add docs for solve_triangular

docs/manual/source/conf.py

@@ -27,7 +27,7 @@ copyright = '2019-2021, Zoltán Vörös and contributors'
 author = 'Zoltán Vörös'
 
 # The full version, including alpha/beta/rc tags
-release = '2.6.0'
+release = '2.7.0'
 
 
 # -- General configuration ---------------------------------------------------

docs/manual/source/index.rst

@@ -22,6 +22,7 @@ Welcome to the ulab book!
    numpy-universal
    numpy-fft
    numpy-linalg
+   scipy-linalg
    scipy-optimize
    scipy-signal
    scipy-special

docs/manual/source/scipy-linalg.rst

@@ -0,0 +1,120 @@
+
+linalg
+======
+
+``scipy``\ ’s ``linalg`` module contains a single function,
+``solve_triangular``, which can be called by prepending it by
+``scipy.linalg.``.
+
+1. `scipy.linalg.solve_triangular <#solve_triangular>`__
+
+solve_triangular
+----------------
+
+``scipy``:
+https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.solve_triangular.html
+
+Solve the linear equation
+
+:raw-latex:`\begin{equation}
+\mathbf{a}\cdot\mathbf{x} = \mathbf{b}
+\end{equation}`
+
+with the assumption that :math:`\mathbf{a}` is a triangular matrix. The
+two position arguments are :math:`\mathbf{a}`, and :math:`\mathbf{b}`,
+and the optional keyword argument is ``lower`` with a default value of
+``False``. ``lower`` determines, whether data are taken from the lower,
+or upper triangle of :math:`\mathbf{a}`.
+
+Note that :math:`\mathbf{a}` itself does not have to be a triangular
+matrix: if it is not, then the values are simply taken to be 0 in the
+upper or lower triangle, as dictated by ``lower``. However,
+:math:`\mathbf{a}\cdot\mathbf{x}` will yield :math:`\mathbf{b}` only,
+when :math:`\mathbf{a}` is triangular. You should keep this in mind,
+when trying to establish the validity of the solution by back
+substitution.
+
+.. code::
+        
+    # code to be run in micropython
+    
+    from ulab import numpy as np
+    from ulab import scipy as spy
+    
+    a = np.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 2, 1, 8]])
+    b = np.array([4, 2, 4, 2])
+    
+    print('a:\n')
+    print(a)
+    print('\nb: ', b)
+    
+    x = spy.linalg.solve_triangular(a, b, lower=True)
+    
+    print('='*20)
+    print('x: ', x)
+    print('\ndot(a, x): ', np.dot(a, x))
+
+.. parsed-literal::
+
+    a:
+    
+    array([[3.0, 0.0, 0.0, 0.0],
+           [2.0, 1.0, 0.0, 0.0],
+           [1.0, 0.0, 1.0, 0.0],
+           [1.0, 2.0, 1.0, 8.0]], dtype=float64)
+    
+    b:  array([4.0, 2.0, 4.0, 2.0], dtype=float64)
+    ====================
+    x:  array([1.333333333333333, -0.6666666666666665, 2.666666666666667, -0.08333333333333337], dtype=float64)
+    
+    dot(a, x):  array([4.0, 2.0, 4.0, 2.0], dtype=float64)
+    
+    
+
+
+With get the same solution, :math:`\mathbf{x}`, with the following
+matrix, but the dot product of :math:`\mathbf{a}`, and
+:math:`\mathbf{x}` is no longer :math:`\mathbf{b}`:
+
+.. code::
+        
+    # code to be run in micropython
+    
+    from ulab import numpy as np
+    from ulab import scipy as spy
+    
+    a = np.array([[3, 2, 1, 0], [2, 1, 0, 1], [1, 0, 1, 4], [1, 2, 1, 8]])
+    b = np.array([4, 2, 4, 2])
+    
+    print('a:\n')
+    print(a)
+    print('\nb: ', b)
+    
+    x = spy.linalg.solve_triangular(a, b, lower=True)
+    
+    print('='*20)
+    print('x: ', x)
+    print('\ndot(a, x): ', np.dot(a, x))
+
+.. parsed-literal::
+
+    a:
+    
+    array([[3.0, 2.0, 1.0, 0.0],
+           [2.0, 1.0, 0.0, 1.0],
+           [1.0, 0.0, 1.0, 4.0],
+           [1.0, 2.0, 1.0, 8.0]], dtype=float64)
+    
+    b:  array([4.0, 2.0, 4.0, 2.0], dtype=float64)
+    ====================
+    x:  array([1.333333333333333, -0.6666666666666665, 2.666666666666667, -0.08333333333333337], dtype=float64)
+    
+    dot(a, x):  array([5.333333333333334, 1.916666666666666, 3.666666666666667, 2.0], dtype=float64)
+    
+    
+
+
+.. code::
+
+    # code to be run in CPython
+    

