Add SVD example

Author: gjbex

source-code/gpu/scikit_cuda.ipynb

@@ -18,24 +18,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "id": "f95a5430-cc82-4e33-9d25-066e558c87b8",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/home/gjb/miniconda3/envs/cuda/lib/python3.9/site-packages/skcuda/cublas.py:284: UserWarning: creating CUBLAS context to get version number\n",
-      "  warnings.warn('creating CUBLAS context to get version number')\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import pycuda.autoinit\n",
     "from pycuda import gpuarray\n",
     "from skcuda import cublas\n",
+    "from skcuda import linalg\n",
     "import sys\n",
     "from time import time"
    ]
@@ -505,7 +497,9 @@
   {
    "cell_type": "markdown",
    "id": "89d7ce40-e25b-4f7c-ae7a-3e67b580486c",
-   "metadata": {},
+   "metadata": {
+    "tags": []
+   },
    "source": [
     "### Benchmarking"
    ]
@@ -702,6 +696,161 @@
    "source": [
     "dev_time"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dfb43514-7195-4292-b1df-f1a6eb4eb9e0",
+   "metadata": {},
+   "source": [
+    "# CuSolver"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d05fb7e8-8064-4159-b4de-3a230bf0e8ff",
+   "metadata": {},
+   "source": [
+    "The CuSolver library contains many algorithms for linear algebra such as matrix decomposition, linear regression and solving systems of linear equations."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "133f7314-bc89-4785-b829-b4b0b5de9abd",
+   "metadata": {},
+   "source": [
+    "## Singular Value Decomposition (SVD)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "348a5c76-aa59-461a-947a-babc0b55a29a",
+   "metadata": {},
+   "source": [
+    "To illustrate some aspects of the library's usage, we will perform a Singular Value Decomposition (SVD) of a large square matrix $A$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "e8c1b888-702c-4ef7-ae2b-afa3ebe92456",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A_nr_rows, A_nr_cols = 2_000, 2_000\n",
+    "A = np.random.uniform(size=(A_nr_rows, A_nr_cols)).astype(np.float32)\n",
+    "A_dev = gpuarray.to_gpu(A)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eb0272e4-6d23-441c-957b-53a9652bd294",
+   "metadata": {},
+   "source": [
+    "### Initialization"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eb92dd10-b5ba-422f-9969-2bb81afa026e",
+   "metadata": {},
+   "source": [
+    "The `linalg` module has to be initialized before it is used to perform computations."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "9ed7e255-9e73-48e5-a392-6ff9796f0390",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "linalg.init()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "100c5d2d-59ad-4992-be0e-4541d66341f2",
+   "metadata": {},
+   "source": [
+    "### Computation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2a00e713-2914-463a-a19b-af7a6a9cbce4",
+   "metadata": {},
+   "source": [
+    "Now we can perform the SVD of the matrix $A$ which results in two device matrices $U$ and $V^t$ as well as a vector $s$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "54715e9a-cbb6-4704-942a-00089ea6dd75",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "U_dev, s_dev, Vt_dev = linalg.svd(A_dev, lib='cusolver')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1df63456-9965-4014-81aa-210e85ac3371",
+   "metadata": {},
+   "source": [
+    "Getting the vector and matrices from the device, we can verify the decomposition by reconstructing $A$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "03db8ca2-a606-48e2-8550-7f624d28cc1f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "U, s, Vt = U_dev.get(), s_dev.get(), Vt_dev.get()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "528acf0f-8aa6-4abd-bccf-6601617810ab",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "S = np.diag(s)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "1fbb598e-8e16-4922-b695-42cf5c903e97",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A_reconstructed = U @ S @ Vt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "ff57f0de-b88a-4099-b013-56d9ca656977",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.allclose(A, A_reconstructed, atol=1.0e-4)"
+   ]
   }
  ],
  "metadata": {