{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": "# Tutorial 2: Sparse Data Structures - CSR, COO, CSC\n\nIn large-scale neural network modeling, connections between neurons are typically **sparse**. For example, in the brain's cortical layers, each neuron connects to only a small fraction of neurons. Using sparse data structures can significantly reduce memory consumption and computation time.\n\nThis tutorial will introduce three sparse matrix formats provided by BrainEvent: **CSR**, **COO**, and **CSC**, and their applications in event-driven computation.\n\n## Contents\n1. Why do we need sparse matrices?\n2. Principles of the three sparse formats\n3. Creating and using sparse matrices\n4. Using with BinaryArray\n5. Performance comparison\n6. Practice: Building a sparse connection network\n7. Visualizing sparse structures"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": "## 1. Why do we need sparse matrices?\n\nIn neural network modeling, connection weight matrices are usually very sparse. Consider the following scenarios:\n\n- **Dense matrix**: 10,000 × 10,000 matrix → requires storing 100,000,000 floats ≈ **400 MB**\n- **Sparse matrix**: Assuming only 1% connections → only needs to store 1,000,000 non-zero elements ≈ **4 MB**\n\n### Core advantages\n- ✅ **Memory efficiency**: Only stores non-zero elements\n- ✅ **Computational efficiency**: Skips multiplication of zero elements\n- ✅ **Event-driven**: Perfect combination with BinaryArray"
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-21T07:02:46.525869Z",
     "start_time": "2025-10-21T07:02:46.521870Z"
    }
   },
   "source": [
    "import brainevent\n",
    "import brainstate\n",
    "import braintools\n",
    "import jax.numpy as jnp\n",
    "import jax\n",
    "import numpy as np\n",
    "\n",
    "print(f\"BrainEvent version: {brainevent.__version__}\")\n",
    "print(f\"JAX version: {jax.__version__}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BrainEvent version: 0.0.4\n",
      "JAX version: 0.7.2\n"
     ]
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": "## 2. Principles of the three sparse formats\n\n### 2.1 COO (Coordinate) Format\n\n**COO format** uses three arrays to store a sparse matrix:\n- `row`: row indices of non-zero elements\n- `col`: column indices of non-zero elements  \n- `data`: values of non-zero elements\n\n**Advantages**: Flexible, easy to build, supports fast incremental updates  \n**Disadvantages**: Slower matrix multiplication\n\n### 2.2 CSR (Compressed Sparse Row) Format\n\n**CSR format** compresses storage by row:\n- `data`: values of non-zero elements (arranged by row)\n- `indices`: column indices of non-zero elements\n- `indptr`: pointer array, `indptr[i]` indicates the starting position of row i\n\n**Advantages**: Fast row access, efficient matrix-vector multiplication  \n**Disadvantages**: Slower to build, not easy to modify\n\n### 2.3 CSC (Compressed Sparse Column) Format\n\n**CSC format** compresses storage by column (similar to CSR, but by column):\n- `data`: values of non-zero elements (arranged by column)\n- `indices`: row indices of non-zero elements\n- `indptr`: pointer array, `indptr[i]` indicates the starting position of column i\n\n**Advantages**: Fast column access, suitable for certain specific operations  \n**Disadvantages**: Similar to CSR"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": "## 3. Creating and using sparse matrices\n\n### 3.1 Creating COO matrix"
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-21T07:02:49.427662Z",
     "start_time": "2025-10-21T07:02:49.423107Z"
    }
   },
   "source": "# Example: Create a simple sparse matrix\n# Matrix shape: 4x5\n# Non-zero elements:\n#   (0, 1) = 1.5\n#   (1, 3) = 2.0\n#   (2, 0) = 0.5\n#   (3, 4) = 3.0\n\nrow = jnp.array([0, 1, 2, 3])\ncol = jnp.array([1, 3, 0, 4])\ndata = jnp.array([1.5, 2.0, 0.5, 3.0])\n\ncoo_matrix = brainevent.COO((data, row, col), shape=(4, 5))\n\nprint(\"COO matrix information:\")\nprint(f\"  shape: {coo_matrix.shape}\")\nprint(f\"  number of non-zero elements: {coo_matrix.nse}\")\nprint(f\"  data type: {coo_matrix.dtype}\")\nprint(f\"\\nDense form:\")\nprint(coo_matrix.todense())",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "COO matrix information:\n",
