Basics of PyTorch (Autograd, mm modules, Distributions, etc.).ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[],"authorship_tag":"ABX9TyNpVUdGDk2eUgvC23V4reTW"},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"code","execution_count":2,"metadata":{"id":"BmvFWAsRTlYi","executionInfo":{"status":"ok","timestamp":1710331434951,"user_tz":240,"elapsed":5376,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"outputs":[],"source":["#Sampling Tensors\n","import torch"]},{"cell_type":"code","source":["#random sampling of tensors\n","torch.manual_seed(1234)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"OMtxMCyGTtV5","executionInfo":{"status":"ok","timestamp":1710274606948,"user_tz":240,"elapsed":5,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"bdd1f16c-a278-4594-db60-7c7ea1214741"},"execution_count":2,"outputs":[{"output_type":"execute_result","data":{"text/plain":["<torch._C.Generator at 0x7f2e785a55d0>"]},"metadata":{},"execution_count":2}]},{"cell_type":"code","source":["torch.rand(4,4)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Vgw9gobzT3VW","executionInfo":{"status":"ok","timestamp":1710274623001,"user_tz":240,"elapsed":274,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"5d7c55f9-20fa-406a-fc10-35d95ee49393"},"execution_count":3,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[0.0290, 0.4019, 0.2598, 0.3666],\n","        [0.0583, 0.7006, 0.0518, 0.4681],\n","        [0.6738, 0.3315, 0.7837, 0.5631],\n","        [0.7749, 0.8208, 0.2793, 0.6817]])"]},"metadata":{},"execution_count":3}]},{"cell_type":"code","source":["#uniform random sampling for tensor\n","torch.Tensor(4,4).uniform_(0,1)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"JnCVNZ2QT7OP","executionInfo":{"status":"ok","timestamp":1710274679462,"user_tz":240,"elapsed":4,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"a70bf49d-148a-42be-f02d-d7bcc37887de"},"execution_count":5,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[0.2837, 0.6567, 0.2388, 0.7313],\n","        [0.6012, 0.3043, 0.2548, 0.6294],\n","        [0.9665, 0.7399, 0.4517, 0.4757],\n","        [0.7842, 0.1525, 0.6662, 0.3343]])"]},"metadata":{},"execution_count":5}]},{"cell_type":"code","source":["#Bernoulli distribution\n","torch.bernoulli(torch.Tensor(4,4).uniform_(0,1))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"lW8rB10xUHHU","executionInfo":{"status":"ok","timestamp":1710274749592,"user_tz":240,"elapsed":232,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"1873e7d8-4cdf-4b63-c3cc-98762bdc1a72"},"execution_count":6,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[0., 0., 0., 0.],\n","        [1., 0., 1., 0.],\n","        [1., 0., 1., 1.],\n","        [0., 0., 0., 0.]])"]},"metadata":{},"execution_count":6}]},{"cell_type":"code","source":["# multinomial distribution picks up without a replacement\n","torch.Tensor([12,23,34,45,56,67,78,89,90])"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"OwusI5gyUaHo","executionInfo":{"status":"ok","timestamp":1710274826636,"user_tz":240,"elapsed":209,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"c8c856f8-6981-494d-e771-fdbd5bd3f203"},"execution_count":7,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([12., 23., 34., 45., 56., 67., 78., 89., 90.])"]},"metadata":{},"execution_count":7}]},{"cell_type":"code","source":["torch.multinomial(torch.tensor([12. ,23. ,34. ,\n","                                45. , 56. ,67. ,\n","                                78. ,89. ,90. ]),\n","                  3)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"lLUBszD9Us8P","executionInfo":{"status":"ok","timestamp":1710274973994,"user_tz":240,"elapsed":5,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"ce104d34-7a8c-4b1e-a9ab-16a160138dd3"},"execution_count":9,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([7, 6, 5])"]},"metadata":{},"execution_count":9}]},{"cell_type":"code","source":["torch.multinomial(torch.tensor([12. ,23. ,34. ,\n","                                45. , 56. ,67. ,\n","                                78. ,89. ,90. ]),\n","                  3, replacement=True)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"fbip7cXLVIKh","executionInfo":{"status":"ok","timestamp":1710275001202,"user_tz":240,"elapsed":192,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"c06487b5-dde9-4248-c1ad-b6d654530bc3"},"execution_count":10,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([1, 6, 5])"]},"metadata":{},"execution_count":10}]},{"cell_type":"code","source":["#creating a set of random weights generated from a normal distribution.