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![@thi.ng/tensors](https://codeberg.org/thi.ng/umbrella/media/branch/develop/assets/banners/thing-tensors.svg?0d90e46c)\n\n[![npm version](https://img.shields.io/npm/v/@thi.ng/tensors.svg)](https://www.npmjs.com/package/@thi.ng/tensors)\n![npm downloads](https://img.shields.io/npm/dm/@thi.ng/tensors.svg)\n[![Mastodon Follow](https://img.shields.io/mastodon/follow/109331703950160316?domain=https%3A%2F%2Fmastodon.thi.ng&style=social)](https://mastodon.thi.ng/@toxi)\n\n> [!NOTE]\n\n> This is one of 217 standalone projects. LLM-free, human-made and\n> cared for software, maintained as part of the\n> [@thi.ng/umbrella](https://codeberg.org/thi.ng/umbrella/) ecosystem and\n> anti-framework.\n>\n> 🚀 Please help me to work full-time on these projects by [sponsoring\n> me](https://codeberg.org/thi.ng/umbrella/src/branch/develop/CONTRIBUTING.md#donations).\n> Thank you! ❤️\n\n- [About](#about)\n- [Built-in tensor operations](#built-in-tensor-operations)\n  - [Broadcasting support](#broadcasting-support)\n  - [Convolution support](#convolution-support)\n  - [Conversions](#conversions)\n- [Status](#status)\n- [Installation](#installation)\n- [Dependencies](#dependencies)\n- [API](#api)\n  - [Basic usage](#basic-usage)\n  - [Matrix-matrix multiplication](#matrix-matrix-multiplication)\n  - [Matrix-vector multiplication](#matrix-vector-multiplication)\n- [Authors](#authors)\n- [License](#license)\n\n## About\n\n0D/1D/2D/3D/4D tensors with extensible polymorphic operations and customizable storage.\n\n> [!NOTE]\n> This package contains code originally written in 2017/18 and has been\n> refactored to be stylistically more aligned with other thi.ng packages.\n\n## Built-in tensor operations\n\nThe [`ITensor`\ninterface](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html) shared\nby all tensor implementations provides the following methods (non-exhaustive\nlist here):\n\n- [.crop(pos, size)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#get-1): Crop tensor region (zero copy)\n- [.get(pos)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#get-1): Get value at position\n- [.hi(pos)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#hi-1): Crop tensor (high end, zero copy)\n- [.index(pos)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#index-1): Get index for position\n- [.lo(pos)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#lo-1): Crop tensor (low end, zero copy)\n- [.pad(pads, n)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#pad-1): Pad tensor along one or more dimensions with constant value\n- [.pack(storage?)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#pack-1): Copy tensor with data tightly packed\n- [.pick(axes)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#pick-1): Select axes only (zero copy)\n- [.position(index)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#position-1): Get position for index\n- [.reshape(newShape, newStride?)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#reshape-1): Reshape tensor (zero copy)\n- [.set(pos)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#set-1): Set value at position\n- [.step(axes)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#step-1): Skip axes (zero copy)\n- [.transpose(order)](https://docs.thi.ng/umbrella/tensors/interfaces/ITensor.html#transpose-1): Re-order axes (zero copy)\n\nThe set of tensor polymorphic component-wise ops is easily extensible via\nprovided higher-order functions in the `defOpXX()` family. Most of the ops\nlisted below are also based on this approach. The function signatures and naming\nconventions are closely aligned to the ones used by the\n[thi.ng/vectors](https://thi.ng/vectors) package.