`mono`/`complexmono`

Creates a TPS corresponding to a specific monomial

Syntax

m = mono(orders [, use=(descriptor|tps)])

m = mono([vars_sparse_mono] [, params=params_sparse_mono] [, use=(descriptor|tps)])

m = mono(idx [, use=(descriptor|tps)])
m = mono(param=param_idx [, use=(descriptor|tps)])

m = complexmono(...)

Description

Indexing by Order

m = mono(orders) creates a TPS equal to the monomial specified by the indexing-by-order vector/tuple orders using the Descriptor in GTPSA.desc_current

m = mono(vars_sparse_mono, params=params_sparse_mono) creates a TPS equal to the monomial specified by the indexing-by-sparse monomial vector/tuple vars_sparse_mono and params_sparse_mono using the Descriptor in GTPSA.desc_current

Indexing by Monomial Index

m = mono(idx) creates a TPS equal to the monomial specified by idx and the Descriptor in GTPSA.desc_current

m = mono(param=param_idx) creates a TPS equal to the monomial specified by param_idx + nv where nv is the number of variables in the GTPSA, using the Descriptor in GTPSA.desc_current

Optional Keyword Argument

use=(descriptor|tps) creates a mono using any of the above methods but using the Descriptor specified by use

Complex Monomial

complexmono will create a ComplexTPS64 using any of the above methods without the overhead of creating a TPS and converting it to a ComplexTPS64

Examples


julia> d1 = Descriptor(3, 15, 2, 15); # 3 vars, 2 params, all to order 15
julia> x1 = mono(1)TPS64:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      1      1   0   0   |   0   0
julia> k1 = mono(param=1)TPS64:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      1      0   0   0   |   1   0
julia> m312 = mono([3,1,2])TPS64:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      6      3   1   2   |   0   0
julia> m31221 = mono((3,1,2,2,1)) # Tuples allowed for indexingTPS64:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      9      3   1   2   |   2   1
julia> m312 = mono([1=>3, 2=>1, 3=>3])TPS64:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      7      3   1   3   |   0   0
julia> m31221 = mono((1=>3, 2=>1, 3=>2), params=(1=>2, 2=>1))TPS64:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      9      3   1   2   |   2   1

Documentation

GTPSA.mono — Function

mono(v::Union{Integer, Vector{<:Union{<:Pair{<:Integer,<:Integer},<:Integer}}, Nothing}=nothing; param::Union{Integer,Nothing}=nothing, params::Union{Vector{<:Pair{<:Integer,<:Integer}}, Nothing}=nothing, use::Descriptor=GTPSA.desc_current)

Returns a TPS{Float64} corresponding to a specific monomial, specified using the variable/parameter index, or monomial indexing-by-order OR monomial indexing-by-sparse monomial.

Input

v – An integer (for variable index), an array of orders for each variable (for indexing-by-order), or an array of pairs (sparse monomial)
param – (Keyword argument, optional) An integer for the parameter index
params – (Keyword argument, optional) An array of pairs for sparse-monomial indexing
use – (Keyword argument, optional) The descriptor to use to generate the monomial. Default is most recently-defined.

Examples: Variable/Parameter Index:

julia> d = Descriptor(3,10,2,10);

julia> mono(1)
TPS{Float64}:
  Coefficient              Order     Exponent
   1.0000000000000000e+00    1        1    0    0    0    0


julia> mono(2, use=d)
TPS{Float64}:
  Coefficient              Order     Exponent
   1.0000000000000000e+00    1        0    1    0    0    0


julia> mono(param=2)
TPS{Float64}:
  Coefficient              Order     Exponent
   1.0000000000000000e+00    1        0    0    0    0    1

Examples: Monomial Index-by-Order

julia> mono([1])
TPS{Float64}:
  Coefficient              Order     Exponent
   1.0000000000000000e+00    1        1    0    0    0    0


julia> mono([0,1])
TPS{Float64}:
  Coefficient              Order     Exponent
   1.0000000000000000e+00    1        0    1    0    0    0


julia> mono([0,0,0,0,1], use=d)
TPS{Float64}:
  Coefficient              Order     Exponent
   1.0000000000000000e+00    1        0    0    0    0    1


julia> mono([1,0,0,0,1])
TPS{Float64}:
  Coefficient              Order     Exponent
   1.0000000000000000e+00    2        1    0    0    0    1

Examples: Monomial Index-by-Sparse Monomial

julia> mono([1=>1])
TPS{Float64}:
  Coefficient              Order     Exponent
   1.0000000000000000e+00    1        1    0    0    0    0


julia> mono([2=>1])
TPS{Float64}:
  Coefficient              Order     Exponent
   1.0000000000000000e+00    1        0    1    0    0    0


julia> mono([1=>1], params=[2=>1], use=d)
TPS{Float64}:
  Coefficient              Order     Exponent
   1.0000000000000000e+00    2        1    0    0    0    1

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