__ __ _ _ _ _ ______ _______
| \/ | | | | | | \ | | ____|__ __|
| \ / | __ _| |_| |__ | \| | |__ | |
| |\/| |/ _` | __| '_ \ | . ` | __| | |
| | | | (_| | |_| | | |_| |\ | |____ | |
|_| |_|\__,_|\__|_| |_(_)_| \_|______| |_|
Math.NET Numerics - http://numerics.mathdotnet.com
Copyright (c) Math.NET - Open Source MIT/X11 License
Math.NET Numerics v3.9.0
### 3.9.0 - 2015-11-25
* Distributions: Normal.CDF avoids problematic subtraction by using Erfc instead of Erf.
* Statistics: geometric and harmonic mean.
* Statistics: DataContracts for ephemeral serialization on RunningStatistics, DescriptiveStatistics and Histogram.
* BUG: Statistics: Histogram did not adjust lower bound correctly when value was equal to the bound *~Volker Breuer*
* Linear Algebra: minor optimization on how we call Array.Copy.
* BUG: Linear Algebra: fix bug in Complex and Complex32 SparseMatrix.ToTypeString.
### 3.8.0 - 2015-09-26
* Distributions: PDF and CDF more robust for large distribution parameters.
* Distributions: BetaScaled distribution.
* Distributions: method to create a PERT distribution (based on BetaScaled) *~John C Barstow*
* Distributions: Weibull.Estimate *~Jon Larborn*
* Random: NextBoolean extensions.
* Root Finding: RootFinding.Secant (based on NewtonRaphson) *~grovesNL*
* Linear Algebra: Matrix Rank calculation now uses a tolerance based on the matrix size.
* Linear Algebra: Alternative CreateMatrix/Vector functions with type parameter on functions instead of type.
* Linear Algebra: MKL LinearAlgebra provider requires at least native provider r9 (linear algebra v2.0).
* Native Providers: automatic handling of intermediate work arrays/buffers in MKL and OpenBLAS providers *~Marcus Cuda, Kuan Bartel*
* Native Providers: automatically use native provider if available.
* Native Providers: new Control.TryUse* to make it simpler to use providers if available but without failing if not.
* Native Providers: improved error state checking and handling *~Marcus Cuda, Kuan Bartel*
* Combinatorics: generate or select random permutation, combination or variation (shuffling)
* Finance: rename CompoundMonthlyReturn to CompoundReturn (old now obsolete).
### 3.7.1 - 2015-09-10
* BUG: Linear Algebra: fix optimized path of adding a sparse matrix to itself.
### 3.7.0 - 2015-05-09
* Statistics: RunningStatistics now propagates min/max on Combine, handles NaN on Push.
* Statistics: new MovingStatistics providing descriptive statistics over a moving window *~Marcus Cuda*
* Statistics: new Statistics.MovingAverage.
* Statistics: Improved Histogram handling of small-width buckets *~Justin Needham*
* Distributions: ChiSquare.InvCDF *~logophobia*
* FFT: Fourier.FrequencyScale to generate the frequency corresponding to each index in frequency space.
* BUG: FFT: fix Bluestein algorithm for sequences with more than 46341 samples but not power-of-two.
* Linear Algebra: SparseVector.AbsoluteMaximumIndex *~Matt Heffron*
* MKL Native Provider: OSX build script *~Marcus Cuda*
* MKL Native Provider: new combined NuGet package with a proper build target (no more manual file handling needed).
* OpenBLAS Native Provider: a new linear algebra provider using OpenBLAS *~Kuan Bartel*
* CUDA Native Provider: a new GPU-based linear algebra provider using Nvidia CUDA *~Matthew A. Johnson*
* Native Providers: now versioned separately for each kind (MKL, CUDA, OpenBLAS).
