![;      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~     None;=>?AVn eigenEComplex number for FFI with the same memory layout as std::complex<T>  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  lmnopkqjihrgsfteudvcwbxay`z_{^|]}\~[ZYXWVUTSRQPONMLKJIHGFEDCBA@?>=<;:9876543210/.-,+*)('&%$#"! None"#V6Peigen<Alias for double prevision mutable matrix of complex numberseigen<Alias for single previsiom mutable matrix of complex numberseigen)Alias for double precision mutable matrixeigen)Alias for single precision mutable matrixeigen'Mutable matrix. You can modify elementseigen*Verify matrix dimensions and memory layouteigenQCreate a mutable matrix of the given size and fill it with 0 as an initial value.eigenOCreate a mutable matrix of the given size and fill it with as an initial value.eigen1Set all elements of the matrix to the given valueeigenLCopy a matrix. The two matrices must have the same size and may not overlap.eigen(Yield the element at the given position.eigen*Replace the element at the given position.eigenCopy a matrix. The two matrices must have the same size and may not overlap however no bounds check performaned to it may SEGFAULT for incorrect input.eigenHYield the element at the given position. No bounds checks are performed.eigenJReplace the element at the given position. No bounds checks are performed.eigenPass a pointer to the matrix's data to the IO action. Modifying data through the pointer is unsafe if the matrix could have been frozen before the modification.None"#&',-;=>?AFQSTVdiVeigen)View matrix as a lower triangular matrix.eigen*View matrix as an upper triangular matrix.eigenDView matrix as a lower triangular matrix with zeros on the diagonal.eigenEView matrix as an upper triangular matrix with zeros on the diagonal.eigenCView matrix as a lower triangular matrix with ones on the diagonal.eigenDView matrix as an upper triangular matrix with ones on the diagonal.eigen4Alias for double prevision matrix of complex numberseigen4Alias for single previsiom matrix of complex numberseigen!Alias for double precision matrixeigen!Alias for single precision matrixeigeniMatrix to be used in pure computations, uses column major memory layout, features copy-free FFI with C++  http://eigen.tuxfamily.orgEigen library. eigen'Encode the matrix as a lazy byte string eigen'Decode matrix from the lazy byte string eigenEmpty 0x0 matrix eigenIs matrix empty?eigenIs matrix square?eigen3Matrix where all coeffs are filled with given valueeigenMatrix where all coeff are 0eigenMatrix where all coeff are 1eigen-The identity matrix (not necessarily square).eigen!The random matrix of a given sizeeigenNumber of rows for the matrixeigen Number of columns for the matrixeigenMtrix size as (rows, cols) paireigen*Matrix coefficient at specific row and coleigen*Matrix coefficient at specific row and coleigenPUnsafe version of coeff function. No bounds check performed so SEGFAULT possibleeigen&List of coefficients for the given coleigen&List of coefficients for the given roweigenVExtract rectangular block from matrix defined by startRow startCol blockRows blockColseigen*Verify matrix dimensions and memory layouteigen%The maximum coefficient of the matrixeigen%The minimum coefficient of the matrix eigenTop N rows of matrix!eigenBottom N rows of matrix"eigenLeft N columns of matrix#eigenRight N columns of matrix$eigenvConstruct matrix from a list of rows, column count is detected as maximum row length. Missing values are filled with 0%eigen Convert matrix to a list of rows&eigenpBuild matrix of given dimensions and values from given list split on rows. Invalid list length results in error.'eigen.Convert matrix to a list by concatenating rows(eigen %generate rows cols ( row col -> val)'Create matrix using generator function  row col -> val)eigen)The sum of all coefficients of the matrix*eigen-The product of all coefficients of the matrix+eigen*The mean of all coefficients of the matrix,eigenjThe trace of a matrix is the sum of the diagonal coefficients and can also be computed as sum (diagonal m)-eigeniApplied to a predicate and a matrix, all determines if all elements of the matrix satisfies the predicate.eigenhApplied to a predicate and a matrix, any determines if any element of the matrix satisfies the predicate/eigenJReturns the number of coefficients in a given matrix that evaluate to true0eigenFor vectors, the l2 norm, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of this with itself.1eigenFor vectors, the squared l2 norm, and for matrices the Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of this with itself.2eigenThe l2 norm of the matrix using the Blue's algorithm. A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM TOMS, Vol 4, Issue 1, 1978.3eigenThe l2 norm of the matrix avoiding undeflow and overflow. This version use a concatenation of hypot calls, and it is very slow.4eigenThe determinant of the matrix5eigenNAdding two matrices by adding the corresponding entries together. You can use (+) function as well.6eigenXSubtracting two matrices by subtracting the corresponding entries together. You can use (-) function as well.7eigen#Matrix multiplication. You can use (*) function as well.8eigen5Apply a given function to each element of the matrix.AHere is an example how to implement scalar matrix multiplication:*let a = fromList [[1,2],[3,4]] :: MatrixXfa Matrix 2x21.0 2.03.0 4.0 map (*10) a Matrix 2x2 10.0 20.0 30.0 40.09eigen5Apply a given function to each element of the matrix.BHere is an example how upper triangular matrix can be implemented:6let a = fromList [[1,2,3],[4,5,6],[7,8,9]] :: MatrixXfa Matrix 3x3 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.06imap (\row col val -> if row <= col then val else 0) a Matrix 3x3 1.0 2.0 3.0 0.0 5.0 6.0 0.0 0.0 9.0:eigen1Triangular view extracted from the current matrix;eigen+Lower trinagle of the matrix. Shortcut for triangularView Lower<eigen+Upper trinagle of the matrix. Shortcut for triangularView Upper=eigenFFilter elements in the matrix. Filtered elements will be replaced by 0>eigenFFilter elements in the matrix. Filtered elements will be replaced by 0?eigenCReduce matrix using user provided function applied to each element.@eigen^Reduce matrix using user provided function applied to each element. This is strict version of ?AeigenQReduce matrix using user provided function applied to each element and it's indexBeigenmReduce matrix using user provided function applied to each element and it's index. This is strict version of ACeigenCReduce matrix using user provided function applied to each element.Deigen^Reduce matrix using user provided function applied to each element. This is strict version of ?EeigenDiagonal of the matrixFeigenInverse of the matrix}For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses PartialPivLU decompositionGeigenAdjoint of the matrixHeigenTranspose of the matrixIeigenConjugate of the matrixJeigen*Nomalize the matrix by deviding it on its 0KeigenApply a destructive operation to a matrix. The operation will be performed in place if it is safe to do so and will modify a copy of the matrix otherwise.LeigenFConvert matrix to different type using user provided element converterMeigen-Yield an immutable copy of the mutable matrixNeigen,Yield a mutable copy of the immutable matrixOeigen}Unsafe convert a mutable matrix to an immutable one without copying. The mutable matrix may not be used after this operation.PeigenUnsafely convert an immutable matrix to a mutable one without copying. The immutable matrix may not be used after this operation.QeigengPass a pointer to the matrix's data to the IO action. The data may not be modified through the pointer.ReigenMatrix binary serializationSeigen0Basic matrix math exposed through Num instance: (*), (+), (-), , , , TeigenPretty prints the matrixW       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQW  $%&'(   !"#)*+,01234?@ABCD-./56789=>EHFGIJKL:;<  NMPOQNone"#Yeigen SDecomposition Requirements on the matrix Speed Accuracy Rank Kernel Image PartialPivLU Invertible ++ + - - - FullPivLU None - +++ + + + HouseholderQR None ++ + - - - ColPivHouseholderQR None + ++ + - - FullPivHouseholderQR None - +++ + - - LLT Positive definite +++ + - - - LDLT Positive or negative semidefinite +++ ++ - - - JacobiSVD None - +++ + - - ZThe best way to do least squares solving for square matrices is with a SVD decomposition (a)Zeigen3LU decomposition of a matrix with partial pivoting.[eigen4LU decomposition of a matrix with complete pivoting.\eigen)Householder QR decomposition of a matrix.]eigenMHouseholder rank-revealing QR decomposition of a matrix with column-pivoting.^eigenKHouseholder rank-revealing QR decomposition of a matrix with full pivoting._eigen3Standard Cholesky decomposition (LL^T) of a matrix.`eigen8Robust Cholesky decomposition of a matrix with pivoting.aeigen;Two-sided Jacobi SVD decomposition of a rectangular matrix.beigen x = solve d a bfinds a solution x of ax = b equation using decomposition dceigen e = relativeError x a b computes norm (ax - b) / norm b where norm is L2 normdeigenThe rank of the matrixeeigen>Return matrix whose columns form a basis of the null-space of AfeigenBReturn a matrix whose columns form a basis of the column-space of Ageigen )(coeffs, error) = linearRegression points$computes multiple linear regression #y = a1 x1 + a2 x2 + ... + an xn + b using ] decompositionpoint format is  [y, x1..xn]coeffs format is  [b, a1..an]error is calculated using c import Data.Eigen.LA main = print $ linearRegression [ [-4.32, 3.02, 6.89], [-3.79, 2.01, 5.39], [-4.01, 2.41, 6.01], [-3.86, 2.09, 5.55], [-4.10, 2.58, 6.32]] produces the following output V([-2.3466569233817127,-0.2534897541434826,-0.1749653335680988],1.8905965120153139e-3) YZ[\]^_`abcdefgYZ[\]^_`abcdefgNoneAleigen1Sets the max number of threads reserved for Eigenmeigen1Gets the max number of threads reserved for EigenlmlmNone"#&'V4neigen<Alias for double prevision mutable matrix of complex numbersoeigen<Alias for single previsiom mutable matrix of complex numberspeigen)Alias for double precision mutable matrixqeigen)Alias for single precision mutable matrixreigen&Mutable version of sparse matrix. See  ! for details about matrix layout.teigen'Creates new matrix with the given size  rows x colsueigen(Returns the number of rows of the matrixveigen+Returns the number of columns of the matrixweigenlReturns the number of rows (resp. columns) of the matrix if the storage order column major (resp. row major)xeigenlReturns the number of columns (resp. rows) of the matrix if the storage order column major (resp. row major)yeigen2Returns whether this matrix is in compressed form.zeigen,Turns the matrix into the compressed format.{eigen,Turns the matrix into the uncompressed mode.|eigen*Reads the value of the matrix at position i, j. This function returns  Scalar(0)$ if the element is an explicit zero.}eigen+Writes the value of the matrix at position i, jY. This function turns the matrix into a non compressed form if that was not the case. This is a  O(log(nnz_j))d operation (binary search) plus the cost of element insertion if the element does not already exist.Cost of element insertion is sorted insertion in O(1) if the elements of each inner vector are inserted in increasing inner index order, and in O(nnz_j) for a random insertion.