      "  shape: (4, 5)\n",
      "  number of non-zero elements: 4\n",
      "  data type: float32\n",
      "\n",
      "Dense form:\n",
      "[[0.  1.5 0.  0.  0. ]\n",
      " [0.  0.  0.  2.  0. ]\n",
      " [0.5 0.  0.  0.  0. ]\n",
      " [0.  0.  0.  0.  3. ]]\n"
     ]
    }
   ],
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": "### 3.2 Creating CSR matrix"
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-21T07:02:52.451153Z",
     "start_time": "2025-10-21T07:02:52.384084Z"
    }
   },
   "source": "# Directly create CSR matrix\n# Same matrix, using CSR format\n\ndata_csr = jnp.array([1.5, 2.0, 0.5, 3.0])\nindices_csr = jnp.array([1, 3, 0, 4])  # column indices\nindptr_csr = jnp.array([0, 1, 2, 3, 4])  # starting position of each row\n\ncsr_matrix = brainevent.CSR((data_csr, indices_csr, indptr_csr), shape=(4, 5))\n\nprint(\"CSR matrix information:\")\nprint(f\"  shape: {csr_matrix.shape}\")\nprint(f\"  number of non-zero elements: {csr_matrix.nse}\")\nprint(f\"  data: {csr_matrix.data}\")\nprint(f\"  indices: {csr_matrix.indices}\")\nprint(f\"  indptr: {csr_matrix.indptr}\")\nprint(f\"\\nDense form:\")\nprint(csr_matrix.todense())\n\n# Verify consistency with COO\nprint(f\"\\nConsistent with COO results: {jnp.allclose(coo_matrix.todense(), csr_matrix.todense())}\")",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CSR matrix information:\n",
      "  shape: (4, 5)\n",
      "  number of non-zero elements: 4\n",
      "  data: [1.5 2.  0.5 3. ]\n",
      "  indices: [1 3 0 4]\n",
      "  indptr: [0 1 2 3 4]\n",
      "\n",
      "Dense form:\n",
      "[[0.  1.5 0.  0.  0. ]\n",
      " [0.  0.  0.  2.  0. ]\n",
      " [0.5 0.  0.  0.  0. ]\n",
      " [0.  0.  0.  0.  3. ]]\n",
      "\n",
      "Consistent with COO results: True\n"
     ]
    }
   ],
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": "### 3.3 Creating CSC matrix"
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-21T07:02:55.160214Z",
     "start_time": "2025-10-21T07:02:55.102180Z"
    }
   },
   "source": "# Directly create CSC matrix\n# Column-wise storage format\n\n# Arrange data in column order\ndata_csc = jnp.array([0.5, 1.5, 2.0, 3.0])  # In order of columns 0,1,3,4\nindices_csc = jnp.array([2, 0, 1, 3])  # Corresponding row indices\nindptr_csc = jnp.array([0, 1, 2, 2, 3, 4])  # Starting position of each column (5 columns + 1)\n\ncsc_matrix = brainevent.CSC((data_csc, indices_csc, indptr_csc), shape=(4, 5))\n\nprint(\"CSC matrix information:\")\nprint(f\"  shape: {csc_matrix.shape}\")\nprint(f\"  number of non-zero elements: {csc_matrix.nse}\")\nprint(f\"  data: {csc_matrix.data}\")\nprint(f\"  indices: {csc_matrix.indices}\")\nprint(f\"  indptr: {csc_matrix.indptr}\")\nprint(f\"\\nDense form:\")\nprint(csc_matrix.todense())\n\n# Verify all three formats produce consistent results\nprint(f\"\\nAll three formats consistent: {jnp.allclose(coo_matrix.todense(), csc_matrix.todense())}\")",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CSC matrix information:\n",
      "  shape: (4, 5)\n",
      "  number of non-zero elements: 4\n",
      "  data: [0.5 1.5 2.  3. ]\n",
      "  indices: [2 0 1 3]\n",
      "  indptr: [0 1 2 2 3 4]\n",
      "\n",
      "Dense form:\n",
      "[[0.  1.5 0.  0.  0. ]\n",
      " [0.  0.  0.  2.  0. ]\n",
      " [0.5 0.  0.  0.  0. ]\n",
      " [0.  0.  0.  0.  3. ]]\n",
      "\n",
      "All three formats consistent: True\n"
     ]
    }
   ],
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": "## 4. Using with BinaryArray\n\nWhen sparse matrices are combined with BinaryArray, it implements **dual optimization**:\n1. Sparse matrices only store non-zero connections\n2. BinaryArray only computes for neurons that fire spikes\n\nThis combination is extremely efficient in spiking neural networks!"