\n","torch.normal(mean=torch.arange(1.,11.),\n","             std=torch.arange(1,0,-0.1))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"37exabFlVXh3","executionInfo":{"status":"ok","timestamp":1710275167765,"user_tz":240,"elapsed":3,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"d2261290-7309-45d1-983e-403943d393ba"},"execution_count":13,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([ 2.2826,  2.1101,  3.3422,  4.2391,  5.6165,  6.5432,  6.4072,  7.8412,\n","         8.9324, 10.0984])"]},"metadata":{},"execution_count":13}]},{"cell_type":"code","source":["torch.normal(mean=3.14,std=torch.arange(0.2,0.67789))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"GZVVZl6SVyGB","executionInfo":{"status":"ok","timestamp":1710319692185,"user_tz":240,"elapsed":493,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"fc4530bd-8fb5-4ce4-f3d1-ba2220559a50"},"execution_count":3,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([3.1352])"]},"metadata":{},"execution_count":3}]},{"cell_type":"code","source":["#Variable Tensors (RANDOM VARIABLE IN PyTorch)\n","#imoplementation of Autograd module\n","from torch.autograd import Variable"],"metadata":{"id":"jbQNxPn9WPS6","executionInfo":{"status":"ok","timestamp":1710319949180,"user_tz":240,"elapsed":4,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"execution_count":4,"outputs":[]},{"cell_type":"code","source":["Variable(torch.ones(2,2),requires_grad=True)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"_M0UpnU1A1O4","executionInfo":{"status":"ok","timestamp":1710319999639,"user_tz":240,"elapsed":3,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"b2b07946-8435-450d-cb99-b42e85b92e61"},"execution_count":5,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[1., 1.],\n","        [1., 1.]], requires_grad=True)"]},"metadata":{},"execution_count":5}]},{"cell_type":"code","source":["a,b=12,23\n","x1=Variable(torch.randn(a,b),requires_grad=True)\n","x2=Variable(torch.randn(a,b),requires_grad=True)\n","x3=Variable(torch.randn(a,b),requires_grad=True)"],"metadata":{"id":"LJH4hbCJBBej","executionInfo":{"status":"ok","timestamp":1710320095084,"user_tz":240,"elapsed":235,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"execution_count":6,"outputs":[]},{"cell_type":"code","source":["c=x2*x1\n","d=a+x2\n","e=torch.sum(d)\n","e.backward()\n","print(e)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"0wCfGyICBY0U","executionInfo":{"status":"ok","timestamp":1710320149350,"user_tz":240,"elapsed":4,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"9b243e34-de2f-4f53-f9f4-05adbd7b1120"},"execution_count":7,"outputs":[{"output_type":"stream","name":"stdout","text":["tensor(3330.1995, grad_fn=<SumBackward0>)\n"]}]},{"cell_type":"code","source":["#introductory statistic in tensors (mean, median, mode). NOTE Torch functions have GPU acceleration\n","#mean for 1D tensor\n","torch.mean(torch.tensor([12.,23.,34.,45.,56.,67.,78.,89.,90.]))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Wm7h8ZEbBmFV","executionInfo":{"status":"ok","timestamp":1710320525783,"user_tz":240,"elapsed":233,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"40602c2e-dffe-49ed-9b17-7dd905295b4d"},"execution_count":8,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor(54.8889)"]},"metadata":{},"execution_count":8}]},{"cell_type":"code","source":["#mean across rows and columns of multi-dimension tensors\n","d=torch.randn(5,5)\n","d"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"1OF_sz-PDB-P","executionInfo":{"status":"ok","timestamp":1710320588284,"user_tz":240,"elapsed":523,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"3e49dcb8-f7de-429f-c975-695b469c4acd"},"execution_count":10,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[ 1.4786,  0.2932, -0.6198, -0.6926, -0.5230],\n","        [ 0.0277,  0.0033, -1.2944, -1.2800,  0.5592],\n","        [-0.7738, -0.0886,  0.1204,  0.7204,  0.3337],\n","        [-1.1497,  0.7606, -1.9451, -1.8636, -0.2904],\n","        [ 0.5290, -0.4065,  0.1078, -0.4989, -0.4873]])"]},"metadata":{},"execution_count":10}]},{"cell_type":"code","source":["torch.mean(d,dim=0)#mean along row"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"EWlqlOzQDOof","executionInfo":{"status":"ok","timestamp":1710320602610,"user_tz":240,"elapsed":3,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"34199e91-677f-42cf-98ad-25ee60b7fc77"},"execution_count":11,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([ 