~eigen&Sets the matrix to the identity matrixeigen/Removes all non zeros but keep allocated memoryeigen#The number of non zero coefficientseigenHPreallocates space for non zeros. The matrix must be in compressed mode.eigenFResizes the matrix to a rows x cols matrix and initializes it to zero.eigenHResizes the matrix to a rows x cols matrix leaving old values untouched.nopqrstuvwxyz{|}~rsqpontuvwxyz{|}~None&'<VV@eigen;Alias for double prevision sparse matrix of complex numberseigen;Alias for single previsiom sparse matrix of complex numberseigen(Alias for double precision sparse matrixeigen(Alias for single precision sparse matrixeigen*A versatible sparse matrix representation.SparseMatrix is the main sparse matrix representation of Eigen's sparse module. It offers high performance and low memory usage. It implements a more versatile variant of the widely-used Compressed Column (or Row) Storage scheme.#It consists of four compact arrays:1: stores the coefficient values of the non-zeros.9: stores the row (resp. column) indices of the non-zeros.`: stores for each column (resp. row) the index of the first non-zero in the previous two arrays.: stores the number of non-zeros of each column (resp. row). The word inner refers to an inner vector that is a column for a column-major matrix, or a row for a row-major matrix. The word outer refers to the other direction.KThis storage scheme is better explained on an example. The following matrix [0 3 0 0 0 22 0 0 0 17 7 5 0 1 0 0 0 0 0 0 0 0 14 0 8  and one of its possible sparse,  column major representation: values: 22 7 _ 3 5 14 _ _ 1 _ 17 8 innerIndices: 1 2 _ 0 2 4 _ _ 2 _ 1 4 outerStarts: 0 3 5 8 10 12 innerNNZs: 2 2 1 1 2  Currently the elements of a given inner vector are guaranteed to be always sorted by increasing inner indices. The "_" indicates available free space to quickly insert new elements. Assuming no reallocation is needed, the insertion of a random element is therefore in O(nnz_j) where nnz_j is the number of nonzeros of the respective inner vector. On the other hand, inserting elements with increasing inner indices in a given inner vector is much more efficient since this only requires to increase the respective  entry that is a O(1) operation.The case where no empty space is available is a special case, and is refered as the compressed mode. It corresponds to the widely used Compressed Column (or Row) Storage schemes (CCS or CRS). Any + can be turned to this form by calling the 1 function. In this case, one can remark that the  array is redundant with  because we the equality: .InnerNNZs[j] = OuterStarts[j+1]-OuterStarts[j]#. Therefore, in practice a call to  frees this buffer.The results of Eigen's operations always produces compressed sparse matrices. On the other hand, the insertion of a new element into a . converts this later to the uncompressed mode.&For more infomration please see Eigen  >http://eigen.tuxfamily.org/dox/classEigen_1_1SparseMatrix.htmldocumentation page.eigen.Encode the sparse matrix as a lazy byte stringeigen.Decode sparse matrix from the lazy byte stringeigen/Stores the coefficient values of the non-zeros.eigen7Stores the row (resp. column) indices of the non-zeros.eigen^Stores for each column (resp. row) the index of the first non-zero in the previous two arrays.eigenStores the number of non-zeros of each column (resp. row). The word inner refers to an inner vector that is a column for a column-major matrix, or a row for a row-major matrix. The word outer refers to the other directioneigen$Number of rows for the sparse matrixeigen'Number of columns for the sparse matrixeigen'Matrix coefficient at given row and coleigen'Matrix coefficient at given row and coleigenFor vectors, the l2 norm, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of this with itself.eigenFor vectors, the squared l2 norm, and for matrices the Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of this with itself.eigenThe l2 norm of the matrix using the Blue's algorithm. A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM TOMS, Vol 4, Issue 1, 1978.eigen]Extract rectangular block from sparse matrix defined by startRow startCol blockRows blockColseigen1Number of non-zeros elements in the sparse matrixeigen#The matrix in the compressed formateigen#The matrix in the uncompressed modeeigenIs this in compressed