Dave Mitchell's DigitalMicrograph™ Scripting Website

// Example script to demonstrate the use of the matrix functions

// available in DM

// D. R. G. Mitchell and J. A. van den Berg, adminsnospam@dmscripting.com (remove the no spam to make this work)

// version:20131110, v1.0, Nov. 2013, www.dmscripting.com

// function to carry out matrix multiplication with checks

image mtxmultiplication(image matrix1, image matrix2)

{

number m1xsize, m2xsize, m1ysize, m2ysize

getsize(matrix1, m1xsize, m1ysize)

getsize(matrix2, m2xsize, m2ysize)

if(m1xsize!=m2ysize)

{

showalert("The x and y dimensions of the two matrices must be the same.",2)

exit(0)

}

image mtxoutput=matrixmultiply(matrix1, matrix2)

return mtxoutput

}

// Function to carry out matrix inversion with checks

image mtxinversion(image matrix1)

{

number m1xsize, m1ysize

getsize(matrix1, m1xsize, m1ysize)

// Matrix inversion requires that the x and y dimensions be the same

if(m1xsize!=m1ysize)

{

showalert("Matrix Inversion: The x and y dimensions of the matrix must be the same",2)

exit(0)

}

image mtxinversion=matrixinverse(matrix1)

return mtxinversion

}

// Function to compute the matrix determinant with checks

// Note: the matrix inverse exists only for matrices whose determinant is not zero

number mtxdeterminant(image matrix1)

{

number m1xsize, m1ysize

getsize(matrix1, m1xsize, m1ysize)

image zerotest=tert(matrix1==0, 0, matrix1)

if(sum(zerotest)==0)

{

showalert("Matrix Determinant: All elements in the matrix can not be zero.",2)

exit(0)

}

// The determinant can only be obtained from square matrices

if(m1xsize!=m1ysize)

{

showalert("Matrix Determinant: The x and y dimensions of the matrix must be the same",2)

exit(0)

}

number mtxdet=matrixdeterminant(matrix1)

return mtxdet

}

// Main program

// Note matrix multiplication requires the x dimension of Matrix 1 to be the same as the y dimension of Matrix 2

// The function checks this and bails out if not

// define a 3 x 3 matrix 1

image matrix1=realimage("",4,3,3)

matrix1=(icol*random())+(irow*random()) // put in some arbitrary numerical values

// To see the effect of setting all the matrix elements to 1 remove the // in front of the following line

//matrix1=1 - this matrix will have a determinant of zere - see below.

showimage(matrix1)

setname(matrix1, "M1")

showimage(matrix1)

// define a 3 x 3 matrix 2

image matrix2=realimage("",4,3,3)

matrix2=(icol*random())+(irow*random())

showimage(matrix2)

setname(matrix2, "M2")

showimage(matrix2)

// Carry out the matrix multiplication

image mtxmultiply=mtxmultiplication(matrix1, matrix2)

showimage(mtxmultiply)

setname(mtxmultiply, "M1 x M2")

// Transpose the matrix so that rows become columns and vice versa

image mtxtranspose=matrixtranspose(matrix1)

showimage(mtxtranspose)

setname(mtxtranspose, "Transpose of M1")

// Compute the matrix determinant. If this has a value of 0 there is no inverse matrix

// Note there appears to be a bug in my version of DM 1.83, wherein the determinant of

// 2x2 matrix of all 1s returns of value of -1e-20. Obviously a very small value

// but not zero as it should be - so checking for mtxdet==0 does not work - hence the cludge below

number mtxdet=mtxdeterminant(matrix1)

if(abs(mtxdet)<1e-9) mtxdet=0 // cludge to deal with DM bug : 1e-9 arbitrarily chosen.

okdialog("Determinant of matrix1 = "+mtxdet)

// Compute the inverse matrix

if(mtxdet!=0) // non-zero determinant means the inverse matrix exists

{

image mtxinverse=mtxinversion(matrix1)

showimage(mtxinverse)

setname(mtxinverse, "Inverse of M1")

}

else

{

Showalert("Determinant of matrix1 is zero - no inverse matrix exists",2)

}