0.0224,  0.1124, -0.7262, -0.7230, -0.0816])"]},"metadata":{},"execution_count":11}]},{"cell_type":"code","source":["torch.mean(d,dim=1)#mean along col"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"zov8wl-PDUtg","executionInfo":{"status":"ok","timestamp":1710320619068,"user_tz":240,"elapsed":3,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"d10dddfc-5fbd-4d0a-8c7d-484ca2afdf95"},"execution_count":12,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([-0.0127, -0.3968,  0.0624, -0.8976, -0.1512])"]},"metadata":{},"execution_count":12}]},{"cell_type":"code","source":["#median\n","torch.median(d,dim=0)#mean along row\n","torch.median(d,dim=1)#mean along col"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"k0o3QPzxDYv1","executionInfo":{"status":"ok","timestamp":1710320660525,"user_tz":240,"elapsed":4,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"9f3ee82e-9d74-4fa4-97fc-efe47a92ae78"},"execution_count":13,"outputs":[{"output_type":"execute_result","data":{"text/plain":["torch.return_types.median(\n","values=tensor([-0.5230,  0.0033,  0.1204, -1.1497, -0.4065]),\n","indices=tensor([4, 1, 2, 0, 1]))"]},"metadata":{},"execution_count":13}]},{"cell_type":"code","source":["#mode\n","torch.mode(d,dim=0)#mean along row\n","torch.mode(d,dim=1)#mean along col"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"lBJKCbG4Di2W","executionInfo":{"status":"ok","timestamp":1710320691048,"user_tz":240,"elapsed":185,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"0c4a3982-c399-4c86-d7e9-92b905cb2d7a"},"execution_count":14,"outputs":[{"output_type":"execute_result","data":{"text/plain":["torch.return_types.mode(\n","values=tensor([-0.6926, -1.2944, -0.7738, -1.9451, -0.4989]),\n","indices=tensor([3, 2, 0, 2, 3]))"]},"metadata":{},"execution_count":14}]},{"cell_type":"code","source":["#standard deviations\n","torch.std(d)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Ny9rouoVDqUb","executionInfo":{"status":"ok","timestamp":1710320734244,"user_tz":240,"elapsed":193,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"b3c37d51-91cf-480b-e7d0-b22a91f9d04f"},"execution_count":15,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor(0.8298)"]},"metadata":{},"execution_count":15}]},{"cell_type":"code","source":["torch.std(d,dim=0)#std along row"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"lUp9p8YvD0Wb","executionInfo":{"status":"ok","timestamp":1710320754603,"user_tz":240,"elapsed":282,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"f5580e84-11ae-4af4-f13c-d975dc52390c"},"execution_count":16,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([1.0470, 0.4400, 0.8989, 0.9677, 0.4965])"]},"metadata":{},"execution_count":16}]},{"cell_type":"code","source":["torch.std(d,dim=1)#std along col"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"4KP55eIVD5z7","executionInfo":{"status":"ok","timestamp":1710320766106,"user_tz":240,"elapsed":192,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"caa2e4f6-cc1d-4179-cbf3-795f1dfa8ea5"},"execution_count":17,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([0.9231, 0.8426, 0.5550, 1.1415, 0.4552])"]},"metadata":{},"execution_count":17}]},{"cell_type":"code","source":["#variance\n","torch.var(d)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"JH0hfsh-D8lG","executionInfo":{"status":"ok","timestamp":1710320785304,"user_tz":240,"elapsed":303,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"c9000af6-8191-4e16-cf7d-2c23695d3a5c"},"execution_count":18,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor(0.6885)"]},"metadata":{},"execution_count":18}]},{"cell_type":"code","source":["torch.var(d,dim=0)#std along row"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"rSjRG2gqEBJf","executionInfo":{"status":"ok","timestamp":1710320800037,"user_tz":240,"elapsed":4,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"759eb393-6f28-4f59-a299-2342a47b1d08"},"execution_count":19,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([1.0962, 0.1936, 0.8080, 0.9364, 0.2465])"]},"metadata":{},"execution_count":19}]},{"cell_type":"code","source":["torch.var(d,dim=1)#std along col"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"3YJfFDUFEE9C","executionInfo":{"status":"ok","timestamp":1710320811353,"user_tz":240,"elapsed":3,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"d07bec57-ef35-4a78-da75-3275955b50c1"},"execution_count":20,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([0.8522, 