1b bisection ported

.gitignore

@@ -0,0 +1 @@
+__pycache__

2/bis.py

@@ -0,0 +1,119 @@
+"bisection tailored to fit lab 1b"
+
+from typing import Callable
+from numbers import Real
+from math import isclose, fabs
+
+
+# this is the already existing bis, see git blame
+def bis(
+    f: Callable[[Real], Real],
+    low: Real,
+    high: Real,
+    *,
+    rel_tol: Real = 1e-9,
+    abs_tol: Real = 0.0,
+    max_loop: int = 100,
+) -> tuple[Real, int]:
+    """real
+
+    rel_tol and abs_tol passes to `math.isclose`
+    """
+
+    def ldaprx(a, b):
+        return isclose(a, b, rel_tol=rel_tol, abs_tol=abs_tol)
+
+    steps = 0
+    fl = f(low)
+    fh = f(high)
+    #     raise ValueError(f"at {low =} f(x) is {fl}, at {high =} f(x) is {fh} which has the same sign")
+
+    if ldaprx(0, fl):
+        return (low, 0)
+    if ldaprx(0, fh):
+        return (high, 0)
+
+    mid = (low + high) / 2
+
+    while (steps := steps + 1) and (max_loop := max_loop - 1) + 1 > 0:
+        match f(mid):
+            case x if ldaprx(0, x):
+                return (mid, steps)
+            case x if x < 0:
+                low = mid
+            case x if x > 0:
+                high = mid
+        mid = (low + high) / 2
+    return (mid, steps)
+
+
+def bis1b(
+    f: Callable[..., Real],
+    bounds: tuple[Real, Real],
+    rel_tol: Real = 1e-6,
+    maxit: int = 50,
+    fa: tuple = None,
+    fkw: dict = None,
+) -> tuple[Real, Real, Real, int]:
+    """bisect: root location zeroes
+
+    uses bisection method to find the root of func
+
+    input:
+        func: name of function
+        bounds: lower and upper guesses
+        rel_tol: desired relative error (default = 0.0001%)
+        maxit: maximum allowable iterations (default = 50)
+        fa, fkw: additional parameters used by func
+    output:
+        root: real root
+        fx: function value at root
+        ea: approximate relative error. not in percent because that is bullshit
+        iter: number of iterations
+
+    function should take one real variable x (Real) + farg and fkwarg like so:
+        `f(x, *fa, **fkw)`
+    """
+    if fa is None:
+        fa = ()
+    if fkw is None:
+        fkw = {}
+
+    def fi(x):
+        return f(x, *fa, **fkw)
+
+    if len(bounds) != 2:
+        raise ValueError("bounds should have two values?")
+    xl, xu = bounds
+    # shit naming competition
+
+    if fi(xl) * fi(xu) > 0:  # maybe incorrect
+        raise ValueError("no sign change")
+
+    it = 0
+    xr = xl
+    ea = 1
+
+    while True:
+        xr_old = xr
+        xr = (xl + xu) / 2
+        it += 1
+
+        if xr != 0:
+            ea = fabs((xr - xr_old) / xr)  # approx
+
+        cur_iter = fi(xl) * fi(xu)
+        match cur_iter:
+            case x if x > 0:
+                xu = xr
+            case x if x < 0:
+                xl = xr
+            case 0:
+                ea = 0
+
+        if ea <= rel_tol or it >= maxit:
+            break
+    root = xr
+    fx = fi(xr)
+
+    return (root, fx, ea, it)

2/symbol.ipynb

@@ -192,7 +192,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -208,7 +208,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -217,7 +217,7 @@
        "np.float64(1.5213797068045676)"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -258,51 +258,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
-    "from typing import Callable\n",
-    "from numbers import Real\n",
-    "from math import isclose\n",
-    "\n",
-    "\n",
-    "def bis(\n",
-    "    f: Callable[[Real], Real],\n",
-    "    low: Real,\n",
-    "    high: Real,\n",
-    "    *,\n",
-    "    rel_tol: Real = 1e-9,\n",
-    "    abs_tol: Real = 0,\n",
-    "    max_loop: int = 100,\n",
-    ") -> tuple[Real, int]:\n",
-    "    ldaprx = lambda a, b: isclose(a, b, rel_tol=rel_tol, abs_tol=abs_tol)\n",
-    "    steps = 0\n",
-    "    fl = f(low)\n",
-    "    fh = f(high)\n",
-    "    #     raise ValueError(f\"at {low =} f(x) is {fl}, at {high =} f(x) is {fh} which has the same sign\")\n",
-    "\n",
-    "    if ldaprx(0, fl):\n",
-    "        return (low, 0)\n",
-    "    elif ldaprx(0, fh):\n",
-    "        return (high, 0)\n",
-    "    else:\n",
-    "        mid = (low + high) / 2\n",
-    "    while (steps := steps + 1) and (max_loop := max_loop - 1) + 1 > 0:\n",
-    "        match f(mid):\n",
-    "            case x if ldaprx(0, x):\n",
-    "                return (mid, steps)\n",
-    "            case x if x < 0:\n",
-    "                low = mid\n",
-    "            case x if x > 0:\n",
-    "                high = mid\n",
-    "        mid = (low + high) / 2\n",
-    "    return (mid, steps)"
+    "from bis import bis # to new file"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -311,7 +276,7 @@
        "(1.5213797068045676, 52)"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }