Îõ³h$ß      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^,Type castings and conversions of array typesPhillip Seeber, 2022AGPL-3phillip.seeber@googlemail.com experimentalPOSIX, WindowsNone #$%/35678:>?ÀÁÂÉÎ×Ùåæì´ ConClusionÈConverts a vector from the HMatrix package to the Massiv representation. ConClusionÏConverts a vector from the Massiv representation to the HMatrix representation. ConClusionÏConverts a matrix from the HMatrix representation to the Massiv representation. ConClusion8Converts a matrix from Massiv to HMatrix representation..Additional tools to work with numerical arraysPhillip Seeber, 2022AGPL-3phillip.seeber@googlemail.com experimentalPOSIX, WindowsNone #$%/35678:>?ÀÁÂÉÎ×Ùåæì^ ConClusion3Exception regarding indexing in some kind of aaray. ConClusionMagnitude of a vector (length). ConClusionNormalise a vector. ConClusionAngle between two vectors.  ConClusionÏFind the minimal distance in a distance matrix, which is not the main diagonal.  ConClusionÓFind the minimal element of a vector, which is at a larger than the supplied index.  ConClusionLike _3 but also returns the index of the minimal element.  3Custom binary tree type with some special functionsPhillip Seeber, 2022AGPL-3phillip.seeber@googlemail.com experimentalPOSIX, WindowsNone #$%/35678:>?ÀÁÂÉÎ×Ùåæìç ConClusionA binary tree. ConClusion"Look at the root of a binary tree. ConClusion•Steps down each branch of a tree until some criterion is satisfied or the end of the branch is reached. Each end of the branch is added to a result. ConClusion Takes the first value in each branch, that does not fullfill the criterion anymore and adds it to the result. Terminal leafes of the branches are always taken.Principal Component AnalysisPhillip Seeber, 2021AGPL-3phillip.seeber@googlemail.com experimentalPOSIX, WindowsNone #$%/35678:>?ÀÁÂÉÎ×Ùåæì ' ConClusion Selections ConClusionÒSelection of a dihedral angle between four atoms. Rotation around the central two.! ConClusion*Selection of an angle between three atoms.# ConClusion&Selection of a bond between two atoms.& ConClusion$A Molecule in cartesian coordinates.' ConClusion*Parser for molecules in Molden XYZ format.( ConClusion;Parser for trajectories in XYZ format as produced by CREST.) ConClusionObtains the feature matrix  \mathbf{X}+ for a principal component analysis. Given m features to analyse in n measurements,  \mathbf{X} will be a  m \times n matrix. !"#$%&'()&%'(#$!" )Statistical FunctionsPhillip Seeber, 2021AGPL-3phillip.seeber@googlemail.com experimentalPOSIX, WindowsNone #$%/35678:>?ÀÁÂÉÎ×Ùåæìv* ConClusion)A strategy/distance measure for clusters.4 ConClusionA dendrogram as a binary tree.5 ConClusionRepresentation of clusters.6 ConClusion'Exception for invalid search distances.8 ConClusion$Distance matrix generator functions.; ConClusionOriginal feature matrix.< ConClusion&Feature matrix in mean deviation form.= ConClusionTransformed data.> ConClusionÉTransformation matrix to transform feature matrix into PCA result matrix.? ConClusion%Mean squared error introduced by PCA.