0.7100, 0.3080, 1.3030, 0.2072])"]},"metadata":{},"execution_count":20}]},{"cell_type":"code","source":["#computation of gradients of sampled tensors\n","#consider a sample datase0074, where two variables (x and y) are present\n","\n","#forward function computes the matrix multiplication of the weight tensor with the input tensor\n","def forward(x):\n","  return x*w"],"metadata":{"id":"lRT3oyWyEHsn","executionInfo":{"status":"ok","timestamp":1710320955593,"user_tz":240,"elapsed":3,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"execution_count":21,"outputs":[]},{"cell_type":"code","source":["import torch\n","from torch.autograd import Variable\n","\n","x_data=[11.0,22.0,33.0]\n","y_data=[54.0,89.09,67.89]\n","\n","w=Variable(torch.Tensor([1,0]),requires_grad=True)\n","\n","#prior of training\n","print(\"predict (before training)\",4,forward(4).data[0])"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"j3Abi9XnEq5W","executionInfo":{"status":"ok","timestamp":1710321170493,"user_tz":240,"elapsed":221,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"5d313bb3-064c-40cc-8c1f-220a375464bf"},"execution_count":22,"outputs":[{"output_type":"stream","name":"stdout","text":["predict (before training) 4 tensor(4.)\n"]}]},{"cell_type":"code","source":["def forward(x):\n","  return x*w"],"metadata":{"id":"7o_2SGtBIXzv","executionInfo":{"status":"ok","timestamp":1710321934606,"user_tz":240,"elapsed":221,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"execution_count":28,"outputs":[]},{"cell_type":"code","source":["#introduce loss function\n","def loss(x,y):\n","  y_pred=forward(x)\n","  return (y_pred-y)*(y_pred-y)"],"metadata":{"id":"XJ4TnlYnFfWO","executionInfo":{"status":"ok","timestamp":1710321947757,"user_tz":240,"elapsed":230,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"execution_count":29,"outputs":[]},{"cell_type":"code","source":["#executing training loop\n","for epoch in range(10):\n","  for x_val, y_val in zip(x_data,y_data):\n","    l=loss(x_val,y_val)\n","    l.backward()\n","    print(\"\\tgrad: \", x_val, y_val, w.grad.data[0])\n","    w.data = w.data-0.01*w.grad.data\n","\n","    #manually setting gradients to 0\n","    w.grad.data.zero_()\n","    print(\"progress:\" , epoch, l.data[0])"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":365},"id":"HZTnNbmjF2x9","executionInfo":{"status":"error","timestamp":1710323234494,"user_tz":240,"elapsed":149,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"d18658a8-492a-4791-f494-d7b2666439ac"},"execution_count":40,"outputs":[{"output_type":"error","ename":"RuntimeError","evalue":"grad can be implicitly created only for scalar outputs","traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)","\u001b[0;32m<ipython-input-40-57a9b215694f>\u001b[0m in \u001b[0;36m<cell line: 2>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m   \u001b[0;32mfor\u001b[0m \u001b[0mx_val\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_val\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_data\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0ml\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mloss\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_val\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my_val\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m     \u001b[0ml\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbackward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"\\tgrad: \"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_val\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_val\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgrad\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0mw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m0.01\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgrad\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n","\u001b[0;32m/usr/local/lib/python3.10/dist-packages/torch/_tensor.py\u001b[0m in \u001b[0;36mbackward\u001b[0;34m(self, gradient, retain_graph, create_graph, inputs)\u001b[0m\n\u001b[1;32m    490\u001b[0m                 \u001b[0minputs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minputs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    491\u001b[0m             )\n\u001b[0;32m--> 492\u001b[0;31m         torch.autograd.backward(\n\u001b[0m\u001b[1;32m    