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-21T07:03:01.058322Z",
     "start_time": "2025-10-21T07:02:58.167913Z"
    }
   },
   "source": "# Create a sparse connection weight matrix (100 -> 50 neurons)\nn_pre = 100\nn_post = 50\nconn_prob = 0.1  # 10% connection probability\n\n# Use brainstate.random to generate sparse connections\nbrainstate.random.seed(42)\n\n# Generate connection matrix mask\nmask = brainstate.random.bernoulli(conn_prob, size=(n_pre, n_post))\nweights_dense = brainstate.random.normal(size=(n_pre, n_post)) * 0.1 * mask\n\n# Convert to COO format\nrow_idx, col_idx = jnp.where(weights_dense != 0)\ndata = weights_dense[row_idx, col_idx]\ncoo_weights = brainevent.COO((data, row_idx, col_idx), shape=(n_pre, n_post))\n\n# Convert to CSR (rebuild from dense matrix)\n# Extract CSR format data\ncsr_data = []\ncsr_indices = []\ncsr_indptr = [0]\n\nfor i in range(n_pre):\n    row_data = weights_dense[i]\n    nz_indices = jnp.where(row_data != 0)[0]\n    csr_indices.extend(nz_indices.tolist())\n    csr_data.extend(row_data[nz_indices].tolist())\n    csr_indptr.append(len(csr_indices))\n\ncsr_weights = brainevent.CSR(\n    (jnp.array(csr_data), jnp.array(csr_indices), jnp.array(csr_indptr)),\n    shape=(n_pre, n_post)\n)\n\nprint(f\"Connection matrix: {n_pre} -> {n_post}\")\nprint(f\"Connection probability: {conn_prob*100}%\")\nprint(f\"Actual connections: {csr_weights.nse}\")\nprint(f\"Expected connections: {int(n_pre * n_post * conn_prob)}\")\nprint(f\"Sparsity: {csr_weights.nse / (n_pre * n_post) * 100:.2f}%\")",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Connection matrix: 100 -> 50\n",
      "Connection probability: 10.0%\n",
      "Actual connections: 542\n",
      "Expected connections: 500\n",
      "Sparsity: 10.84%\n"
     ]
    }
   ],
   "execution_count": 8
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-21T07:03:03.575775Z",
     "start_time": "2025-10-21T07:03:02.545098Z"
    }
   },
   "source": "# Generate input spikes (sparse)\nspike_rate = 0.05  # 5% firing rate\n\nbrainstate.random.seed(123)\nspikes_bool = brainstate.random.bernoulli(spike_rate, size=(n_pre,))\nspikes = brainevent.BinaryArray(spikes_bool)\n\nprint(f\"Input spikes:\")\nprint(f\"  Number of neurons: {n_pre}\")\nprint(f\"  Firing rate: {spike_rate*100}%\")\nprint(f\"  Actual firing: {spikes.sum()} neurons\")\n\n# Event-driven sparse matrix multiplication\npost_input = spikes @ csr_weights\n\nprint(f\"\\nPost-synaptic input:\")\nprint(f\"  shape: {post_input.shape}\")\nprint(f\"  maximum input: {post_input.max():.4f}\")\nprint(f\"  average input: {post_input.mean():.4f}\")\nprint(f\"  number of non-zero inputs: {jnp.sum(post_input != 0)}\")",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input spikes:\n",
      "  Number of neurons: 100\n",
      "  Firing rate: 5.0%\n",
      "  Actual firing: 6 neurons\n",
      "\n",
      "Post-synaptic input:\n",
      "  shape: (50,)\n",
      "  maximum input: 0.2411\n",
      "  average input: 0.0142\n",
      "  number of non-zero inputs: 23\n"
     ]
    }
   ],
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": "## 5. Performance comparison\n\nLet's compare the performance of sparse matrices and dense matrices in practical applications."
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-21T07:03:35.250975Z",
     "start_time": "2025-10-21T07:03:05.337638Z"
    }
   },
   "source": "import time\n\n# Large-scale network parameters\nn_pre = 5000\nn_post = 5000\nconn_prob = 0.05  # 5% connections\nspike_rate = 0.02  # 2% firing rate\n\n# Generate sparse weight matrix\nbrainstate.random.seed(0)\nmask = brainstate.random.bernoulli(conn_prob, size=(n_pre, n_post))\nweights_dense = brainstate.random.normal(size=(n_pre, n_post)) * 0.1 * mask\n\n# Create CSR format\ncsr_data = []\ncsr_indices = []\ncsr_indptr = [0]\n\nfor i in range(n_pre):\n    row_data = weights_dense[i]\n    nz_indices = jnp.where(row_data != 0)[0]\n    csr_indices.extend(nz_indices.tolist())\n    csr_data.extend(row_data[nz_indices].tolist())\n    csr_indptr.append(len(csr_indices))\n\ncsr_w = brainevent.CSR(\n    (jnp.array(csr_data), jnp.array(csr_indices), jnp.array(csr_indptr)),\n    shape=(n_pre, n_post)\n)\n\n# Generate input spikes\nbrainstate.random.seed(999)\nspikes_bool = brainstate.random.bernoulli(spike_rate, size=(n_pre,))\nspikes = brainevent.BinaryArray(spikes_bool)\n\nprint(f\"Test configuration:\")\nprint(f\"  Network size: {n_pre} -> {n_post}\")\nprint(f\"  Number of connections: {csr_w.nse}\")\nprint(f\"  Number of firing neurons: {spikes.sum()}\")\nprint(f\"\\nWarming up...\")\n\n# Warm-up\n_ = jax.block_until_ready(spikes @ csr_w)\n_ = jax.block_until_ready(spikes @ weights_dense)\n\nn_trials = 50\n\n# Test CSR\nstart = time.time()\nfor _ in range(n_trials):\n    result = jax.block_until_ready(spikes @ csr_w)\ncsr_time = (time.time() - start) / n_trials\n\n# Test dense matrix\nstart = time.time()\nfor _ in range(n_trials):\n    result = jax.block_until_ready(spikes @ weights_dense)\ndense_time = (time.time() - start) / n_trials\n\nprint(f\"\\nPerformance test results (average time):\")\nprint(f\"  CSR format:    {csr_time*1000:.3f} ms\")\nprint(f\"  Dense matrix:   {dense_time*1000:.3f} ms\")\nprint(f\"\\nSpeedup ratio:\")\nprint(f\"  CSR vs dense: {dense_time/csr_time:.2f}x\")\nprint(f\"\\nMemory comparison:\")\nprint(f\"  CSR: ~{csr_w.nse * 8 / 1024 / 1024:.2f} MB\")\nprint(f\"  Dense: ~{n_pre * n_post * 4 / 1024 / 1024:.2f} MB\")\nprint(f\"  Memory saved: {(1 - csr_w.nse / (n_pre * n_post)) * 100:.1f}%\")",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test configuration:\n",
      "  Network size: 5000 -> 5000\n",
      "  Number of connections: 1249192\n",
      "  Number of firing neurons: 110\n",
      "\n",
      "Warming up...\n",
      "\n",
      "Performance test results (average time):\n",
      "  CSR format:    0.020 ms\n",
      "  Dense matrix:   0.360 ms\n",
      "\n",
      "Speedup ratio:\n",
      "  CSR vs dense: 18.03x\n",
      "\n",
      "Memory comparison:\n",
      "  CSR: ~9.53 MB\n",
      "  Dense: ~95.37 MB\n",
      "  Memory saved: 95.0%\n"
     ]
    }
   ],
   "execution_count": 10
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": "## 6. Practice: Building a sparse connection neural network\n\nLet's build a real spiking neural network using sparse connections to improve efficiency."