form?eigen1Minor dimension with respect to the storage ordereigen1Major dimension with respect to the storage ordereigenRSuppresses all nonzeros which are much smaller than reference under the tolerence epsiloneigen!Multiply matrix on a given scalareigenTranspose of the sparse matrixeigenAdjoint of the sparse matrixeigenUAdding two sparse matrices by adding the corresponding entries together. You can use (+) function as well.eigen_Subtracting two sparse matrices by subtracting the corresponding entries together. You can use (-) function as well.eigen#Matrix multiplication. You can use (*) function as well.eigenOConstruct sparse matrix of given size from the list of triplets (row, col, val)eigenZConstruct sparse matrix of given size from the storable vector of triplets (row, col, val)eigengConvert sparse matrix to the list of triplets (row, col, val). Compressed elements will not be includedeigenrConvert sparse matrix to the storable vector of triplets (row, col, val). Compressed elements will not be includedeigenConstruct sparse matrix of two-dimensional list of values. Matrix dimensions will be detected automatically. Zero values will be compressed.eigen;Convert sparse matrix to (rows X cols) dense list of valueseigenKConstruct sparse matrix from dense matrix. Zero elements will be compressedeigen)Construct dense matrix from sparse matrixeigen-Yield an immutable copy of the mutable matrixeigen,Yield a mutable copy of the immutable matrixeigen}Unsafe convert a mutable matrix to an immutable one without copying. The mutable matrix may not be used after this operation.eigenUnsafely convert an immutable matrix to a mutable one without copying. The immutable matrix may not be used after this operation.eigen#Map over values of a sparse matrix.eigen0Map over values of a sparse matrix with indices.eigenGet a row of a sparse matrix.eigen Get a column of a sparse matrix.eigen Get all rows of a sparse matrix.eigen#Get all columns of a sparse matrix.eigenGet all row sums.eigenGet all column sums.eigenGet sum of matrix.eigenGet the ones vector.eigenGet the identity matrix.eigen*Transform a column into a diagonal matrix.eigen'Transform a row into a diagonal matrix.eigen#Update the row indices of a matrix.eigen&Update the column indices of a matrix.eigen!Get a matrix from a list of rows.eigen!Get a matrix from a list of cols.eigen Get a subset of a square matrix.eigen7Basic sparse matrix math exposed through Num instance: (*), (+), (-), , , , eigenPretty prints the sparse matrix==None "#;=>?AK%eigenComputation was successful.eigen4The provided data did not satisfy the prerequisites.eigen%Iterative procedure did not converge.eigenThe inputs are invalid, or the algorithm has been improperly called. When assertions are enabled, such errors trigger an error.eigen4Sparse left-looking rank-revealing QR factorization.This class implements a left-looking rank-revealing QR decomposition of sparse matrices. When a column has a norm less than a given tolerance it is implicitly permuted to the end. The QR factorization thus obtained is given by  A*P = Q*R where R$ is upper triangular or trapezoidal.Pi is the column permutation which is the product of the fill-reducing and the rank-revealing permutations.QL is the orthogonal matrix represented as products of Householder reflectors.RG is the sparse triangular or trapezoidal matrix. The later occurs when A is rank-deficient.eigen8Sparse supernodal LU factorization for general matrices.This class implements the supernodal LU factorization for general matrices. It uses the main techniques from the sequential  *http://crd-legacy.lbl.gov/~xiaoye/SuperLU/SuperLU package4. It handles transparently real and complex arithmetics with single and double precision, depending on the scalar type of your input matrix. The code has been optimized to provide BLAS-3 operations during supernode-panel updates. It benefits directly from the built-in