MAT #TRANSFORM X BY <expression(X#,I#,J#)>
or
MAT #TRANSFORM X BY Y AND <expression(X#,Y#,I#,J#)>
works as MAT TRANSFORM but allows a larger set of functions to be used.
In fact, all features of the VAR operation are available
except those related to data sets like lags and leads, etc.
Thus, for example, temporary functions defined in the edit field
library functions (on disk), and random deviates (rand function etc.)
are permitted.
Examples:
m=8 / Generating m x m matrix A
MAT A=ZER(m,m) / with all elements
MAT #TRANSFORM A BY probit(rand(1995)) / independently distributed as N(0,1)
MAT C=ZER(m,m) / Generating m x m matrix C
MAT #TRANSFORM C BY C(I#,J#) / of binomial coefficients
MAT #TRANSFORM C BY RECURRENCE N
transforms matrix C by a recurrence relation N of two integer variables.
N must be defined like a temporary function in editorial computing in the form
N(m,n):=function(m,n,N(i1,j1),N(i2,j2),...) where i1,i2,...<m, j1,j2,...<=n .
Before using this MAT #TRANSFORM operation the initial conditions
must be given by filling certain first rows/columns/elements with
suitable values. The starting position of iteration is supplied by
a START=i0,j0 specification where i0,j0 are row and column indices.
Rows and columns are implicitly labelled by 0,1,2,... (i.e. starting
from 0 instead of 1). Operations
MAT RLABELS NUM(0) TO C
MAT CLABELS NUM(0) TO C
are available for such labelling.
If C is a column vector, also functions of one integer variable are allowed.
........................................................................
Example: Stirling numbers of the second kind
S2(n,k):=S2(n-1,k-1)+k*S2(n-1,k) Initial condition S2(n,1)=1
n=10 k=n / Numbers for n=1,..,10 k=1,...,10 to be computed
MAT A=ZER(n+1,k+1) / Matrix A initialized by 0's
MAT C=CON(n,1)
MAT A(2,2)=C / Column 2 (corresponding to k=1) filled with 1's
MAT RLABELS NUM(0) TO A
MAT CLABELS NUM(0) TO A
/MATSHOW A,12 / See matrix A in initial state
START=2,2 / Starting point for recursion
MAT #TRANSFORM A BY RECURRENCE S2
/MATSHOW A,12345 / See the table of Stirling numbers
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MAT #TRANSFORM X BY #RAND(seed_number)
works as
MAT #TRANSFORM X BY RAND(seed_number)
but is about two times faster.
MAT #TRANSFORM X BY #DISTR(P,seed_number)
transforms X to a random matrix with elements as a sample from
a discrete distribution defined by a matrix P.
P is defined as in the command
TRANSFORM <data> BY #DISTR(P) (See TRANSFORM?).
A = More about additional MAT #operations
M = More about MAT operations
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