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-21T07:03:58.209576Z",
     "start_time": "2025-10-21T07:03:50.022442Z"
    }
   },
   "source": "class SparseSpikingNetwork:\n    \"\"\"Spiking neural network using sparse connections\"\"\"\n    \n    def __init__(self, n_input, n_hidden, n_output, \n                 conn_prob=0.1, seed=0):\n        \"\"\"\n        Args:\n            n_input: number of input layer neurons\n            n_hidden: number of hidden layer neurons\n            n_output: number of output layer neurons\n            conn_prob: connection probability\n            seed: random seed\n        \"\"\"\n        self.n_input = n_input\n        self.n_hidden = n_hidden\n        self.n_output = n_output\n        \n        brainstate.random.seed(seed)\n        \n        # Create first layer sparse connections (input -> hidden)\n        mask1 = brainstate.random.bernoulli(conn_prob, size=(n_input, n_hidden))\n        w1_dense = brainstate.random.normal(size=(n_input, n_hidden)) * 0.1 * mask1\n        \n        # Convert to CSR\n        csr_data1 = []\n        csr_indices1 = []\n        csr_indptr1 = [0]\n        for i in range(n_input):\n            row = w1_dense[i]\n            nz = jnp.where(row != 0)[0]\n            csr_indices1.extend(nz.tolist())\n            csr_data1.extend(row[nz].tolist())\n            csr_indptr1.append(len(csr_indices1))\n        \n        self.w1 = brainevent.CSR(\n            (jnp.array(csr_data1), jnp.array(csr_indices1), jnp.array(csr_indptr1)),\n            shape=(n_input, n_hidden)\n        )\n        \n        # Create second layer sparse connections (hidden -> output)\n        mask2 = brainstate.random.bernoulli(conn_prob, size=(n_hidden, n_output))\n        w2_dense = brainstate.random.normal(size=(n_hidden, n_output)) * 0.1 * mask2\n        \n        # Convert to CSR\n        csr_data2 = []\n        csr_indices2 = []\n        csr_indptr2 = [0]\n        for i in range(n_hidden):\n            row = w2_dense[i]\n            nz = jnp.where(row != 0)[0]\n            csr_indices2.extend(nz.tolist())\n            csr_data2.extend(row[nz].tolist())\n            csr_indptr2.append(len(csr_indices2))\n        \n        self.w2 = brainevent.CSR(\n            (jnp.array(csr_data2), jnp.array(csr_indices2), jnp.array(csr_indptr2)),\n            shape=(n_hidden, n_output)\n        )\n        \n        print(f\"Network structure: {n_input} -> {n_hidden} -> {n_output}\")\n        print(f\"First layer connections: {self.w1.nse} / {n_input * n_hidden} ({self.w1.nse/(n_input*n_hidden)*100:.1f}%)\")\n        print(f\"Second layer connections: {self.w2.nse} / {n_hidden * n_output} ({self.w2.nse/(n_hidden*n_output)*100:.1f}%)\")\n    \n    def forward(self, input_spikes, threshold_hidden=0.3, threshold_output=0.5):\n        \"\"\"Forward propagation\"\"\"\n        # First layer\n        hidden_input = input_spikes @ self.w1\n        hidden_spikes = brainevent.BinaryArray(hidden_input > threshold_hidden)\n        \n        # Second layer\n        output_input = hidden_spikes @ self.w2\n        output_spikes = brainevent.BinaryArray(output_input > threshold_output)\n        \n        return output_input, output_spikes, hidden_spikes\n\n# Create network\nnetwork = SparseSpikingNetwork(\n    n_input=500,\n    n_hidden=200,\n    n_output=10,\n    conn_prob=0.15,\n    seed=42\n)",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Network structure: 500 -> 200 -> 10\n",
