j1] = c[2]

 
     # for X, f_X in [(A, f_A), (B, f_B)]:
     # n = torch.arange(self.height * self.width).reshape(self.height, self.width)
 
     # for X, f_X in [(A, f_A), (B, f_B)]:
     # n = torch.arange(self.height * self.width).reshape(self.height, self.width)


@@ -722,24 +968,104 @@ class Grids(problem.Problem):
     # i,j=q%self.height,q//self.height
     # if
 
     # i,j=q%self.height,q//self.height
     # if
 

-    ######################################################################
+    # @torch.compile
+    def task_puzzle(self, A, f_A, B, f_B):
+        S = 4
+        i0, j0 = (self.height - S) // 2, (self.width - S) // 2
+        c = torch.randperm(len(self.colors) - 1)[:4] + 1
+        for X, f_X in [(A, f_A), (B, f_B)]:
+            while True:
+                f_X[...] = 0
+                h = list(torch.randperm(c.size(0)))
+                n = torch.zeros(c.max() + 1)
+                for _ in range(2):
+                    k = torch.randperm(S * S)
+                    for q in k:
+                        i, j = q % S + i0, q // S + j0
+                        if f_X[i, j] == 0:
+                            r, s, t, u = (
+                                f_X[i - 1, j],
+                                f_X[i, j - 1],
+                                f_X[i + 1, j],
+                                f_X[i, j + 1],
+                            )
+                            r, s, t, u = torch.tensor([r, s, t, u])[torch.randperm(4)]
+                            if r > 0 and n[r] < 6:
+                                n[r] += 1
+                                f_X[i, j] = r
+                            elif s > 0 and n[s] < 6:
+                                n[s] += 1
+                                f_X[i, j] = s
+                            elif t > 0 and n[t] < 6:
+                                n[t] += 1
+                                f_X[i, j] = t
+                            elif u > 0 and n[u] < 6:
+                                n[u] += 1
+                                f_X[i, j] = u
+                            else:
+                                if len(h) > 0:
+                                    d = c[h.pop()]
+                                    n[d] += 1
+                                    f_X[i, j] = d
+
+                if n.sum() == S * S:
+                    break

 
 

-    def all_tasks(self):
-        return [
-            self.task_replace_color,
-            self.task_translate,
-            self.task_grow,
-            self.task_color_grow,
-            self.task_frame,
-            self.task_detect,
-            self.task_count,
-            self.task_trajectory,
-            self.task_bounce,
-            self.task_scale,
-            self.task_symbols,
-            self.task_ortho,
-            # self.task_islands,
-        ]
+            k = 0
+            for d in range(4):
+                while True:
+                    ii, jj = (
+                        torch.randint(self.height, (1,)).item(),
+                        torch.randint(self.width, (1,)).item(),
+                    )
+                    e = 0
+                    for i in range(S):
+                        for j in range(S):
+                            if (
+                                ii + i >= self.height
+                                or jj + j >= self.width
+                                or (
+                                    f_X[i + i0, j + j0] == c[d]
+                                    and X[ii + i, jj + j] > 0
+                                )
+                            ):
+                                e = 1
+                    if e == 0:
+                        break
+                for i in range(S):
+                    for j in range(S):
+                        if f_X[i + i0, j + j0] == c[d]:
+                            X[ii + i, jj + j] = c[d]
+
+    def task_islands(self, A, f_A, B, f_B):
+        c = torch.randperm(len(self.colors) - 1)[:2] + 1
+        for X, f_X in [(A, f_A), (B, f_B)]:
+            if not hasattr(self, "cache_islands") or len(self.cache_islands) == 0:
+                self.cache_islands = list(
+                    grow_islands(
+                        1000,
+                        self.height,
+                        self.width,
+                        nb_seeds=self.height * self.width // 20,
+                        nb_iterations=self.height * self.width // 2,
+                    )
+                )
+
+            A = self.cache_islands.pop()
+
+            while True:
+                i, j = (
+                    torch.randint(self.height // 2, (1,)).item(),
+                    torch.randint(self.width // 2, (1,)).item(),
+                )
+                if A[i, j] > 0:
+                    break
+
+            X[...] = (A > 0) * c[0]
+            X[i, j] = c[1]
+            f_X[...] = (A == A[i, j]) * c[1] + ((A > 0) & (A != A[i, j])) * c[0]
+
+    ######################################################################

 
     def trivial_prompts_and_answers(self, prompts, answers):
         S = self.height * self.width
 
     def trivial_prompts_and_answers(self, prompts, answers):
         S = self.height * self.width


@@ -747,11 +1073,9 @@ class Grids(problem.Problem):
         f_Bs = answers
         return (Bs == f_Bs).long().min(dim=-1).values > 0
 
         f_Bs = answers
         return (Bs == f_Bs).long().min(dim=-1).values > 0
 

-    def generate_prompts_and_answers(
-        self, nb, tasks=None, progress_bar=False, device="cpu"
-    ):
+    def generate_prompts_and_answers_(self, nb, tasks=None, progress_bar=False):

         if tasks is None:
         if tasks is None:

