From 1f7da92727094c607ad51a74fa917ca859e8f4c1 Mon Sep 17 00:00:00 2001 From: "Kwabena W. Agyeman" Date: Sat, 7 Nov 2020 16:48:22 -0800 Subject: [PATCH] Remove external libraries ulab replaces --- scripts/libraries/mtx.py | 96 ---- scripts/libraries/rv/LICENSE.txt | 674 --------------------------- scripts/libraries/rv/README.md | 173 ------- scripts/libraries/rv/__init__.py | 1 - scripts/libraries/rv/moments.py | 86 ---- scripts/libraries/rv/planar.py | 20 - scripts/libraries/rv/quickshiftpp.py | 162 ------- scripts/libraries/ulinalg.py | 173 ------- scripts/libraries/umatrix.py | 473 ------------------- scripts/libraries/vec/LICENSE.md | 20 - scripts/libraries/vec/README.md | 28 -- scripts/libraries/vec/__init__.py | 17 - scripts/libraries/vec/distance.py | 13 - 13 files changed, 1936 deletions(-) delete mode 100644 scripts/libraries/mtx.py delete mode 100644 scripts/libraries/rv/LICENSE.txt delete mode 100644 scripts/libraries/rv/README.md delete mode 100644 scripts/libraries/rv/__init__.py delete mode 100644 scripts/libraries/rv/moments.py delete mode 100644 scripts/libraries/rv/planar.py delete mode 100644 scripts/libraries/rv/quickshiftpp.py delete mode 100644 scripts/libraries/ulinalg.py delete mode 100644 scripts/libraries/umatrix.py delete mode 100644 scripts/libraries/vec/LICENSE.md delete mode 100644 scripts/libraries/vec/README.md delete mode 100644 scripts/libraries/vec/__init__.py delete mode 100644 scripts/libraries/vec/distance.py diff --git a/scripts/libraries/mtx.py b/scripts/libraries/mtx.py deleted file mode 100644 index e53fdda63..000000000 --- a/scripts/libraries/mtx.py +++ /dev/null @@ -1,96 +0,0 @@ -# The MIT License (MIT) -# -# Copyright (c) 2019 Nick Lee -# -# Permission is hereby granted, free of charge, to any person obtaining a copy of -# this software and associated documentation files (the "Software"), to deal in -# the Software without restriction, including without limitation the rights to -# use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of -# the Software, and to permit persons to whom the Software is furnished to do so, -# subject to the following conditions: -# -# The above copyright notice and this permission notice shall be included in all -# copies or substantial portions of the Software. -# -# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS -# FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR -# COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER -# IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN -# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. - -def _dot(a, b): - s = 0 - for i in range(0, len(b)): - s += a[i] * b[i] - return s - -def mul(A, b): - return [_dot(row, b) for row in A] - -def _height(A): - return len(A) - -def _width(A): - return len(A[0]) - -def _max_magnitude_row(A, column): - first_row = column - - max_row = first_row - max_value = A[first_row][column] - - for i in range(first_row+1, _height(A)): - if abs(A[i][column]) > abs(max_value): - max_row = i - max_value = A[i][column] - - return max_row - -def _subtract_rows_below(A, row, column, pivot_value): - # Fill in factors where entries will become zero. - for i in range(row+1, _height(A)): - A[i][column] /= pivot_value - - for i in range(row+1, _height(A)): - for j in range(column+1, _width(A)): - A[i][j] -= (A[i][column] * A[row][j]) - -def lu(A): - P = None - for pivot_column in range(0, _width(A)-1): - pivot_row = pivot_column - max_row = _max_magnitude_row(A, pivot_column) - pivot_value = A[max_row][pivot_column] - - if max_row != pivot_row: - A[pivot_row], A[max_row] = A[max_row], A[pivot_row] - - if P is None: - P = list(range(0, _height(A))) - - P[pivot_row], P[max_row] = P[max_row], P[pivot_row] - - _subtract_rows_below(A, pivot_row, pivot_column, pivot_value) - return P,A - -def _forward_substitute(A, b): - for i in range(1, len(b)): - for j in range(0, i): - b[i] = b[i] - (b[j] * A[i][j]) - -def _backward_substitute(A, b): - size = len(b) - b[-1] = b[-1] / A[-1][-1] - for i in range(size-2, -1, -1): - for j in range(i+1, size): - b[i] = b[i] - (b[j] * A[i][j]) - b[i] = b[i] / A[i][i] - -def solve(PLU, b): - P, LU = PLU - - x = b[:] if P is None else [b[i] for i in P] # permutation - _forward_substitute(LU, x) - _backward_substitute(LU, x) - return x diff --git a/scripts/libraries/rv/LICENSE.txt b/scripts/libraries/rv/LICENSE.txt deleted file mode 100644 index f288702d2..000000000 --- a/scripts/libraries/rv/LICENSE.txt +++ /dev/null @@ -1,674 +0,0 @@ - GNU GENERAL PUBLIC LICENSE - Version 3, 29 June 2007 - - Copyright (C) 2007 Free Software Foundation, Inc. - Everyone is permitted to copy and distribute verbatim copies - of this license document, but changing it is not allowed. - - Preamble - - The GNU General Public License is a free, copyleft license for -software and other kinds of works. - - The licenses for most software and other practical works are designed -to take away your freedom to share and change the works. 