493\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgradient\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mretain_graph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcreate_graph\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minputs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minputs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    494\u001b[0m         )\n","\u001b[0;32m/usr/local/lib/python3.10/dist-packages/torch/autograd/__init__.py\u001b[0m in \u001b[0;36mbackward\u001b[0;34m(tensors, grad_tensors, retain_graph, create_graph, grad_variables, inputs)\u001b[0m\n\u001b[1;32m    242\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    243\u001b[0m     \u001b[0mgrad_tensors_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_tensor_or_tensors_to_tuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrad_tensors\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtensors\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 244\u001b[0;31m     \u001b[0mgrad_tensors_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_make_grads\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtensors\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_tensors_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mis_grads_batched\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    245\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mretain_graph\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    246\u001b[0m         \u001b[0mretain_graph\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcreate_graph\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n","\u001b[0;32m/usr/local/lib/python3.10/dist-packages/torch/autograd/__init__.py\u001b[0m in \u001b[0;36m_make_grads\u001b[0;34m(outputs, grads, is_grads_batched)\u001b[0m\n\u001b[1;32m    115\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrequires_grad\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    116\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnumel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 117\u001b[0;31m                     raise RuntimeError(\n\u001b[0m\u001b[1;32m    118\u001b[0m                         \u001b[0;34m\"grad can be implicitly created only for scalar outputs\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    119\u001b[0m                     )\n","\u001b[0;31mRuntimeError\u001b[0m: grad can be implicitly created only for scalar outputs"]}]},{"cell_type":"code","source":["from torch import FloatTensor\n","from torch.autograd import Variable"],"metadata":{"id":"H9Lxjcf0HV9E","executionInfo":{"status":"ok","timestamp":1710331460702,"user_tz":240,"elapsed":122,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"execution_count":5,"outputs":[]},{"cell_type":"code","source":["a=Variable(FloatTensor([5]))\n","\n","weights= [Variable(FloatTensor([i]),requires_grad=True) for i in (12,91,89,56)]\n","w1,w2, w3, w4=weights\n","b=w1*a\n","c=w2*a\n","d=w3*b+w4*c\n","loss=(10-d)\n","loss.backward()\n","\n","for index, weights in enumerate(weights,start=1):\n","  gradient,*__=weights.grad.data\n","  print(f\"gradient of w{index} with respect to loss: {gradient}\")"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"PwNsYx4jNmwZ","executionInfo":{"status":"ok","timestamp":1710331464579,"user_tz":240,"elapsed":328,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"3a5810f3-e7ef-4518-c877-b71a0c0b64b6"},"execution_count":6,"outputs":[{"output_type":"stream","name":"stdout","text":["gradient of w1 with respect to loss: -445.0\n","gradient of w2 with respect to loss: -280.0\n","gradient of w3 with respect to loss: -60.0\n","gradient of w4 with respect to loss: -455.0\n"]}]},{"cell_type":"code","source":["#Tensor Operations (grad, volatile, gradient)\n","#Perform matrix multiplication by mm modeule\n","x=Variable(torch.Tensor(4,4).uniform_(-4,5))\n","y=Variable(torch.Tensor(4,4).uniform_(-3,2))"],"metadata":{"id":"X62CerjENvoG","executionInfo":{"status":"ok","timestamp":1710331466986,"user_tz":240,"elapsed":129,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"execution_count":7,"outputs":[]},{"cell_type":"code","source":["x"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"U-3-PxjLP9pQ","executionInfo":{"status":"ok","timestamp":1710331469422,"user_tz":240,"elapsed":137,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"16daae00-9c2a-46a4-ff6b-93bbc5e7a7d5"},"execution_count":8,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[ 