EzDevInfo.com

inverting a 4x4 matrix

i am looking for a sample code implementation on how to invert a 4x4 matrix. i know there is gaussian eleminiation, LU decomposition, etc. but instead of looking at them in detail i am really just looking for the code to do this.

language ideally C++, data is available in array of 16 floats in cloumn-major order.

thank you!

A Transpose/Unzip Function in Python (inverse of zip)

I have a list of 2-item tuples and I'd like to convert them to 2 lists where the first contains the first item in each tuple and the second list holds the second item.

For example:

original = [('a', 1), ('b', 2), ('c', 3), ('d', 4)]
# and I want to become...
result = (['a', 'b', 'c', 'd'], [1, 2, 3, 4])

Is there a builtin function that does that?

How do you rotate a two dimensional array?

Inspired by Raymond Chen's 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, but I'd like to see some real world stuff.

[1][2][3][4]
[5][6][7][8]
[9][0][1][2]
[3][4][5][6]

Becomes:

[3][9][5][1]
[4][0][6][2]
[5][1][7][3]
[6][2][8][4]

Update: Nick's answer is the most straightforward, but is there a way to do it better than n^2? What if the matrix was 10000x10000?

How can I index a MATLAB array returned by a function without first assigning it to a local variable?

For example, if I want to read the middle value from magic(5), I can do so like this:

M = magic(5);
value = M(3,3);

to get value == 13. I'd like to be able to do something like one of these:

value = magic(5)(3,3);
value = (magic(5))(3,3);

to dispense with the intermediate variable. However, MATLAB complains about Unbalanced or unexpected parenthesis or bracket on the first parenthesis before the 3.

Is it possible to read values from an array/matrix without first assigning it to a variable?

Numpy ‘smart’ symmetric matrix

Is there a smart and space-efficient symmetric matrix in numpy which automatically (and transparently) fills the position at [j][i] when [i][j] is written to?

a = numpy.symmetric((3, 3))
a[0][1] = 1
a[1][0] == a[0][1]
# True
print a
# [[0 1 0], [1 0 0], [0 0 0]]

assert numpy.all(a == a.T) # for any symmetric matrix

An automatic Hermitian would also be nice, although I won’t need that at the time of writing.

Bomb dropping algorithm

I have an n x m matrix consisting of non-negative integers. For example:

2 3 4 7 1
1 5 2 6 2
4 3 4 2 1
2 1 2 4 1
3 1 3 4 1
2 1 4 3 2
6 9 1 6 4

"Dropping a bomb" decreases by one the number of the target cell and all eight of its neighbours, to a minimum of zero.

x x x 
x X x
x x x

What is an algorithm that would determine the minimum number of bombs required to reduce all the cells to zero?

B Option (Due to me not being a careful reader)

Actually the first version of problem is not the one I'm seeking answer for. I didn't carefully read whole task, there's additional constraints, let us say:

What about simple problem, when sequence in row must be non-increasing:

8 7 6 6 5 is possible input sequence

7 8 5 5 2 is not possible since 7 -> 8 growing in a sequence.

Maybe finding answer for "easier" case would help in finding solution for harder one.

PS: I believe that when we have several same situations require minimum bombs to clear upper line, we choose one that use most bombs on "left side" of the row. Still any proof that might be correct?

What are the most widely used C++ vector/matrix math/linear algebra libraries, and their cost and benefit tradeoffs?

It seems that many projects slowly come upon a need to do matrix math, and fall into the trap of first building some vector classes and slowly adding in functionality until they get caught building a half-assed custom linear algebra library, and depending on it.

I'd like to avoid that while not building in a dependence on some tangentially related library (e.g. OpenCV, OpenSceneGraph).

What are the commonly used matrix math/linear algebra libraries out there, and why would decide to use one over another? Are there any that would be advised against using for some reason? I am specifically using this in a geometric/time context*(2,3,4 Dim)* but may be using higher dimensional data in the future.

I'm looking for differences with respect to any of: API, speed, memory use, breadth/completeness, narrowness/specificness, extensibility, and/or maturity/stability.

(Edit/note: There's a bit of information in the answers, but it's scattered and without context. I'm unsure if I should pull it together in another answer, but I'm still not particularly clear on the benefits or downsides to any of these choices over another)

I ended up using Eigen3 which I am extremely happy with

Numpy matrix to array

I am using numpy. I have a matrix with 1 column and N rows and I want to get an array from with N elements.