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If not, see . - -Also add information on how to contact you by electronic and paper mail. - - If the program does terminal interaction, make it output a short -notice like this when it starts in an interactive mode: - - Copyright (C) - This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. - This is free software, and you are welcome to redistribute it - under certain conditions; type `show c' for details. - -The hypothetical commands `show w' and `show c' should show the appropriate -parts of the General Public License. Of course, your program's commands -might be different; for a GUI interface, you would use an "about box". - - You should also get your employer (if you work as a programmer) or school, -if any, to sign a "copyright disclaimer" for the program, if necessary. -For more information on this, and how to apply and follow the GNU GPL, see -. - - The GNU General Public License does not permit incorporating your program -into proprietary programs. If your program is a subroutine library, you -may consider it more useful to permit linking proprietary applications with -the library. If this is what you want to do, use the GNU Lesser General -Public License instead of this License. But first, please read -. diff --git a/scripts/libraries/rv/README.md b/scripts/libraries/rv/README.md deleted file mode 100644 index e96cbd386..000000000 --- a/scripts/libraries/rv/README.md +++ /dev/null @@ -1,173 +0,0 @@ -# OpenRV - Robot Vision routines for OpenMV - -[OpenMV](https://openmv.io) is a small camera board for machine vision. I use it -to direct my robot. [The software -library](http://docs.openmv.io/library/index.html) is adequate, but lacks some -algorithms I need. Out comes this project, in which I implement a few missing -pieces myself. I hope it could save time for someone who tries to do the same. - -**Everything is tested on OpenMV Cam H7** - -## Prerequisites - -Vector and matrix are mainstay in machine vision. Finding no satisfactory -libraries, I have again implemented my own. - -#### Vector Operations on MicroPython - -- [Project](https://gitlab.com/nickoala/micropython-vec) -- [Package](https://pypi.org/project/micropython-vec/) - -#### Fast Matrix Multiplication and Linear Solver on MicroPython - -- [Project](https://gitlab.com/nickoala/micropython-mtx) -- [Package](https://pypi.org/project/micropython-mtx/) - -Along with this project's `rv` package, the OpenMV camera's SD card should -contain: - -``` -/ -├── mtx.py -├── rv -│   ├── __init__.py -│   ├── moments.py -│   ├── planar.py -│   └── quickshiftpp.py -└── vec - ├── distance.py - └── __init__.py -``` - -**In addition, you need some theoretical backgrounds to use vision algorithms -effectively. This page does not give you those backgrounds. Study them -yourself.** - -## Hu moments - -[Hu moments](https://docs.opencv.org/2.4/modules/imgproc/doc/structural_analysis_and_shape_descriptors.html#humoments) -[is a shape descriptor](https://www.pyimagesearch.com/2014/10/27/opencv-shape-descriptor-hu-moments-example/) -[invariant to translation, scale, and rotation](https://www.learnopencv.com/shape-matching-using-hu-moments-c-python/). -That means it can recognize the same shape no matter its location, size, and orientation in the picture. - -#### Usage - -The last element of Hu moments is somewhat of an oddball. It indicates -reflection rather than the general shape. For matching, the last element should -be dropped. - -Use the function `vec.distance.euclidean()` to see how close two vectors are. - -```python -import rv.moments -import vec.distance -import image - -a = image.Image('/images/a.pgm') -b = image.Image('/images/b.pgm') - -ha = rv.moments.hu(a) -hb = rv.moments.hu(b) - -print(vec.distance.euclidean(ha[:-1], hb[:-1])) -``` - -**Remark:** Although accepting gray-level images, this implementation treats -pixels as either 0 or 1. Pixels having a non-zero brightness are treated as 1. -This speeds up calculation. - -**More:** [test_moments.py](test/test_moments.py) - -## Planar homography - -Map points from one coordinate system to another. For example, a red ball sits -at (90, 50) on the image and you know it is on the floor (not floating in air), -planar homography can map the image point (90, 50) to a position on the floor, -telling you how far the red ball is in front of the robot and how much left or -right. In this case, points are essentially mapped from the *image coordinate -system* to the *floor coordinate system*. - -Once you can map points, finding out the size of objects is straight-forward. - -#### Usage - -It works only when two coordinate systems (i.e. the two planes) are fixed -relative to each other. In other words, the camera's height and orientation -relative to the floor cannot change. - -**[First, you have to calibrate for a homography matrix, which is a very long -story. I have devoted an entire directory to discuss the process. Take a look -there.](homography)** - -Once you have the matrix, the rest is easy. - -```python -import rv.planar - -H = [[ 3.14916496e+01, -9.79038178e+02, 