common lisp 张量，矩阵计算库介绍

clvt

clvt (common lisp vector tensor) library. 这是一个纯 common lisp 语言编写的张量库，是使用'智谱清言'AI(GLM5.1)和'DeepSeek'(v4pro) AI共同编写，目标就是为 common lisp 生态构建一个简洁而强大的张量计算库。虽然 lisp 社区拥有 magicl 和 numcl 这两个比较流行的库，但是 magicl 缺乏对高维张量的支持以及缺少一些重要的函数，numcl 注重类型推理并且一些函数接口和CL语言标准重合。clvt 这库的核心基础是 vt-einsum，vt-map, vt-reduce 三个函数, 其余操作大多数都是基于这三个核心函数组合完成，易于理解，同时这个库有完美的打印输出功能。目前这个库已经实现了许多张量的基础操作，未来将进一步完善，目标是尽可能实现 numpy 众多功能, 部分函数功能向pytorch看齐。这个库的函数都是以 vt- 开头，配合 slime 一起使用非常方便，易于查看已经实现了哪些函数。目前在sbcl上完成了大部分的测试。

This is a tensor library written entirely in Common Lisp, collaboratively developed by the AI 'Zhipu Qingyan' (GLM5.1) and 'DeepSeek' (v4pro). The goal is to build a concise yet powerful tensor computation library for the Common Lisp ecosystem. Although the Lisp community already has two relatively popular libraries, magicl and numcl, magicl lacks support for high-dimensional tensors and some important functions, while numcl emphasizes type inference and has some function interfaces that overlap with standard CL functions. The core foundation of the clvt library consists of three functions: vt-einsum, vt-map, and vt-reduce. Most other operations are built by combining these three core functions, making them easy to understand. Additionally, this library features excellent pretty-printing capabilities. Currently, the library has already implemented many basic tensor operations, and further improvements will be made in the future, aiming to implement as many NumPy features as possible, with some functions modeled after PyTorch. Functions in this library are all prefixed with vt-, which, when used with Slime, makes it very convenient to see which functions have been implemented. The majority of tests have been completed on SBCL.

clvt 举例:

CLVT> (defparameter *m* (vt-arange 27 :start 0 :step 1 :type 'fixnum)) *M* CLVT> *m* #<VT shape:(27) dtype:FIXNUM [ 0, 1, 2, 3, ..., 23, 24, 25, 26]> CLVT> (setf *m* (vt-reshape *m* '(3 3 3))) #<VT shape:(3 3 3) dtype:FIXNUM [[[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8]], [[ 9, 10, 11], [ 12, 13, 14], [ 15, 16, 17]], [[ 18, 19, 20], [ 21, 22, 23], [ 24, 25, 26]]]> CLVT> (vt-amax *m*) #<VT shape:NIL dtype:FIXNUM 26> CLVT> (vt-amax *m* :axis 0) #<VT shape:(3 3) dtype:FIXNUM [[ 18, 19, 20], [ 21, 22, 23], [ 24, 25, 26]]> CLVT> (vt-argmin *m* :axis 0) #<VT shape:(3 3) dtype:FIXNUM [[ 0, 0, 0], [ 0, 0, 0], [ 0, 0, 0]]> CLVT> (vt-sum *m*) #<VT shape:NIL dtype:FIXNUM 351> CLVT> (vt-sum *m* :axis 0) #<VT shape:(3 3) dtype:FIXNUM [[ 27, 30, 33], [ 36, 39, 42], [ 45, 48, 51]]> CLVT> (vt-+ *m* 5) #<VT shape:(3 3 3) dtype:FIXNUM [[[ 5, 6, 7], [ 8, 9, 10], [ 11, 12, 13]], [[ 14, 15, 16], [ 17, 18, 19], [ 20, 21, 22]], [[ 23, 24, 25], [ 26, 27, 28], [ 29, 30, 31]]]> CLVT> (vt-+ *m* *m*) #<VT shape:(3 3 3) dtype:FIXNUM [[[ 0, 2, 4], [ 6, 8, 10], [ 12, 14, 16]], [[ 18, 20, 22], [ 24, 26, 28], [ 30, 32, 34]], [[ 36, 38, 40], [ 42, 44, 46], [ 48, 50, 52]]]> CLVT> (vt-* *m* *m*) #<VT shape:(3 3 3) dtype:FIXNUM [[[ 0, 1, 4], [ 9, 16, 25], [ 36, 49, 64]], [[ 81, 100, 121], [ 144, 169, 196], [ 225, 256, 289]], [[ 324, 361, 400], [ 441, 484, 529], [ 576, 625, 676]]]> CLVT> (vt-sin *m*) #<VT shape:(3 3 3) dtype:DOUBLE-FLOAT [[[ 0.0, 0.8415, 0.9093], [ 0.1411, -0.7568, -0.9589], [ -0.2794, 0.657, 0.9894]], [[ 0.4121, -0.544, -1.0], [ -0.5366, 0.4202, 0.9906], [ 0.6503, -0.2879, -0.9614]], [[ -0.751, 0.1499, 0.9129], [ 0.8367, -0.0089, -0.8462], [ -0.9056, -0.1324, 0.7626]]]> CLVT> (vt-slice *m* '(0)) #<VT shape:(3 3) dtype:FIXNUM [[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8]]> CLVT> (setf (vt-slice *m* '(1)) (vt-slice *m* '(0))) #<VT shape:(3 3) dtype:FIXNUM [[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8]]> CLVT> *m* #<VT shape:(3 3 3) dtype:FIXNUM [[[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8]], [[ 0, 1, 2], [ 3, 4, 5], [ 6, 7, 8]], [[ 18, 19, 20], [ 21, 22, 23], [ 24, 25, 26]]]>