### 3.6.0 - 2015-03-22
* Distributions: ChiSquare.CDF more robust for large numbers *~Baltazar Bieniek*
* Linear Algebra: MatrixStorage.Map2 equivalent to VectorStorage.Map2
* Linear Algebra: Matrix and Vector Find/Find2, Exists/Exists2, ForAll/ForAll2
* Linear Algebra: more consistent range checking in MatrixStorage.Clear and related
* Linear Algebra: mixed-storage fall back implementations now leverage higher-order functions
* BUG: Linear Algebra: fix loop range in MatrixStorage.ClearColumns (built-in storage not affected)
* BUG: Linear Algebra: fix sparse matrix equality.
* BUG: Linear Algebra: ArgumentException instead of index exception when trying to create an empty matrix.
* Generate: Unfold, Fibonacci; Normal and Standard replacing Gaussian and Stable.
* Native Providers: NativeProviderLoader to automatically load the provider for the matching processor architecture (x86, x64) *~Kuan Bartel*
* Native Providers: Control.NativeProviderPath allowing to explicitly declare where to load binaries from.
* MKL Native Provider: support for native complex eigen-value decomposition *~Marcus Cuda*
* MKL Native Provider: non-convergence checks in singular-value and eigen-value decompositions *~Marcus Cuda*
### 3.5.0 - 2015-01-10
* Differentiation: derivative, partial and mixed partial; hessian & jacobian *~Hythem Sidky*
* Differentiation: Differentiate facade class for simple use cases
* Differentiation: F# module for better F# function support.
* Linear Algebra: matrix ToRowArrays/ToColumnArrays
* Linear Algebra: F# insertRow, appendRow, prependRow and same also for columns
* Linear Algebra: F# append, stack and ofMatrixList2
* Precision: measured machine epsilon, positive vs negative epsilon
### 3.4.0 - 2015-01-04
* Special Functions: Generalized Exponential Integral *~Ashley Messer*
* Special Functions: Regularized Incomplete Gamma domain extended to a=0 *~Ashley Messer*
* Statistics: weighted Pearson correlation *~ViK*
* MKL Native Provider: memory functions to free buffers and gather usage statistics *~Marcus Cuda*
* F#: depend on new official FSharp.Core NuGet package instead of FSharp.Core.Microsoft.Signed
* F#: simpler NuGet package dependencies (no more need for framework groups)
* Build: vagrant bootstrap now uses the latest xamarin mono packages
### 3.3.0 - 2014-11-26
* Linear Algebra: Vector.Fold2 (fold2 in F#), storage optimized
* Linear Algebra: Minor change how matrix products call the LA provider
* Linear Algebra: Random generation now leveraging array sampling routines
* BUG: Linear Algebra: fix bug when manually assigning System.Random to random distribution
* Root Finding: Change Brent tolerance check, add bracket check *~Hythen Sidky*
* Root Finding: Auto zero-crossing bracketing in FindRoots facade (not in algorithms)
* Statistics: RootMeanSquare (RMS)
* Distributions: Array sampling routines now available through interface
* Distributions: Categorical sampling now explicitly skips p=0 categories
* Generate: leverage array sampling routines for random data generation
* Generate: square, triangle and sawtooth waves
* Distance: Jaccard Index
* F#: explicitly depend on official FSharp.Core NuGet packages
* F#: NuGet package with iPython IfSharp F# module integration load script
* F#: load scripts with better packet support (and NuGet with -ExcludeVersion)
* Build: unified build.sh and buildn.sh into combined build.sh
* Build: use Paket instead of NuGet to maintain NuGet dependencies
* Build: for core add PCL profiles 7, 78 and 259; for F# extensions drop PCL profile 328
### 3.2.3 - 2014-09-06
* BUG: MatrixNormal distribution: fix density for non-square matrices *~Evelina Gabasova*
### 3.2.2 - 2014-09-05
* BUG: MatrixNormal distribution: density computation switched row and column covariance *~Evelina Gabasova*
### 3.2.1 - 2014-08-05
* Package fix: make sure .Net 3.5-only dependencies are not installed on .Net 4 and newer.
