mirror of
https://gitlab.kitware.com/vtk/vtk-m
synced 2024-10-05 09:59:12 +00:00
374 lines
13 KiB
ReStructuredText
374 lines
13 KiB
ReStructuredText
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==============================
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Math
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==============================
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.. index:: math
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|VTKm| comes with several math functions that tend to be useful for visualization algorithms.
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The implementation of basic math operations can vary subtly on different accelerators, and these functions provide cross platform support.
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All math functions are located in the ``vtkm`` package.
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The functions are most useful in the execution environment, but they can also be used in the control environment when needed.
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------------------------------
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Basic Math
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------------------------------
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The :file:`vtkm/Math.h` header file contains several math functions that replicate the behavior of the basic POSIX math functions as well as related functionality.
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.. didyouknow::
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When writing worklets, you should favor using these math functions provided by |VTKm| over the standard math functions in :file:`vtkm/Math.h`.
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|VTKm|'s implementation manages several compiling and efficiency issues when porting.
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Exponentials
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==============================
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.. doxygenfunction:: vtkm::Exp(vtkm::Float32)
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.. doxygenfunction:: vtkm::Exp(vtkm::Float64)
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.. doxygenfunction:: vtkm::Exp(const T&)
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.. doxygenfunction:: vtkm::Exp(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::Exp10(vtkm::Float32)
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.. doxygenfunction:: vtkm::Exp10(vtkm::Float64)
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.. doxygenfunction:: vtkm::Exp10(T)
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.. doxygenfunction:: vtkm::Exp10(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::Exp2(vtkm::Float32)
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.. doxygenfunction:: vtkm::Exp2(vtkm::Float64)
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.. doxygenfunction:: vtkm::Exp2(const T&)
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.. doxygenfunction:: vtkm::Exp2(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::ExpM1(vtkm::Float32)
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.. doxygenfunction:: vtkm::ExpM1(vtkm::Float64)
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.. doxygenfunction:: vtkm::ExpM1(const T&)
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.. doxygenfunction:: vtkm::ExpM1(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::Log(vtkm::Float32)
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.. doxygenfunction:: vtkm::Log(vtkm::Float64)
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.. doxygenfunction:: vtkm::Log(const T&)
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.. doxygenfunction:: vtkm::Log(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::Log10(vtkm::Float32)
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.. doxygenfunction:: vtkm::Log10(vtkm::Float64)
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.. doxygenfunction:: vtkm::Log10(const T&)
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.. doxygenfunction:: vtkm::Log10(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::Log1P(vtkm::Float32)
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.. doxygenfunction:: vtkm::Log1P(vtkm::Float64)
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.. doxygenfunction:: vtkm::Log1P(const T&)
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.. doxygenfunction:: vtkm::Log1P(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::Log2(vtkm::Float32)
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.. doxygenfunction:: vtkm::Log2(vtkm::Float64)
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.. doxygenfunction:: vtkm::Log2(const T&)
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.. doxygenfunction:: vtkm::Log2(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::Pow(vtkm::Float32, vtkm::Float32)
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.. doxygenfunction:: vtkm::Pow(vtkm::Float64, vtkm::Float64)
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Non-finites
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==============================
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.. doxygenfunction:: Infinity
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.. doxygenfunction:: Infinity32
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.. doxygenfunction:: Infinity64
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.. doxygenfunction:: IsFinite
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.. doxygenfunction:: IsInf
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.. doxygenfunction:: IsNan
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.. doxygenfunction:: IsNegative(vtkm::Float32)
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.. doxygenfunction:: IsNegative(vtkm::Float64)
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.. doxygenfunction:: Nan
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.. doxygenfunction:: Nan32
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.. doxygenfunction:: Nan64
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.. doxygenfunction:: NegativeInfinity
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.. doxygenfunction:: NegativeInfinity32
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.. doxygenfunction:: NegativeInfinity64
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Polynomials
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==============================
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.. doxygenfunction:: vtkm::Cbrt(vtkm::Float32)
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.. doxygenfunction:: vtkm::Cbrt(vtkm::Float64)
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.. doxygenfunction:: vtkm::Cbrt(const T&)
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.. doxygenfunction:: vtkm::Cbrt(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::QuadraticRoots
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.. doxygenfunction:: vtkm::RCbrt(vtkm::Float32)
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.. doxygenfunction:: vtkm::RCbrt(vtkm::Float64)
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.. doxygenfunction:: vtkm::RCbrt(T)
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.. doxygenfunction:: vtkm::RCbrt(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::RSqrt(vtkm::Float32)
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.. doxygenfunction:: vtkm::RSqrt(vtkm::Float64)
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.. doxygenfunction:: vtkm::RSqrt(T)
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.. doxygenfunction:: vtkm::RSqrt(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::Sqrt(vtkm::Float32)
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.. doxygenfunction:: vtkm::Sqrt(vtkm::Float64)
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.. doxygenfunction:: vtkm::Sqrt(const T&)
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.. doxygenfunction:: vtkm::Sqrt(const vtkm::Vec<T, N>&)
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Remainders and Quotient
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==============================
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.. doxygenfunction:: vtkm::ModF(vtkm::Float32, vtkm::Float32&)
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.. doxygenfunction:: vtkm::ModF(vtkm::Float64, vtkm::Float64&)
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.. doxygenfunction:: vtkm::Remainder(vtkm::Float32, vtkm::Float32)
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.. doxygenfunction:: vtkm::Remainder(vtkm::Float64, vtkm::Float64)
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.. doxygenfunction:: RemainderQuotient(vtkm::Float32, vtkm::Float32, QType&)
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.. doxygenfunction:: RemainderQuotient(vtkm::Float64, vtkm::Float64, QType&)
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Rounding and Precision
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==============================
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.. doxygenfunction:: vtkm::Ceil(vtkm::Float32)
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.. doxygenfunction:: vtkm::Ceil(vtkm::Float64)
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.. doxygenfunction:: vtkm::Ceil(const T&)
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.. doxygenfunction:: vtkm::Ceil(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::CopySign(vtkm::Float32, vtkm::Float32)
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.. doxygenfunction:: vtkm::CopySign(vtkm::Float64, vtkm::Float64)
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.. doxygenfunction:: vtkm::CopySign(const vtkm::Vec<T, N>&, const vtkm::Vec<T, N>&)
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.. doxygenfunction:: Epsilon
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.. doxygenfunction:: Epsilon32
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.. doxygenfunction:: Epsilon64
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.. doxygenfunction:: vtkm::FMod(vtkm::Float32, vtkm::Float32)
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.. doxygenfunction:: vtkm::FMod(vtkm::Float64, vtkm::Float64)
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.. doxygenfunction:: vtkm::Round(vtkm::Float32)
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.. doxygenfunction:: vtkm::Round(vtkm::Float64)
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.. doxygenfunction:: vtkm::Round(const T&)
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.. doxygenfunction:: vtkm::Round(const vtkm::Vec<T, N>&)
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Sign
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==============================
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.. doxygenfunction:: vtkm::Abs(vtkm::Int32)
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.. doxygenfunction:: vtkm::Abs(vtkm::Int64)
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.. doxygenfunction:: vtkm::Abs(vtkm::Float32)
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.. doxygenfunction:: vtkm::Abs(vtkm::Float64)
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.. doxygenfunction:: vtkm::Abs(T)
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.. doxygenfunction:: vtkm::Abs(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::Floor(vtkm::Float32)
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.. doxygenfunction:: vtkm::Floor(vtkm::Float64)
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.. doxygenfunction:: vtkm::Floor(const T&)
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.. doxygenfunction:: vtkm::Floor(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::SignBit(vtkm::Float32)
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.. doxygenfunction:: vtkm::SignBit(vtkm::Float64)
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Trigonometry
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==============================
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.. doxygenfunction:: vtkm::ACos(vtkm::Float32)
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.. doxygenfunction:: vtkm::ACos(vtkm::Float64)
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.. doxygenfunction:: vtkm::ACos(const T&)
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.. doxygenfunction:: vtkm::ACos(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::ACosH(vtkm::Float32)
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.. doxygenfunction:: vtkm::ACosH(vtkm::Float64)
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.. doxygenfunction:: vtkm::ACosH(const T&)
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.. doxygenfunction:: vtkm::ACosH(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::ASin(vtkm::Float32)
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.. doxygenfunction:: vtkm::ASin(vtkm::Float64)
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.. doxygenfunction:: vtkm::ASin(const T&)
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.. doxygenfunction:: vtkm::ASin(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::ASinH(vtkm::Float32)
