Initial commit. I can successfully create random tensor.

lib/src/app.dart

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+import 'package:flutter/material.dart';
+import 'package:flutter_gen/gen_l10n/app_localizations.dart';
+import 'package:flutter_localizations/flutter_localizations.dart';
+
+import 'sample_feature/sample_item_details_view.dart';
+import 'sample_feature/sample_item_list_view.dart';
+import 'settings/settings_controller.dart';
+import 'settings/settings_view.dart';
+
+/// The Widget that configures your application.
+class MyApp extends StatelessWidget {
+  const MyApp({
+    super.key,
+    required this.settingsController,
+  });
+
+  final SettingsController settingsController;
+
+  @override
+  Widget build(BuildContext context) {
+    // Glue the SettingsController to the MaterialApp.
+    //
+    // The ListenableBuilder Widget listens to the SettingsController for changes.
+    // Whenever the user updates their settings, the MaterialApp is rebuilt.
+    return ListenableBuilder(
+      listenable: settingsController,
+      builder: (BuildContext context, Widget? child) {
+        return MaterialApp(
+          // Providing a restorationScopeId allows the Navigator built by the
+          // MaterialApp to restore the navigation stack when a user leaves and
+          // returns to the app after it has been killed while running in the
+          // background.
+          restorationScopeId: 'app',
+
+          // Provide the generated AppLocalizations to the MaterialApp. This
+          // allows descendant Widgets to display the correct translations
+          // depending on the user's locale.
+          localizationsDelegates: const [
+            AppLocalizations.delegate,
+            GlobalMaterialLocalizations.delegate,
+            GlobalWidgetsLocalizations.delegate,
+            GlobalCupertinoLocalizations.delegate,
+          ],
+          supportedLocales: const [
+            Locale('en', ''), // English, no country code
+          ],
+
+          // Use AppLocalizations to configure the correct application title
+          // depending on the user's locale.
+          //
+          // The appTitle is defined in .arb files found in the localization
+          // directory.
+          onGenerateTitle: (BuildContext context) =>
+              AppLocalizations.of(context)!.appTitle,
+
+          // Define a light and dark color theme. Then, read the user's
+          // preferred ThemeMode (light, dark, or system default) from the
+          // SettingsController to display the correct theme.
+          theme: ThemeData(),
+          darkTheme: ThemeData.dark(),
+          themeMode: settingsController.themeMode,
+
+          // Define a function to handle named routes in order to support
+          // Flutter web url navigation and deep linking.
+          onGenerateRoute: (RouteSettings routeSettings) {
+            return MaterialPageRoute<void>(
+              settings: routeSettings,
+              builder: (BuildContext context) {
+                switch (routeSettings.name) {
+                  case SettingsView.routeName:
+                    return SettingsView(controller: settingsController);
+                  case SampleItemDetailsView.routeName:
+                    return const SampleItemDetailsView();
+                  case SampleItemListView.routeName:
+                  default:
+                    return const SampleItemListView();
+                }
+              },
+            );
+          },
+        );
+      },
+    );
+  }
+}

lib/src/localization/app_en.arb

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+{
+  "appTitle": "archimedes_test",
+  "@appTitle": {
+    "description": "The title of the application"
+  }
+}

lib/src/sample_feature/sample_item.dart

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+/// A placeholder class that represents an entity or model.
+class SampleItem {
+  const SampleItem(this.id);
+
+  final int id;
+}

lib/src/sample_feature/sample_item_details_view.dart

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+import 'package:flutter/material.dart';
+
+/// Displays detailed information about a SampleItem.
+class SampleItemDetailsView extends StatelessWidget {
+  const SampleItemDetailsView({super.key});
+
+  static const routeName = '/sample_item';
+
+  @override
+  Widget build(BuildContext context) {
+    return Scaffold(
+      appBar: AppBar(
+        title: const Text('Item Details'),
+      ),
+      body: const Center(
+        child: Text('More Information Here'),
+      ),
+    );
+  }
+}