      "First layer connections: 15017 / 100000 (15.0%)\n",
      "Second layer connections: 312 / 2000 (15.6%)\n"
     ]
    }
   ],
   "execution_count": 11
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-21T07:04:02.915011Z",
     "start_time": "2025-10-21T07:04:01.101597Z"
    }
   },
   "source": "# Test network\nn_samples = 100\n\n# Record statistics\ninput_counts = []\nhidden_counts = []\noutput_counts = []\noutput_activities = []\n\nbrainstate.random.seed(999)\nfor i in range(n_samples):\n    # Generate random input spikes\n    input_pattern = brainstate.random.bernoulli(0.1, size=(500,))\n    input_spikes = brainevent.BinaryArray(input_pattern)\n    \n    # Forward propagation\n    output_act, output_spk, hidden_spk = network.forward(input_spikes)\n    \n    # Record statistics\n    input_counts.append(int(input_spikes.sum()))\n    hidden_counts.append(int(hidden_spk.sum()))\n    output_counts.append(int(output_spk.sum()))\n    output_activities.append(output_act)\n\n# Statistical analysis\nprint(f\"Tested {n_samples} samples:\")\nprint(f\"\\nInput layer:\")\nprint(f\"  Average firing: {np.mean(input_counts):.1f} / 500 ({np.mean(input_counts)/500*100:.1f}%)\")\nprint(f\"  Firing range: [{min(input_counts)}, {max(input_counts)}]\")\n\nprint(f\"\\nHidden layer:\")\nprint(f\"  Average firing: {np.mean(hidden_counts):.1f} / 200 ({np.mean(hidden_counts)/200*100:.1f}%)\")\nprint(f\"  Firing range: [{min(hidden_counts)}, {max(hidden_counts)}]\")\n\nprint(f\"\\nOutput layer:\")\nprint(f\"  Average firing: {np.mean(output_counts):.1f} / 10 ({np.mean(output_counts)/10*100:.1f}%)\")\nprint(f\"  Firing range: [{min(output_counts)}, {max(output_counts)}]\")",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tested 100 samples:\n",
      "\n",
      "Input layer:\n",
      "  Average firing: 50.5 / 500 (10.1%)\n",
      "  Firing range: [37, 67]\n",
      "\n",
      "Hidden layer:\n",
      "  Average firing: 27.1 / 200 (13.6%)\n",
      "  Firing range: [13, 41]\n",
      "\n",
      "Output layer:\n",
      "  Average firing: 0.2 / 10 (1.9%)\n",
      "  Firing range: [0, 2]\n"
     ]
    }
   ],
   "execution_count": 12
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": "## 7. Visualizing sparse connection structures"
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-21T07:04:11.518116Z",
     "start_time": "2025-10-21T07:04:11.080459Z"
    }
   },
   "source": "import matplotlib.pyplot as plt\n\n# Extract dense form of weight matrices\nw1_dense = network.w1.todense()\nw2_dense = network.w2.todense()\n\n# Create figure\nfig, axes = plt.subplots(1, 2, figsize=(16, 6))\n\n# First layer weight connection pattern\nw1_binary = np.array(w1_dense != 0, dtype=int)\nim1 = axes[0].imshow(w1_binary, aspect='auto', cmap='binary', interpolation='nearest')\naxes[0].set_title(f'Layer 1 Connectivity Pattern\\n{network.w1.nse} connections ({network.w1.nse/(500*200)*100:.1f}% density)',\n                 fontsize=13, fontweight='bold')\naxes[0].set_xlabel('Hidden Neurons (200)', fontsize=11)\naxes[0].set_ylabel('Input Neurons (500)', fontsize=11)\naxes[0].grid(False)\n\n# Add sparsity statistics\nsparsity1 = 100 - (network.w1.nse / (500 * 200) * 100)\naxes[0].text(0.02, 0.98, f'Sparsity: {sparsity1:.1f}%',\n            transform=axes[0].transAxes,\n            fontsize=10, verticalalignment='top',\n            bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n\n# Second layer