docs/scipy-linalg.ipynb

@@ -0,0 +1,437 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-01-13T18:54:58.722373Z",
+     "start_time": "2021-01-13T18:54:57.178438Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Populating the interactive namespace from numpy and matplotlib\n"
+     ]
+    }
+   ],
+   "source": [
+    "%pylab inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Notebook magic"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-05-09T05:37:22.600510Z",
+     "start_time": "2021-05-09T05:37:22.595924Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from IPython.core.magic import Magics, magics_class, line_cell_magic\n",
+    "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n",
+    "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n",
+    "import subprocess\n",
+    "import os"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-05-09T05:37:26.429136Z",
+     "start_time": "2021-05-09T05:37:26.403191Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "@magics_class\n",
+    "class PyboardMagic(Magics):\n",
+    "    @cell_magic\n",
+    "    @magic_arguments()\n",
+    "    @argument('-skip')\n",
+    "    @argument('-unix')\n",
+    "    @argument('-pyboard')\n",
+    "    @argument('-file')\n",
+    "    @argument('-data')\n",
+    "    @argument('-time')\n",
+    "    @argument('-memory')\n",
+    "    def micropython(self, line='', cell=None):\n",
+    "        args = parse_argstring(self.micropython, line)\n",
+    "        if args.skip: # doesn't care about the cell's content\n",
+    "            print('skipped execution')\n",
+    "            return None # do not parse the rest\n",
+    "        if args.unix: # tests the code on the unix port. Note that this works on unix only\n",
+    "            with open('/dev/shm/micropython.py', 'w') as fout:\n",
+    "                fout.write(cell)\n",
+    "            proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n",
+    "                                    stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n",
+    "            print(proc.stdout.read().decode(\"utf-8\"))\n",
+    "            print(proc.stderr.read().decode(\"utf-8\"))\n",
+    "            return None\n",
+    "        if args.file: # can be used to copy the cell content onto the pyboard's flash\n",
+    "            spaces = \"    \"\n",
+    "            try:\n",
+    "                with open(args.file, 'w') as fout:\n",
+    "                    fout.write(cell.replace('\\t', spaces))\n",
+    "                    printf('written cell to {}'.format(args.file))\n",
+    "            except:\n",
+    "                print('Failed to write to disc!')\n",
+    "            return None # do not parse the rest\n",
+    "        if args.data: # can be used to load data from the pyboard directly into kernel space\n",
+    "            message = pyb.exec(cell)\n",
+    "            if len(message) == 0:\n",
+    "                print('pyboard >>>')\n",
+    "            else:\n",
+    "                print(message.decode('utf-8'))\n",
+    "                # register new variable in user namespace\n",
+    "                self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n",
+    "        \n",
+    "        if args.time: # measures the time of executions\n",
+    "            pyb.exec('import utime')\n",
+    "            message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n",
+    "                               \"\\nprint('execution time: {:d} us'.format(delta))\")\n",
+    "            print(message.decode('utf-8'))\n",
+    "        \n",
+    "        if args.memory: # prints out memory information \n",
+    "            message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n",
+    "            print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n",
+    "            message = pyb.exec(cell)\n",
+    "            print(\">>> \", message.decode('utf-8'))\n",
+    "            message = pyb.exec('print(mem_info())')\n",
+    "            print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n",
+    "\n",
+    "        if args.pyboard:\n",
+    "            message = pyb.exec(cell)\n",
+    "            print(message.decode('utf-8'))\n",
+    "\n",
+    "ip = get_ipython()\n",
+    "ip.register_magics(PyboardMagic)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## pyboard"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-05-07T07:35:35.126401Z",
+     "start_time": "2020-05-07T07:35:35.105824Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import pyboard\n",
+    "pyb = pyboard.Pyboard('/dev/ttyACM0')\n",
+    "pyb.enter_raw_repl()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-05-19T19:11:18.145548Z",
+     "start_time": "2020-05-19T19:11:18.137468Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "pyb.exit_raw_repl()\n",
+    "pyb.close()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2020-05-07T07:35:38.725924Z",
+     "start_time": "2020-05-07T07:35:38.645488Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%micropython -pyboard 1\n",
+    "\n",
+    "import utime\n",
+    "import ulab as np\n",
+    "\n",
+    "def timeit(n=1000):\n",
+    "    def wrapper(f, *args, **kwargs):\n",
+    "        func_name = str(f).split(' ')[1]\n",
+    "        def new_func(*args, **kwargs):\n",
+    "            run_times = np.zeros(n, dtype=np.uint16)\n",
+    "            for i in range(n):\n",
+    "                t = utime.ticks_us()\n",
+    "                result = f(*args, **kwargs)\n",
+    "                run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n",
+    "            print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n",
+    "            print('\\tbest: %d us'%np.min(run_times))\n",
+    "            print('\\tworst: %d us'%np.max(run_times))\n",
+    "            print('\\taverage: %d us'%np.mean(run_times))\n",