lib/src/sample_feature/sample_item_list_view.dart

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+import 'package:flutter/material.dart';
+
+import '../settings/settings_view.dart';
+import 'sample_item.dart';
+import 'sample_item_details_view.dart';
+
+/// Displays a list of SampleItems.
+class SampleItemListView extends StatelessWidget {
+  const SampleItemListView({
+    super.key,
+    this.items = const [SampleItem(1), SampleItem(2), SampleItem(3)],
+  });
+
+  static const routeName = '/';
+
+  final List<SampleItem> items;
+
+  @override
+  Widget build(BuildContext context) {
+    return Scaffold(
+      appBar: AppBar(
+        title: const Text('Sample Items'),
+        actions: [
+          IconButton(
+            icon: const Icon(Icons.settings),
+            onPressed: () {
+              // Navigate to the settings page. If the user leaves and returns
+              // to the app after it has been killed while running in the
+              // background, the navigation stack is restored.
+              Navigator.restorablePushNamed(context, SettingsView.routeName);
+            },
+          ),
+        ],
+      ),
+
+      // To work with lists that may contain a large number of items, it’s best
+      // to use the ListView.builder constructor.
+      //
+      // In contrast to the default ListView constructor, which requires
+      // building all Widgets up front, the ListView.builder constructor lazily
+      // builds Widgets as they’re scrolled into view.
+      body: ListView.builder(
+        // Providing a restorationId allows the ListView to restore the
+        // scroll position when a user leaves and returns to the app after it
+        // has been killed while running in the background.
+        restorationId: 'sampleItemListView',
+        itemCount: items.length,
+        itemBuilder: (BuildContext context, int index) {
+          final item = items[index];
+
+          return ListTile(
+            title: Text('SampleItem ${item.id}'),
+            leading: const CircleAvatar(
+              // Display the Flutter Logo image asset.
+              foregroundImage: AssetImage('assets/images/flutter_logo.png'),
+            ),
+            onTap: () {
+              // Navigate to the details page. If the user leaves and returns to
+              // the app after it has been killed while running in the
+              // background, the navigation stack is restored.
+              Navigator.restorablePushNamed(
+                context,
+                SampleItemDetailsView.routeName,
+              );
+            }
+          );
+        },
+      ),
+    );
+  }
+}

lib/src/settings/settings_controller.dart

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+import 'package:flutter/material.dart';
+
+import 'settings_service.dart';
+
+/// A class that many Widgets can interact with to read user settings, update
+/// user settings, or listen to user settings changes.
+///
+/// Controllers glue Data Services to Flutter Widgets. The SettingsController
+/// uses the SettingsService to store and retrieve user settings.
+class SettingsController with ChangeNotifier {
+  SettingsController(this._settingsService);
+
+  // Make SettingsService a private variable so it is not used directly.
+  final SettingsService _settingsService;
+
+  // Make ThemeMode a private variable so it is not updated directly without
+  // also persisting the changes with the SettingsService.
+  late ThemeMode _themeMode;
+
+  // Allow Widgets to read the user's preferred ThemeMode.
+  ThemeMode get themeMode => _themeMode;
+
+  /// Load the user's settings from the SettingsService. It may load from a
+  /// local database or the internet. The controller only knows it can load the
+  /// settings from the service.
+  Future<void> loadSettings() async {
+    _themeMode = await _settingsService.themeMode();
+
+    // Important! Inform listeners a change has occurred.
+    notifyListeners();
+  }
+
+  /// Update and persist the ThemeMode based on the user's selection.
+  Future<void> updateThemeMode(ThemeMode? newThemeMode) async {
+    if (newThemeMode == null) return;
+
+    // Do not perform any work if new and old ThemeMode are identical
+    if (newThemeMode == _themeMode) return;
+
+    // Otherwise, store the new ThemeMode in memory
+    _themeMode = newThemeMode;
+
+    // Important! Inform listeners a change has occurred.
+    notifyListeners();
+
+    // Persist the changes to a local database or the internet using the
+    // SettingService.
+    await _settingsService.updateThemeMode(newThemeMode);
+  }
+}

lib/src/settings/settings_service.dart

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+import 'package:flutter/material.dart';
+
+/// A service that stores and retrieves user settings.
+///
+/// By default, this class does not persist user settings. If you'd like to
+/// persist the user settings locally, use the shared_preferences package. If
+/// you'd like to store settings on a web server, use the http package.
+class SettingsService {
+  /// Loads the User's preferred ThemeMode from local or remote storage.
+  Future<ThemeMode> themeMode() async => ThemeMode.system;
+
+  /// Persists the user's preferred ThemeMode to local or remote storage.
+  Future<void> updateThemeMode(ThemeMode theme) async {
+    // Use the shared_preferences package to persist settings locally or the
+    // http package to persist settings over the network.
+  }
+}