1.03951636e+05], - [ 7.57939015e+02, -3.31912533e+01, -5.86807545e+04], - [ 2.06572544e-01, 2.03579263e+00, 1.00000000e+00]] - -p = rv.planar.Planar(H) - -image_points = [[83, 109], - [70, 100], - [51, 92]] - -print(p.project(image_points)) -``` - -**More:** [test_planar.py](test/test_planar.py) - -## Quickshift++ - -[The latest member](https://github.com/google/quickshift) [of the -Meanshift](http://www.chioka.in/meanshift-algorithm-for-the-rest-of-us-python/) -[family of clustering -algorithms](https://github.com/Nick-Ol/MedoidShift-and-QuickShift), Quickshift++ -accepts a bunch of points and group them. I use it to "discover" the colors of -disks on the floor, before using colors to pick out the disks. This saves me -from hard-coding the colors beforehand, and makes the robot adaptive. - -It is not optimized to handle a large number of points. OpenMV's limited memory -precludes handling a lot of points anyway. Don't expect to use it to segment an -entire image. - -#### Usage - -```python -import rv.quickshiftpp - -points = [ - # cluster 1 - [1, 1], - [1.0, 1.2], - [0.9, 1.1], - [0.95, 0.99], - - # cluster 2 - [3.3, 3.0], - - # cluster 3 - [5.0, 8.2], - [5.5, 7.9], - [4.8, 8.1], - [5.1, 7.7], -] - -print(rv.quickshiftpp.cluster(points, - k=2, - beta=0.2)) -``` - -The parameter `k` determines how density is estimated. It uses *distance to the -k-th nearest neighbor* to estimate density around each point. - -The parameter `beta` determines how much density is allowed to vary within -cluster cores. Here is not the place to explain what "cluster core" means. Some -theoretical understanding cannot be avoided. - -In short, use `k` and `beta` to tune the clustering. - -**More:** [test_quickshiftpp.py](test/test_quickshiftpp.py) and - [test_quickshiftpp_colors.py](test/test_quickshiftpp_colors.py) diff --git a/scripts/libraries/rv/__init__.py b/scripts/libraries/rv/__init__.py deleted file mode 100644 index 8b1378917..000000000 --- a/scripts/libraries/rv/__init__.py +++ /dev/null @@ -1 +0,0 @@ - diff --git a/scripts/libraries/rv/moments.py b/scripts/libraries/rv/moments.py deleted file mode 100644 index 8c8dd6db8..000000000 --- a/scripts/libraries/rv/moments.py +++ /dev/null @@ -1,86 +0,0 @@ -import math - -def _sum(img, roi, f): - x, y, w, h = roi or (0, 0, img.width(), img.height()) - s = 0 - for i in range(x, x + w): - for j in range(y, y + h): - if img.get_pixel(i,j) != 0: - s += f(i, j) - return s - -def centroid(img, roi=None, return_intermediate=False): - m10 = _sum(img, roi, lambda x,y: x) - m01 = _sum(img, roi, lambda x,y: y) - m00 = _sum(img, roi, lambda x,y: 1) - - c = [0, 0] if m00 == 0 else [float(m10 / m00), float(m01 / m00)] - - return [m00, c] if return_intermediate else c - -def central(img, roi=None, return_intermediate=False): - results = centroid(img, roi, return_intermediate=True) - cx, cy = results[-1] - - u20 = _sum(img, roi, lambda x,y: (x-cx)**2) - u11 = _sum(img, roi, lambda x,y: (x-cx) * (y-cy)) - u02 = _sum(img, roi, lambda x,y: (y-cy)**2) - - u30 = _sum(img, roi, lambda x,y: (x-cx)**3) - u21 = _sum(img, roi, lambda x,y: (x-cx)**2 * (y-cy)) - u12 = _sum(img, roi, lambda x,y: (x-cx) * (y-cy)**2) - u03 = _sum(img, roi, lambda x,y: (y-cy)**3) - - us = [u20, u11, u02, u30, u21, u12, u03] - - return (results + [us]) if return_intermediate else us - -def normalized_central(img, roi=None, return_intermediate=False): - results = central(img, roi, return_intermediate=True) - m00, _, [u20, u11, u02, u30, u21, u12, u03] = results - - if m00 == 0: - ns = [0, 0, 0, 0, 0, 0, 0] - else: - m2 = m00**2 - m3 = m00**2.5 - n20, n11, n02 = u20/m2, u11/m2, u02/m2 - n30, n21, n12, n03 = u30/m3, u21/m3, u12/m3, u03/m3 - - ns = [n20, n11, n02, n30, n21, n12, n03] - - return (results + [ns]) if return_intermediate else ns - -def hu(img, roi=None, return_intermediate=False): - results = normalized_central(img, roi, return_intermediate=True) - n20, n11, n02, n30, n21, n12, n03 = results[-1] - - h0 = n20 + n02 - - h1 = (n20 - n02)**2 + 4 * n11 * n11 - - _n30_3n12 = n30 - 3 * n12 - _3n21_n03 = 3 * n21 - n03 - - h2 = _n30_3n12**2 + _3n21_n03**2 - - n3012 = n30 + n12 - n3012_2 = n3012 * n3012 - - n2103 = n21 + n03 - n2103_2 = n2103 * n2103 - - h3 = n3012_2 + n2103_2 - - h4 = (_n30_3n12 * n3012 * ( n3012_2 - 3 * n2103_2 ) - + _3n21_n03 * n2103 * ( 3 * n3012_2 - n2103_2 )) - - h5 = ( n20 - n02 ) * ( n3012_2 - n2103_2 ) + 4 * n11 * n3012 * n2103 - - h6 = (_3n21_n03 * n2103 * ( 3 * n3012_2 - n2103_2 ) - - _n30_3n12 * n2103 * ( 3 * n3012_2 - n2103_2 )) - - hs = [0 if h == 0 else math.copysign(math.log10(math.fabs(h)), h) - for h in [h0, h1, h2, h3, h4, h5, h6]] - - return (results + [hs]) if return_intermediate else hs diff --git a/scripts/libraries/rv/planar.py b/scripts/libraries/rv/planar.py deleted file mode 100644 index f5bcc639c..000000000 --- a/scripts/libraries/rv/planar.py +++ /dev/null @@ -1,20 +0,0 @@ -import mtx, vec - -class Planar(object): - def __init__(self, H, offset=[0,0]): - self.H = H - self.H_ = None # LU factorization of H - self.offset = offset - - def project(self, points, reverse=False): - if reverse: - if self.H_ is None: - self.H_ = mtx.lu([r[:] for r in self.H]) - - qs = [mtx.solve(self.H_, - vec.sub(p, self.offset)+[1]) for p in points] - return [vec.div(q[:-1], q[-1]) for q in qs] - else: - qs = [mtx.mul(self.H, p+[1]) for p in points] - return [vec.add(self.offset, - vec.div(q[:-1], q[-1])) for q in qs] diff --git a/scripts/libraries/rv/quickshiftpp.py b/scripts/libraries/rv/quickshiftpp.py deleted file mode 100644 index b373f5d64..000000000 --- a/scripts/libraries/rv/quickshiftpp.py +++ /dev/null @@ -1,162 +0,0 @@ -import vec.distance - -def distance_to_kth_nearest_neighbor(points, i, k): - fix = points[i] - d = [vec.distance.euclidean(fix, p) for p in points] - d.sort() - return d[k] - # Smallest distance is always to the point itself. - # First element can be ignored. - # Distance to k-th nearest neighbor is at index == k. - -def calculate_threshold(r, d, beta): - return r / (1 - beta)**(1 / d) - -def find_threshold_position(threshold, ascending): - lower = 0 - upper = len(ascending) - 1 - - if ascending[upper][0] <= threshold: - return upper - - # binary search - while upper - lower > 1: - i = (upper + lower) // 2 - r = ascending[i][0] - - if r == threshold: - # push `i` to last element equal to threshold - while i+1 < len(ascending) and ascending[i+1][0] == threshold: - i += 1 - return i - elif r < threshold: - lower = i - else: - upper = i - - if ascending[upper][0] <= threshold: - return upper - else: - return lower - -def in_which(x, sets): - for s in sets: - if x in s: - return s - return None - -def form_cluster_core(core_set, - existing_cores, - points, - sorted_radii, - seed_position, - threshold_position): - - def include(current_position): - current_radius, current_index = sorted_radii[current_position] - - core_set.add(current_index) - - for other_position in range(0, threshold_position + 1): - other_radius, other_index = sorted_radii[other_position] - - if other_index == current_index or other_index in core_set: - continue - - distance = vec.distance.euclidean( - points[current_index], points[other_index]) - - if distance <= min(current_radius, other_radius): - # Connect current point to the other point - - if in_which(other_index, existing_cores) is not None: - # The other point is already in another core. - # Current set will not be disjoint from existing cores. - # Current set cannot form a new core. - return False - else: - # Continue making connections, starting from new point. - clean = include(other_position) - if not clean: - return False - return True - - return include(seed_position) - -def assign_cluster(clusters, - points, - sorted_radii, - position): - - def find_cluster_to_belong(current_position): - _, current_index = sorted_radii[current_position] - - cluster_set = in_which(current_index, clusters) - if cluster_set is not None: - # already belong to a cluster - return cluster_set - - nearest_neighbor_distance = None - nearest_neighbor_position = None - - # find nearest neighbor - for i in range(0, current_position): - _, other_index = sorted_radii[i] - - distance = vec.distance.euclidean( - points[current_index], points[other_index]) - - if nearest_neighbor_distance is None \ - or distance < nearest_neighbor_distance: - nearest_neighbor_distance = distance - nearest_neighbor_position = i - - # join nearest neighbor's cluster - cluster_set = find_cluster_to_belong(nearest_neighbor_position) - cluster_set.add(current_index) - return cluster_set - - find_cluster_to_belong(position) - -def cluster(points, - k, - beta, - return_modes=False): - dimension = len(points[0]) - - sorted_radii = [(distance_to_kth_nearest_neighbor(points, i, k=k), i) - for i in range(0, len(points))] - sorted_radii.sort() - # smallest radius first, i.e. highest density first. - - modes = [] - clusters = [] - proposed_core = set() - - for position in range(0, len(sorted_radii)): - radius, index = sorted_radii[position] - - threshold = calculate_threshold(radius, dimension, beta) - threshold_position = find_threshold_position(threshold, sorted_radii) - - if form_cluster_core(proposed_core, - clusters, - points, - sorted_radii, - seed_position=position, - threshold_position=threshold_position): - clusters.append(proposed_core) - proposed_core = set() - - if return_modes: - modes.append(index) - else: - proposed_core.clear() - - for position in range(0, len(sorted_radii)): - assign_cluster(clusters, - points, - sorted_radii, - position=position) - - return (clusters, modes) if return_modes else clusters diff --git a/scripts/libraries/ulinalg.py b/scripts/libraries/ulinalg.py deleted file mode 100644 index 7ad79c911..000000000 --- a/scripts/libraries/ulinalg.py +++ /dev/null @@ -1,173 +0,0 @@ -''' - -Part of the micro-linalg project to provide a small -matrix / linear algebra package for Micropython (Python3) - -The MIT License (MIT) - -Copyright (c) 2015 Jamie Lawson - -Permission is hereby granted, free of charge, to any person obtaining a copy -of this software