-            tasks = self.all_tasks()
+            tasks = self.all_tasks

 
         S = self.height * self.width
         prompts = torch.zeros(nb, 3 * S + 2, dtype=torch.int64)
 
         S = self.height * self.width
         prompts = torch.zeros(nb, 3 * S + 2, dtype=torch.int64)


@@ -772,12 +1096,12 @@ class Grids(problem.Problem):
             f_A = prompt[1 * (S + 1) : 1 * (S + 1) + S].view(self.height, self.width)
             B = prompt[2 * (S + 1) : 2 * (S + 1) + S].view(self.height, self.width)
             f_B = answer.view(self.height, self.width)
             f_A = prompt[1 * (S + 1) : 1 * (S + 1) + S].view(self.height, self.width)
             B = prompt[2 * (S + 1) : 2 * (S + 1) + S].view(self.height, self.width)
             f_B = answer.view(self.height, self.width)

-            task = tasks[torch.randint(len(tasks), (1,))]
+            task = tasks[torch.randint(len(tasks), (1,)).item()]

             task(A, f_A, B, f_B)
 
         return prompts.flatten(1), answers.flatten(1)
 
             task(A, f_A, B, f_B)
 
         return prompts.flatten(1), answers.flatten(1)
 

-    def save_quizzes(
+    def save_quiz_illustrations(

         self,
         result_dir,
         filename_prefix,
         self,
         result_dir,
         filename_prefix,


@@ -797,12 +1121,22 @@ class Grids(problem.Problem):
             nrow,
         )
 
             nrow,
         )
 

+    def save_some_examples(self, result_dir):
+        nb, nrow = 72, 4
+        for t in self.all_tasks:
+            print(t.__name__)
+            prompts, answers = self.generate_prompts_and_answers_(nb, tasks=[t])
+            self.save_quiz_illustrations(
+                result_dir, t.__name__, prompts[:nb], answers[:nb], nrow=nrow
+            )
+

 
 ######################################################################
 
 if __name__ == "__main__":
     import time
 
 
 ######################################################################
 
 if __name__ == "__main__":
     import time
 

+    # grids = Grids(max_nb_cached_chunks=5, chunk_size=100, nb_threads=4)

     grids = Grids()
 
     # nb = 1000
     grids = Grids()
 
     # nb = 1000


@@ -816,22 +1150,26 @@ if __name__ == "__main__":
     # print(f"{prompts.size(0)/delay:02f} seq/s")
     # exit(0)
 
     # print(f"{prompts.size(0)/delay:02f} seq/s")
     # exit(0)
 

-    if True:
-        nb = 72
+    # if True:
+    nb, nrow = 72, 4
+    # nb, nrow = 8, 2

 
 

-        for t in grids.all_tasks():
-            # for t in [grids.task_ortho]:
-            print(t.__name__)
-            prompts, answers = grids.generate_prompts_and_answers(nb, tasks=[t])
-            grids.save_quizzes("/tmp", t.__name__, prompts[:nb], answers[:nb], nrow=4)
+    # for t in grids.all_tasks:
+    for t in [grids.task_distance]:
+        print(t.__name__)
+        prompts, answers = grids.generate_prompts_and_answers_(nb, tasks=[t])
+        grids.save_quiz_illustrations(
+            "/tmp", t.__name__, prompts[:nb], answers[:nb], nrow=nrow
+        )

 
 

-        exit(0)
+    # exit(0)

 
 

-    nb = 500
+    nb = 1000

 
 

-    for t in grids.all_tasks():
+    # for t in grids.all_tasks:
+    for t in [grids.task_distance]:

         start_time = time.perf_counter()
         start_time = time.perf_counter()

-        prompts, answers = grids.generate_prompts_and_answers(nb, tasks=[t])
+        prompts, answers = grids.generate_prompts_and_answers_(nb, tasks=[t])

         delay = time.perf_counter() - start_time
         print(f"{t.__name__} {prompts.size(0)/delay:02f} seq/s")
 
         delay = time.perf_counter() - start_time
         print(f"{t.__name__} {prompts.size(0)/delay:02f} seq/s")
 


@@ -841,7 +1179,7 @@ if __name__ == "__main__":
     predicted_prompts = m * (torch.randint(2, (prompts.size(0),)) * 2 - 1)
     predicted_answers = (1 - m) * (torch.randint(2, (prompts.size(0),)) * 2 - 1)
 
     predicted_prompts = m * (torch.randint(2, (prompts.size(0),)) * 2 - 1)
     predicted_answers = (1 - m) * (torch.randint(2, (prompts.size(0),)) * 2 - 1)
 

-    grids.save_quizzes(
+    grids.save_quiz_illustrations(

         "/tmp",
         "test",
         prompts[:nb],
         "/tmp",
         "test",
         prompts[:nb],