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.. doxygenfunction:: vtkm::ASinH(vtkm::Float64)
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.. doxygenfunction:: vtkm::ASinH(const T&)
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.. doxygenfunction:: vtkm::ASinH(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::ATan(vtkm::Float32)
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.. doxygenfunction:: vtkm::ATan(vtkm::Float64)
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.. doxygenfunction:: vtkm::ATan(const T&)
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.. doxygenfunction:: vtkm::ATan(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::ATan2(vtkm::Float32, vtkm::Float32)
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.. doxygenfunction:: vtkm::ATan2(vtkm::Float64, vtkm::Float64)
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.. doxygenfunction:: vtkm::ATanH(vtkm::Float32)
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.. doxygenfunction:: vtkm::ATanH(vtkm::Float64)
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.. doxygenfunction:: vtkm::ATanH(const T&)
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.. doxygenfunction:: vtkm::ATanH(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::Cos(vtkm::Float32)
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.. doxygenfunction:: vtkm::Cos(vtkm::Float64)
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.. doxygenfunction:: vtkm::Cos(const T&)
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.. doxygenfunction:: vtkm::Cos(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::CosH(vtkm::Float32)
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.. doxygenfunction:: vtkm::CosH(vtkm::Float64)
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.. doxygenfunction:: vtkm::CosH(const T&)
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.. doxygenfunction:: vtkm::CosH(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: Pi
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.. doxygenfunction:: Pi_2
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.. doxygenfunction:: Pi_3
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.. doxygenfunction:: Pi_4
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.. doxygenfunction:: Pi_180
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.. doxygenfunction:: vtkm::Sin(vtkm::Float32)
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.. doxygenfunction:: vtkm::Sin(vtkm::Float64)
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.. doxygenfunction:: vtkm::Sin(const T&)
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.. doxygenfunction:: vtkm::Sin(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::SinH(vtkm::Float32)
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.. doxygenfunction:: vtkm::SinH(vtkm::Float64)
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.. doxygenfunction:: vtkm::SinH(const T&)
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.. doxygenfunction:: vtkm::SinH(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::Tan(vtkm::Float32)
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.. doxygenfunction:: vtkm::Tan(vtkm::Float64)
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.. doxygenfunction:: vtkm::Tan(const T&)
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.. doxygenfunction:: vtkm::Tan(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: vtkm::TanH(vtkm::Float32)
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.. doxygenfunction:: vtkm::TanH(vtkm::Float64)
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.. doxygenfunction:: vtkm::TanH(const T&)
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.. doxygenfunction:: vtkm::TanH(const vtkm::Vec<T, N>&)
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.. doxygenfunction:: TwoPi
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Miscellaneous
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==============================
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.. doxygenfunction:: FloatDistance(vtkm::Float64, vtkm::Float64)
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.. doxygenfunction:: FloatDistance(vtkm::Float32, vtkm::Float32)
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.. doxygenfunction:: Max(const T&, const T&)
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.. doxygenfunction:: Min(const T&, const T&)
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------------------------------
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Vector Analysis
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------------------------------
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.. index:: vector analysis
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Visualization and computational geometry algorithms often perform vector analysis operations.
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The :file:`vtkm/VectorAnalysis.h` header file provides functions that perform the basic common vector analysis operations.
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.. doxygenfunction:: vtkm::Cross
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.. doxygenfunction:: vtkm::Lerp(const ValueType&, const ValueType&, const WeightType&)
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.. doxygenfunction:: vtkm::Magnitude
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.. doxygenfunction:: vtkm::MagnitudeSquared
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.. doxygenfunction:: vtkm::Normal
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.. doxygenfunction:: vtkm::Normalize
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.. doxygenfunction:: vtkm::Orthonormalize
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.. doxygenfunction:: vtkm::Project
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.. doxygenfunction:: vtkm::ProjectedDistance
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.. doxygenfunction:: vtkm::RMagnitude
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.. doxygenfunction:: vtkm::TriangleNormal
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------------------------------
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Matrices
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------------------------------
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.. index:: matrix
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Linear algebra operations on small matrices that are done on a single thread are located in :file:`vtkm/Matrix.h`.
