SymLargestEigenval

This function computes the largest eigenvalue of a symmetric matrix.

This function calls ARPACK's SSAUPD or DSAUPD routine.

Currently, there are two interfaces under this generic method.

ans = SymLargestEigenVal(real::mat(:,:), char::which, int::NCV, int::maxIter, real::tol)
ans(1:nev) = SymLargestEigenVal(real::mat(:,:), int::nev, char::which, int::NCV, int::maxIter, real::tol)

܀ Interface 1

INTERFACE
  MODULE FUNCTION SymLargestEigenVal(mat, which, NCV, maxIter, tol) &
    & RESULT(ans)
    REAL(DFP), INTENT(IN) :: mat(:, :)
    !! dense matrix
    CHARACTER(LEN=*), OPTIONAL, INTENT(IN) :: which
    !! `which = "LM"` ⇨ absolute largest eigenvalue
    !! `which = "LA"` ⇨ algebraic largest eigenvalue
    !! default is "LA"
    INTEGER(I4B), OPTIONAL, INTENT(IN) :: NCV
    !! Number of Lanczos vectors generated
    !! It must be greater than 1 and smaller than `size(mat,1)`
    !! Default is `NCV = MIN(n, 20)`
    INTEGER(I4B), OPTIONAL, INTENT(IN) :: maxIter
    !! Maximum number of iteration default = `N*10`
    REAL(DFP), OPTIONAL, INTENT(IN) :: tol
    !! tolerance, default = 0.0
    REAL(DFP) :: ans
    !! maximum eigenvalue
  END FUNCTION SymLargestEigenVal
END INTERFACE

• mat is dense matrix
• which = "LM" ⇨ absolute largest eigenvalue
• which = "LA" ⇨ algebraic largest eigenvalue
• Default value of which is "LA"
• NCV Number of Lanczos vectors generated. It must be greater than 1 and smaller than size(mat,1). Default is NCV = MIN(n, 20)
• maxIter Maximum number of iteration default = N*10
• tol tolerance, default = 0.0
• ans maximum eigenvalue.

܀ Interface 2

INTERFACE
  MODULE FUNCTION SymLargestEigenVal(mat, nev, which, NCV, maxIter, tol) &
    & RESULT(ans)
    REAL(DFP), INTENT(IN) :: mat(:, :)
    !! dense matrix
    INTEGER(I4B), INTENT(IN) :: nev
    !! number of eigenvalues requested
    CHARACTER(LEN=*), OPTIONAL, INTENT(IN) :: which
    !! `which = "LM"` ⇨ absolute largest eigenvalue
    !! `which = "LA"` ⇨ algebraic largest eigenvalue
    !! default is "LA"
    INTEGER(I4B), OPTIONAL, INTENT(IN) :: NCV
    !! Number of Lanczos vectors generated
    !! It must be greater than 1 and smaller than `size(mat,1)`
    !! Default is `NCV = MIN(n, MAX(2*nev+1, 20))`
    INTEGER(I4B), OPTIONAL, INTENT(IN) :: maxIter
    !! Maximum number of iteration default = `N*10`
    REAL(DFP), OPTIONAL, INTENT(IN) :: tol
    !! tolerance, default = 0.0
    REAL(DFP) :: ans(nev)
    !! first k, largest eigenvalue
  END FUNCTION SymLargestEigenVal
END INTERFACE

• mat dense matrix
• nev number of eigenvalues requested
• which = "LM" ⇨ absolute largest eigenvalue
• which = "LA" ⇨ algebraic largest eigenvalue
• Default value of which is "LA"
• NCV Number of Lanczos vectors generated. It must be greater than 1 and smaller than size(mat,1). Default is NCV = MIN(n, MAX(2*nev+1, 20))
• maxIter Maximum number of iteration default = N*10
• tol tolerance, default = 0.0
• ans(nev) first k, the largest eigenvalue.

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