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Just playing around.

This commit is contained in:
Simon Forman 2021-11-24 14:53:26 -08:00
parent 0ce58872ac
commit 0c51a3fc7d
1 changed files with 399 additions and 76 deletions
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475
docs/Newton-Raphson.ipynb
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@ -74,18 +74,43 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"Let's try out this function `over / + 2 /` on an example:" "Let's try out this function `over / + 2 /` on an example:\n",
"\n",
" F == over / + 2 /"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 14, "execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": []
}
],
"source": [
"[F over / + 2 /] inscribe"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to use this function `F` we have to provide an initial estimate for the value of the square root, and we want to keep the input value `n` handy for iterations (we don't want the user to have to keep reentering it.)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
" 5 36 • F\n",
" 5 36 • over / + 2 /\n", " 5 36 • over / + 2 /\n",
"5 36 5 • / + 2 /\n", "5 36 5 • / + 2 /\n",
" 5 7 • + 2 /\n", " 5 7 • + 2 /\n",
@ -100,16 +125,368 @@
"source": [ "source": [
"clear\n", "clear\n",
"\n", "\n",
"5 36 [over / + 2 /] trace" "5 36 [F] trace"
] ]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"The function we want has the argument `n` in it:\n", "The initial estimate can be 2, and we can `cons` the input value onto a quote with `F`:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6"
]
}
],
"source": [
"[F1 2 swap [F] cons] inscribe"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 36 • F1\n",
" 36 • 2 swap [F] cons\n",
" 36 2 • swap [F] cons\n",
" 2 36 • [F] cons\n",
"2 36 [F] • cons\n",
"2 [36 F] • \n",
"\n",
"2 [36 F]"
]
}
],
"source": [
"clear\n",
"\n", "\n",
" n over / + 2 /" "36 [F1] trace"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 2 • 36 F\n",
" 2 36 • F\n",
" 2 36 • over / + 2 /\n",
"2 36 2 • / + 2 /\n",
" 2 18 • + 2 /\n",
" 20 • 2 /\n",
" 20 2 • /\n",
" 10 • \n",
"\n",
"10"
]
}
],
"source": [
"trace"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6"
]
}
],
"source": [
"36 F"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": []
}
],
"source": [
"clear"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[2 [36 F] codireco]"
]
}
],
"source": [
"36 F1 make_generator"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6"
]
}
],
"source": [
"x x x first"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6 12"
]
}
],
"source": [
"144 F1 make_generator x x x x first"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2 [36 F]"
]
}
],
"source": [
"clear\n",
"\n",
"2 [36 F]"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2 [36 F] false"
]
}
],
"source": [
"[first] [pop sqr] fork - abs 3 <"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10"
]
}
],
"source": [
"pop i"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10 [36 F] false"
]
}
],
"source": [
"[36 F] [first] [pop sqr] fork - abs 3 <"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6"
]
}
],
"source": [
"pop i"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6 [36 F] true"
]
}
],
"source": [
"[36 F] [first] [pop sqr] fork - abs 3 <"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2"
]
}
],
"source": [
"clear\n",
"\n",
"2"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6"
]
}
],
"source": [
"[] true [i [36 F] [first] [pop sqr] fork - abs 3 >] loop pop"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"12"
]
}
],
"source": [
"clear\n",
"\n",
"7 [] true [i [144 F] [first] [pop sqr] fork - abs 3 >] loop pop"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"120"
]
}
],
"source": [
"clear\n",
"\n",
"7 [] true [i [14400 F] [first] [pop sqr] fork - abs 3 >] loop pop"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"broken due to no float div\n",
"\n",
" clear\n",
"\n",
" 7 [] true [i [1000 F] [first] [pop sqr] fork - abs 10 >] loop pop"
] ]
}, },
{ {
@ -140,7 +517,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 2, "execution_count": null,
"metadata": { "metadata": {
"scrolled": true "scrolled": true
}, },
@ -151,17 +528,9 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [],
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1 [dup 23 over / + 2 /] codireco]\n"
]
}
],
"source": [ "source": [
"J('23 gsra')" "J('23 gsra')"
] ]
@ -175,17 +544,9 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [],
{
"name": "stdout",
"output_type": "stream",
"text": [
"23.0000000001585\n"
]
}
],
"source": [ "source": [
"J('23 gsra 6 [x popd] times first sqr')" "J('23 gsra 6 [x popd] times first sqr')"
] ]
@ -232,7 +593,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -253,7 +614,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 6, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -286,7 +647,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 7, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -307,7 +668,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -324,38 +685,22 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 9, "execution_count": null,
"metadata": { "metadata": {
"scrolled": true "scrolled": true
}, },
"outputs": [ "outputs": [],
{
"name": "stdout",
"output_type": "stream",
"text": [
"6.0\n"
]
}
],
"source": [ "source": [
"J('36 sqrt')" "J('36 sqrt')"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 10, "execution_count": null,
"metadata": { "metadata": {
"scrolled": true "scrolled": true
}, },
"outputs": [ "outputs": [],
{
"name": "stdout",
"output_type": "stream",
"text": [
"4.795831523312719\n"
]
}
],
"source": [ "source": [
"J('23 sqrt')" "J('23 sqrt')"
] ]
@ -369,42 +714,20 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 11, "execution_count": null,
"metadata": { "metadata": {
"scrolled": true "scrolled": true
}, },
"outputs": [ "outputs": [],
{
"data": {
"text/plain": [
"22.999999999999996"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [ "source": [
"4.795831523312719**2" "4.795831523312719**2"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 12, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [],
{
"data": {
"text/plain": [
"4.795831523312719"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [ "source": [
"from math import sqrt\n", "from math import sqrt\n",
"\n", "\n",