weight connection pattern\nw2_binary = np.array(w2_dense != 0, dtype=int)\nim2 = axes[1].imshow(w2_binary, aspect='auto', cmap='binary', interpolation='nearest')\naxes[1].set_title(f'Layer 2 Connectivity Pattern\\n{network.w2.nse} connections ({network.w2.nse/(200*10)*100:.1f}% density)',\n                 fontsize=13, fontweight='bold')\naxes[1].set_xlabel('Output Neurons (10)', fontsize=11)\naxes[1].set_ylabel('Hidden Neurons (200)', fontsize=11)\naxes[1].grid(False)\n\n# Add sparsity statistics\nsparsity2 = 100 - (network.w2.nse / (200 * 10) * 100)\naxes[1].text(0.02, 0.98, f'Sparsity: {sparsity2:.1f}%',\n            transform=axes[1].transAxes,\n            fontsize=10, verticalalignment='top',\n            bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n\nplt.tight_layout()\nplt.show()\n\n# Print connection statistics\nprint(f\"\\nConnection pattern analysis:\")\nprint(f\"  Layer 1: {network.w1.nse:,} connections, {sparsity1:.2f}% sparse\")\nprint(f\"  Layer 2: {network.w2.nse:,} connections, {sparsity2:.2f}% sparse\")\nprint(f\"  Total parameters: {network.w1.nse + network.w2.nse:,}\")\nprint(f\"  Saved memory vs dense: {((500*200 + 200*10) - (network.w1.nse + network.w2.nse)) / (500*200 + 200*10) * 100:.1f}%\")\nprint(f\"\\nLegend: Black = connected, White = not connected\")",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1600x600 with 2 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Connection pattern analysis:\n",
      "  Layer 1: 15,017 connections, 84.98% sparse\n",
      "  Layer 2: 312 connections, 84.40% sparse\n",
      "  Total parameters: 15,329\n",
      "  Saved memory vs dense: 85.0%\n",
      "\n",
      "Legend: Black = connected, White = not connected\n"
     ]
    }
   ],
   "execution_count": 13
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-21T07:04:18.603336Z",
     "start_time": "2025-10-21T07:04:16.872030Z"
    }
   },
   "source": "# Record spike activity over multiple time steps\nn_timesteps = 100\nspike_history_input = []\nspike_history_hidden = []\nspike_history_output = []\n\nbrainstate.random.seed(888)\nfor t in range(n_timesteps):\n    # Generate input spikes\n    input_pattern = brainstate.random.bernoulli(0.1, size=(500,))\n    input_spikes = brainevent.BinaryArray(input_pattern)\n\n    # Forward propagation\n    output_act, output_spk, hidden_spk = network.forward(input_spikes)\n\n    # Record first 50 neurons' activity (for visualization)\n    spike_history_input.append(np.array(input_pattern[:50], dtype=int))\n    spike_history_hidden.append(np.array(hidden_spk.value[:50], dtype=int))\n    spike_history_output.append(np.array(output_spk.value, dtype=int))\n\n# Convert to time×neuron matrix\nspike_matrix_input = np.array(spike_history_input)  # (100, 50)\nspike_matrix_hidden = np.array(spike_history_hidden)  # (100, 50)\nspike_matrix_output = np.array(spike_history_output)  # (100, 10)\n\n# Use braintools.visualize.raster_plot to plot spike raster\nfig, axes = plt.subplots(3, 1, figsize=(14, 10))\n\n# Input layer spikes\nts = np.arange(n_timesteps)\nax = plt.subplot(3, 1, 1)\nbraintools.visualize.raster_plot(\n    ts,\n    spike_matrix_input,\n    markersize=3,\n    ax=ax,\n    xlim=(0, n_timesteps),\n    ylim=(-1, 50),\n    xlabel='Time Step',\n    ylabel='Input Neuron ID (first 50)',\n    title=f'Input Layer Spike Raster (Avg rate: {spike_matrix_input.mean():.2%})',\n    show=False\n)\n\n# Hidden layer spikes\nax = plt.subplot(3, 