+    "            print('\\tdeviation: +/-%.3f us'%np.std(run_times))            \n",
+    "            return result\n",
+    "        return new_func\n",
+    "    return wrapper\n",
+    "\n",
+    "def timeit(f, *args, **kwargs):\n",
+    "    func_name = str(f).split(' ')[1]\n",
+    "    def new_func(*args, **kwargs):\n",
+    "        t = utime.ticks_us()\n",
+    "        result = f(*args, **kwargs)\n",
+    "        print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n",
+    "        return result\n",
+    "    return new_func"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "__END_OF_DEFS__"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# linalg\n",
+    "\n",
+    "`scipy`'s `linalg` module contains a single function, `solve_triangular`, which can be called by prepending it  by `scipy.linalg.`.\n",
+    "\n",
+    "1. [scipy.linalg.solve_triangular](#solve_triangular)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## solve_triangular\n",
+    "\n",
+    "`scipy`: https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.solve_triangular.html \n",
+    "\n",
+    "Solve the linear equation \n",
+    "\n",
+    "\\begin{equation}\n",
+    "\\mathbf{a}\\cdot\\mathbf{x} = \\mathbf{b}\n",
+    "\\end{equation}\n",
+    "\n",
+    "with the assumption that $\\mathbf{a}$ is a triangular matrix. The two position arguments are $\\mathbf{a}$, and $\\mathbf{b}$, and the optional keyword argument is `lower` with a default value of `False`. `lower` determines, whether data are taken from the lower, or upper triangle of $\\mathbf{a}$. \n",
+    "\n",
+    "Note that $\\mathbf{a}$ itself does not have to be a triangular matrix: if it is not, then the values are simply taken to be 0 in the upper or lower triangle, as dictated by `lower`. However, $\\mathbf{a}\\cdot\\mathbf{x}$ will yield $\\mathbf{b}$ only, when $\\mathbf{a}$ is triangular. You should keep this in mind, when trying to establish the validity of the solution by back substitution."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-05-09T05:56:57.449996Z",
+     "start_time": "2021-05-09T05:56:57.422515Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "a:\n",
+      "\n",
+      "array([[3.0, 0.0, 0.0, 0.0],\n",
+      "       [2.0, 1.0, 0.0, 0.0],\n",
+      "       [1.0, 0.0, 1.0, 0.0],\n",
+      "       [1.0, 2.0, 1.0, 8.0]], dtype=float64)\n",
+      "\n",
+      "b:  array([4.0, 2.0, 4.0, 2.0], dtype=float64)\n",
+      "====================\n",
+      "x:  array([1.333333333333333, -0.6666666666666665, 2.666666666666667, -0.08333333333333337], dtype=float64)\n",
+      "\n",
+      "dot(a, x):  array([4.0, 2.0, 4.0, 2.0], dtype=float64)\n",
+      "\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%micropython -unix 1\n",
+    "\n",
+    "from ulab import numpy as np\n",
+    "from ulab import scipy as spy\n",
+    "\n",
+    "a = np.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 2, 1, 8]])\n",
+    "b = np.array([4, 2, 4, 2])\n",
+    "\n",
+    "print('a:\\n')\n",
+    "print(a)\n",
+    "print('\\nb: ', b)\n",
+    "\n",
+    "x = spy.linalg.solve_triangular(a, b, lower=True)\n",
+    "\n",
+    "print('='*20)\n",
+    "print('x: ', x)\n",
+    "print('\\ndot(a, x): ', np.dot(a, x))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "With get the same solution, $\\mathbf{x}$, with the following matrix, but the dot product of $\\mathbf{a}$, and $\\mathbf{x}$ is no longer $\\mathbf{b}$:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2021-05-09T06:03:30.853054Z",
+     "start_time": "2021-05-09T06:03:30.841500Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "a:\n",
+      "\n",
+      "array([[3.0, 2.0, 1.0, 0.0],\n",
+      "       [2.0, 1.0, 0.0, 1.0],\n",
+      "       [1.0, 0.0, 1.0, 4.0],\n",
+      "       [1.0, 2.0, 1.0, 8.0]], dtype=float64)\n",
+      "\n",
+      "b:  array([4.0, 2.0, 4.0, 2.0], dtype=float64)\n",
+      "====================\n",
+      "x:  array([1.333333333333333, -0.6666666666666665, 2.666666666666667, -0.08333333333333337], dtype=float64)\n",
+      "\n",
+      "dot(a, x):  array([5.333333333333334, 1.916666666666666, 3.666666666666667, 2.0], dtype=float64)\n",
+      "\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%micropython -unix 1\n",
+    "\n",
+    "from ulab import numpy as np\n",
+    "from ulab import scipy as spy\n",
+    "\n",
+    "a = np.array([[3, 2, 1, 0], [2, 1, 0, 1], [1, 0, 1, 4], [1, 2, 1, 8]])\n",
+    "b = np.array([4, 2, 4, 2])\n",
+    "\n",
+    "print('a:\\n')\n",
+    "print(a)\n",
+    "print('\\nb: ', b)\n",
+    "\n",
+    "x = spy.linalg.solve_triangular(a, b, lower=True)\n",
+    "\n",
+    "print('='*20)\n",
+    "print('x: ', x)\n",
+    "print('\\ndot(a, x): ', np.dot(a, x))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.5"
+  },
+  "toc": {
+   "base_numbering": 1,
+   "nav_menu": {},
+   "number_sections": true,
+   "sideBar": true,
+   "skip_h1_title": false,
+   "title_cell": "Table of Contents",
+   "title_sidebar": "Contents",
+   "toc_cell": false,
+   "toc_position": {
+    "height": "calc(100% - 180px)",
+    "left": "10px",
+    "top": "150px",
+    "width": "382.797px"
+   },
+   "toc_section_display": true,
+   "toc_window_display": true
+  },
+  "varInspector": {
+   "cols": {
+    "lenName": 16,
+    "lenType": 16,
+    "lenVar": 40
+   },
+   "kernels_config": {
+    "python": {
+     "delete_cmd_postfix": "",
+     "delete_cmd_prefix": "del ",
+     "library": "var_list.py",
+     "varRefreshCmd": "print(var_dic_list())"
+    },
+    "r": {
+     "delete_cmd_postfix": ") ",
+     "delete_cmd_prefix": "rm(",
+     "library": "var_list.r",
+     "varRefreshCmd": "cat(var_dic_list()) "
+    }
+   },
+   "types_to_exclude": [
+    "module",
+    "function",
+    "builtin_function_or_method",
+    "instance",
+    "_Feature"
+   ],
+   "window_display": false
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

