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mono/complexmono

Creates a TPS corresponding to a specific monomial

Syntax

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

# Static Descriptor resolution:
m = mono(TPS{Float64|ComplexF64, descriptor}, monomialindex)

# Dynamic Descriptor
m = mono(monomialindex [, use=(descriptor|tps)])
m = mono(TPS{Float64|ComplexF64 [, GTPSA.Dynamic]} monomialindex [, use=(descriptor|tps)])

Description

monomialindex can be any of kind monomial indexing: by index, by order, and by sparse monomial. See the monomial indexing for more details on each.

Examples


julia> d15 = Descriptor(3, 15, 2, 15); # 3 vars, 2 params, all to order 15
julia> mono(1)TPS64{GTPSA.Dynamic}:
Descriptor(NV=3, MO=15, NP=2, PO=15)
 Coefficient                Order   Exponent
  1.0000000000000000e+00      1      1   0   0   |   0   0
julia> mono(TPS64{d15}, 1)TPS64{Descriptor(NV=3, MO=15, NP=2, PO=15)}:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      1      1   0   0   |   0   0
julia> mono(ComplexTPS64{d15}, param=1)ComplexTPS64{Descriptor(NV=3, MO=15, NP=2, PO=15)}:
 Real                     Imag                       Order   Exponent
  1.0000000000000000e+00   0.0000000000000000e+00      1      0   0   0   |    ⋯
                                                               2 columns omitted
julia> mono(TPS64, [3,1,2], use=d15)TPS64{GTPSA.Dynamic}:
Descriptor(NV=3, MO=15, NP=2, PO=15)
 Coefficient                Order   Exponent
  1.0000000000000000e+00      6      3   1   2   |   0   0
julia> mono(TPS64{d15}, (3,1,2,2,1))TPS64{Descriptor(NV=3, MO=15, NP=2, PO=15)}:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      9      3   1   2   |   2   1
julia> mono([1=>3, 2=>1, 3=>3])TPS64{GTPSA.Dynamic}:
Descriptor(NV=3, MO=15, NP=2, PO=15)
 Coefficient                Order   Exponent
  1.0000000000000000e+00      7      3   1   3   |   0   0
julia> mono((1=>3, 2=>1, 3=>2), params=(1=>2, 2=>1), use=d15)TPS64{GTPSA.Dynamic}:
Descriptor(NV=3, MO=15, NP=2, PO=15)
 Coefficient                Order   Exponent
  1.0000000000000000e+00      9      3   1   2   |   2   1

Documentation

GTPSA.mono — Function
mono([tpstype, ] monomialindex [, use=(descriptor|tps)])

Returns a TPS of type tpstype (which defaults to TPS{Float64,GTPSA.Dynamic}) with the specified monomial set to 1. Any of the three monomial indexing schemes (by order, sparse monomial, or monomial index – see the Monomial Indexing section of the GTPSA manual for more details) may be used to specify the monomial to set to one. E.g. a call to this function is equivalent to doing t = (tpstype)(use=use); t[monomialindex] = 1

use may only be specified if tpstype <: TPS{T where {T},<:GTPSA.Dynamic}.

Examples: Variable/Parameter Index:

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

julia> mono(1)
TPS64{GTPSA.Dynamic}:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      1      1   0   0   |   0   0


julia> mono(ComplexTPS64, 1)
ComplexTPS64{GTPSA.Dynamic}:
 Real                     Imag                       Order   Exponent
  1.0000000000000000e+00   0.0000000000000000e+00      1      1   0   0   |   0   0


julia> mono(ComplexTPS64{d}, param=2)
ComplexTPS64{Descriptor(NV=3, MO=10, NP=2, PO=10)}:
 Real                     Imag                       Order   Exponent
  1.0000000000000000e+00   0.0000000000000000e+00      1      0   0   0   |   0   1

Examples: Monomial Index-by-Order

julia> mono([1,2,3])
TPS64{GTPSA.Dynamic}:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      6      1   2   3   |   0   0


julia> mono([0,0,3,2,1], use=d)
TPS64{GTPSA.Dynamic}:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      6      0   0   3   |   2   1


julia> mono(TPS64{d}, [1,0,0,0,1])
TPS64{Descriptor(NV=3, MO=10, NP=2, PO=10)}:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      2      1   0   0   |   0   1

Examples: Monomial Index-by-Sparse Monomial

julia> mono([1=>1])
TPS64{GTPSA.Dynamic}:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      1      1   0   0   |   0   0


julia> mono([2=>1])
TPS64{GTPSA.Dynamic}:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      1      0   1   0   |   0   0


julia> mono([1=>1], params=[2=>1], use=d)
TPS64{GTPSA.Dynamic}:
 Coefficient                Order   Exponent
  1.0000000000000000e+00      2      1   0   0   |   0   1
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