2.9111, -1.1113,  2.0239,  1.3368],\n","        [-2.3053,  1.3786, -0.7065,  4.6133],\n","        [ 0.2035,  2.8672,  2.1076,  4.8294],\n","        [-0.7025,  0.0271, -2.7841, -2.5639]])"]},"metadata":{},"execution_count":8}]},{"cell_type":"code","source":["y"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"e69iXArrP-1J","executionInfo":{"status":"ok","timestamp":1710323922841,"user_tz":240,"elapsed":6,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"553180f9-0342-4739-ce11-db64aa20acb8"},"execution_count":46,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[-1.9156, -1.8726,  1.0226, -2.3292],\n","        [-2.0001,  0.1279,  0.5313, -1.6413],\n","        [-0.4996, -2.3758,  1.2876, -0.6267],\n","        [-2.7291, -2.9486, -2.2718, -2.7632]])"]},"metadata":{},"execution_count":46}]},{"cell_type":"code","source":["xmultiplyy=torch.mm(x,y)"],"metadata":{"id":"OZ19F7SPP_YN","executionInfo":{"status":"ok","timestamp":1710331474315,"user_tz":240,"elapsed":110,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"execution_count":9,"outputs":[]},{"cell_type":"code","source":["z=xmultiplyy"],"metadata":{"id":"vinKkKfFQF3I","executionInfo":{"status":"ok","timestamp":1710331477048,"user_tz":240,"elapsed":146,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"execution_count":10,"outputs":[]},{"cell_type":"code","source":["z"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"BTzF7cGNQKp9","executionInfo":{"status":"ok","timestamp":1710323970712,"user_tz":240,"elapsed":169,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"27d59218-56c6-4e8e-b3ae-4f5c05d83673"},"execution_count":49,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[-21.0577, -18.9734,  -2.8621, -21.1509],\n","        [ 14.8348,   3.7486,   3.8594,  14.2648],\n","        [ -7.0854, -11.6179,   4.0567,  -6.5713],\n","        [  7.0754,  -7.5367,   2.7598,   5.7408]])"]},"metadata":{},"execution_count":49}]},{"cell_type":"code","source":["z.size()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"iZRo8LrCQLBd","executionInfo":{"status":"ok","timestamp":1710331479597,"user_tz":240,"elapsed":118,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"eed555f1-3a21-4049-d8e8-2f0bfabde8ae"},"execution_count":11,"outputs":[{"output_type":"execute_result","data":{"text/plain":["torch.Size([4, 4])"]},"metadata":{},"execution_count":11}]},{"cell_type":"code","source":["#properties of the variable\n","z=Variable(torch.Tensor(4,4).uniform_(-5,5))\n","print(z)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"fO9nLbYaQNGN","executionInfo":{"status":"ok","timestamp":1710331482085,"user_tz":240,"elapsed":86,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"59459147-eb6c-4bc0-d8da-6be47d1c97f8"},"execution_count":12,"outputs":[{"output_type":"stream","name":"stdout","text":["tensor([[ 3.9654,  2.8418,  4.5645,  0.5791],\n","        [-3.4296, -4.2381, -3.8777,  1.4841],\n","        [-1.0304,  1.2935, -2.4219,  0.0192],\n","        [-2.6667, -3.5739,  2.0413, -2.0858]])\n"]}]},{"cell_type":"code","source":["print('Required Gradient: %s ' % (z.requires_grad))\n","print('Volatile: %s ' % (z.volatile))\n","print('Grad: %s ' % (z.grad))\n","print(z.data)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"diM6H5B0QmxC","executionInfo":{"status":"ok","timestamp":1710331484825,"user_tz":240,"elapsed":109,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"8127be0c-6aef-48af-dc85-b70855cc8b64"},"execution_count":13,"outputs":[{"output_type":"stream","name":"stdout","text":["Required Gradient: False \n","Volatile: False \n","Grad: None \n","tensor([[ 3.9654,  2.8418,  4.5645,  0.5791],\n","        [-3.4296, -4.2381, -3.8777,  1.4841],\n","        [-1.0304,  1.2935, -2.4219,  0.0192],\n","        [-2.6667, -3.5739,  2.0413, -2.0858]])\n"]},{"output_type":"stream","name":"stderr","text":["<ipython-input-13-69d0e6fb4537>:2: UserWarning: volatile was removed (Variable.volatile is always False)\n","  print('Volatile: %s ' % (z.volatile))\n"]}]},{"cell_type":"code","source":["#tensor operations (matrix-vector computation, and matrix-matrix and vector-vector calculation)\n","some_mat1=torch.FloatTensor(4,4).uniform_(0,1)\n","some_mat1"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"J5u0nNN-RF7B","executionInfo":{"status":"ok","timestamp":1710331538479,"user_tz":240,"elapsed":102,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"a1bf33fd-33a7-4fba-c597-700338750c3d"},"execution_count":15,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[0.7848, 