lib/src/settings/settings_view.dart

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+import 'package:flutter/material.dart';
+
+import 'settings_controller.dart';
+
+/// Displays the various settings that can be customized by the user.
+///
+/// When a user changes a setting, the SettingsController is updated and
+/// Widgets that listen to the SettingsController are rebuilt.
+class SettingsView extends StatelessWidget {
+  const SettingsView({super.key, required this.controller});
+
+  static const routeName = '/settings';
+
+  final SettingsController controller;
+
+  @override
+  Widget build(BuildContext context) {
+    return Scaffold(
+      appBar: AppBar(
+        title: const Text('Settings'),
+      ),
+      body: Padding(
+        padding: const EdgeInsets.all(16),
+        // Glue the SettingsController to the theme selection DropdownButton.
+        //
+        // When a user selects a theme from the dropdown list, the
+        // SettingsController is updated, which rebuilds the MaterialApp.
+        child: DropdownButton<ThemeMode>(
+          // Read the selected themeMode from the controller
+          value: controller.themeMode,
+          // Call the updateThemeMode method any time the user selects a theme.
+          onChanged: controller.updateThemeMode,
+          items: const [
+            DropdownMenuItem(
+              value: ThemeMode.system,
+              child: Text('System Theme'),
+            ),
+            DropdownMenuItem(
+              value: ThemeMode.light,
+              child: Text('Light Theme'),
+            ),
+            DropdownMenuItem(
+              value: ThemeMode.dark,
+              child: Text('Dark Theme'),
+            )
+          ],
+        ),
+      ),
+    );
+  }
+}

lib/src/splat/camera.dart

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+import 'dart:typed_data';
+
+import 'package:archimedes_test/src/splat/tensor.dart';
+import 'package:camera/camera.dart';
+
+class Camera {
+  int id = -1;
+  int width = 0;
+  int height = 0;
+  double fx = 0;
+  double fy = 0;
+  double cx = 0;
+  double cy = 0;
+  double k1 = 0;
+  double k2 = 0;
+  double k3 = 0;
+  double p1 = 0;
+  double p2 = 0;
+
+  ByteBuffer? image;
+  Tensor? camToWorld;
+
+  List<List<double>> getIntrinsicsMatrix() {
+    return [
+      [fx, 0.0, cx],
+      [0.0, fy, cy],
+      [0.0, 0.0, 1.0]
+    ];
+  }
+
+  Future<CameraDescription?> getFrontCameraDescription() async {
+    List<CameraDescription> cameras = await availableCameras();
+    for (CameraDescription cd in cameras) {
+      if (cd.lensDirection == CameraLensDirection.front) {
+        return cd;
+      }
+    }
+    return null;
+  }
+}

lib/src/splat/input_data.dart

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+import 'package:archimedes_test/src/splat/camera.dart';
+
+class InputData {
+  List<Camera>? cameras;
+}

lib/src/splat/listutil.dart

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+

lib/src/splat/model.dart

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+import 'dart:math';
+
+import 'package:archimedes_test/src/splat/tensor.dart';
+
+double minus(double i) {
+  return 1 - i;
+}
+
+Tensor randomQuantTensor(int n) {
+  Tensor u = Tensor.random([n]);
+  Tensor v = Tensor.random([n]);
+  Tensor w = Tensor.random([n]);
+
+  Tensor a1 = u.each((f, _, __) {
+    return sin(2 * pi * f);
+  });
+  Tensor a2 = u.each((f, _, __) {
+    return sqrt(1 - f);
+  });
+  Tensor a = a1 * a2;
+
+  Tensor b1 = v.each((f, _, __) {
+    return cos(2 * pi * f);
+  });
+  Tensor b2 = v.each((f, _, __) {
+    return sqrt(1 - f);
+  });
+
+  Tensor b = b1 * b2;
+
+  Tensor c1 = u.each((f, _, __) {
+    return sqrt(f);
+  });
+  Tensor c2 = w.each((f, _, __) {
+    return sin(2 * pi * f);
+  });
+  Tensor c = c1 * c2;
+
+  Tensor d1 = u.each((f, _, __) {
+    return sqrt(f);
+  });
+  Tensor d2 = w.each((f, _, __) {
+    return cos(2 * pi * f);
+  });
+  Tensor d = d1 * d2;
+
+  return Tensor.stack(Tensor([a[0], b[0], c[0], d[0]]));
+}

