
Numeric.LinearAlgebra.LAPACK  Portability  portable (uses FFI)  Stability  provisional  Maintainer  Alberto Ruiz (aruiz at um dot es) 



Description 
Wrappers for a few LAPACK functions (http://www.netlib.org/lapack).


Synopsis 

svdR :: Matrix Double > (Matrix Double, Vector Double, Matrix Double)   svdRdd :: Matrix Double > (Matrix Double, Vector Double, Matrix Double)   svdC :: Matrix (Complex Double) > (Matrix (Complex Double), Vector Double, Matrix (Complex Double))   eigC :: Matrix (Complex Double) > (Vector (Complex Double), Matrix (Complex Double))   eigR :: Matrix Double > (Vector (Complex Double), Matrix (Complex Double))   eigS :: Matrix Double > (Vector Double, Matrix Double)   eigH :: Matrix (Complex Double) > (Vector Double, Matrix (Complex Double))   eigS'   eigH'   linearSolveR :: Matrix Double > Matrix Double > Matrix Double   linearSolveC :: Matrix (Complex Double) > Matrix (Complex Double) > Matrix (Complex Double)   linearSolveLSR :: Matrix Double > Matrix Double > Matrix Double   linearSolveLSC :: Matrix (Complex Double) > Matrix (Complex Double) > Matrix (Complex Double)   linearSolveSVDR :: Maybe Double > Matrix Double > Matrix Double > Matrix Double   linearSolveSVDC :: Maybe Double > Matrix (Complex Double) > Matrix (Complex Double) > Matrix (Complex Double)   luR :: Matrix Double > (Matrix Double, [Int])   luC :: Matrix (Complex Double) > (Matrix (Complex Double), [Int])   cholS :: Matrix Double > Matrix Double   cholH :: Matrix (Complex Double) > Matrix (Complex Double)   qrR :: Matrix Double > (Matrix Double, Vector Double)   qrC :: Matrix (Complex Double) > (Matrix (Complex Double), Vector (Complex Double))   hessR :: Matrix Double > (Matrix Double, Vector Double)   hessC :: Matrix (Complex Double) > (Matrix (Complex Double), Vector (Complex Double))   schurR :: Matrix Double > (Matrix Double, Matrix Double)   schurC :: Matrix (Complex Double) > (Matrix (Complex Double), Matrix (Complex Double)) 


Documentation 


Wrapper for LAPACK's dgesvd, which computes the full svd decomposition of a real matrix.
(u,s,v)=full svdR m so that m=u <> s <> trans v.



Wrapper for LAPACK's dgesvd, which computes the full svd decomposition of a real matrix.
(u,s,v)=full svdRdd m so that m=u <> s <> trans v.



Wrapper for LAPACK's zgesvd, which computes the full svd decomposition of a complex matrix.
(u,s,v)=full svdC m so that m=u <> comp s <> trans v.



Wrapper for LAPACK's zgeev, which computes the eigenvalues and right eigenvectors of a general complex matrix:
if (l,v)=eigC m then m <> v = v <> diag l.
The eigenvectors are the columns of v.
The eigenvalues are not sorted.



Wrapper for LAPACK's dgeev, which computes the eigenvalues and right eigenvectors of a general real matrix:
if (l,v)=eigR m then m <> v = v <> diag l.
The eigenvectors are the columns of v.
The eigenvalues are not sorted.



Wrapper for LAPACK's dsyev, which computes the eigenvalues and right eigenvectors of a symmetric real matrix:
if (l,v)=eigSl m then m <> v = v <> diag l.
The eigenvectors are the columns of v.
The eigenvalues are sorted in descending order (use eigS' for ascending order).



Wrapper for LAPACK's zheev, which computes the eigenvalues and right eigenvectors of a hermitian complex matrix:
if (l,v)=eigH m then m <> s v = v <> diag l.
The eigenvectors are the columns of v.
The eigenvalues are sorted in descending order (use eigH' for ascending order).


eigS' 

eigH' 


Wrapper for LAPACK's dgesv, which solves a general real linear system (for several righthand sides) internally using the lu decomposition.



Wrapper for LAPACK's zgesv, which solves a general complex linear system (for several righthand sides) internally using the lu decomposition.



Wrapper for LAPACK's dgels, which obtains the least squared error solution of an overconstrained real linear system or the minimum norm solution of an underdetermined system, for several righthand sides. For rank deficient systems use linearSolveSVDR.



Wrapper for LAPACK's zgels, which obtains the least squared error solution of an overconstrained complex linear system or the minimum norm solution of an underdetermined system, for several righthand sides. For rank deficient systems use linearSolveSVDC.



:: Maybe Double  rcond
 > Matrix Double  coefficient matrix
 > Matrix Double  right hand sides (as columns)
 > Matrix Double  solution vectors (as columns)
 Wrapper for LAPACK's dgelss, which obtains the minimum norm solution to a real linear least squares problem Ax=B using the svd, for several righthand sides. Admits rank deficient systems but it is slower than linearSolveLSR. The effective rank of A is determined by treating as zero those singular valures which are less than rcond times the largest singular value. If rcond == Nothing machine precision is used.




:: Maybe Double  rcond
 > Matrix (Complex Double)  coefficient matrix
 > Matrix (Complex Double)  right hand sides (as columns)
 > Matrix (Complex Double)  solution vectors (as columns)
 Wrapper for LAPACK's zgelss, which obtains the minimum norm solution to a complex linear least squares problem Ax=B using the svd, for several righthand sides. Admits rank deficient systems but it is slower than linearSolveLSC. The effective rank of A is determined by treating as zero those singular valures which are less than rcond times the largest singular value. If rcond == Nothing machine precision is used.




Wrapper for LAPACK's dgetrf, which computes a LU factorization of a general real matrix.



Wrapper for LAPACK's zgees, which computes a Schur factorization of a square complex matrix.



Wrapper for LAPACK's dpotrf, which computes the Cholesky factorization of a
real symmetric positive definite matrix.



Wrapper for LAPACK's zpotrf, which computes the Cholesky factorization of a
complex Hermitian positive definite matrix.



Wrapper for LAPACK's dgeqr2, which computes a QR factorization of a real matrix.



Wrapper for LAPACK's zgeqr2, which computes a QR factorization of a complex matrix.



Wrapper for LAPACK's dgehrd, which computes a Hessenberg factorization of a square real matrix.



Wrapper for LAPACK's zgehrd, which computes a Hessenberg factorization of a square complex matrix.



Wrapper for LAPACK's dgees, which computes a Schur factorization of a square real matrix.



Wrapper for LAPACK's zgees, which computes a Schur factorization of a square complex matrix.


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