high-performant Eigen BLAS routines. Moreover, when the size of a supernode is very small, the BLAS calls are avoided to enable a better optimization from the compiler. For best performance, you should compile it with NDEBUG flag to avoid the numerous bounds checking on vectors.An important parameter of this class is the ordering method. It is used to reorder the columns (and eventually the rows) of the matrix to reduce the number of new elements that are created during numerical factorization. The cheapest method available is COLAMD. See  Bhttp://eigen.tuxfamily.org/dox/group__OrderingMethods__Module.htmlOrderingMethods module< for the list of built-in and external ordering methods.eigenEA bi conjugate gradient stabilized solver for sparse square problems.This class allows to solve for A.x = b\ sparse linear problems using a bi conjugate gradient stabilized algorithm. The vectors x and b can be either dense or sparse.OThe maximal number of iterations and tolerance value can be controlled via the  and ` methods. The defaults are the size of the problem for the maximal number of iterations and epsilon for the toleranceeigen=A conjugate gradient solver for sparse self-adjoint problems.This class allows to solve for A.x = bP sparse linear problems using a conjugate gradient algorithm. The sparse matrix A must be selfadjoint.OThe maximal number of iterations and tolerance value can be controlled via the  and ` methods. The defaults are the size of the problem for the maximal number of iterations and epsilon for the toleranceeigenSometimes, the solution need not be too accurate. In this case, the iterative methods are more suitable and the desired accuracy can be set before the solve step using .eigenFFor direct methods, the solution is computed at the machine precision.eigen-A preconditioner based on the digonal entriesIt allows to approximately solve for A.x = b problems assuming A is a diagonal matrix. In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for: 3 A.diagonal().asDiagonal() . x = b  This preconditioner is suitable for both selfadjoint and general problems. The diagonal entries are pre-inverted and stored into a dense vector.[A variant that has yet to be implemented would attempt to preserve the norm of each column.eigenKA naive preconditioner which approximates any matrix as the identity matrixeigenOrdering methods for sparse matrices. They are typically used to reduce the number of elements during the sparse matrix decomposition (LLT, LU, QR<). Precisely, in a preprocessing step, a permutation matrix P is computed using those ordering methods and applied to the columns of the matrix. Using for instance the sparse Cholesky decomposition, it is expected that the nonzeros elements in LLT(A*P)# will be much smaller than that in LLT(A).eigeniThe column approximate minimum degree ordering The matrix should be in column-major and compressed formateigenThe natural ordering (identity)eigenHInitializes the iterative solver for the sparsity pattern of the matrix A for further solving Ax=b problems.eigenIInitializes the iterative solver with the numerical values of the matrix A for further solving Ax=b problems.eigen1Initializes the iterative solver with the matrix A for further solving Ax=b problems.The & method is equivalent to calling both  and .eigenAn expression of the solution x of Ax=b$ using the current decomposition of A.eigen9 if the iterations converged or computation was succesful1 if the factorization reports a numerical problem$ if the iterations are not converged if the input matrix is invalideigen6The tolerance threshold used by the stopping criteria.eigen;Sets the tolerance threshold used by the stopping criteria.EThis value is used as an upper bound to the relative residual error:  |Ax-b|/|b|6. The default value is the machine precision given by epsiloneigenThe max number of iterations. It is either the value setted by setMaxIterations