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Memory Spaces - Power Iteration - SOLUTION: Fix %timeit synchronization and regenerate output.
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Lines changed: 198 additions & 24 deletions

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‎notebooks/5__memory_spaces__power_iteration__SOLUTION.ipynb‎

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"metadata": {
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"id": "ZHpg3aVXSeix"
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},
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"execution_count": null,
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"execution_count": 1,
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"outputs": []
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},
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{
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"metadata": {
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"id": "BCToOdVdSONp"
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},
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"execution_count": null,
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"execution_count": 2,
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"outputs": []
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 3,
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"metadata": {
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"id": "5ak3mn2hIsKo"
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"id": "5ak3mn2hIsKo",
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"outputId": "0d415d45-535a-4a2d-e757-f0c4a7a1efb0",
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"colab": {
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"base_uri": "https://localhost:8080/"
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}
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},
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"outputs": [],
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"[[-0.4937 -0.519 -0.2935 ... -0.1628 0.8361 0.531 ]\n",
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" [-1.0859 0.0087 -0.0661 ... -0.1706 1.0955 0.7075]\n",
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" [-0.4291 -0.3628 0.3393 ... 0.1813 0.2238 -0.2124]\n",
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" ...\n",
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" [-1.1089 -0.4564 -0.3024 ... 0.2075 1.2864 0.9066]\n",
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" [-0.8714 -0.5109 -0.1201 ... -0.072 1.3048 0.4372]\n",
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" [-1.6421 -0.6629 -0.2001 ... -0.2997 1.8579 1.5576]]\n"
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]
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}
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],
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"source": [
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"def generate_host(cfg=PowerIterationConfig()):\n",
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" np.random.seed(42)\n",
@@ -150,10 +168,44 @@
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"print(lam_est_host)"
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],
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"metadata": {
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"id": "q0x0_p4pvAdD"
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"id": "q0x0_p4pvAdD",
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"outputId": "78e0d606-1d79-4a89-8bcc-79dd9282f4cf",
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"colab": {
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"base_uri": "https://localhost:8080/"
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}
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},
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"execution_count": null,
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"outputs": []
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"execution_count": 4,
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"step 0: residual = 7.594e+00\n",
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"step 10: residual = 1.699e-02\n",
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"step 20: residual = 2.148e-02\n",
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"step 30: residual = 1.295e-02\n",
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"step 40: residual = 4.494e-03\n",
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"step 50: residual = 1.366e-03\n",
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"step 60: residual = 4.129e-04\n",
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"step 70: residual = 1.274e-04\n",
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"step 80: residual = 4.013e-05\n",
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"step 90: residual = 1.286e-05\n",
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"step 100: residual = 4.181e-06\n",
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"step 110: residual = 1.374e-06\n",
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"step 120: residual = 4.550e-07\n",
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"step 130: residual = 1.517e-07\n",
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"step 140: residual = 5.085e-08\n",
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"step 150: residual = 1.712e-08\n",
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"step 160: residual = 5.784e-09\n",
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"step 170: residual = 1.961e-09\n",
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"step 180: residual = 6.655e-10\n",
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"step 190: residual = 2.269e-10\n",
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"step 200: residual = 7.746e-11\n",
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"\n",
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"0.9999999999604734\n"
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]
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}
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]
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},
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{
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"cell_type": "markdown",
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"print(lam_est_device)"
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],
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"metadata": {
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"id": "sulx6gabBd1w"
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"id": "sulx6gabBd1w",
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"outputId": "2b929e25-6bd7-4533-bf93-1a7d1f912f00",
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"colab": {
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"base_uri": "https://localhost:8080/"
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}
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},
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"execution_count": null,
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"outputs": []
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"execution_count": 5,
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"step 0: residual = 7.594e+00\n",
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"step 10: residual = 1.699e-02\n",
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"step 20: residual = 2.148e-02\n",
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"step 30: residual = 1.295e-02\n",
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"step 40: residual = 4.494e-03\n",
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"step 50: residual = 1.366e-03\n",
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"step 60: residual = 4.129e-04\n",
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"step 70: residual = 1.274e-04\n",
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"step 80: residual = 4.013e-05\n",
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"step 90: residual = 1.286e-05\n",
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"step 100: residual = 4.181e-06\n",
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"step 110: residual = 1.374e-06\n",
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"step 120: residual = 4.550e-07\n",
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"step 130: residual = 1.517e-07\n",
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"step 140: residual = 5.085e-08\n",
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"step 150: residual = 1.712e-08\n",
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"step 160: residual = 5.784e-09\n",
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"step 170: residual = 1.960e-09\n",
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"step 180: residual = 6.659e-10\n",
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"step 190: residual = 2.269e-10\n",
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"step 200: residual = 7.736e-11\n",
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"\n",
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"0.9999999999593268\n"
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]
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}
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]
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},
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{
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"cell_type": "markdown",
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"print(lam_est_device_generation)"
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],
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"metadata": {
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"id": "HXFZXGhU1Xj2"
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"id": "HXFZXGhU1Xj2",
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"outputId": "fd52bba4-839b-42c6-c7d3-80d1a39f80e3",
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"colab": {
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"base_uri": "https://localhost:8080/"