0.1165, 0.8236, 0.9971],\n","        [0.9884, 0.4494, 0.7886, 0.6796],\n","        [0.4086, 0.4149, 0.3651, 0.2848],\n","        [0.7076, 0.7932, 0.2800, 0.8026]])"]},"metadata":{},"execution_count":15}]},{"cell_type":"code","source":["some_mat2=torch.FloatTensor(4,4).uniform_(0,1)\n","some_mat2"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"DRbSdlM6tB_k","executionInfo":{"status":"ok","timestamp":1710331557348,"user_tz":240,"elapsed":5,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"36c5504b-9ef3-43b6-8900-50548126a66a"},"execution_count":16,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[0.1174, 0.0982, 0.2957, 0.8359],\n","        [0.3346, 0.4318, 0.2329, 0.4929],\n","        [0.6346, 0.8150, 0.1193, 0.6444],\n","        [0.7579, 0.3256, 0.5988, 0.8430]])"]},"metadata":{},"execution_count":16}]},{"cell_type":"code","source":["some_vec1=torch.FloatTensor(4).uniform_(0,1)\n","some_vec1"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"wTi5gYKAtGkU","executionInfo":{"status":"ok","timestamp":1710331595329,"user_tz":240,"elapsed":4,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"5e0c8b31-e412-4bc0-94bc-bdf6e9173e72"},"execution_count":18,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([0.8065, 0.3862, 0.0899, 0.5788])"]},"metadata":{},"execution_count":18}]},{"cell_type":"code","source":["some_mat2+some_mat1"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"j9pzqJS2tPbK","executionInfo":{"status":"ok","timestamp":1710331607567,"user_tz":240,"elapsed":3,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"4c8900c8-a085-4b4a-d3e1-156f5a563b8d"},"execution_count":19,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[0.9022, 0.2147, 1.1193, 1.8329],\n","        [1.3230, 0.8811, 1.0215, 1.1725],\n","        [1.0432, 1.2300, 0.4844, 0.9292],\n","        [1.4655, 1.1188, 0.8788, 1.6456]])"]},"metadata":{},"execution_count":19}]},{"cell_type":"code","source":["some_mat2+some_mat1+.0998123"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"waxq9zNXtO1c","executionInfo":{"status":"ok","timestamp":1710331629165,"user_tz":240,"elapsed":91,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"a743c4ab-0516-4608-f53a-964082f4f311"},"execution_count":20,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[1.0020, 0.3145, 1.2191, 1.9327],\n","        [1.4229, 0.9809, 1.1213, 1.2723],\n","        [1.1431, 1.3298, 0.5842, 1.0290],\n","        [1.5653, 1.2186, 0.9786, 1.7454]])"]},"metadata":{},"execution_count":20}]},{"cell_type":"code","source":["some_mat2+some_mat1-.0998123"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"A_glM1iDtY1U","executionInfo":{"status":"ok","timestamp":1710331651053,"user_tz":240,"elapsed":128,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"7ff8ad52-7968-4b70-a585-977eb4337129"},"execution_count":21,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[0.8024, 0.1149, 1.0195, 1.7331],\n","        [1.2232, 0.7813, 0.9217, 1.0727],\n","        [0.9434, 1.1301, 0.3845, 0.8294],\n","        [1.3657, 1.0190, 0.7790, 1.5458]])"]},"metadata":{},"execution_count":21}]},{"cell_type":"code","source":["#matrix and vector addition\n","some_mat1+some_mat2+some_vec1"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Kr4JUwKXteI3","executionInfo":{"status":"ok","timestamp":1710331680954,"user_tz":240,"elapsed":90,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"eb6c961a-56bb-462d-9333-931f76ca6cb4"},"execution_count":22,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([[1.7087, 0.6009, 1.2092, 2.4117],\n","        [2.1295, 1.2673, 1.1114, 1.7513],\n","        [1.8497, 1.6161, 0.5742, 1.5080],\n","        [2.2720, 1.5049, 0.9687, 2.2243]])"]},"metadata":{},"execution_count":22}]},{"cell_type":"code","source":["some_mat3=torch.FloatTensor(5,4)"],"metadata":{"id":"I_VpLJwptldz","executionInfo":{"status":"ok","timestamp":1710331746947,"user_tz":240,"elapsed":92,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"execution_count":23,"outputs":[]},{"cell_type":"code","source":["some_mat3+some_mat1#obviously not possible due to different sizes of tensors"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":144},"id":"cU6CtRvet1iF","executionInfo":{"status":"error","timestamp":1710331772213,"user_tz":240,"elapsed":126,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"74c42038-2253-4259-b5b5-55e42d86ddcc"},"execution_count":24,"outputs":[{"output_type":"error","ename":"RuntimeError","evalue":"The