or, by default, twice the number of columns of the matrix.eigenXSets the max number of iterations. Default is twice the number of columns of the matrix.eigensThe tolerance error reached during the last solve. It is a close approximation of the true relative residual error  |Ax-b|/|b|.eigen8The number of iterations performed during the last solveeigen Returns the b sparse upper triangular matrix R of the QR factorization.eigenReturns the matrix Q. as products of sparse Householder reflectors.eigenaSets the threshold that is used to determine linearly dependent columns during the factorization.In practice, if during the factorization the norm of the column that has to be eliminated is below this threshold, then the entire column is treated as zero, and it is moved at the end.eigen]Returns the number of non linearly dependent columns as determined by the pivoting threshold.eigen:Indicate that the pattern of the input matrix is symmetriceigenReturns the matrix LeigenReturns the matrix UeigenThe determinant of the matrix.eigenlThe natural log of the absolute value of the determinant of the matrix of which this is the QR decompositionsThis method is useful to work around the risk of overflow/underflow that's inherent to the determinant computation.eigen[The absolute value of the determinant of the matrix of which *this is the QR decomposition.A determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow. One way to work around that is to use  instead.eigen1A number representing the sign of the determinant..      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~     {z !"#$%&'()*+,-|}~./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijk  lmnod`a_]^pq|}~&r'stuvw=>?@xyz{|}~$eigen-3.3.4.1-37WyQM43XFu7Rc83oyjAnmData.Eigen.InternalData.Eigen.Matrix.MutableData.Eigen.Matrix Data.Eigen.LAData.Eigen.ParallelData.Eigen.SparseMatrix.MutableData.Eigen.SparseMatrixData.Eigen.SparseLA SparseMatrix MagicCodeCodecode CSolverPtrCSolverCSparseMatrixPtr CSparseMatrixCTripletCComplexCastcastElemc_sparse_la_signDeterminantc_sparse_la_absDeterminantc_sparse_la_logAbsDeterminantc_sparse_la_determinantc_sparse_la_setSymmetricc_sparse_la_matrixUc_sparse_la_matrixLc_sparse_la_rankc_sparse_la_setPivotThresholdc_sparse_la_matrixRc_sparse_la_matrixQc_sparse_la_solvec_sparse_la_iterationsc_sparse_la_errorc_sparse_la_infoc_sparse_la_setMaxIterationsc_sparse_la_maxIterationsc_sparse_la_setTolerancec_sparse_la_tolerancec_sparse_la_computec_sparse_la_analyzePatternc_sparse_la_factorizec_sparse_la_freeSolverc_sparse_la_newSolverc_sparse_uncompressInplacec_sparse_compressInplacec_sparse_conservativeResizec_sparse_resizec_sparse_reservec_sparse_setIdentityc_sparse_setZeroc_sparse_innerNNZsc_sparse_innerIndicesc_sparse_outerStartsc_sparse_valuesc_sparse_toMatrixc_sparse_fromMatrixc_sparse_block c_sparse_mul c_sparse_sub c_sparse_addc_sparse_blueNormc_sparse_squaredNorm c_sparse_norm c_sparse_rows c_sparse_colsc_sparse_coeffRefc_sparse_coeffc_sparse_outerSizec_sparse_innerSizec_sparse_nonZerosc_sparse_scalec_sparse_prunedRefc_sparse_prunedc_sparse_adjointc_sparse_transposec_sparse_isCompressedc_sparse_uncompressc_sparse_makeCompressed c_sparse_freec_sparse_toListc_sparse_fromListc_sparse_clone c_sparse_newc_relativeErrorc_solvec_kernelc_imagec_rank c_determinant c_hypotNorm c_blueNorm c_squaredNormc_tracec_normc_meanc_prodc_sum c_normalize c_conjugate c_adjoint c_inverse c_transpose c_diagonalc_mulc_subc_add c_identityc_randomc_getNbThreadsc_setNbThreadsfree c_freeStringintSize encodeInt decodeInt performIOplusForeignPtrcall magicCoderandomidentityaddsubmuldiagonal transposeinverseadjoint conjugate normalizesumprodmeannormtrace squaredNormblueNorm hypotNorm determinantrankimagekernelsolve relativeError sparse_new sparse_clonesparse_fromList sparse_toList sparse_freesparse_makeCompressedsparse_uncompresssparse_isCompressedsparse_transposesparse_adjoint sparse_prunedsparse_prunedRef