docs/ulab-convert.ipynb

@@ -14,11 +14,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 1,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2021-03-23T16:27:42.273017Z",
+     "end_time": "2021-05-09T06:05:50.855683Z",
-     "start_time": "2021-03-23T16:27:42.261057Z"
+     "start_time": "2021-05-09T06:05:50.838482Z"
     }
    },
    "outputs": [
@@ -61,7 +61,7 @@
     "author = 'Zoltán Vörös'\n",
     "\n",
     "# The full version, including alpha/beta/rc tags\n",
-    "release = '2.6.0'\n",
+    "release = '2.7.0'\n",
     "\n",
     "\n",
     "# -- General configuration ---------------------------------------------------\n",
@@ -151,8 +151,8 @@
    "execution_count": 2,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2021-03-04T18:23:33.312441Z",
+     "end_time": "2021-05-09T06:06:28.491158Z",
-     "start_time": "2021-03-04T18:23:33.298784Z"
+     "start_time": "2021-05-09T06:06:28.477127Z"
     }
    },
    "outputs": [
@@ -190,10 +190,11 @@
     "   numpy-universal\n",
     "   numpy-fft\n",
     "   numpy-linalg\n",
+    "   scipy-linalg\n",
     "   scipy-optimize\n",
     "   scipy-signal\n",
     "   scipy-special\n",
-    "    ulab-utils\n",
+    "   ulab-utils\n",
     "   ulab-programming\n",
     "\n",
     "Indices and tables\n",
@@ -213,11 +214,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 3,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2021-03-23T16:27:30.647984Z",
+     "end_time": "2021-05-09T06:06:35.839960Z",
-     "start_time": "2021-03-23T16:27:28.144633Z"
+     "start_time": "2021-05-09T06:06:33.112686Z"
     }
    },
    "outputs": [],
@@ -254,11 +255,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2021-03-23T16:27:35.399254Z",
+     "end_time": "2021-05-09T06:07:00.143083Z",
-     "start_time": "2021-03-23T16:27:30.656938Z"
+     "start_time": "2021-05-09T06:06:56.719659Z"
     }
    },
    "outputs": [],