size of tensor a (5) must match the size of tensor b (4) at non-singleton dimension 0","traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)","\u001b[0;32m<ipython-input-24-53285d95e0cf>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0msome_mat3\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0msome_mat1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m","\u001b[0;31mRuntimeError\u001b[0m: The size of tensor a (5) must match the size of tensor b (4) at non-singleton dimension 0"]}]},{"cell_type":"code","source":["#Distributions on tensors for weight normalization, weight initialization, and computation of gradients in neural network– based operations using PyTorch\n","#targetting Bernoulli distribution\n","from torch.distributions.bernoulli import Bernoulli\n"],"metadata":{"id":"KYtgxUXTt7vV","executionInfo":{"status":"ok","timestamp":1710331913258,"user_tz":240,"elapsed":90,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}}},"execution_count":25,"outputs":[]},{"cell_type":"code","source":["dist=Bernoulli(torch.tensor([0.3,0.6,0.9]))\n","dist.sample()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"83cVxKS0ueLk","executionInfo":{"status":"ok","timestamp":1710331984878,"user_tz":240,"elapsed":94,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"fac2895b-e5ec-4ac3-cdb7-25a2d0a612eb"},"execution_count":28,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([0., 1., 1.])"]},"metadata":{},"execution_count":28}]},{"cell_type":"code","source":["#Beta distribution\n","from torch.distributions.beta import Beta\n","dist=Beta(torch.tensor([0.9]),torch.tensor([0.9]))\n","dist.sample()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"FCB_GEvzur5f","executionInfo":{"status":"ok","timestamp":1710332080067,"user_tz":240,"elapsed":4,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"1eb7862d-745c-47da-8cbc-13407041633e"},"execution_count":33,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([0.0913])"]},"metadata":{},"execution_count":33}]},{"cell_type":"code","source":["#Binomial distribution\n","from torch.distributions.binomial import Binomial\n","dist=Binomial(100,torch.tensor([0.9]))\n","dist.sample()\n"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Ti-cDBexu3Gw","executionInfo":{"status":"ok","timestamp":1710332225167,"user_tz":240,"elapsed":90,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"35da1b68-f404-4402-c4fc-0d28c25f2b00"},"execution_count":35,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([90.])"]},"metadata":{},"execution_count":35}]},{"cell_type":"code","source":["#a generalized Bernoulli distribution called as categorical\n","from torch.distributions.categorical import Categorical\n","dist=Categorical(torch.tensor([0.7,0.7,0.7]))\n","dist.sample()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"zNTQvgfOvYkG","executionInfo":{"status":"ok","timestamp":1710332281022,"user_tz":240,"elapsed":247,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"764ac867-d22e-4790-bc59-b99303dcc944"},"execution_count":40,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor(0)"]},"metadata":{},"execution_count":40}]},{"cell_type":"code","source":["#Laplacian distribution\n","from torch.distributions.laplace import Laplace\n","dist=Laplace(torch.tensor([7.0]),torch.tensor([0.99]))\n","dist.sample()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"3qH-Gs4wvsNI","executionInfo":{"status":"ok","timestamp":1710332435910,"user_tz":240,"elapsed":4,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"6c85b98c-1b48-41e9-cba4-97a7c2d043bb"},"execution_count":44,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([5.7971])"]},"metadata":{},"execution_count":44}]},{"cell_type":"code","source":["# normal distribution\n","from torch.distributions.normal import Normal\n","dist=Normal(torch.tensor([7.0]),torch.tensor([0.99]))\n","dist.sample()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"1zYCFzM4wQ6J","executionInfo":{"status":"ok","timestamp":1710332498846,"user_tz":240,"elapsed":102,"user":{"displayName":"HIMANSHU SINGH","userId":"15356404559194605405"}},"outputId":"d6c120a6-fdd0-4536-a50b-927a09d104b1"},"execution_count":46,"outputs":[{"output_type":"execute_result","data":{"text/plain":["tensor([6.4637])"]},"metadata":{},"execution_count":46}]},{"cell_type":"code","source":[],"metadata":{"id":"FzcD6BTxwhU5"},"execution_count":null,"outputs":[]}]}