tensorgrid

tensor.jl

# approximating tensor grids
# computing the approximating coefficients on 
# a tensor product of basis functions
# NOTE: the fastest varying index in v is the one with highest 
# index in ibm
function getTensorCoef{T<:Real}(ibm::Dict{Integer,Array{T,2}},v::Vector{T})

	# ibm are usually inverse basis matrices

	nall = length(v)	# length value vector
	nbm  = length(ibm)	# number of basis functions / dimensions of v

	# dim(matrices) must be same as length v
	prod = 1
	for (k,va) in ibm
		prod *= size(va,1)
		if !(size(va,1) == size(va,2))
			throw(ArgumentError("all matrices must be square"))
		end
	end
	if !(prod == nall)
		throw(ArgumentError("sizes of matrices not consistent with v"))
	end

	# compute product for first matrix
	ks = sort(collect(keys(ibm)))
	v0    = copy(v)
	stemp = ibm[ks[1]]
	n     = size(stemp,1)
	m     = nall / n
	v1    = zeros(nall)
	for i in 1:m
		v1[m*(0:(n-1)) + i] = stemp * v0[(n*(i-1)) + (1:n)]
	end

	# compute for all other matrics
	if nbm > 1
		for imat in 2:nbm
			v0    = copy(v1)
			stemp = ibm[ks[imat]]
			n     = size(stemp,1)
			m     = nall / n
			# fill!(v1,0.0)
			for i in 1:m
				v1[m*(0:(n-1)) + i] = stemp * v0[(n*(i-1)) + (1:n)]
			end
		end
	end
	return v1
end




# running the test
 d = Dict{Integer,Array{Float64,2}}()
 for i=1:4
	d[i] = rand(10+i,10+i)
end
y = rand(11*12*13*14)

function myfun()
    for i in 1:100
       getTensorCoef(d,y)
    end
end

@profile myfun()

julia> Profile.print()

1     LineEdit.jl; activate; line: 1304
 1 LineEdit.jl; activate; line: 1299
  1 LineEdit.jl; refresh_multi_line; line: 953
5     abstractarray.jl; stride; line: 30
1     array.jl; getindex; line: 271
14    array.jl; setindex!; line: 337
1     dict.jl; ht_keyindex; line: 469
1     linalg/blas.jl; gemv!; line: 263
10    linalg/matmul.jl; gemv!; line: 207
2     operators.jl; to_index; line: 309
11152 task.jl; anonymous; line: 96
 11152 REPL.jl; eval_user_input; line: 54
  11152 profile.jl; anonymous; line: 14
   11152 none; myfun; line: 3
    2    ...swald/git/BSplines.jl/src/approx.jl; getTensorCoef; line: 32
     1 array.jl; collect; line: 226
     1 array.jl; collect; line: 228
      1 dict.jl; skip_deleted; line: 669
    2    ...swald/git/BSplines.jl/src/approx.jl; getTensorCoef; line: 34
     1 dict.jl; ht_keyindex; line: 479
    535  ...swald/git/BSplines.jl/src/approx.jl; getTensorCoef; line: 37
    329  ...swald/git/BSplines.jl/src/approx.jl; getTensorCoef; line: 38
    3812 ...swald/git/BSplines.jl/src/approx.jl; getTensorCoef; line: 39
     2244 array.jl; getindex; line: 271
      281 operators.jl; to_index; line: 309
     26   array.jl; setindex!; line: 337
     23   array.jl; setindex!; line: 344
     108  array.jl; setindex!; line: 345
     2    array.jl; setindex!; line: 348
     32   linalg/matmul.jl; gemv!; line: 207
     1    linalg/matmul.jl; gemv!; line: 208
     2    linalg/matmul.jl; gemv!; line: 209
     2    linalg/matmul.jl; gemv!; line: 211
     4    linalg/matmul.jl; gemv!; line: 213
     1    linalg/matmul.jl; gemv!; line: 215
     9    linalg/matmul.jl; gemv!; line: 216
     997  linalg/matmul.jl; gemv!; line: 217
      1   abstractarray.jl; stride; line: 37
      8   linalg/blas.jl; gemv!; line: 263
      7   linalg/blas.jl; gemv!; line: 264
      977 linalg/blas.jl; gemv!; line: 265
       5 abstractarray.jl; stride; line: 30
       1 abstractarray.jl; stride; line: 34
    1    ...swald/git/BSplines.jl/src/approx.jl; getTensorCoef; line: 45
    23   ...swald/git/BSplines.jl/src/approx.jl; getTensorCoef; line: 46
     1 dict.jl; ht_keyindex; line: 469
     6 dict.jl; ht_keyindex; line: 479
    724  ...swald/git/BSplines.jl/src/approx.jl; getTensorCoef; line: 50
    5691 ...swald/git/BSplines.jl/src/approx.jl; getTensorCoef; line: 51
     3791 array.jl; getindex; line: 271
      1725 operators.jl; to_index; line: 309
     21   array.jl; setindex!; line: 337
     42   array.jl; setindex!; line: 344
     246  array.jl; setindex!; line: 345
     5    array.jl; setindex!; line: 348
     1    linalg/blas.jl; gemv!; line: 272
     21   linalg/matmul.jl; gemv!; line: 207
     1    linalg/matmul.jl; gemv!; line: 211
     2    linalg/matmul.jl; gemv!; line: 213
     1    linalg/matmul.jl; gemv!; line: 214
     2    linalg/matmul.jl; gemv!; line: 215
     9    linalg/matmul.jl; gemv!; line: 216
     814  linalg/matmul.jl; gemv!; line: 217
      3   abstractarray.jl; stride; line: 37
      6   linalg/blas.jl; gemv!; line: 263
      7   linalg/blas.jl; gemv!; line: 264
      789 linalg/blas.jl; gemv!; line: 265
       4 abstractarray.jl; stride; line: 30
      6   linalg/blas.jl; gemv!; line: 272