and associated documentation files (the "Software"), to deal -in the Software without restriction, including without limitation the rights -to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -copies of the Software, and to permit persons to whom the Software is -furnished to do so, subject to the following conditions: - -The above copyright notice and this permission notice shall be included in all -copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -SOFTWARE. -''' -import math -import umatrix - - -def zeros(m, n, dtype=umatrix.ddtype): - return umatrix.matrix([[0 for i in range(n)] for j in range(m)], dtype=dtype) - - -def ones(m, n, dtype=umatrix.ddtype): - return zeros(m, n, dtype) + 1 - - -def eye(m, dtype=umatrix.ddtype): - Z = zeros(m, m, dtype=dtype) - for i in range(m): - Z[i, i] = 1 - return Z - -def det_inv(x): - ''' Return (det(x) and inv(x)) - - Operates on a copy of x - Using elementary row operations convert X to an upper matrix - the product of the diagonal = det(X) - Continue to convert X to the identity matrix - All the operation carried out on the original identity matrix - makes it the inverse of X - ''' - if not x.is_square: - raise ValueError('Matrix must be square') - else: - # divide each row element by [0] to give a one in the first position - # (may have to find a row to switch with if first element is 0) - x = x.copy() - inverse = eye(len(x), dtype=float) - sign = 1 - factors = [] - p = 0 - while p < len(x): - d = x[p, p] - if abs(d) < umatrix.flt_eps: - # pivot == 0 need to swap a row - # check if swap row also has a zero at the same position - np = 1 - while (p + np) < len(x) and abs(x[p + np, p]) < umatrix.flt_eps: - np += 1 - if (p + np) == len(x): - # singular - return [0, []] - # swap rows - z = x[p + np] - x[p + np, :] = x[p] - x[p, :] = z - # do identity - z = inverse[p + np] - inverse[p + np, :] = inverse[p] - inverse[p, :] = z - # change sign of det - sign = -sign - continue - factors.append(d) - # change target row - for n in range(p, len(x)): - x[p, n] = x[p, n] / d - # need to do the entire row for the inverse - for n in range(len(x)): - inverse[p, n] = inverse[p, n] / d - # eliminate position in the following rows - for i in range(p + 1, len(x)): - # multiplier is that column entry - t = x[i, p] - for j in range(p, len(x)): - x[i, j] = x[i, j] - (t * x[p, j]) - for j in range(len(x)): - inverse[i, j] = inverse[i, j] - (t * inverse[p, j]) - p = p + 1 - s = sign - for i in factors: - s = s * i # determinant - # travel through the rows eliminating upper diagonal non-zero values - for i in range(len(x) - 1): - # final row should already be all zeros - # except for the final position - for p in range(i + 1, len(x)): - # multiplier is that column entry - t = x[i, p] - for j in range(i + 1, len(x)): - x[i, j] = x[i, j] - (t * x[p, j]) - for j in range(len(x)): - inverse[i, j] = inverse[i, j] - (t * inverse[p, j]) - return (s, inverse) - - -def pinv(X): - ''' Calculates the pseudo inverse Adagger = (A'A)^-1.A' ''' - Xt = X.transpose() - d, Z = det_inv(dot(Xt, X)) - return dot(Z, Xt) - - -def dot(X, Y): - ''' Dot product ''' - if X.size(2) == Y.size(1): - Z = [] - for k in range(X.size(1)): - for j in range(Y.size(2)): - Z.append(sum([X[k, i] * Y[i, j] for i in range(Y.size(1))])) - return umatrix.matrix(Z, cstride=1, rstride=Y.size(2)) - else: - raise ValueError('shapes not aligned') - - -def cross(X, Y, axis=1): - ''' Cross product - axis=1 Numpy default - axis=0 MATLAB, Octave, SciLab default - ''' - if axis == 0: - X = X.T - Y = Y.T - if (X.n in (2, 3)) and (Y.n in (2, 3)): - if X.m == Y.m: - Z = [] - for k in range(min(X.m, Y.m)): - z = X[k, 0] * Y[k, 1] - X[k, 1] * Y[k, 0] - if (X.n == 3) and (Y.n == 3): - Z.append([X[k, 1] * Y[k, 2] - X[k, 2] * Y[k, 1], - X[k, 2] * Y[k, 0] - X[k, 0] * Y[k, 2], z]) - else: - Z.append([z]) - if axis == 0: - return umatrix.matrix(Z).T - else: - return umatrix.matrix(Z) - else: - raise ValueError('shape mismatch') - else: - raise ValueError('incompatible dimensions for cross product' - ' (must be 2 or 3)') - -def eps(x = 0): - # ref. numpy.spacing(), Octave/MATLAB eps() function - if x: - return 2**(math.floor(math.log(abs(x))/math.log(2)))*umatrix.flt_eps - else: - return umatrix.flt_eps diff --git a/scripts/libraries/umatrix.py b/scripts/libraries/umatrix.py deleted file mode 100644 index e7597864e..000000000 --- a/scripts/libraries/umatrix.py +++ /dev/null @@ -1,473 +0,0 @@ -''' - -Part of the micro-linalg project to provide a small -matrix / linear algebra package for MicroPython (Python3) - -The MIT License (MIT) - -Copyright (c) 2015 Jamie Lawson - -Permission is hereby granted, free of charge, to any person obtaining a copy -of this software and associated documentation files (the "Software"), to deal -in the Software without restriction, including without limitation the rights -to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -copies of the Software, and to permit persons to whom the Software is -furnished to do so, subject to the following conditions: - -The