\n\n- [abs](https://docs.thi.ng/umbrella/tensors/variables/abs.html): Componentwise `Math.abs`\n- [add](https://docs.thi.ng/umbrella/tensors/variables/add.html): Tensor-tensor addition\n- [addN](https://docs.thi.ng/umbrella/tensors/variables/addN.html): Tensor-scalar addition\n- [argMax](https://docs.thi.ng/umbrella/tensors/functions/argMax.html): Maximum component index/value\n- [argMin](https://docs.thi.ng/umbrella/tensors/functions/argMin.html): Minimum component index/value\n- [cdf](https://docs.thi.ng/umbrella/tensors/variables/cdf.html): Cumulative distribution of 1D tensor\n- [clamp](https://docs.thi.ng/umbrella/tensors/variables/clamp.html): Tensor-tensor interval clamping\n- [clampN](https://docs.thi.ng/umbrella/tensors/variables/clampN.html): Tensor-scalar interval clamping\n- [convolve](https://docs.thi.ng/umbrella/tensors/variables/convolve.html): Tensor convolution (1D/2D/3D only)\n- [cos](https://docs.thi.ng/umbrella/tensors/variables/cos.html): Componentwise `Math.cos`\n- [diagonal](https://docs.thi.ng/umbrella/tensors/functions/diagonal.html): Diagonal extraction\n- [div](https://docs.thi.ng/umbrella/tensors/variables/div.html): Tensor-tensor division\n- [divN](https://docs.thi.ng/umbrella/tensors/variables/divN.html): Tensor-scalar division\n- [dot](https://docs.thi.ng/umbrella/tensors/variables/dot.html): Dot product\n- [equalizeHistogram](https://docs.thi.ng/umbrella/tensors/functions/equalizeHistogram.html): histogram equalization\n- [exp](https://docs.thi.ng/umbrella/tensors/variables/exp.html): Componentwise `Math.exp`\n- [exp2](https://docs.thi.ng/umbrella/tensors/variables/exp2.html): Componentwise `2^x`\n- [histogramUint](https://docs.thi.ng/umbrella/tensors/functions/histogramUint.html): histogram of uint-based tensor\n- [identity](https://docs.thi.ng/umbrella/tensors/functions/identity.html): Square identity matrix tensor\n- [integrate](https://docs.thi.ng/umbrella/tensors/functions/integrate.html): Integrate tensor along innermost dimension\n- [log](https://docs.thi.ng/umbrella/tensors/variables/log.html): Componentwise `Math.log`\n- [log2](https://docs.thi.ng/umbrella/tensors/variables/log2.html): Componentwise `Math.log2`\n- [mag](https://docs.thi.ng/umbrella/tensors/functions/mag.html): Tensor magnitude\n- [magSq](https://docs.thi.ng/umbrella/tensors/variables/magSq.html): Tensor squared magnitude\n- [max](https://docs.thi.ng/umbrella/tensors/variables/max.html): Tensor-tensor maximum\n- [maxN](https://docs.thi.ng/umbrella/tensors/variables/maxN.html): Tensor-scalar maximum\n- [mean](https://docs.thi.ng/umbrella/tensors/functions/mean.html): Tensor mean value\n- [min](https://docs.thi.ng/umbrella/tensors/functions/min.html): Tensor-tensor minimum\n- [minN](https://docs.thi.ng/umbrella/tensors/variables/minN.html): Tensor-scalar maximum\n- [mul](https://docs.thi.ng/umbrella/tensors/variables/mul.html): Tensor-tensor multiplication\n- [mulN](https://docs.thi.ng/umbrella/tensors/variables/mulN.html): Tensor-scalar multiplication\n- [mulM](https://docs.thi.ng/umbrella/tensors/functions/mulM.html): Matrix-matrix product\n- [mulV](https://docs.thi.ng/umbrella/tensors/functions/mulV.html): Matrix-vector product\n- [negativeIndices](https://docs.thi.ng/umbrella/tensors/variables/negativeIndices.html): Indices of negative component values\n- [nonZeroIndices](https://docs.thi.ng/umbrella/tensors/variables/nonZeroIndices.html): Indices of non-zero component values\n- [normalize](https://docs.thi.ng/umbrella/tensors/functions/normalize.html): Tensor normalization (w/ optional length)\n- [ones](https://docs.thi.ng/umbrella/tensors/functions/ones.html): One-filled tensor creation\n- [positiveIndices](https://docs.thi.ng/umbrella/tensors/variables/positiveIndices.html): Indices of positive component values\n- [pow](https://docs.thi.ng/umbrella/tensors/variables/pow.html): Tensor-tensor `Math.pow`\n- [powN](https://docs.thi.ng/umbrella/tensors/variables/powN.html): Tensor-scalar `Math.pow`\n- [print](https://docs.thi.ng/umbrella/tensors/functions/print.html): Formatted tensor output\n- [product](https://docs.thi.ng/umbrella/tensors/variables/product.html): Component product\n- [randDistrib](https://docs.thi.ng/umbrella/tensors/variables/randDistrib.html): Fill with random data from distribution fn\n- [range](https://docs.thi.ng/umbrella/tensors/functions/range.html): Create 1D tensor of monotonically increasing/decreasing values\n- [relu](https://docs.thi.ng/umbrella/tensors/variables/relu.html): ReLU activation\n- [reluN](https://docs.thi.ng/umbrella/tensors/variables/reluN.html): Leaky ReLU activation\n- [select](https://docs.thi.ng/umbrella/tensors/functions/select.html): Generalization of argMin/Max\n- [set](https://docs.thi.ng/umbrella/tensors/functions/set.html): Tensor setter\n- [setN](https://docs.thi.ng/umbrella/tensors/functions/setN.html): Tensor setter w/ uniform scalar\n- [sigmoid](https://docs.thi.ng/umbrella/tensors/variables/sigmoid.html): Sigmoid activation\n- [sin](https://docs.thi.ng/umbrella/tensors/variables/sin.html): Componentwise `Math.sin`\n- [smoothStep](https://docs.thi.ng/umbrella/tensors/variables/smoothStep.html): Smooth threshold function (as as GLSL `smoothstep()`)\n- [smoothStepN](https://docs.thi.ng/umbrella/tensors/variables/smoothStepN.html): Smooth threshold function (as as GLSL `smoothstep()`)\n- [softMax](https://docs.thi.ng/umbrella/tensors/functions/softMax.html): Soft Max activation\n- [sqrt](https://docs.thi.ng/umbrella/tensors/variables/sqrt.html): Componentwise `Math.sqrt`\n- [step](https://docs.thi.ng/umbrella/tensors/variables/step.html): Threshold function (as as GLSL `step()`)\n- [stepN](https://docs.thi.ng/umbrella/tensors/variables/stepN.html): Threshold function (as as GLSL `step()`)\n- [sub](https://docs.thi.ng/umbrella/tensors/variables/sub.html): Tensor-tensor subtraction\n- [subN](https://docs.thi.ng/umbrella/tensors/variables/subN.html): Tensor-scalar subtraction\n- [sum](https://docs.thi.ng/umbrella/tensors/variables/sum.html): Component sum\n- [svd](https://docs.thi.ng/umbrella/tensors/functions/svd.html): Singular value decomposition\n- [swap](https://docs.thi.ng/umbrella/tensors/functions/swap.html): Swap tensor values\n- [tan](https://docs.thi.ng/umbrella/tensors/variables/tan.html): Componentwise `Math.tan`\n- [tanh](https://docs.thi.ng/umbrella/tensors/variables/tanh.html): Componentwise `Math.tanh`\n- [trace](https://docs.thi.ng/umbrella/tensors/functions/trace.html): Matrix trace (diagonal component sum)\n- [zeroes](https://docs.thi.ng/umbrella/tensors/functions/zeroes.html): Zero-filled tensor creation\n\n### Broadcasting support\n\nMost of the built-in functions taking two or more tensors as input are\nsupporting broadcasting, i.e. the shapes of the individual arguments only need\nto be compatible, not identical. The operators attempt to adjust the tensor\nshape & stride configurations to be compatible, applying the steps and rules\nbelow:\n\n- If the dimensions are unequal, the smaller tensor's dimensions will be\n  increased as needed. The size of each added dimension will be set to 1 and its\n  stride set to zero.\n- The size of each dimension will be compared and only the following cases are\n  accepted (otherwise will throw an error): sizes are equal or one side is 1\n- Any of the tensors requiring shape adjustments will be shallow copied with\n  new shape/stride config applied.