lib/src/splat/points.dart

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+import 'package:archimedes_test/src/splat/tensor.dart';
+
+class Points {
+  Tensor xyz;
+  Tensor rgb;
+
+  Points(this.xyz, this.rgb);
+}

lib/src/splat/tensor.dart

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+import 'dart:math';
+
+import 'package:collection/collection.dart';
+
+class Tensor extends DelegatingList<DelegatingList<double>> {
+  Tensor(super.base);
+
+  Tensor each(Function(double, int, int) f) {
+    Tensor other = Tensor([]);
+    for (int j = 0; j < length; ++j) {
+      other[j] = const DelegatingList([]);
+      for (int k = 0; k < this[j].length; ++k) {
+        other[j][k] = f(this[j][k], j, k);
+      }
+    }
+    return other;
+  }
+
+  /// Generate a random tensor of shape `shape`
+  static Tensor random(List<int> shape) {
+    Random r = Random();
+
+    int d1 = 0, d2 = 0;
+    if (shape.length == 1) {
+      d1 = shape[0];
+    } else if (shape.length == 2) {
+      d1 = shape[0];
+      d2 = shape[1];
+    } else if (shape.length == 3) {
+      // d3 = shapes[2];
+    }
+    Tensor ret = Tensor(List.filled(d1, DelegatingList(List.filled(d2, 0.0))));
+
+    for (int i = 0; i < d1; ++i) {
+      for (int j = 0; j < d2; ++j) {
+        ret[i][j] = r.nextDouble();
+      }
+    }
+
+    return ret;
+  }
+
+  static Tensor stack(Tensor tensors, {int axis = 0}) {
+    if (axis < -1 || axis > tensors.length - 1) {
+      throw ArgumentError('Invalid axis value');
+    }
+
+    int newAxisSize = tensors.length;
+    for (var tensor in tensors) {
+      newAxisSize *= tensor.length;
+    }
+
+    Tensor result = Tensor([]);
+    for (int i = 0; i < newAxisSize; i++) {
+      int index = i;
+      int currentAxisIndex = axis;
+      List<int> currentAxisIndexes = List.filled(tensors.length, -1);
+      int currentTensorIndex = 0;
+
+      while (currentAxisIndexes[currentTensorIndex] < tensors.length) {
+        if (currentAxisIndexes[currentTensorIndex] == currentAxisIndex) {
+          index = currentAxisIndexes[currentTensorIndex] +
+              (index ~/ tensors.length);
+          currentAxisIndexes[currentTensorIndex]++;
+        }
+        currentAxisIndex += (axis > 0 ? 1 : -1);
+        currentTensorIndex =
+            (currentAxisIndex < 0 || currentTensorIndex >= tensors.length)
+                ? 0
+                : currentTensorIndex + 1;
+      }
+
+      result.add(tensors[
+          currentTensorIndex]); // Access tensors[currentTensorIndex] as a List<double> rather than using the index operator [] with it
+    }
+
+    return Tensor(result);
+  }
+
+  operator *(Tensor other) {
+    return each((d, i, j) {
+      return [i][j] * other[i][j];
+    });
+  }
+}

lib/src/test/splat/tensor_test.dart

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+import 'package:archimedes_test/src/splat/tensor.dart';
+import 'package:collection/collection.dart';
+import 'package:test/test.dart';
+
+void main() {
+  group('stack', () {
+    test('A random tensor can be generated', () {
+      Tensor generated = Tensor.random([2, 4]);
+      expect(generated.length, equals(2));
+      expect(generated[0].length, equals(4));
+    });
+
+    test("A tensor can be stacked", () {
+      Tensor x = Tensor(const DelegatingList([
+        DelegatingList([0.3367, 0.1288, 0.2345]),
+        DelegatingList([0.2303, -1.1229, -0.1863])
+      ]));
+
+      expect(Tensor.stack(x)[0], equals(x));
+    });
+  });
+}