mat2sum {lazy.symbolic}

R Documentation

Express the i-j element of an Matrix Expression using Summation Operators

Description

Express the i-j element of an Matrix Expression using Summation Operators

Usage

mat2sum(
  exp,
  row = "i",
  col = "j",
  root = "s",
  sublist = NA,
  simple = 1,
  expand = 1,
  print = 0,
  debug = 0
)

Arguments

exp	An full symbplic matrix expression
row	row subscript name
col	column subscript name
root	root of the intermediate subscripts
sublist	a character vector containing the intermediate subscript names
simple	= 0 to use full spec: subscript, from , to
expand	= 0 not to expand (A+B) or (A*B) etc.
print	= 1 to print the result
debug	= 1 to print the intermediate result

Details

The summation of an expression over subscript k is expressed as
s( exp, {k} )
or
s( exp, {k, from, to} )

The lowercase object is treated as a column vector. (See examples below.)

When row="i" and col="j":

 mat2sum( "A %*% B" ) -> s(A[i,s1]*B[s1,j], {s1})
 mat2sum( "A %*% B", root="z" ) -> s(A[ij,z1]*B[z1,j], {z1})
 mat2sum( "A %*% B", simple=0 ) -> s(A[i,s1]*B[s1,j], {s1,1,ncol(A)})
 mat2sum( "t(A) %*% B" ) -> s(A[s1,i]*B[s1,j], {s1})
 mat2sum( "A %*% t(B)" ) -> s(A[i,s1]*B[j,s1], {s1})
 mat2sum( "A %*%Diag(B)%*%C" ) -> s(A[i,s1]*B[s1,s1]*C[s1,j],{s1})
 mat2sum( "A %*% b" ) -> s(A[i,s1]*b[s1],{s1})
 mat2sum( "t(a) %*% B" ) -> s(a[s1]*B[s1,j],{s1})
 

Identity matrix, I, and vec function are not recognized.

Diag or diag function will be recognized.

Use parentheses to mark Hadamar and Kronecker products.

The resulting summation expression can be expanded and evaluated by sumEval function. (lazy.symbolic2 package is required.)

Examples

mat2sum( "A %*% B" )
mat2sum( "A %*% B", root="z" )
mat2sum( "A %*% B", simple=0 )
mat2sum( "t(A) %*% B" )
mat2sum( "A %*% t(B)" )
mat2sum( "A %*%Diag(B)%*%C" )
mat2sum( "A %*% b" )
mat2sum( "t(a) %*% B" )
mat2sum( "a %*% t(b)" )
mat2sum( "A%*%(B+C)" )
mat2sum( "A%*%(B+C)", expand=0 )

exp="t(A)%*%t(B)%*%C - D%*%t(E)"
mat2sum( exp )
mat2sum( exp, root="k" )
mat2sum( exp, sublist=letters[11:20] )
exp="A%*%diag(B)%*%C - diag(D)%*%E%*%diag(F)%*%G + diag(H)"
mat2sum( exp )


sexp0=mat2sum( "A%*%(B+C)", expand=0 )
sexp=mat2sum( "A%*%(B+C)" )
sexpe=Expand(c(sexp0,sexp))
Print(sexp0,sexp,sexpe)

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