;; 已经实现并导出的函数有 ;; 张量结构访问器 vt vt-shape vt-strides vt-offset vt-data vt-element-type vt-order vt-size vt-p vt-itemsize vt-nbytes vt-contiguous-p vt-shape-to-size vt-compute-strides ;; 张量创建 vt-zeros vt-ones vt-full vt-empty vt-zeros-like vt-ones-like vt-full-like vt-empty-like vt-const vt-arange vt-linspace vt-logspace vt-eye vt-diag vt-identity vt-from-sequence vt-from-array vt-from-function vt-flatten-sequence vt-to-list vt-to-array vt-astype ;; 形状操作与视图 vt-view vt-reshape vt-transpose vt-squeeze vt-unsqueeze vt-expand-dims vt-flatten vt-ravel vt-swapaxes vt-rot90 vt-narrow vt-split vt-vsplit vt-hsplit vt-dsplit vt-stack vt-vstack vt-hstack vt-dstack vt-concatenate vt-concat vt-repeat vt-tile vt-pad vt-broadcast-to vt-broadcast-shapes vt-broadcast-strides vt-contiguous vt-flip vt-roll vt-triu vt-tril vt-diagonal vt-flatten-to-nested ;; 索引、切片与选择 vt-ref ;; (setf vt-ref ... vt-slice ;; (setf vt-slice ... vt-item vt-take vt-put vt-where vt-argwhere vt-nonzero vt-choose vt-select vt-extract vt-searchsorted vt-digitize vt-bincount vt-ensure-shape-compatible vt-normalize-axis ;; 算术运算 vt-+ vt-- vt-* vt-/ vt-add vt-sub vt-mul vt-div vt-scale vt-square vt-expt vt-pow vt-sqrt vt-abs vt-signum vt-mod vt-rem vt-round vt-floor vt-ceiling vt-trancate vt-rint vt-log vt-log2 vt-log10 vt-exp vt-clip ;; 三角函数与双曲函数 vt-sin vt-cos vt-tan vt-asin vt-acos vt-atan vt-atan2 vt-sinh vt-cosh vt-tanh vt-hypot vt-sinc vt-deg2rad vt-rad2deg ;; 比较与逻辑 vt-= vt-/= vt-< vt-<= vt-> vt->= vt-positive-p vt-negative-p vt-zero-p vt-nonzero-p vt-even-p vt-odd-p vt-logical-and vt-logical-or vt-logical-not vt-logical-xor vt-all vt-any vt-isclose vt-allclose vt-isfinite vt-isinf vt-isnan ;; 归约与统计 vt-sum vt-mean vt-average vt-std vt-var vt-amax vt-amin vt-argmax vt-argmin vt-prod vt-cumsum vt-cumprod vt-median vt-percentile vt-quantile vt-ptp vt-histogram vt-trapz vt-gradient vt-diff vt-correlate vt-convolve vt-sort vt-argsort vt-maximum vt-minimum ;; 线性代数 vt-matmul vt-matmul-df vt-@ vt-einsum vt-dot vt-outer vt-trace vt-norm vt-l1-norm vt-frobenius-norm vt-solve vt-inv vt-det vt-lu vt-diag vt-triu vt-tril vt-diagonal vt-qr vt-svd vt-matrix-rank ;; 激活函数 vt-sigmoid vt-relu vt-leaky-relu vt-swish vt-softplus vt-gelu vt-mish vt-hard-tanh vt-hard-sigmoid ;; 损失函数与概率 vt-softmax vt-log-softmax vt-mean-squared-error vt-binary-cross-entropy vt-cross-entropy ;; 集合操作 vt-unique vt-intersect1d vt-union1d vt-setdiff1d vt-setxor1d vt-in1d ;; 随机数生成 vt-random vt-random-uniform vt-random-normal vt-random-int vt-random-integers vt-random-seed ;; nan的相关 vt-float-nan vt-float-nan-p vt-float-nan-= vt-float-pos-inf vt-float-neg-inf vt-float-pos-inf-p vt-float-neg-inf-p vt-float-inf-= vt-float-nan-inf-= +vt-float-nan+ +vt-float-pos-inf+ +vt-float-neg-inf+ ;; 核心迭代与映射 vt-map vt-do-each vt-reduce vt-copy-into vt-copy vt-get-contiguous-df-data ;; 通用辅助与宏 vt-normalize-axis vt-broadcast-shapes vt-broadcast-strides vt-compute-strides vt-compute-logical-strides vt-ensure-shape-compatible with-float-safe

测试在 example/example.lisp 文件中。

(load "~/quicklisp/local-projects/clvt/example/example.lisp") (run-all-tests)

License

MIT

仓库代码链接：https://github.com/anranyicheng/clvt