Program For Bisection Method In Fortran 90' title='Program For Bisection Method In Fortran 90' />Inspired by Raymond Chens post, say you have a 4x4 two dimensional array, write a function that rotates it 90 degrees. Raymond links to a solution in pseudo code. The inductor calculator presented on this page is unique in that it employs the n0 sheath helix waveguide mode to determine the inductance of a coil, irrespective of. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. Easily share your publications and get. ComputationalPhysics/Book/Computer/emacsFile.png' alt='Program For Bisection Method In Fortran 90' title='Program For Bisection Method In Fortran 90' />How do you rotate a two dimensional array Id like to add a little more detail. In this answer, key concepts are repeated, the pace is slow and intentionally repetitive. The solution provided here is not the most syntactically compact, it is however intended for those who wish to learn what matrix rotation is and the resulting implementation. Firstly, what is a matrixFor the purposes of this answer, a matrix is just a grid where the width and height are the same. Note, the width and height of a matrix can be different, but for simplicity, this tutorial considers only matrices with equal width and height and yes, matrices is the plural of matrix. Example matrices are 22, 33 or 55. Or, more generally, NN. A 22 matrix will have 4 squares because 224. A 55 matrix will have 2. Each square is called an element or entry. Well represent each element with a period. So, what does it mean to rotate a matrix Lets take a 22 matrix and put some numbers in each element so the rotation can be observed 0 1. Rotating this by 9. We literally turned the whole matrix once to the right just like turning the steering wheel of a car. It may help to think of tipping the matrix onto its right side. We want to write a function, in Python, that takes a matrix and rotates in once to the right. The function signature will be def rotatematrix. Algorithm goes here. The matrix will be defined using a two dimensional array matrix. Therefore the first index position accesses the row. The second index position accesses the column matrixrowcolumn. Well define a utility function to print a matrix. One method of rotating a matrix is to do it a layer at a time. But what is a layer Think of an onion. Just like the layers of an onion, as each layer is removed, we move towards the center. Other analogies is a Matryoshka doll or a game of pass the parcel. The width and height of a matrix dictate the number of layers in that matrix. Lets use different symbols for each layer A 22 matrix has 1 layer. A 33 matrix has 2 layers. A 44 matrix has 2 layers. A 55 matrix has 3 layers. A 66 matrix has 3 layers. A 77 matrix has 4 layers. You may notice that incrementing the width and height of a matrix by one, does not always increase the number of layers. Taking the above matrices and tabulating the layers and dimensions, we see the number of layers increases once for every two increments of width and height. NN Layers. However, not all layers need rotating. A 11 matrix is the same before and after rotation. The central 11 layer is always the same before and after rotation no matter how large the overall matrix. NN Layers Rotatable Layers. Given NN matrix, how can we programmatically determine the number of layers we need to rotate If we divide the width or height by two and ignore the remainder we get the following results. NN Layers Rotatable Layers N2. Notice how N2 matches the number of layers that need to be rotatedSometimes the number of rotatable layers is one less the total number of layers in the matrix. This occurs when the innermost layer is formed of only one element i. It simply gets ignored. We will undoubtedly need this information in our function to rotate a matrix, so lets add it now def rotatematrix. Rotatable layers only. Now we know what layers are and how to determine the number of layers that actually need rotating, how do we isolate a single layer so we can rotate it Firstly, we inspect a matrix from the outermost layer, inwards, to the innermost layer. A 55 matrix has three layers in total and two layers that need rotating. Lets look at columns first. The position of the columns defining the outermost layer, assuming we count from 0, are 0 and 4. Column 0 1 2 3 4. O x. Row. O x. 3. Emmegi Cnc Software. This will always be the case since the width and height are the same. Therefore we can define the column and row positions of a layer with just two values rather than four. Moving inwards to the second layer, the position of the columns are 1 and 3. And, yes, you guessed it, its the same for rows. Its important to understand we had to both increment and decrement the row and column positions when moving inwards to the next layer. Layer Rows Columns Rotate Outermost 0 and 4 0 and 4 Yes. Inner 1 and 3 1 and 3 Yes. Innermost 2 2 No. So, to inspect each layer, we want a loop with both increasing and decreasing counters that represent moving inwards, starting from the outermost layer. Well call this our layer loop. Layer d first d, last d layer, first, last. The code above loops through the row and column positions of any layers that need rotating. Layer 0 first 0, last 4. Layer 1 first 1, last 3. We now have a loop providing the positions of the rows and columns of each layer. The variables first and last identify the index position of the first and last rows and columns. Referring back to our row and column tables. Column 0 1 2 3 4. O x. Row. O x. 3. So we can navigate through the layers of a matrix. Now we need a way of navigating within a layer so we can move elements around that layer. Note, elements never jump from one layer to another, but they do move within their respective layers. Rotating each element in a layer rotates the entire layer. Rotating all layers in a matrix rotates the entire matrix. This sentence is very important, so please try your best to understand it before moving on. Now, we need a way of actually moving elements, i. For simplicity, well revert to a 3x. Our layer loop provides the indexes of the first and last columns, as well as first and last rows. Col 0 1 2. Row. Because our matrices are always square, we need just two variables, first and last, since index positions are the same for rows and columns. Our layer loop i0, i1, i2. We want to move within a layer here. The variables first and last can easily be used to reference the four corners of a matrix. This is because the corners themselves can be defined using various permutations of first and last with no subtraction, addition or offset of those variables. Corner Position 3x. Values. For this reason, we start our rotation at the outer four corners well rotate those first. Lets highlight them with. We want to swap each with the to the right of it. So lets go ahead a print out our corners defined using only various permutations of first and last def rotatematrix. Output should be topleft 0, 0. Now we could quite easily swap each of the corners from within our layer loop def rotatematrix. Matrix before rotating corners 0, 1, 2. Matrix after rotating corners 6, 1, 0. Great We have successfully rotated each corner of the matrix. But, we havent rotated the elements in the middle of each layer. Clearly we need a way of iterating within a layer.