above copyright notice and this permission notice shall be included in all -copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -SOFTWARE. -''' - -import sys - -stypes = [bool, int] -ddtype = int -estypes = [] -flt_eps = 1 - - -class matrix(object): - - def __init__(self, data, cstride=0, rstride=0, dtype=None): - ''' Builds a matrix representation of 'data'. - 'data' can be a list (columns) of lists (rows) - [[1,2,3],[4,5,6]] or - a simple list organized as determined by rstride and cstride: - [1,2,3,4,5,6] cstride=1, rstride=3. - Elements will be of highest type included in 'data' or - 'dtype' can be used to force the type. - ''' - if cstride != 0: - if cstride == 1: - self.n = rstride - self.m = int(len(data) / self.n) - else: - self.m = cstride - self.n = int(len(data) / self.m) - self.cstride = cstride - self.rstride = rstride - self.data = data - else: - # else determine shape from list passed in - self.n = 1 - if type(data) == int: - self.m = 1 - else: # it is a list - self.m = len(data) - # is data[0] a list - if (type(data[0]) == list): - self.n = len(data[0]) - self.data = [data[i][j] - for i in range(self.m) for j in range(self.n)] - self.cstride = 1 - self.rstride = self.n - # ensure all elements are of the same type - if dtype is None: - self.dtype = stypes[max([stypes.index(type(i)) for i in self.data])] - else: - if dtype in stypes: - self.dtype = dtype - else: - raise TypeError('unsupported type', dtype) - self.data = [self.dtype(i) for i in self.data] - - def __len__(self): - return self.m - - def __eq__(self, other): - if self.shape == other.shape: - res = all([self.data[i] == other.data[i] for i in range(self.size())]) - return res and (self.shape == other.shape) - else: - raise ValueError('shapes not equal') - - def __ne__(self, other): - return not __eq__(other) - - def __iter__(self): - self.cur = 0 - # determine proper axis - if self.m == 1: - self.cnt_lim = self.n - else: - self.cnt_lim = self.m - return self - - def __next__(self): - ''' - Returns a matrix if m > 1 - else the next numeric element of the vector. - (Numpy returns vectors if selected via slice) - ''' - if self.cur >= self.cnt_lim: - raise StopIteration - self.cur = self.cur + 1 - if self.m == 1: - return self.data[self.cur - 1] - else: - return self[self.cur - 1] - - def slice_to_offset(self, r0, r1, c0, c1): - # check values and limit them - nd = [self.data[i * self.rstride + j * self.cstride] - for i in range(r0, r1) for j in range(c0, c1)] - return matrix(nd, cstride=1, rstride=(c1 - c0)) - - def slice_indices(self, index, axis=0): - # handles the unsupported slice.indices() method in uPy. - # If implemented: - # midx = index.indices(self.m) - # should work. - if isinstance(index.start, type(None)): - s0 = 0 - else: - s0 = min(int(index.start), self.shape[axis]) - if isinstance(index.stop, type(None)): - p0 = self.shape[axis] - else: - p0 = min(int(index.stop), self.shape[axis]) - return (s0, p0) - - def __getitem__(self, index): - if type(index) == tuple: - # int and int - # int and slice - # slice and int - # slice and slice - if isinstance(index[0], int): - s0 = index[0] - p0 = s0 + 1 - else: # row slice - s0, p0 = self.slice_indices(index[0], 0) - if isinstance(index[1], int): - s1 = index[1] - p1 = s1 + 1 - else: # column slice - s1, p1 = self.slice_indices(index[1], 1) - elif type(index) == list: - # list of indices etc - raise NotImplementedError('Fancy indexing') - else: - # type is int? This will default to returning a row - s0 = index - p0 = s0 + 1 - s1 = 0 - p1 = self.n - # resultant matrix - z = self.slice_to_offset(s0, p0, s1, p1) - # if it's a single entry then return that entry as int, float etc. - if (p0 == s0 + 1) and (p1 == s1 + 1): - return z.data[0] - else: - return z - - def __setitem__(self, index, val): - if type(index) != tuple: - # need to make it a slice without the slice function - raise NotImplementedError('Need to use the slice [1,:] format.') - # int and int => single entry gets changed - # combinations of int and slice => row and columns take on elements from val - if isinstance(index[0], int): - s0 = index[0] - p0 = s0 + 1 - else: # slice - s0, p0 = self.slice_indices(index[0], 0) - if isinstance(index[1], int): - s1 = index[1] - p1 = s1 + 1 - else: # slice - s1, p1 = self.slice_indices(index[1], 1) - if type(val) == matrix: - val = val.data - elif type(val) not in [list, tuple]: - val = [val] - if not all([type(i) in stypes for i in val]): - raise ValueError('Non numeric entry') - else: - # assign list values wrapping as necessary to fill destination - k = 0 - for i in range(s0, p0): - for j in range(s1, p1): - self.data[i * self.rstride + j * self.cstride] = (self.dtype(val[k])) - k = (k + 1) % len(val) - - # there is also __delitem__ - - # def __str__(self): - def __repr__(self): - # things that use __str__ will fallback to __repr__ - # find max string field size for formatting - l = 0 - for i in self.data: - l = max(l, len(repr(i))) - s = 'mat([' - r = 0 - for i in range(self.m): - c = 0 - s = s + '[' - for j in