@ ConClusionÁPercentage of the behaviour captured in the remaining dimensions.A ConClusionÂAll eigenvalues from the diagonalisation of the covariance matrix.B ConClusion#Eigenvalues that were kept for PCA.C ConClusionÃAll eigenvectors from the diagonalisation of the covariance matrix.D ConClusion$Eigenvectors that were kept for PCA.E ConClusion%Performs a PCA on the feature matrix  \mathbf{X}î by solving the eigenproblem of the covariance matrix. The function takes the feature matrix directly and perfoms the conversion to mean deviation form, the calculation of the covariance matrix and the eigenvalue problem automatically.F ConClusionòSubtract the mean value of all columns from the feature matrix. Brings the feature matrix to mean deviation form.G ConClusionObtains the covariance matrix  \mathbf{C_X} from the feature matrix  \mathbf{X}. Á \mathbf{C_X} \equiv \frac{1}{n - 1} \mathbf{X} \mathbf{X}^T  where n( is the number of columns in the matrix.9The feature matrix should be in mean deviation form, see F.H ConClusionÐNormalise each value so that the maximum absolute value in each row becomes one.I ConClusionThe L_pÑ norm between two vectors. Generalisation of Manhattan and Euclidean distances. € d(\mathbf{a}, \mathbf{b}) = \left( \sum \limits_{i=1}^n \lvert \mathbf{a}_i - \mathbf{b}_i \rvert ^p \right) ^ \frac{1}{p} J ConClusionÂThe Manhattan distance between two vectors. Specialisation of the L_p norm for p = 1. à d(\mathbf{a}, \mathbf{b}) = \sum \limits_{i=1}^n \lvert \mathbf{a}_i - \mathbf{b}_i \rvert K ConClusionÂThe Euclidean distance between two vectors. Specialisation of the L_p norm for p = 2. Ý d(\mathbf{a}, \mathbf{b}) = \sqrt{\sum \limits_{i=1}^n (\mathbf{a}_i - \mathbf{b}_i)^2} L ConClusionÈMahalanobis distance between points. Suitable for non correlated axes. î d(\mathbf{a}, \mathbf{b}) = \sqrt{(\mathbf{a} - \mathbf{b})^T \mathbf{S}^{-1} (\mathbf{a} - \mathbf{b})}  where  \mathbf{S} is the covariance matrix.M ConClusionDBScan algorithm.N ConClusionCut a 45 at a given distance and obtain all clusters from it.O ConClusion8Performance improved hierarchical clustering algorithm. GENERIC_LINKAGE from figure 3,  #https://arxiv.org/pdf/1109.2378.pdf.E ConClusion'Dimensionalty after PCA transformation. ConClusion m \times n Feaute matrix  \mathbf{X}, with m# different measurements (rows) in n different trials (columns).M ConClusion==?ÀÁÂÉÎ×Ùåæì`abcdefgè       !"#$%%&&''()*+,-./01234567899:;;<=>?@ABCDEFGH IJKLMNOPQRSTUVWXYZ[\]^_`abcdefghiê'ConClusion-0.2.0-CJTr1MxRC5h6RE4MqNcODaConClusion.Array.ConversionConClusion.Array.UtilConClusion.BinaryTreeConClusion.Chemistry.TopologyConClusion.Numeric.StatisticsPaths_ConClusionvecH2MvecM2HmatH2MmatM2HIndexException magnitude normaliseangle minDistAt minDistAtVec iMinimumM$fExceptionIndexException$fShowIndexExceptionBinTreeLeafNoderoottakeBranchesWhiletakeLeafyBranchesWhile$fFunctorBinTree$fToJSONBinTree$fFromJSONBinTree $fEqBinTree $fShowBinTree$fGenericBinTreeFeatureEnergyBondAngleDihedralDAB TrajectoryMoleculexyz trajectory getFeatures JoinStrat SingleLinkageCompleteLinkageMedianUPGMAWPGMACentroidWardLWFBLW DendrogramClustersDistanceInvalidExceptionDistFnPCA $sel:x:PCA $sel:x':PCA $sel:y:PCA $sel:a:PCA $sel:mse:PCA$sel:remaining:PCA$sel:allEigenValues:PCA$sel:pcaEigenValues:PCA$sel:allEigenVecs:PCA$sel:pcaEigenVecs:PCApca meanDeviation covariancelpNorm manhattan euclidean mahalanobisdbscan cutDendroAthca#$fExceptionDistanceInvalidException$fToJSONDendroNode$fFromJSONDendroNode$fFromJSONDendrogram$fToJSONDendrogram $fEqJoinStrat$fShowJoinStrat$fShowDendrogram$fEqDendrogram$fGenericDendrogram$fEqDendroNode$fShowDendroNode$fGenericDendroNode$fShowDistanceInvalidException$fEqDistanceInvalidException%massiv-1.0.1.1-AeELM7LQxcH3yig0mraLZOData.Massiv.Array.Ops.FoldminimumMversion getBinDir getLibDir getDynLibDir getDataDir getLibexecDir getSysconfDirgetDataFileName