Why doesn’t Fortran have a built-in matrix inverse function? This function is used a lot, and I feel like it would be easier if people don’t have to use Lapack.

I created a small GitHub repo Matrix_Inversion Matrix inversion using Crout’s method, calling Fortran code by Alan Miller.

Perhaps because the user can write her own or find code to compute the inverse, and because some users would translate A * x = b to x = matmul(inv(A),b) which is a suboptimal way to solve a set of linear equations. Maybe stdlib should define a .div. operator so that one can write x = b .div. A …

[image] Beliavsky: In Matlab one writes x = b \ A Rather, one writes x = A \ b, because x = b \ A means “multiply the Penrose-Moore pseudoinverse of b by A”, which is quite different!

Some relevant reading for those looking for matrix inverses: Don’t invert that matrix Why Shouldn’t I Invert That Matrix?

[image] fortran4r: This function is used a lot, Actually it’s mostly solve that is used a lot, not matrix inversion, since it is not as accurate and has other issues as @ivanpribec pointed out. That being said, inv(x) is useful for just experimenting or testing or debugging, I’ve used it a f…

Two examples where matrix inversion is used quite a bit are in FEM codes where you need to compute the inverse of the Jacobian matrix for isoparametric elements and in some constitutive models where you need to compute the inverse of the deformation tensor. Fortunately these are at most 3x3 matrices…

Does anyone have any suggestions/links or Fortran code snippets for the matrix inverse using the Krylov method?

[image] ivanpribec: Some relevant reading for those looking for matrix inverses: Don’t invert that matrix Why Shouldn’t I Invert That Matrix? What is the matrix rank/size for this to be true ? I am sure for the use of a symmetric Jacobian (3x3), it is best to use the inverse. Probably…

[image] rwmsu: Fortunately these are at most 3x3 matrices so you can write your own MATLAB like inv function using direct inversion or Cramers rule For these kinds of matrices you don’t want to call lapack, but rather some specialized inversion that you write. [image] rwmsu: Don’t presum…

In addition to the comments of others, where for example a linear equation solution is needed rather than an actual matrix inverse, there are other reasons to avoid computing an actual matrix inverse. Consider the situation where multiple A*x=b solutions are needed for the same A but different vecto…

As rwmsu says, there are niche applications where matrix inverse is actually what you want. But most of the time, you want to solve a linear system. Computing the inverse and multiplying by the RHS is about twice as much work as factoring the system and back solving. If the matrix is symmetric, use …

Why doesn't Fortran have a built-in matrix inverse function?

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ivanpribec January 31, 2022, 5:53pm 4

Some relevant reading for those looking for matrix inverses:

Don’t invert that matrix
Why Shouldn’t I Invert That Matrix?

What is the best pseudo inverse (Moore-Penrose inverse) subroutine?

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Why doesn't Fortran have a built-in matrix inverse function?

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