h&3d0      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^,Type castings and conversions of array typesPhillip Seeber, 2023AGPL-3phillip.seeber@googlemail.com experimentalPOSIX, Windows Safe-Inferred"%&'1689:;= ConClusionConverts a vector from the HMatrix package to the Massiv representation. ConClusionConverts a vector from the Massiv representation to the HMatrix representation. ConClusionConverts 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, 2023AGPL-3phillip.seeber@googlemail.com experimentalPOSIX, Windows Safe-Inferred"%&'1689:;=| ConClusion3Exception regarding indexing in some kind of aaray. ConClusionMagnitude of a vector (length). ConClusionNormalise a vector. ConClusionAngle between two vectors.  ConClusionFind the minimal distance in a distance matrix, which is not the main diagonal.  ConClusionFind 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, 2023AGPL-3phillip.seeber@googlemail.com experimentalPOSIX, Windows Safe-Inferred"%&'1689:;=  ConClusionA binary tree. ConClusion"Look at the root of a binary tree. ConClusionSteps 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. ConClusionTakes 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, 2023AGPL-3phillip.seeber@googlemail.com experimentalPOSIX, Windows Safe-Inferred"%&'1689:;= ConClusion Selections ConClusionSelection 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$A Molecule in cartesian coordinates.` ConClusionThe energy of the molecule.a ConClusion(Chemical symbols or names of the atoms. N vector.b ConClusion6Cartesian coordinates. Atoms as rows, xyz as columns.  N \times 3 matrix.' ConClusion*Parser for molecules in Molden XYZ format.( ConClusion;Parser for trajectories in XYZ format as produced by CREST.c ConClusionCalculate a bond distance.d ConClusion8Calculates the sinus of an angle defined by three atoms.e ConClusionCalculates the dihedral angle defined by four atoms. Respects rotation direction. Obtains the result in radian.f ConClusionCalculates a metric value of the dihedral angle defined by four atoms. This must create 2 values in the feature matrix, instead of one. See  ConClusionTransformation matrix to transform feature matrix into PCA result matrix.? ConClusion%Mean squared error introduced by PCA.@ ConClusionPercentage of the behaviour captured in the remaining dimensions.A ConClusionAll eigenvalues from the diagonalisation of the covariance matrix.B ConClusion#Eigenvalues that were kept for PCA.C ConClusionAll eigenvectors from the diagonalisation of the covariance matrix.D ConClusion$Eigenvectors that were kept for PCA.m ConClusionSolves eigenvalue problem of a square matrix and obtains its eigenvalues and eigenvectors.n ConClusionSort eigenvalues and eigenvectors by magnitude of the eigenvalues in descending order (largest eigenvalues first). Eigenvectors are the columns of the input matrix.o ConClusionAdjust function for priority queues. Updates the priority at a given key if present.p ConClusion8Transform the input values with a transformation matrix  \mathbf{A}, where  \mathbf{A} is constructed from the eigenvectors associated to the largest eigenvalues.E ConClusion%Performs a PCA on the feature matrix  \mathbf{X} 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 ConClusionSubtract 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}. [ 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 ConClusionNormalise each value so that the maximum absolute value in each row becomes one.q ConClusionBuilds the distance measures in a permutation matrix/distance matrix.I ConClusionThe L_p 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 ConClusionThe Manhattan distance between two vectors. Specialisation of the L_p norm for p = 1. [ d(mathbf{a}, mathbf{b}) = sum limits_{i=1}^n lvert mathbf{a}_i - mathbf{b}_i rvert ]K ConClusionThe Euclidean distance between two vectors. Specialisation of the L_p norm for p = 2. [ d(mathbf{a}, mathbf{b}) = sqrt{sum limits_{i=1}^n (mathbf{a}_i - mathbf{b}_i)^2} ]L ConClusionMahalanobis distance between points. Suitable for non correlated axes. [ 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.r ConClusion+Lance Williams formula to update distances.O ConClusion8Performance improved hierarchical clustering algorithm. GENERIC_LINKAGE from figure 3,  #https://arxiv.org/pdf/1109.2378.pdf.s ConClusionAgglomerative clustering by the improved generic linkage algorithm. This is the main loop recursion L 10-43.t ConClusionObtain candidates for the clusters to join by looking at the minimal distance in the priority queue and the neighbourlist. L 11-13u ConClusionIf the minimal distance d# found is not the distance between a and b recalculate the neighbour list, update the priority queue and obtain a new set of a,b and a distance between them. L 14-20.v ConClusionJoins the selected clusters A and B and updates the dendrogram accumulator at index b. A will not be removed so that the accumulator never shrinks. L 21-24w ConClusionUpdate the distance matrix with a Lance-Williams update in the rows and columns of cluster b. L 25-27x ConClusionUpdates the neighbourlist. All elements with a smaller index than a, that had a as a nearest neighbour are blindly redirected to the union of a and b, now at index b. L 28-32y ConClusionUpdates the list of nearest neighbours for all combinations that might have changed by recalculation with the joined cluster AB at index b. L 33-38z ConClusionUpdates the list of nearest neighbours and the priority queue at key b. L 39-40{ ConClusionFind the nearest neighbour for each point from a distance matrix. For each point it stores the minimum distance and the index of the other point, that is the nearest neighbour but at a higher index.| ConClusionMake a search row for distances. Takes row x from a distance matrix and zips them with their column index. Then keeps only the valid elements of the row, that are still part of the available points. A minimum or maximum search can be performed on the resulting vector and a valid pair of distance and index can be obtained.p ConClusion&Number of dimensions to keep from PCA. ConClusionMatrix of the eigenvectors, sorted descendingly by eigenvalues, where the eigenvectors are the columns of the matrix. ConClusion&Feature matrix in mean deviation form. ConClusionInput data transformed by PCA to lower dimensions, and the transformation matrix  \mathbf{A}.E ConClusion'Dimensionalty after PCA transformation. ConClusion m \times n Feaute matrix  \mathbf{X}, with m# different measurements (rows) in n different trials (columns).q ConClusion0Zip function to combine the elements of vectors  \mathbf{a}  \mathbf{b} . Usually (-). , f(\mathbf{a}_i, \mathbf{b}_i) = \mathbf{c}  ConClusionFold the vector  \mathbf{c} elementwise to a distance d. ConClusion!Accumulator of the fold function. ConClusion m \times n matrix, with n m3-dimensional points (column vectors of the matrix). ConClusionResulting distance matrix.M ConClusion==?@ABCDEFGH IJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~&ConClusion-0.2.2-Ccij1JjHpTsxLxVT4fULWConClusion.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-1.0.4.0-3TS4GWpPz54ANCUKc4UrrbData.Massiv.Array.Ops.FoldminimumM$sel:energy:Molecule$sel:atoms:Molecule$sel:coordinates:Moleculebond dihedral'dihedral getFeatureDistanceMatrix Neighbourlist DendroAccM DendroAcc DendroNodeeigeigSortpqAdjusttransformToPCABasis buildDistMat lanceWilliams agglomerategetJoinCandidatesrecalculateNghbr joinClusters updateDistMatredirectNeighboursupdateWithNewBDistsupdateBNeighbournearestNeighbours searchRowversiongetDataFileName getBinDir getLibDir getDynLibDir getDataDir getLibexecDir getSysconfDir