1, 2)\nbraintools.visualize.raster_plot(\n    ts,\n    spike_matrix_hidden,\n    markersize=3,\n    ax=ax,\n    xlim=(0, n_timesteps),\n    ylim=(-1, 50),\n    xlabel='Time Step',\n    ylabel='Hidden Neuron ID (first 50)',\n    title=f'Hidden Layer Spike Raster (Avg rate: {spike_matrix_hidden.mean():.2%})',\n    show=False\n)\n\n# Output layer spikes\nax = plt.subplot(3, 1, 3)\nbraintools.visualize.raster_plot(\n    ts,\n    spike_matrix_output,\n    markersize=5,\n    ax=ax,\n    xlim=(0, n_timesteps),\n    ylim=(-1, 10),\n    xlabel='Time Step',\n    ylabel='Output Neuron ID',\n    title=f'Output Layer Spike Raster (Avg rate: {spike_matrix_output.mean():.2%})',\n    show=False\n)\n\nplt.tight_layout()\nplt.show()\n\nprint(f\"\\nSpike statistics:\")\nprint(f\"  Input layer: {spike_matrix_input.sum()} spikes over {n_timesteps} timesteps\")\nprint(f\"  Hidden layer: {spike_matrix_hidden.sum()} spikes over {n_timesteps} timesteps\")\nprint(f\"  Output layer: {spike_matrix_output.sum()} spikes over {n_timesteps} timesteps\")",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1400x1000 with 3 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Spike statistics:\n",
      "  Input layer: 498 spikes over 100 timesteps\n",
      "  Hidden layer: 631 spikes over 100 timesteps\n",
      "  Output layer: 13 spikes over 100 timesteps\n"
     ]
    }
   ],
   "execution_count": 14
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": "## 8. Format selection guide\n\n### When to use COO?\n- ✅ Building phase (flexible element addition)\n- ✅ Frequent matrix modifications needed\n- ✅ Intermediate step for conversion to other formats\n\n### When to use CSR?\n- ✅ **Matrix-vector multiplication** (most common!)\n- ✅ Row-wise data access\n- ✅ Spiking neural network forward propagation\n- ✅ BinaryArray @ CSR operations\n\n### When to use CSC?\n- ✅ Column-wise data access\n- ✅ Certain special algorithms (e.g., solving linear systems)\n- ✅ Efficient column slicing operations needed\n\n**Recommendation**: For most spiking neural network applications, use **CSR format** combined with **BinaryArray**!"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9. Summary\n",
    "\n",
    "In this tutorial, we learned:\n",
    "\n",
    "1. ✅ **Necessity of sparse matrices**: Memory and computational efficiency\n",
    "2. ✅ **Three formats**: Principles and characteristics of COO, CSR, CSC\n",
    "3. ✅ **Creation and usage**: How to create and operate sparse matrices\n",
    "4. ✅ **Combination with BinaryArray**: Dual optimization strategy\n",
    "5. ✅ **Performance comparison**: Actual performance advantages of sparse matrices\n",
    "6. ✅ **Practical application**: Building a sparse connection spiking neural network\n",
    "7. ✅ **Visualization**: Visualizing sparse structures with braintools and matplotlib\n",
    "8. ✅ **Format selection**: Choosing the appropriate format based on application scenarios\n",
    "\n",
    "## Next Steps\n",
    "\n",
    "In the next tutorial, we will learn:\n",
    "- 📚 **Tutorial 3**: JIT connection matrices - JITCHomoR, JITCNormalR, JITCUniformR\n",
    "- Learn about just-in-time compiled connection structures without pre-storing weight matrices\n",
    "- Suitable for ultra-large-scale network modeling"
   ]
  }
 ],
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   "name": "python",
   "version": "3.10.0"
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