\n\nSome examples:\n\n```ts tangle:export/readme-broadcast.ts\nimport { add, sub, print, tensor } from \"@thi.ng/tensors\";\n\n// 2D + 1D\nprint(add(null, tensor([[1,2], [3,4]]), tensor([10, 20])));\n//   11.0000   22.0000\n//   13.0000   24.0000\n\n// 2D + 1D (as column vector)\nprint(add(null, tensor([[1, 2], [3, 4]]), tensor([10, 20]).reshape([2,1])));\n//   11.0000   12.0000\n//   23.0000   24.0000\n\n// 1D - 2D\nprint(sub(null, tensor([10, 20]), tensor([[1,2], [3,4]])));\n//    9.0000   18.0000\n//    7.0000   16.0000\n\n// 1D + 3D\nprint(add(null, tensor([10, 20]), tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])));\n// --- 0: ---\n//   11.0000   22.0000\n//   13.0000   24.0000\n// --- 1: ---\n//   15.0000   26.0000\n//   17.0000   28.0000\n\n// 2D + 3D\nprint(add(null, tensor([[10, 20], [100, 200]]), tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])));\n// --- 0: ---\n//   11.0000   22.0000\n//  103.0000  204.0000\n// --- 1: ---\n//   15.0000   26.0000\n//  107.0000  208.0000\n```\n\n### Convolution support\n\nTensor convolution is only possible if both the domain tensor and the kernel\ntensor have same dimensionality. No broadcasting support.\n\nThe following kernel presets and tensor factories are included and can be used\nwith\n[`convolve()`](https://docs.thi.ng/umbrella/tensors/variables/convolve.html):\n\n- `BOX_BLUR2(radius)`: Box blur kernel factory\n- `GAUSSION2(radius)`: Gaussian blur kernel factory\n- `EDGE2(radius)`: Edge/ridge detection kernel factory\n- `SOBEL1`: 1D Sobel kernel\n- `SOBEL2`: 2D Sobel kernel\n- `SOBEL3`: 3D Sobel kernel\n\nFor more generalized convolution-like functionality, the following kernel\nfactories can be used with\n[`applyKernel()`](https://docs.thi.ng/umbrella/tensors/variables/applyKernel.html):\n\n- `MAX2_POOL(width,height?)`: max pooling\n- `MIN2_POOL(width,height?)`: min pooling\n- `MAXIMA2(radius)`: local maxima detection\n- `MINIMA2(radius)`: local minima detection\n\n### Conversions\n\nThe following functions can be used to convert/coerce other data structures into\ntensors:\n\n- [`asTensor()`](https://docs.thi.ng/umbrella/tensors/functions/asTensor.html):\n  Convert/wrap data as tensor\n- [`fromFloatBuffer()`](https://docs.thi.ng/umbrella/tensors/functions/fromFloatBuffer.html):\n  Coerce [thi.ng/pixel] float buffer/image (or compatible data structures) into\n  a 2D/3D tensor\n\n## Status\n\n**ALPHA** - bleeding edge / work-in-progress\n\n[Search or submit any issues for this package](https://codeberg.org/thi.ng/umbrella/issues?q=%5Btensors%5D)\n\n## Installation\n\n```bash\nyarn add @thi.ng/tensors\n```\n\nESM import:\n\n```ts\nimport * as ten from \"@thi.ng/tensors\";\n```\n\nBrowser ESM import:\n\n```html\n<script type=\"module\" src=\"https://esm.run/@thi.ng/tensors\"></script>\n```\n\n[JSDelivr documentation](https://www.jsdelivr.com/)\n\nFor Node.js REPL:\n\n```js\nconst ten = await import(\"@thi.ng/tensors\");\n```\n\nPackage sizes (brotli'd, pre-treeshake): ESM: 12.19 KB\n\n## Dependencies\n\n- [@thi.ng/api](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/api)\n- [@thi.ng/arrays](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/arrays)\n- [@thi.ng/checks](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/checks)\n- [@thi.ng/equiv](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/equiv)\n- [@thi.ng/errors](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/errors)\n- [@thi.ng/math](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/math)\n- [@thi.ng/random](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/random)\n- [@thi.ng/strings](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/strings)\n- [@thi.ng/vectors](https://codeberg.org/thi.ng/umbrella/src/branch/develop/packages/vectors)\n\nNote: @thi.ng/api is in _most_ cases a type-only import (not used at runtime)\n\n## API\n\n[Generated API docs](https://docs.thi.ng/umbrella/tensors/)\n\nTODO\n\n### Basic usage\n\n```ts tangle:export/readme-1.ts\nimport * as t from \"@thi.ng/tensors\";\n\n// create 4x4x4 3D tensor and fill with values\nconst a = t.range(64).reshape([4, 4, 4]);\n\nt.print(a);\n// --- 0: ---\n//         0    1.0000    2.0000    3.0000\n//    4.0000    5.0000    6.0000    7.0000\n//    8.0000    9.0000   10.0000   11.0000\n//   12.0000   13.0000   14.0000   