eigen_mod Module Reference

DERIVED TYPE eigen for eigenvalue / eigenvector problems More...

Data Types
interface	clear
	destructor More...
interface	eigen
	Derived type for eigenvalue problem resolution. More...
interface	print
	print a short description More...
interface	set
	set the solver More...
interface	solve
	Solver for: More...

Functions/Subroutines
subroutine	eigen_clear (eig)
	Destructor. More...
type(eigen) function	eigen_create (size, nev, sym, std)
	constructor for the type eigen More...
subroutine	eigen_set (eig, type, mode, which, tol, itMax, shift, verb)
	Eigen-solver settings More...
subroutine	eigen_print (eig)
	Print a short description. More...
subroutine	eigen_solve (eig, A, B, Op)
	Eigen-problem resolution More...
subroutine	arpack_solve (eig, A, B, Op)
subroutine	arpack_ds (eig, A, B, Op)
	ARPACK, symmetric case. More...

Detailed Description

DERIVED TYPE eigen for eigenvalue / eigenvector problems

Choral constants for eigenvalue problems: EIG_xxx, see the list.

A variable 'eig' of type eigen contains the settings for an eigen-solver.
It is created in two steps

1. eig = eigen(args)

   defines the eigen-problem parameters (standard, symmetric, size), see eigen doc.

2. call set(eig, optional args)

   define the eigen-solver parameters (mode, tolerance, ...), see set doc.

Problems

• standard eigenvalue problems: \(~~ A\,x = \lambda \,x \)
• geeralised eigenvalue problems: \(~~ A\,x = \lambda \, B \,x \)

Modes.

• Standard problems.
  • Regular mode EIG_REGULAR: solve \( A\,x = \lambda \,x \)
  • Shift invert mode EIG_SHIFT INVERT: solve \( \frac{1}{\lambda -s}x = (A-sId)^{-1}x \),
    • \( s \) is the shift parameter
    • by default \( s=0 \) and the problem is \( \lambda^{-1} x = A^{-1}x \)
• Geeralised problems.
  • inverse mode EIG_INVERSE: solve \( B^{-1} A x = \lambda x \)
  • Shift invert mode EIG_SHIFT INVERT: solve \( \frac{1}{\lambda -s}x = (A-sB)^{-1}Bx \),
    • \( s \) is the shift parameter
    • by default \( s=0 \) and the problem is \( \lambda^{-1} x = A^{-1}Bx \)

Solvers

• EIG_ARPACK: Arnoldi methods, library ARPACK
  https://www.caam.rice.edu/software/ARPACK/

Eigen-problem resolution: after creation of the eigen-solver 'eig' of type eigen:

call solve(eig, args) 

• The computed eigen-values are in the 1D-array

  eig%lambda 

• The associated eigen-vectors are in the 2D-array

  eig%v 

see solve description for the argument list.

Author

Charles PIERRE, January 2020

Function/Subroutine Documentation

arpack_ds()

subroutine eigen_mod::arpack_ds ( type(eigen), intent(inout)  eig, procedure(rntorn), optional  A, procedure(rntorn), optional  B, procedure(rntornxl), optional  Op  )

private

ARPACK, symmetric case.

Definition at line 638 of file eigen_mod.F90.

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arpack_solve()

subroutine eigen_mod::arpack_solve ( type(eigen), intent(inout)  eig, procedure(rntorn), optional  A, procedure(rntorn), optional  B, procedure(rntornxl), optional  Op  )

private

Definition at line 614 of file eigen_mod.F90.

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eigen_clear()

subroutine eigen_mod::eigen_clear ( type(eigen), intent(inout)  eig )

private

Destructor.

Definition at line 249 of file eigen_mod.F90.

eigen_create()

type(eigen) function eigen_mod::eigen_create ( integer, intent(in)  size, integer, intent(in)  nev, logical, intent(in)  sym, logical, intent(in)  std  )

private

constructor for the type eigen

Parameters

[out]	eig	eigen-solver settings
[in]	size	problem size ( \( x\in\R^{\rm size}\))
[in]	nev	number of eigen-modes to be computed
[in]	sym	symmetric problem ? [TRUE/FALSE]
[in]	std	standard problem ? [TRUE/FALSE]

Definition at line 268 of file eigen_mod.F90.

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eigen_print()

subroutine eigen_mod::eigen_print ( type(eigen), intent(in)  eig )

private

Print a short description.

Definition at line 389 of file eigen_mod.F90.

eigen_set()

subroutine eigen_mod::eigen_set ( type(eigen), intent(inout)  eig, integer, intent(in), optional  type, integer, intent(in), optional  mode, integer, intent(in), optional  which, real(rp), intent(in), optional  tol, integer, intent(in), optional  itMax, real(rp), intent(in), optional  shift, integer, intent(in), optional  verb  )

private

Eigen-solver settings

Pre-defined eigen-solver settings are modified by a list of optional arguments.

Parameters

[in,out]	eig	eigen-solver settings
[in]	type	solver type (default EIG_ARPACK)
[in]	which	targetted eigenvalues (default EIG_WHICH_SM')
[in]	mode	method (default EIG_REGULAR)
[in]	tol	tolerance (default 1E-8_RP)
[in]	itMax	Max iteration number (default 100)
[in]	verb	verbosity (default 0)
[in]	shift	shift value (default 0.0_RP)

Definition at line 325 of file eigen_mod.F90.

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eigen_solve()

subroutine eigen_mod::eigen_solve ( type(eigen), intent(inout)  eig, procedure(rntorn), optional  A, procedure(rntorn), optional  B, procedure(rntornxl), optional  Op  )

private

Eigen-problem resolution

Parameters

[in,out]

eig

eigen-solver settings

See solve for the output description.

Optional arguments:

Parameters

[in]	A	eigen-problem matrix, procedural arguments with interface RnToRn
[in]	B	eigen-problem matrix (generalised problems), procedural arguments with interface RnToRn
[in]	Op	linear problem solver, procedural arguments with interface RnToRnxL.

See solve for the argument list description.

Definition at line 458 of file eigen_mod.F90.

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