套件：liblip-dev（2.0.0-2.1）

[ 原始碼： liblip  ]

reliable interpolation of multivariate scattered data

Lip interpolates scattered multivariate data with a Lipschitz function.

Methods of interpolation of multivariate scattered data are scarce. The programming library Lip implements a new method by G. Beliakov, which relies on building reliable lower and upper approximations of Lipschitz functions. If we assume that the function that we want to interpolate is Lipschitz-continuous, we can provide tight bounds on its values at any point, in the worse case scenario. Thus we obtain the interpolant, which approximates the unknown Lipschitz function f best in the worst case scenario. This translates into reliable learning of f, something that other methods cannot do (the error of approximation of most other methods can be infinitely large, depending on what f generated the data).

Lipschitz condition implies that the rate of change of the function is bounded:

|f(x)-f(y)|<M||x-y||.

It is easily interpreted as the largest slope of the function f. f needs not be differentiable.

The interpolant based on the Lipschitz properties of the function is piecewise linear, it possesses many useful properties, and it is shown that it is the best possible approximation to f in the worst case scenario. The value of the interpolant depends on the data points in the immediate neigbourhood of the point in question, and in this sense, the method is similar to the natural neighbour interpolation.

There are two methods of construction and evaluation of the interpolant. The explicit method processes all data points to find the neighbours of the point in question. It does not require any preprocessing, but the evaluation of the interpolant has linear complexity O(K) in terms of the number of data.

"Fast" method requires substantial preprocessing in the case of more than 3-4 variables, but then it provides O(log K) evaluation time, and thus is suitable for very large data sets (K of order of 500000) and modest dimension (n=1-4). For larger dimension, explicit method becomes practically more efficient. The class library Lip implements both fast and explicit methods.

標籤: 軟體開發: 函式庫, 領域: 數學, 角色: 開發用函式庫

其他與 liblip-dev 有關的套件

• dep: libc6 (>= 2.27) [riscv64]

  GNU C 函式庫：共用函式庫
  同時作為一個虛擬套件由這些套件填實： libc6-udeb

  dep: libc6 (>= 2.29) [除 alpha, ia64, riscv64, sh4]

  dep: libc6 (>= 2.37) [sh4]

• dep: libc6.1 (>= 2.29) [alpha]

  GNU C 函式庫：共用函式庫
  同時作為一個虛擬套件由這些套件填實： libc6.1-udeb

  dep: libc6.1 (>= 2.37) [ia64]

• dep: libgcc-s1 (>= 3.0) [amd64, arm64, i386, mips64el, ppc64, ppc64el, s390x, x32]

  GCC 支援函式庫

  dep: libgcc-s1 (>= 3.4) [alpha, riscv64, sh4, sparc64]

  dep: libgcc-s1 (>= 3.5) [armel, armhf]

  dep: libgcc-s1 (>= 4.2) [ia64]

• dep: libgcc-s2 (>= 4.2.1) [m68k]

  GCC 支援函式庫

• dep: libgcc-s4 (>= 4.1.1) [hppa]

  GCC 支援函式庫

• dep: liblip2t64 (= 2.0.0-2.1)

  reliable interpolation of multivariate scattered data

• dep: libstdc++6 (>= 13.1)

  GNU Standard C++ Library v3

• dep: libtnt-dev

  interface for scientific computing in C++

• dep: libunwind8 [ia64]

  library to determine the call-chain of a program - runtime

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硬體架構	套件大小	安裝後大小	檔案
alpha （非官方移植版）	71。8 kB	377。0 kB	[檔案列表]
amd64	65。7 kB	278。0 kB	[檔案列表]
arm64	61。2 kB	270。0 kB	[檔案列表]
armel	61。5 kB	248。0 kB	[檔案列表]
armhf	57。5 kB	204。0 kB	[檔案列表]
hppa （非官方移植版）	71。3 kB	270。0 kB	[檔案列表]
i386	66。6 kB	249。0 kB	[檔案列表]
ia64 （非官方移植版）	87。0 kB	436。0 kB	[檔案列表]
m68k （非官方移植版）	59。0 kB	229。0 kB	[檔案列表]
mips64el	71。8 kB	345。0 kB	[檔案列表]
ppc64 （非官方移植版）	71。3 kB	338。0 kB	[檔案列表]
ppc64el	72。2 kB	324。0 kB	[檔案列表]
riscv64	156。4 kB	1，397。0 kB	[檔案列表]
s390x	72。2 kB	307。0 kB	[檔案列表]
sh4 （非官方移植版）	68。0 kB	222。0 kB	[檔案列表]
sparc64 （非官方移植版）	60。6 kB	307。0 kB	[檔案列表]
x32 （非官方移植版）	64。3 kB	239。0 kB	[檔案列表]