determinants

matrix determinant differentiation in tensorflow

由 南楼画角 提交于 2019-11-29 07:18:18
I am interested in computing the derivative of a matrix determinant using TensorFlow. I can see from experimentation that TensorFlow has not implemented a method of differentiating through a determinant: LookupError: No gradient defined for operation 'MatrixDeterminant' (op type: MatrixDeterminant) A little further investigation revealed that it is actually possible to compute the derivative; see for example Jacobi's formula . I determined that in order to implement this means of differentiating through a determinant that I need to use the function decorator, @tf.RegisterGradient(

Gaussian elimination without result for acceleration

由 淺唱寂寞╮ 提交于 2019-11-28 09:58:51
问题 Good day, I'm working on a C library (for myself, code: https://github.com/BattlestarSC/matrixLibrary.git) to handle matrix functions. This is mostly a learning/practice activity. One of my challenges is to take the determinant of a matrix efficiently. As my current attempts have failed, I wanted to take a different approach. I was reading though this method from MIT docs: http://web.mit.edu/18.06/www/Spring17/Determinants.pdf and it made a lot of sense. The issue I'm having is how to get to

Python Numpy - Treat really small numbers as zero

由 半腔热情 提交于 2019-11-28 04:59:21
问题 I want to calculate the Determinant of a Singular Matrix (which has a 0 determinant) with Numpy and when I print the determinant it shows a really small number (which is nearly zero = -7.09974814699e-30) but not zero itself... when I try to print the determinant either with %s, %d or %f, sometimes it's zero, sometimes -0 and sometimes -7.09974814699e-30 . Here's the Code : import numpy as np array = np.arange(16) array = array.reshape(4, -1) determinant = np.linalg.det(array) print(

What is the best algorithm to find a determinant of a matrix?

由 半腔热情 提交于 2019-11-27 20:55:41
问题 Can anyone tell me which is the best algorithm to find the value of determinant of a matrix of size N x N ? 回答1: Here is an extensive discussion. There are a lot of algorithms. A simple one is to take the LU decomposition. Then, since det M = det LU = det L * det U and both L and U are triangular, the determinant is a product of the diagonal elements of L and U . That is O(n^3) . There exist more efficient algorithms. 回答2: Row Reduction The simplest way (and not a bad way, really) to find the

Java inverse matrix calculation

由 僤鯓⒐⒋嵵緔 提交于 2019-11-27 14:06:09
I'm trying to calculate the inverse matrix in Java. I'm following the adjoint method (first calculation of the adjoint matrix, then transpose this matrix and finally, multiply it for the inverse of the value of the determinant). It works when the matrix is not too big. I've checked that for matrixes up to a size of 12x12 the result is quickly provided. However, when the matrix is bigger than 12x12 the time it needs to complete the calculation increases exponentially. The matrix I need to invert is 19x19, and it takes too much time. The method that more time consumes is the method used for the

Calculating an NxN matrix determinant in C#

由 那年仲夏 提交于 2019-11-27 08:27:20
问题 How do you calculate the determinant of an NxN matrix C# ? 回答1: The OP posted another question asking specifically about 4x4 matrices, which has been closed as an exact duplicate of this question. Well, if you're not looking for a general solution but instead are constrained to 4x4 matrices alone, then you can use this ugly looking but tried-and-true code: public double GetDeterminant() { var m = _values; return m[12] * m[9] * m[6] * m[3] - m[8] * m[13] * m[6] * m[3] - m[12] * m[5] * m[10] *

Java inverse matrix calculation

由 我与影子孤独终老i 提交于 2019-11-26 18:21:56
问题 I'm trying to calculate the inverse matrix in Java. I'm following the adjoint method (first calculation of the adjoint matrix, then transpose this matrix and finally, multiply it for the inverse of the value of the determinant). It works when the matrix is not too big. I've checked that for matrixes up to a size of 12x12 the result is quickly provided. However, when the matrix is bigger than 12x12 the time it needs to complete the calculation increases exponentially. The matrix I need to
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