15.0000\n// --- 1: ---\n//   16.0000   17.0000   18.0000   19.0000\n//   20.0000   21.0000   22.0000   23.0000\n//   24.0000   25.0000   26.0000   27.0000\n//   28.0000   29.0000   30.0000   31.0000\n// --- 2: ---\n//   32.0000   33.0000   34.0000   35.0000\n//   36.0000   37.0000   38.0000   39.0000\n//   40.0000   41.0000   42.0000   43.0000\n//   44.0000   45.0000   46.0000   47.0000\n// --- 3: ---\n//   48.0000   49.0000   50.0000   51.0000\n//   52.0000   53.0000   54.0000   55.0000\n//   56.0000   57.0000   58.0000   59.0000\n//   60.0000   61.0000   62.0000   63.0000\n\n// pick a tensor slice/axis (view only, 2d tensor)\nt.print(a.pick([3]));\n//   48.0000   49.0000   50.0000   51.0000\n//   52.0000   53.0000   54.0000   55.0000\n//   56.0000   57.0000   58.0000   59.0000\n//   60.0000   61.0000   62.0000   63.0000\n\n// any axis set to -1 will be skipped\n// here we select slice 3 and column 2 only (1d tensor)\nt.print(a.pick([3, -1, 2]));\n//   50.0000   54.0000   58.0000   62.0000\n\n// use `.pack()` to apply view to standalone densely packed tensor (own data)\nconsole.log(a.pick([3, 2]).pack().data);\n// [ 56, 57, 58, 59 ]\n\n// only select every second value along each axis\nt.print(a.step([2, 2, 2]));\n// --- 0: ---\n//         0    2.0000\n//    8.0000   10.0000\n// --- 1: ---\n//   32.0000   34.0000\n//   40.0000   42.0000\n\n// extract an axis range (view only, use `.pack()` to extract)\nt.print(a.lo([1, 1, 1]).hi([2, 2, 2]));\n// --- 0: ---\n//   21.0000   22.0000\n//   25.0000   26.0000\n// --- 1: ---\n//   37.0000   38.0000\n//   41.0000   42.0000\n\n// read & write elements (no bounds checking!)\na.set([1, 2, 3], 100);\n\nconsole.log(a.get([1, 2, 3]));\n// 100\n\n// or via direct array access\nconsole.log(a.data[a.index([1, 2, 3])]);\n// 100\n\n// tensors are iterables (in current stride order)\nconsole.log([...a]);\n// [ 0, 1, 2, 3, 4, ... 60, 61, 62, 63 ]\n\n// create a 2D tensor w/ random values (by default normal distribution, bias=0, std=1)\nconst b = t.randDistrib(t.tensor(\"f64\", [4, 2]));\n\nt.print(b);\n//    0.3854    0.6597\n//    0.5775    0.9201\n//   -0.7276   -0.1069\n//    1.0550    0.4903\n\n// apply sigmoid\n// (null as output arg means mutate original [in 99% of all provided ops])\nt.print(t.sigmoid(null, b));\n//    0.5952    0.6592\n//    0.6405    0.7151\n//    0.3257    0.4733\n//    0.7417    0.6202\n```\n\n### Matrix-matrix multiplication\n\n```ts tangle:export/readme-mulm.ts\nimport { tensor, mulM, print } from \"@thi.ng/tensors\";\n\n// create 2x3 matrix\nconst m1 = tensor([[1, 2, 3], [4, 5, 6]]);\n\nprint(m1);\n//    1.0000    2.0000    3.0000\n//    4.0000    5.0000    6.0000\n\n// create transposed view (view only, zero-copy)\nconst m2 = m1.transpose([1, 0]);\n\nprint(m2);\n//    1.0000    4.0000\n//    2.0000    5.0000\n//    3.0000    6.0000\n\n// matrix multiplication\n// (here if 1st arg is null, a new tensor will be created)\nprint(mulM(null, m1, m2));\n//   14.0000   32.0000\n//   32.0000   77.0000\n```\n\n### Matrix-vector multiplication\n\n```ts tangle:export/readme-mulv.ts\nimport { tensor, mulV, print } from \"@thi.ng/tensors\";\n\n// create 2x3 transformation matrix (row-major)\nconst mat = tensor([[10, 0, 100], [0, 5, 200]]);\n\nprint(mat);\n//   10.0000         0  100.0000\n//         0    5.0000  200.0000\n\n// create vector\nconst vec = tensor([1, 1, 1]);\n\n// matrix-vector multiply\nprint(mulV(null, mat, vec));\n//  110.0000  205.0000\n```\n\n## Authors\n\n- [Karsten Schmidt](https://thi.ng)\n\nIf this project contributes to an academic publication, please cite it as:\n\n```bibtex\n@misc{thing-tensors,\n  title = \"@thi.ng/tensors\",\n  author = \"Karsten Schmidt\",\n  note = \"https://thi.ng/tensors\",\n  year = 2018\n}\n```\n\n## License\n\n&copy; 2018 - 2026 Karsten Schmidt // Apache License 2.0\n","readmeFilename":"README.md"}