Need Matrix Mathematics

[transpower]

I request that FileMaker add a matrix field type so that matrices can be entered and matrix mathematics performed (with new functions). I also request a contains operator and field event trapping. Also, FileMaker should work with Microsoft to use protected memory so that if FileMaker freezes it wouldn't freeze the whole darn machine.

[Ender]

It's been a while since I've worked with matricies. A matrix is essentially a multi-dimensional array, correct? Can you give examples of what you would want to see.

[transpower]

OK. I'd like one and two-dimensional arrays (I don't think that three-dimensional or higher-dimensional arrays would usually be needed). I'd like to be able to multiply matrix A and vector x and add that to the product of matrix B and vector u, for instance. So, I'd like matrix addition, subtraction, multiplication, powers, inverses, transposes, and also have functions that can work with each element of an array.

[Fenton]

If you can get your hands on a Mac, this is available using AppleScript, via a free Scripting Addition, Satimage, from:

http://www.satimage-software.com

They are into mathematics and graphics. Maybe someone will create a FileMaker plug-in that does this; I've never heard of one. Maybe Visual Basic? (I have no idea)

Here's a some of its dictionary:

creatematrix plain text -- "1": array of 1.0, "x": array of x values, "y": array of y values

ncols integer -- or a list of real with the "x" option, will make an array with identical rows

nrows integer -- or a list of real with the "y" option, will make an array with identical columns

[range a list of real] -- {min,max}

[as type class] -- array of real or matrix, default: array of real

Result: array of real -- or matrix

transpose matrix -- the matrix

Result: matrix -- the transposed matrix

extractarray array of real

[at integer] -- the first item to read or a list of indexes (in which case, the "for", "step" and "blocksize" parameters are not taken into account). 1-based. Default 1

[for integer] -- the number of blocks to read. Default 1

[blocksize integer] -- size of the block to read at each step. blocksize must be smaller than step

[step integer] -- the interval between the beginnings of successive blocks to read. Must be larger than blocksize. Default: blocksize

[as type class] -- default is array of real, you can provide small real or real for 1 item

Result: array of real

evalformula: apply C-like mathematical expressions to arrays of real. Ex: evalformula "a*x^2+y^2" with {a:2.4,x:anarray,y:anotherarray}

evalformula plain text -- the formula to compute

[with a list of real] -- the definition of the variables occurring in the formula.

Result: array of real -- or real

[RalphL]

I would like to know why and how you would use a matrix in a database. It seems counter to the first normal form of relational database design.

[transpower]

Fenton:

Thanks, but I work with Windows and UNIX only. I do a lot of matrix programming using MATLAB, Maple, and Mathcad. (I used to use TrueBASIC quite a lot--it had all kinds of matrix manipulations.) It would be nice to be able to do it in FileMaker.

Ralph:

The matrix field type would be just another field type; a calculation involving matrices would be another matrix.

[The Shadow]

I can't see matrices ever being added as a field type, I think its too technical.

I added an example to my web page that does some of the easier matrix manipulation as custom functions:

http://www.spf-15.com/fmExamples/

(see Matrix Math)

The matrices are stored as a semi-colon seperated list, ie:

-1; 3.5; 17;

0; 14; 72;

It implements transpose, matrix multiplication with another matrix or a scalar, addition / subtraction of matrices, an identity matrix creator, and various functions to extract rows, columns, or a single element.

No determinant or inverse functions at the moment, those look quite a bit more complex.

[transpower]

The Shadow:

Very good--it makes sense to use custom functions for this.

[transpower]

The Shadow:

I finally got around to testing your custom functions. Unfortunately the matrix multiplication routine doesn't work. If I multiply [1 0 5 ; -1 3 2] by [3 3 ; 2 1 ; 1 0] (MATLAB notation) I should get [8 3 ; 5 0]. Your custom function returns [3 3 ; 5 0].

[The Shadow]

I'm not seeing that problem. I added a new record with:

MatrixMultiply( A; B )

with A: "1; 0; 5;

[The Shadow]

I have updated the example on my website to incorporate a few fixes to some of the routines that were leaving extra elements around in some cases. I also changed records to be examples, with short descriptions of the public functions.

http://www.spf-15.com/fmExamples/

[transpower]

The Shadow:

I've tried several different matrix multiplicands; the custom function gives the wrong 1,1 element in each case.

[transpower]

OOPS: When I was playing with the A or B matrix I was inadvertently leaving off the ";" at the end of the first row (out of habit in working with other computer languages like MATLAB and Maple). With the ";" in place at the end of each row and between each element, your custom function produces the correct result. Thank you very much.

[bruceR]

If you're working with Unix then of course the Mac is a perfect fit because it Is Unix. The Satimage capabailities are amazing.