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}
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},
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"execution_count": null,
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"outputs": []
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"execution_count": 6,
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"A_host:\n",
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"[[-0.4937 -0.519 -0.2935 ... -0.1628 0.8361 0.531 ]\n",
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" [-1.0859 0.0087 -0.0661 ... -0.1706 1.0955 0.7075]\n",
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" [-0.4291 -0.3628 0.3393 ... 0.1813 0.2238 -0.2124]\n",
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" ...\n",
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" [-1.1089 -0.4564 -0.3024 ... 0.2075 1.2864 0.9066]\n",
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" [-0.8714 -0.5109 -0.1201 ... -0.072 1.3048 0.4372]\n",
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" [-1.6421 -0.6629 -0.2001 ... -0.2997 1.8579 1.5576]]\n",
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"\n",
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"A_device:\n",
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"[[-0.3175 -0.227 0.0765 ... -0.2411 0.9861 -0.6663]\n",
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" [-1.8135 -0.6378 -0.4466 ... -0.4503 3.2291 -1.3058]\n",
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" [-0.6443 0.3033 0.9719 ... 0.1302 0.4531 -0.3723]\n",
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" ...\n",
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" [-1.8697 -0.7714 -0.2048 ... 0.0244 2.859 -1.1147]\n",
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" [-1.1404 -0.9935 -0.4077 ... -0.2789 2.8553 -0.7879]\n",
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" [-0.5979 -0.6596 0.1047 ... -0.1826 1.4195 -0.0636]]\n",
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"\n",
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"step 0: residual = 2.346e+01\n",
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"step 10: residual = 2.859e-02\n",
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"step 20: residual = 2.984e-02\n",
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"step 30: residual = 1.433e-02\n",
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"step 40: residual = 5.035e-03\n",
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"step 50: residual = 1.643e-03\n",
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"step 60: residual = 5.309e-04\n",
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"step 70: residual = 1.726e-04\n",
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"step 80: residual = 5.663e-05\n",
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"step 90: residual = 1.875e-05\n",
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"step 100: residual = 6.253e-06\n",
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"step 110: residual = 2.098e-06\n",
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"step 120: residual = 7.077e-07\n",
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"step 130: residual = 2.396e-07\n",
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"step 140: residual = 8.140e-08\n",
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"step 150: residual = 2.772e-08\n",
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"step 160: residual = 9.461e-09\n",
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"step 170: residual = 3.234e-09\n",
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"step 180: residual = 1.107e-09\n",
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"step 190: residual = 3.792e-10\n",
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"step 200: residual = 1.299e-10\n",
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"step 210: residual = 4.454e-11\n",
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"\n",
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"0.9999999999558278\n"
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]
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}
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "fL7QYIVesehd"
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},
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"execution_count": null,
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"execution_count": 7,
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"outputs": []
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},
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{
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"np.testing.assert_allclose(lam_est_device, lam_ref, rtol=1e-4)"
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],
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"metadata": {
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"id": "7E7MUYsYsjwO"
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"id": "7E7MUYsYsjwO",
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"outputId": "b9e3bb4e-f9d9-4311-ba18-5896be23eb8e",
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"colab": {
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"base_uri": "https://localhost:8080/"
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}
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},
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"execution_count": null,
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"outputs": []
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"execution_count": 8,
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"Solution\n",
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"\n",
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"Power iteration (host) = 1.000000e+00\n",
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"Power iteration (device) = 1.000000e+00\n",
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"`eigvals` reference = 1.000000e+00\n",
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"\n",
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"Relative error (host) = 3.938e-11\n",
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"Relative error (device) = 4.053e-11\n"
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]
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}
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]
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},
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{
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"cell_type": "markdown",
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"print(f\"Execution Time\")\n",
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"print()\n",
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"\n",
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"time_host = %timeit -q -o estimate_host(A_host, PowerIterationConfig(progress=False))\n",
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"time_host = %timeit -q -o estimate_host(A_host, PowerIterationConfig(progress=False)).item()\n",
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"print(f\"Power iteration (host) = {time_host}\")\n",
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"\n",
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"# We intentionally use `A_host`, not `A_device`, because they're not\n",
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"# the same matrices due to differences in NumPy and CuPy's random facilities.\n",
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"time_device = %timeit -q -o estimate_device(A_host, PowerIterationConfig(progress=False))\n",
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"time_device = %timeit -q -o estimate_device(A_host, PowerIterationConfig(progress=False)).item()\n",
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"print(f\"Power iteration (device) = {time_device}\")\n",
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"\n",
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"time_ref = %timeit -q -o -r 1 -n 1 np.linalg.eigvals(A_host).real.max()\n",
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"print(f\"`eigvals` reference = {time_ref}\")"
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],
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"metadata": {
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"id": "v_2HmcBFERhE"
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"id": "v_2HmcBFERhE",
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"outputId": "43c4da5f-6164-4088-ac5e-685f26b58c95",
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"colab": {
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"base_uri": "https://localhost:8080/"
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}
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},
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"execution_count": null,
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"outputs": []
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"execution_count": 9,
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"outputs": [
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{
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"Execution Time\n",
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"\n",
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"Power iteration (host) = 2.38 s ± 382 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
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"Power iteration (device) = 324 ms ± 7.39 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
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"`eigvals` reference = 49.1 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
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]
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}
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]
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}
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]
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}
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}

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