sparse_scalesparse_nonZerossparse_innerSizesparse_outerSize sparse_coeffsparse_coeffRef sparse_cols sparse_rows sparse_normsparse_squaredNormsparse_blueNorm sparse_add sparse_sub sparse_mul sparse_blocksparse_fromMatrixsparse_toMatrix sparse_valuessparse_outerStartssparse_innerIndicessparse_innerNNZssparse_setZerosparse_setIdentitysparse_reserve sparse_resizesparse_conservativeResizesparse_compressInplacesparse_uncompressInplacesparse_la_newSolversparse_la_freeSolversparse_la_factorizesparse_la_analyzePatternsparse_la_computesparse_la_tolerancesparse_la_setTolerancesparse_la_maxIterationssparse_la_setMaxIterationssparse_la_infosparse_la_errorsparse_la_iterationssparse_la_solvesparse_la_matrixQsparse_la_matrixRsparse_la_setPivotThresholdsparse_la_ranksparse_la_matrixLsparse_la_matrixUsparse_la_setSymmetricsparse_la_determinantsparse_la_logAbsDeterminantsparse_la_absDeterminantsparse_la_signDeterminant$fBinaryVector$fCastDoubleCDouble$fCastCDoubleDouble$fCastFloatCFloat$fCastCFloatFloat $fCastIntCInt $fCastCIntInt$fCastComplexCComplex$fCastCComplexComplex$fCastComplexCComplex0$fCastCComplexComplex0$fStorableCComplex$fCast(,,)CTriplet$fCastCTriplet(,,)$fStorableCTriplet$fCodeCComplex$fCodeCComplex0 $fCodeCDouble $fCodeCFloat$fElemComplexCComplex$fElemComplexCComplex0$fElemDoubleCDouble$fElemFloatCFloat$fBinaryMagicCode$fShowCComplex$fShowCTriplet $fEqMagicCodeSTMatrixIOMatrix MMatrixXcd MMatrixXcf MMatrixXd MMatrixXfMMatrixmm_rowsmm_colsmm_valsvalidnew replicatesetcopyreadwrite unsafeCopy unsafeRead unsafeWrite unsafeWithTriangularModeLowerUpper StrictlyLower StrictlyUpper UnitLower UnitUpper MatrixXcd MatrixXcfMatrixXdMatrixXfMatrixencodedecodeemptynullsquareconstantzeroonesrowscolsdims!coeff unsafeCoeffcolrowblockmaxCoeffminCoefftopRows bottomRowsleftCols rightColsfromListtoList fromFlatList toFlatListgenerateallanycountmapimaptriangularView lowerTriangle upperTrianglefilterifilterfoldfold'ifoldifold'fold1fold1'modifyconvertfreezethaw unsafeFreeze unsafeThaw$fBinaryMatrix $fNumMatrix $fShowMatrix$fEqTriangularMode$fEnumTriangularMode$fShowTriangularMode$fReadTriangularMode Decomposition PartialPivLU FullPivLU HouseholderQRColPivHouseholderQRFullPivHouseholderQRLLTLDLT JacobiSVDlinearRegression$fEqDecomposition$fEnumDecomposition$fShowDecomposition$fReadDecomposition setNbThreads getNbThreadsIOSparseMatrixXcdIOSparseMatrixXcfIOSparseMatrixXdIOSparseMatrixXfIOSparseMatrix innerSize outerSize compressedcompress uncompress setIdentitysetZerononZerosreserveresizeconservativeResizeSparseMatrixXcdSparseMatrixXcfSparseMatrixXdSparseMatrixXfvalues innerIndices outerStarts innerNNZsprunedscale fromVectortoVector fromDenseList toDenseList fromMatrixtoMatrix_map_imapgetRowgetColgetRowsgetCols getRowSums getColSumsgetSumidentdiagColdiagRowfromRowsfromCols squareSubset$fBinarySparseMatrix$fNumSparseMatrix$fShowSparseMatrixSolverTComputationInfoSuccessNumericalIssue NoConvergence InvalidInputSparseQRSparseLUBiCGSTABConjugateGradientIterativeSolver DirectSolverSolverPreconditionerDiagonalPreconditionerIdentityPreconditionerOrderingMethodCOLAMDOrderingNaturalOrdering runSolverTanalyzePattern factorizecomputeinfo tolerance setTolerance maxIterationssetMaxIterationserror iterationsmatrixRmatrixQsetPivotThreshold setSymmetricmatrixLmatrixUlogAbsDeterminantabsDeterminantsignDeterminant$fCodeConjugateGradient"$fIterativeSolverConjugateGradient$fSolverConjugateGradient$fCodeBiCGSTAB$fIterativeSolverBiCGSTAB$fSolverBiCGSTAB$fCodeSparseLU$fDirectSolverSparseLU$fSolverSparseLU$fCodeSparseQR$fDirectSolverSparseQR$fSolverSparseQR$fShowOrderingMethod$fReadOrderingMethod$fShowPreconditioner$fReadPreconditioner$fShowConjugateGradient$fReadConjugateGradient$fShowBiCGSTAB$fReadBiCGSTAB$fShowSparseLU$fReadSparseLU$fShowSparseQR$fReadSparseQR$fEqComputationInfo$fEnumComputationInfo$fShowComputationInfo$fReadComputationInfobaseGHC.Num fromIntegersignumabsnegate updateRowIdx updateColIdx