For example, if i have M = matrix([[1], [2], [3], [4]]), I want to get A = array([1,2,3,4]).

To achieve it, I use A = np.array(M.T)[0]. Does anyone know a more elegant way to get the same result?

Thanks!

Performance of Java matrix math libraries? [closed]

We are computing something whose runtime is bound by matrix operations. (Some details below if interested.) This experience prompted the following question:

Do folk have experience with the performance of Java libraries for matrix math (e.g., multiply, inverse, etc.)? For example:

• JAMA
• COLT
• Apache commons math

I searched and found nothing.

Details of our speed comparison:

We are using Intel FORTRAN (ifort (IFORT) 10.1 20070913). We have reimplemented it in Java (1.6) using Apache commons math 1.2 matrix ops, and it agrees to all of its digits of accuracy. (We have reasons for wanting it in Java.) (Java doubles, Fortran real*8). Fortran: 6 minutes, Java 33 minutes, same machine. jvisualm profiling shows much time spent in RealMatrixImpl.{getEntry,isValidCoordinate} (which appear to be gone in unreleased Apache commons math 2.0, but 2.0 is no faster). Fortran is using Atlas BLAS routines (dpotrf, etc.).

Obviously this could depend on our code in each language, but we believe most of the time is in equivalent matrix operations.

In several other computations that do not involve libraries, Java has not been much slower, and sometimes much faster.

What are the differences between numpy arrays and matrices? Which one should I use?

What are the advantages and disadvantages of each?

From what I've seen, either one can work as a replacement for the other if need be, so should I bother using both or should I stick to just one of them?

Will the style of the program influence my choice? I am doing some machine learning using numpy, so there are indeed lots of matrices, but also lots of vectors (arrays).

how does multiplication differ for NumPy Matrix vs Array classes?

The numpy docs recommend using array instead of matrix for working with matrices. However, unlike octave (which I was using till recently), * doesn't perform matrix multiplication, you need to use the function matrixmultipy(). I feel this makes the code very unreadable.

Does anybody share my views, and has found a solution?

Finding row index containing maximum value using R

Given the following matrix lets assume I want to find the maximum value in column two.

mat <- matrix(c(1:3,7:9,4:6),byrow=T,nc=3)

     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    7    8    9
[3,]    4    5    6

I know max(mat[,2]) will return 8. How can I return the row index, in this case row two?

Data frame or matrix?

When to use data frame and when to use matrix?

I know data frame can have other than numeric vectors. Sometimes different packages doing similar analysis use different data type. The end results are sometimes different if I feed it different data type. And I'm getting tired to remember that this package uses data frame and the other uses matrix.

I also started to program in R and not sure which one to use.

Is there a general guide how to choose which data type?

Looping in a spiral

A friend was in need of an algorithm that would let him loop through the elements of an NxM matrix (N and M are odd). I came up with a solution, but I wanted to see if my fellow SO'ers could come up with a better solution.

I'm posting my solution as an answer to this question.

Example Output:

For a 3x3 matrix, the output should be:

(0, 0) (1, 0) (1, 1) (0, 1) (-1, 1) (-1, 0) (-1, -1) (0, -1) (1, -1)

Furthermore, the algorithm should support non-square matrices, so for example for a 5x3 matrix, the output should be:

(0, 0) (1, 0) (1, 1) (0, 1) (-1, 1) (-1, 0) (-1, -1) (0, -1) (1, -1) (2, -1) (2, 0) (2, 1) (-2, 1) (-2, 0) (-2, -1)

Android: How to rotate a bitmap on a center point

I've been looking for over a day for a solution to this problem but nothing helps, even the answers here. Documentation doesn't explain anything too.

I am simply trying to get a rotation in the direction of another object. The problem is that the bitmap is not rotated around a fixed point, but rather around the bitmaps (0,0).

Here is the code I am having troubles with:

  Matrix mtx = new Matrix();
  mtx.reset();
  mtx.preTranslate(-centerX, -centerY);
  mtx.setRotate((float)direction, -centerX, -centerY);
  mtx.postTranslate(pivotX, pivotY);
  Bitmap rotatedBMP = Bitmap.createBitmap(bitmap, 0, 0, spriteWidth, spriteHeight, mtx, true);
  this.bitmap = rotatedBMP;

The weird part is, it doesn't matter how I change the values within pre/postTranslate() and the float arguments in setRotation(). Can someone please help and push me in the right direction? :)