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This header defines the :class:`vtkm::Matrix` templated class.
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The template parameters are first the type of component, then the number of rows, then the number of columns.
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The overloaded parentheses operator can be used to retrieve values based on row and column indices.
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Likewise, the bracket operators can be used to reference the :class:`vtkm::Matrix` as a 2D array (indexed by row first).
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.. doxygenclass:: vtkm::Matrix
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:members:
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The following example builds a :class:`vtkm::Matrix` that contains the values
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.. math::
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\left|
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\begin{array}{ccc}
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0 & 1 & 2 \\
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10 & 11 & 12
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\end{array}
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\right|
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.. load-example:: BuildMatrix
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:file: GuideExampleMatrix.cxx
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:caption: Creating a :class:`vtkm::Matrix`.
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The :file:`vtkm/Matrix.h` header also defines the following functions
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that operate on matrices.
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.. index::
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single: matrix; determinant
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single: determinant
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.. doxygenfunction:: vtkm::MatrixDeterminant(const vtkm::Matrix<T, Size, Size>&)
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.. doxygenfunction:: vtkm::MatrixGetColumn
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.. doxygenfunction:: vtkm::MatrixGetRow
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.. index::
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double: identity; matrix
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.. doxygenfunction:: vtkm::MatrixIdentity()
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.. doxygenfunction:: vtkm::MatrixIdentity(vtkm::Matrix<T, Size, Size>&)
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.. index::
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double: inverse; matrix
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.. doxygenfunction:: vtkm::MatrixInverse
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.. doxygenfunction:: vtkm::MatrixMultiply(const vtkm::Matrix<T, NumRow, NumInternal>&, const vtkm::Matrix<T, NumInternal, NumCol>&)
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.. doxygenfunction:: vtkm::MatrixMultiply(const vtkm::Matrix<T, NumRow, NumCol>&, const vtkm::Vec<T, NumCol>&)
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.. doxygenfunction:: vtkm::MatrixMultiply(const vtkm::Vec<T, NumRow>&, const vtkm::Matrix<T, NumRow, NumCol>&)
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.. doxygenfunction:: vtkm::MatrixSetColumn
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.. doxygenfunction:: vtkm::MatrixSetRow
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.. index::
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double: transpose; matrix
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.. doxygenfunction:: vtkm::MatrixTranspose
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.. index:: linear system
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.. doxygenfunction:: vtkm::SolveLinearSystem
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------------------------------
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Newton's Method
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------------------------------
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.. index:: Newton's method
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|VTKm|'s matrix methods (documented in :secref:`math:Matrices`)
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provide a method to solve a small linear system of equations. However,
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sometimes it is necessary to solve a small nonlinear system of equations.
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This can be done with the :func:`vtkm::NewtonsMethod` function defined in the
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:file:`vtkm/NewtonsMethod.h` header.
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The :func:`vtkm::NewtonsMethod` function assumes that the number of
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variables equals the number of equations. Newton's method operates on an
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iterative evaluate and search. Evaluations are performed using the functors
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passed into the :func:`vtkm::NewtonsMethod`.
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.. doxygenfunction:: vtkm::NewtonsMethod
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The :func:`vtkm::NewtonsMethod` function returns a \vtkm{NewtonsMethodResult} object.
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\textidentifier{NewtonsMethodResult} is a \textcode{struct} templated on the type and number of input values of the nonlinear system.
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\textidentifier{NewtonsMethodResult} contains the following items.
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.. doxygenstruct:: vtkm::NewtonsMethodResult
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:members:
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.. load-example:: NewtonsMethod
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:file: GuideExampleNewtonsMethod.cxx
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:caption: Using :func:`vtkm::NewtonsMethod` to solve a small system of nonlinear equations.
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