Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Clarify variable p is a 2D array #70

Open
wants to merge 1 commit into
base: master
Choose a base branch
from
Open

Clarify variable p is a 2D array #70

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
60 changes: 26 additions & 34 deletions lessons/12_Step_9.ipynb
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -126,9 +126,7 @@
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [],
"source": [
"import numpy\n",
Expand All @@ -140,9 +138,7 @@
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [],
"source": [
"def plot2D(x, y, p):\n",
Expand All @@ -162,7 +158,13 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"The function `plot2D` takes three arguments, an x-vector, a y-vector and our p matrix. Given these three values, it produces a 3D projection plot, sets the plot limits and gives us a nice viewing angle. "
"The function `plot2D` takes three arguments:\n",
"\n",
"* `x`: 1D array with point locations along an horizontal gridline,\n",
"* `y`: 1D array with point locations along a vertical gridline,\n",
"* `p`: 2D array containing the numerical solution in the domain.\n",
"\n",
"Given these three values, it produces a 3D projection plot, sets the plot limits and gives us a nice viewing angle. "
]
},
{
Expand All @@ -175,9 +177,7 @@
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [],
"source": [
"def laplace2d(p, y, dx, dy, l1norm_target):\n",
Expand All @@ -204,17 +204,21 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"`laplace2d` takes five arguments, the `p` matrix, the `y`-vector, `dx`, `dy` and the value `l1norm_target`. This last value defines how close the `p` matrix should be in two consecutive iterations before the loop breaks and returns the calculated `p` value. \n",
"`laplace2d` takes five arguments:\n",
"\n",
"* `p`: 2D array containing the initial solution in the domain,\n",
"* `y`: 1D array with point locations along a vertical gridline,\n",
"* `dx`: $x$-distance between two gridlines,\n",
"* `dy`: $y$-distance between two gridlines,\n",
"* `l1norm_target`: value to define convergence; we stop the iterative process (i.e., exit the `while` loop) when the relative difference between two consecutive solutions (in the $L_1$-norm) is lower or equal than `l1norm_target`.\n",
"\n",
"Note that when executing the cells above in your own notebook, there will be no output. You have *defined* the function but you have not yet *called* the function. It is now available for you to use, the same as `numpy.linspace` or any other function in our namespace. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [],
"source": [
"##variable declarations\n",
Expand Down Expand Up @@ -250,9 +254,7 @@
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
Expand Down Expand Up @@ -281,9 +283,7 @@
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [],
"source": [
"p = laplace2d(p, y, dx, dy, 1e-4)"
Expand All @@ -299,9 +299,7 @@
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
Expand Down Expand Up @@ -342,9 +340,7 @@
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
Expand Down Expand Up @@ -384,9 +380,7 @@
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
Expand Down Expand Up @@ -419,9 +413,7 @@
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"metadata": {},
"outputs": [
{
"data": {
Expand Down Expand Up @@ -551,9 +543,9 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
"version": "3.6.10"
}
},
"nbformat": 4,
"nbformat_minor": 0
"nbformat_minor": 1
}