range(self.n): - s1 = repr(self.data[r + c]) - s = s + s1 + ' ' * (l - len(s1)) - if (j < (self.n - 1)): - s = s + ', ' - c = c + self.cstride - if (i < (self.m - 1)): - s = s + '],\n ' - else: - s = s + ']' - r = r + self.rstride - s = s + '])' - return s - - # Reflected operations are not yet implemented in MicroPython - # __rmul__ for example will not be invoked - - def __neg__(self): - ndat =[self.data[i] * (-1) for i in range(len(self.data))] - return matrix(ndat, cstride=self.cstride, rstride=self.rstride) - - def __do_op__(self, a, b, op): - if op == '+': - return (a + b) - elif op == '-': - return (a - b) - elif op == '*': - return (a * b) - elif op == '**': - return (a ** b) - elif op == '/': - try: - return (a / b) - except ZeroDivisionError: - raise ZeroDivisionError('division by zero') - elif op == '//': - try: - return (a // b) - except ZeroDivisionError: - raise ZeroDivisionError('division by zero') - else: - raise NotImplementedError('Unknown operator ', op) - - def __OP__(self, a, op): - if type(a) in stypes: - # matrix - scaler elementwise operation - ndat = [self.__do_op__(self.data[i], a, op) for i in range(len(self.data))] - return matrix(ndat, cstride=self.cstride, rstride=self.rstride) - elif (type(a) == list): - # matrix - list elementwise operation - # hack - convert list to matrix and resubmit then it gets handled below - # if self.n = 1 try transpose otherwise broadcast error to match numpy - if (self.n == 1) and (len(a) == self.m): - return self.__OP__(matrix([a]).T, op) - elif len(a) == self.n: - return self.__OP__(matrix([a]), op) - else: - raise ValueError('could not be broadcast') - elif (type(a) == matrix): - if (self.m == a.m) and (self.n == a.n): - # matrix - matrix elementwise operation - # use matrix indices to handle views - ndat = [self.__do_op__(self[i, j], a[i, j], op) for i in range(self.m) for j in range(self.n)] - return matrix(ndat, cstride=1, rstride=self.n) - # generalize the following two elif for > 2 dimensions? - elif (self.m == a.m): - # m==m n!=n => column-wise row operation - Y = self.copy() - for i in range(self.n): - # this call _OP_ once for each row and __do_op__ for each element - for j in range(self.m): - Y[j, i] = self.__do_op__(Y[j, i], a[j, 0], op) - return Y - elif (self.n == a.n): - # m!=m n==n => row-wise col operation - Y = self.copy() - for i in range(self.m): - # this call _OP_ once for each col and __do_op__ for each element - for j in range(self.n): - Y[i, j] = self.__do_op__(Y[i, j], a[0, j], op) - return Y - else: - raise ValueError('could not be broadcast') - raise NotImplementedError('__OP__ matrix + ', type(a)) - - def __add__(self, a): - ''' matrix - scaler elementwise addition''' - return self.__OP__(a, '+') - - def __radd__(self, a): - ''' scaler - matrix elementwise addition''' - ''' commutative ''' - return self.__add__(a) - - def __sub__(self, a): - ''' matrix - scaler elementwise subtraction ''' - if type(a) in estypes: - return self.__add__(-a) - raise NotImplementedError('__sub__ matrix -', type(a)) - - def __rsub__(self, a): - ''' scaler - matrix elementwise subtraction ''' - self = -self - return self.__add__(a) - - def __mul__(self, a): - ''' matrix scaler elementwise multiplication ''' - return self.__OP__(a, '*') - - def __rmul__(self, a): - ''' scaler * matrix elementwise multiplication - commutative - ''' - return self.__mul__(a) - - def __truediv__(self, a): - ''' matrix / scaler elementwise division ''' - return self.__OP__(a, '/') - - def __rtruediv__(self, a): - ''' scaler / matrix elementwise division ''' - return self.__OP__(a, '/') - - def __floordiv__(self, a): - ''' matrix // scaler elementwise integer division ''' - return self.__OP__(a, '//') - - def __rfloordiv__(self, a): - ''' scaler // matrix elementwise integer division ''' - return self.__OP__(a, '//') - - def __pow__(self, a): - ''' matrix ** scaler elementwise power ''' - return self.__OP__(a, '**') - - def __rpow__(self, a): - ''' scaler ** matrix elementwise power ''' - return self.__OP__(a, '**') - - def copy(self): - """ Return a copy of matrix, not just a view """ - return matrix([i for i in self.data], - cstride=self.cstride, rstride=self.rstride) - - def size(self, axis=0): - """ 0 entries - 1 rows - 2 columns - """ - return [self.m * self.n, self.m, self.n][axis] - - @property - def shape(self): - return (self.m, self.n) - - @shape.setter - def shape(self, nshape): - """ check for proper length """ - if (nshape[0] * nshape[1]) == self.size(): - self.m, self.n = nshape - self.cstride = 1 - self.rstride = self.n - else: - raise ValueError('total size of new matrix must be unchanged') - return self - - @property - def is_square(self): - return self.m == self.n - - def reshape(self, nshape): - """ check for proper length """ - X = self.copy() - X.shape = nshape - return X - - @property - def T(self): - return self.transpose() - - def transpose(self): - """ Return a view """ - X = matrix(self.data, cstride=self.rstride, rstride=self.cstride) - if self.cstride == self.rstride: - # handle