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The following\nsections provide more in depth commentary.\n\nmat provides:\n\nIn the documentation below, we use \"matrix\" as a short-hand for all of\nthe FooDense types implemented in this package. We use \"Matrix\" to\nrefer to the Matrix interface.\n\nA matrix may be constructed through the corresponding New function. If no\nbacking array is provided the matrix will be initialized to all zeros.\n\nIf a backing data slice is provided, the matrix will have those elements.\nAll matrices are stored in row-major format and users should consider\nthis when expressing matrix arithmetic to ensure optimal performance.\n\nOperations involving matrix data are implemented as functions when the values\nof the matrix remain unchanged\n\nand are implemented as methods when the operation modifies the receiver.\n\nNote that the input arguments to most functions and methods are interfaces\nrather than concrete types `func Trace(Matrix)` rather than\n`func Trace(*Dense)` allowing flexible use of internal and external\nMatrix types.\n\nWhen a matrix is the destination or receiver for a function or method,\nthe operation will panic if the matrix is not the correct size.\nAn exception to this is when the destination is empty (see below).\n\nAn empty matrix is one that has zero size. Empty matrices are used to allow\nthe destination of a matrix operation to assume the correct size automatically.\nThis operation will re-use the backing data, if available, or will allocate\nnew data if necessary. The IsEmpty method returns whether the given matrix\nis empty. The zero-value of a matrix is empty, and is useful for easily\ngetting the result of matrix operations.\n\nThe Reset method can be used to revert a matrix to an empty matrix.\nReset should not be used when multiple different matrices share the same backing\ndata slice. This can cause unexpected data modifications after being resized.\nAn empty matrix can not be sliced even if it does have an adequately sized\nbacking data slice, but can be expanded using its Grow method if it exists.\n\nThe Matrix interface is the common link between the concrete types of real\nmatrices. The Matrix interface is defined by three functions: Dims, which\nreturns the dimensions of the Matrix, At, which returns the element in the\nspecified location, and T for returning a Transpose (discussed later). All of\nthe matrix types can perform these behaviors and so implement the interface.\nMethods and functions are designed to use this interface, so in particular the method\n\nconstructs a *Dense from the result of a multiplication with any Matrix types,\nnot just *Dense. Where more restrictive requirements must be met, there are also\nadditional interfaces like Symmetric and Triangular. For example, in\n\nthe Symmetric interface guarantees a symmetric result.\n\nThe CMatrix interface plays the same role for complex matrices. The difference\nis that the CMatrix type has the H method instead T, for returning the conjugate\ntranspose.\n\n(Conjugate) Transposes\n\nThe T method is used for transposition on real matrices, and H is used for\nconjugate transposition on complex matrices. For example, c.Mul(a.T(), b) computes\nc = aᵀ * b. The mat types implement this method implicitly —\nsee the Transpose and Conjugate types for more details. Note that some\noperations have a transpose as part of their definition, as in *SymDense.SymOuterK.\n\nMatrix factorizations, such as the LU decomposition, typically have their own\nspecific data storage, and so are each implemented as a specific type. The\nfactorization can be computed through a call to Factorize\n\nThe elements of the factorization can be extracted through methods on the\nfactorized type, for example *LU.UTo. The factorization types can also be used\ndirectly, as in *Cholesky.SolveTo. Some factorizations can be updated directly,\nwithout needing to update the original matrix and refactorize, for example with\n*LU.RankOne.\n\nBLAS and LAPACK are the standard APIs for linear algebra routines. Many\noperations in mat are implemented using calls to the wrapper functions\nin gonum/blas/blas64 and gonum/lapack/lapack64 and their complex equivalents.\nBy default, blas64 and lapack64 call the native Go implementations of the\nroutines. Alternatively, it is possible to use C-based implementations of the\nAPIs through the respective cgo packages and the wrapper packages' \"Use\"\nfunctions. The Go implementation of LAPACK makes calls through blas64, so if\na cgo BLAS implementation is registered, the lapack64 calls will be partially\nexecuted in Go and partially executed in C.\n\nThe Matrix abstraction enables efficiency as well as interoperability. Go's\ntype reflection capabilities are used to choose the most efficient routine\ngiven the specific concrete types. For example, in\n\nif a and b both implement RawMatrixer, that is, they can be represented as a\nblas64.General, blas64.Gemm (general matrix multiplication) is called, while\ninstead if b is a RawSymmetricer blas64.Symm is used (general-symmetric\nmultiplication), and if b is a *VecDense blas64.Gemv is used.\n\nThere are many possible type combinations and special cases. No specific guarantees\nare made about the performance of any method, and in particular, note that an\nabstract matrix type may be copied into a concrete type of the corresponding\nvalue. If there are specific special cases that are needed, please submit a\npull-request or file an issue.\n\nMatrix input arguments to package functions are never directly modified. If an\noperation changes Matrix data, the mutated matrix will be the receiver of a\nmethod, or will be the first, dst, argument to a method named with a To suffix.\n\nFor convenience, a matrix may be used as both a receiver and as an input, e.g.\n\nthough in many cases this will cause an allocation (see Element Aliasing).\nAn exception to this rule is Copy, which does not allow a.Copy(a.T()).\n\nMost methods in mat modify receiver data. It is forbidden for the modified\ndata region of the receiver to overlap the used data area of the input\narguments. The exception to this rule is when the method receiver is equal to one\nof the input arguments, as in the a.Pow(a, 6) call above, or its implicit transpose.\n\nThis prohibition is to help avoid subtle mistakes when the method needs to read\nfrom and write to the same data region. 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