From Newsgroup: comp.lang.fortran

I came across some old NASA Fortran subroutines for inverting small
matrices. Basically, no loops just long equations for each cell (and a determinant). So efficient for speed, not memory. Interestingly for 5x5 matrix, there are extra lines like
A11=A(1,1)
A12=A(1,2)
then the scalar variables are used thereafter. So I presume the 25 copy operations are offset by faster access later using scalar instead of
indexed array fetch?
--- Synchronet 3.21f-Linux NewsLink 1.2

From Newsgroup: comp.lang.fortran

Woozy Song wrote:

I came across some old NASA Fortran subroutines for inverting small
matrices. Basically, no loops just long equations for each cell (and a determinant). So efficient for speed, not memory. Interestingly for
5x5 matrix, there are extra lines like
A11=A(1,1)
A12=A(1,2)
then the scalar variables are used thereafter. So I presume the 25
copy operations are offset by faster access later using scalar instead
of indexed array fetch?

Must be a very old compiler where those assignments would gain anything. Determinant? Don't tell me it's using Cramer's rule!
--
*********** To reply by e-mail, make w single in address **************
--- Synchronet 3.21f-Linux NewsLink 1.2

From Newsgroup: comp.lang.fortran

Woozy Song <suzyw0ng@outlook.com> schrieb:

I came across some old NASA Fortran subroutines for inverting small matrices. Basically, no loops just long equations for each cell (and a determinant). So efficient for speed, not memory. Interestingly for 5x5 matrix, there are extra lines like
A11=A(1,1)
A12=A(1,2)
then the scalar variables are used thereafter. So I presume the 25 copy operations are offset by faster access later using scalar instead of
indexed array fetch?

I very much doubt this would make a difference for modern optimizing
compilers.

Do these routines actually invert matrices? This is rarely needed.
What is the dimension of these matrices?
--
This USENET posting was made without artificial intelligence,
artificial impertinence, artificial arrogance, artificial stupidity,
artificial flavorings or artificial colorants.
--- Synchronet 3.21f-Linux NewsLink 1.2

From Newsgroup: comp.lang.fortran

Thomas Koenig wrote:

Woozy Song <suzyw0ng@outlook.com> schrieb:

I came across some old NASA Fortran subroutines for inverting small
matrices. Basically, no loops just long equations for each cell (and a
determinant). So efficient for speed, not memory. Interestingly for 5x5
matrix, there are extra lines like
A11=A(1,1)
A12=A(1,2)
then the scalar variables are used thereafter. So I presume the 25 copy
operations are offset by faster access later using scalar instead of
indexed array fetch?

I very much doubt this would make a difference for modern optimizing compilers.

Do these routines actually invert matrices? This is rarely needed.
What is the dimension of these matrices?

dimensions 3x3 to 6x6. I have seen similar snippets elsewhere, but only
for 3x3 and 4x4. I presume there are niche algorithms that do lots of
small matrix inversions.

So if it doesn't gain anything, I guess it was to make the code text
less unwieldly replacing 6 characters with 3.
--- Synchronet 3.21f-Linux NewsLink 1.2

From Newsgroup: comp.lang.fortran

On 4/16/2026 8:48 PM, Woozy Song wrote:

Thomas Koenig wrote:

Woozy Song <suzyw0ng@outlook.com> schrieb:

I came across some old NASA Fortran subroutines for inverting small
matrices. Basically, no loops just long equations for each cell (and a
determinant). So efficient for speed, not memory. Interestingly for 5x5
matrix, there are extra lines like
   A11=A(1,1)
   A12=A(1,2)
then the scalar variables are used thereafter. So I presume the 25 copy
operations are offset by faster access later using scalar instead of
indexed array fetch?

I very much doubt this would make a difference for modern optimizing
compilers.

Do these routines actually invert matrices?  This is rarely needed.
What is the dimension of these matrices?

dimensions 3x3 to 6x6. I have seen similar snippets elsewhere, but only
for 3x3 and 4x4. I presume there are niche algorithms that do lots of
small matrix inversions.

So if it doesn't gain anything, I guess it was to make the code text
less unwieldly replacing 6 characters with 3.

It might have gain something in some historical context (and for a
particular problem set).
--- Synchronet 3.21f-Linux NewsLink 1.2

From Newsgroup: comp.lang.fortran

Woozy Song <suzyw0ng@outlook.com> schrieb:

Thomas Koenig wrote:

Woozy Song <suzyw0ng@outlook.com> schrieb:

I came across some old NASA Fortran subroutines for inverting small
matrices. Basically, no loops just long equations for each cell (and a
determinant). So efficient for speed, not memory. Interestingly for 5x5
matrix, there are extra lines like
A11=A(1,1)
A12=A(1,2)
then the scalar variables are used thereafter. So I presume the 25 copy
operations are offset by faster access later using scalar instead of
indexed array fetch?

I very much doubt this would make a difference for modern optimizing
compilers.

Do these routines actually invert matrices? This is rarely needed.
What is the dimension of these matrices?

dimensions 3x3 to 6x6. I have seen similar snippets elsewhere, but only
for 3x3 and 4x4. I presume there are niche algorithms that do lots of
small matrix inversions.

So if it doesn't gain anything, I guess it was to make the code text
less unwieldly replacing 6 characters with 3.

This might have gained something in the grey mists of time, when
dinosaurs roamed the computer centers. Compilers these days have
progressed enormously, from ongoing development and from having
much more computing power available, so much many more and more
expensive passes can be run.
--
This USENET posting was made without artificial intelligence,
artificial impertinence, artificial arrogance, artificial stupidity,
artificial flavorings or artificial colorants.
--- Synchronet 3.21f-Linux NewsLink 1.2

From Newsgroup: comp.lang.fortran

Thomas Koenig wrote:

Woozy Song <suzyw0ng@outlook.com> schrieb:

I came across some old NASA Fortran subroutines for inverting small
matrices. Basically, no loops just long equations for each cell (and a
determinant). So efficient for speed, not memory. Interestingly for 5x5
matrix, there are extra lines like
A11=A(1,1)
A12=A(1,2)
then the scalar variables are used thereafter. So I presume the 25 copy
operations are offset by faster access later using scalar instead of
indexed array fetch?

I very much doubt this would make a difference for modern optimizing compilers.

Do these routines actually invert matrices? This is rarely needed.
What is the dimension of these matrices?

I can see a need for that if matrices were to be used with programs
written in other languages.
Just as a reminder,
a (3,3) matrix would be stored in Fortran as 1,1 2,1 3,1 1,2 2,2
3,2 1,3 2,3 3,3.
in other languages it would be 1,1 1,2 1,3 2,1 2,2 2,3 3,1 3,2 3,3
One of a couple of weird decisions made with the original language specs.
--- Synchronet 3.21f-Linux NewsLink 1.2