column vector - X.shape = (self.n, self.m) - return X - - def reciprocal(self, n=1): - return matrix([n / i for i in self.data], cstride=self.cstride, rstride=self.rstride) - - def apply(self, func, *args, **kwargs): - """ call a scalar function on each element, returns a new matrix - passes *args and **kwargs to func unmodified - note: this is not useful for matrix-matrix operations - e.g. - y = x.apply(math.sin) - y = x.apply(lambda a,b: a>b, 5) # equivalent to y = x > 5 - y = x.apply(operators.gt, 5) # equivalent to y = x > 5 (not in micropython) - """ - return matrix([func(i, *args, **kwargs) for i in self.data], - cstride=self.cstride, rstride=self.rstride) - -def matrix_isclose(x, y, rtol=1E-05, atol=flt_eps): - ''' Returns a matrix indicating equal elements within tol''' - for i in range(x.size()): - try: - data = [abs(x.data[i] - y.data[i]) <= atol+rtol*abs(y.data[i]) for i in range(len(x.data))] - except (AttributeError, IndexError): - data = [False for i in range(len(x.data))] - return matrix(data, cstride=x.cstride, rstride=x.rstride, dtype=bool) - - -def matrix_equal(x, y, tol=0): - ''' Matrix equality test with tolerance same shape''' - res = False - if type(y) == matrix: - if x.shape == y.shape: - res = all([abs(x.data[i] - y.data[i]) <= tol for i in range(x.size())]) - return res - - -def matrix_equiv(x, y): - ''' Returns a boolean indicating if X and Y share the same data and are broadcastable''' - res = False - if type(y) == matrix: - if x.size() == y.size(): - res = all([x.data[i] == y.data[i] for i in range(len(x.data))]) - return res - -def fp_eps(): - ''' Determine floating point resolution ''' - e = 1 - while 1 + e > 1: - e = e / 2 - return 2 * e - -flt_eps = fp_eps() -try: - if sys.implementation.name == 'micropython' and sys.platform == 'linux': - # force this as there seems to be some interaction with - # some operations done using the C library with a smaller epsilon (doubles) - flt_eps = 1.19E-7 # single precision IEEE 2**-23 double 2.22E-16 == 2**-52 -except: - pass -# Determine supported types -try: - stypes.append(float) - ddtype = float -except: - pass -try: - stypes.append(complex) -except: - pass -# extended types -estypes = [matrix] -estypes.extend(stypes) diff --git a/scripts/libraries/vec/LICENSE.md b/scripts/libraries/vec/LICENSE.md deleted file mode 100644 index 88e3dffbd..000000000 --- a/scripts/libraries/vec/LICENSE.md +++ /dev/null @@ -1,20 +0,0 @@ -The MIT License (MIT) - -Copyright (c) 2019 Nick Lee - -Permission is hereby granted, free of charge, to any person obtaining a copy of -this software and associated documentation files (the "Software"), to deal in -the Software without restriction, including without limitation the rights to -use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of -the Software, and to permit persons to whom the Software is furnished to do so, -subject to the following conditions: - -The above copyright notice and this permission notice shall be included in all -copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS -FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR -COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER -IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN -CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. diff --git a/scripts/libraries/vec/README.md b/scripts/libraries/vec/README.md deleted file mode 100644 index 3a1136913..000000000 --- a/scripts/libraries/vec/README.md +++ /dev/null @@ -1,28 +0,0 @@ -# Vector Operations on MicroPython - -Nothing fancy. Treating list as vector, this library performs common -operations. I personally use it on [OpenMV](https://openmv.io) for robot vision. - -```python -import vec - -a = [1, 2, 3] -b = [4, 5, 6] - -vec.add(a, b) # [5, 7, 9] -vec.sub(a, b) # [-3, -3, -3] -vec.dot(a, b) # 32 - -vec.mul(a, 2) # [2, 4, 6] -vec.div(a, 2) # [0.5, 1.0, 1.5] -``` - -```python -import vec.distance - -a = [2, 3] -b = [5, 7] - -vec.distance.manhattan(a, b) # 7 -vec.distance.euclidean(a, b) # 5 -``` diff --git a/scripts/libraries/vec/__init__.py b/scripts/libraries/vec/__init__.py deleted file mode 100644 index 45ca5b380..000000000 --- a/scripts/libraries/vec/__init__.py +++ /dev/null @@ -1,17 +0,0 @@ -def add(a, b): - return [a[i] + b[i] for i in range(0, min(len(a), len(b)))] - -def sub(a, b): - return [a[i] - b[i] for i in range(0, min(len(a), len(b)))] - -def mul(a, n): - return [a[i] * n for i in range(0, len(a))] - -def div(a, n): - return [a[i] / n for i in range(0, len(a))] - -def dot(a, b): - s = 0 - for i in range(0, min(len(a), len(b))): - s += a[i] * b[i] - return s diff --git a/scripts/libraries/vec/distance.py b/scripts/libraries/vec/distance.py deleted file mode 100644 index 7042a369e..000000000 --- a/scripts/libraries/vec/distance.py +++ /dev/null @@ -1,13 +0,0 @@ -import math - -def manhattan(a, b): - s = 0 - for i in range(0, min(len(a), len(b))): - s += abs(a[i] - b[i]) - return s - -def euclidean(a, b): - s = 0 - for i in range(0, min(len(a), len(b))): - s += (a[i] - b[i])**2 - return math.sqrt(s)