### 3.2.0 - 2014-08-05
* Linear Algebra: Vector.Map2 (map2 in F#), storage-optimized
* Linear Algebra: fix RemoveColumn/Row early index bound check (was not strict enough)
* Statistics: Entropy *~Jeff Mastry*
* Interpolation: use Array.BinarySearch instead of local implementation *~Candy Chiu*
* Resources: fix a corrupted exception message string
* Portable Build: support .Net 4.0 as well by using profile 328 instead of 344.
* .Net 3.5: F# extensions now support .Net 3.5 as well
* .Net 3.5: NuGet package now contains p
克里金插值算法绘制云图,生成DEM等高线
需积分: 0 162 浏览量
更新于2023-05-16
2
收藏 5.71MB ZIP 举报
克里金插值(Kriging Interpolation)是一种在地理信息系统(GIS)和地球科学领域广泛应用的统计插值方法,由南非矿业工程师丹尼尔·嘉士伯·克里金提出。该算法主要用于填补空间数据的空白区域,通过考虑已知数据点之间的空间相关性,预测未知位置的值。克里金插值不仅考虑了数据点的值,还考虑了它们之间的距离和方向,以提供更为精确的估计。
云图通常用于可视化三维数据,将数据投影到二维平面上,通过颜色梯度或等高线来表示不同数值的分布。在克里金插值中,云图可以清晰地展示地形高度变化,帮助我们理解地理特征的连续性和不连续性。生成DEM(数字高程模型)等高线是这一过程中的关键步骤,DEM是地形表面的数字表示,包含每个网格点的海拔高度信息。
克里金插值算法主要包括以下几个步骤:
1. 数据收集:我们需要收集一系列空间分布的测量点,这些点包含了我们要插值的高度信息。
2. 半变异函数:这是克里金插值的核心,它描述了两个数据点之间的空间相关性随它们之间距离的变化。半变异函数可以通过实际数据进行拟合,选择合适的模型,如球状、指数、高斯等。
3. 权重计算:根据半变异函数,为每个已知数据点计算权重。权重的大小取决于数据点与待插值点的距离和方向,以及它们之间的相关性。
4. 插值预测:利用所有数据点的权重,对未知位置的值进行预测。这通常通过解决一个系统线性方程组来实现。
5. 图形化输出:将插值结果以云图或等高线的形式展示出来。云图可以直观地展示地形的连续性,而等高线则能突出地形的起伏和特征。
6. 可变参数调整:为了提高插值精度,可能需要多次尝试不同的克里金参数,如 nugget 效应、结构参数等,以找到最佳模型。
克里金插值算法的优势在于其灵活性和适应性,能够处理非正态分布的数据,同时考虑到空间自相关性,使得预测结果更为可靠。然而,计算量相对较大,尤其是在大数据集上。此外,合理选择半变异函数和参数对结果有很大影响,需要根据实际问题进行选择和优化。
克里金插值算法在地理数据分析中扮演着重要角色,特别是在创建精确的DEM和可视化复杂地形特征时。通过理解和应用这个方法,我们可以更好地理解地球表面的自然现象,并为环境研究、城市规划和资源管理等领域提供有价值的工具。


幽兰的天空
- 粉丝: 4007
最新资源
- 基于Android的社交分享平台的设计论文.doc
- 网络宣传管理工作总结.docx
- 董老师研发多项目管理.doc
- 基因工程的步骤.ppt
- 国际货物买卖法MicrosoftPowerPoint演示文稿.pptx
- 金蝶软件初始化准备及基础资料编码规则培训.ppt
- 软件售后服务人员提成方案附表.docx
- 设施网络规划与物流管理.pptx
- 网络侵权的界定是什么?.doc
- 基于MATLAB彩色图像及增强处理设计方法.doc
- 项目管理人员安全生产责任制考核记录表.doc
- 天骄联盟网网络推广策划书.doc
- 中小企业会计信息化综述.doc
- 门户网站Web及应用服务器加速及负载均衡方案.doc
- 信息系统项目管理师九大项目管理知识点整合.pdf
- 根源性创新与计算机产业.ppt