In this module the Short Iterative Lanczos routines are collected. More...

Public Member Functions
subroutine	silstep (Psi, DtPsi, PsiDim, IntPeriod, IntOrder, TolError, Relax, Restart, StdForm, Stepsize, ErrorCode, Time, Func, STATE, Also_BackProp, MinOrder)
	SHORT ITERATIVE LANCZOS (sillib.f) * Library module containing a short iterative Lanczos integrator. * Contains: * SILStep: The (real) Lanczos integration routine. * SILErrorMsg: Returns for a given error number a corresponding * error message. * SILDiag: The (real) Lanczos diagonalisation routine. * More...

subroutine	silerrormsg (Error, Msg)
	SUBROUTINE SILERRORMSG * Generates for a given error number returned by "SILStep/SILStep2/ * SILStep3" a corresponding error message. * Input parameters: * Error: Error code returned by SILStep/SILStep2. * Output parameters: * Msg: Error message. * V7.0 MB * More...

subroutine	sildiag (Psi, DtPsi, PsiDim, IntOrder, TolError, StdForm, Steps, ErrorCode, rlaxnum, Time, ortho, Func, minorder)
	SUBROUTINE SILDIAG * Diagonalises a (complex) Hermitian matrix by Lanczos-iterations. * This routine is used for improved relaxation and for meigenf. * Input parameters: * Psi: The (complex) initial-value vector. * DtPsi: Action of Hamiltonian on the initial-value vector, * i.e. H\|Psi> or -i H\|Psi>, depending on "StdForm". * PsiDim Length of Psi and DtPsi vectors. * IntPeriod: Lenght of time interval to be integrated. * IntOrder: Maximum integration order. * TolError: Maximum error that is tolerated. * StdForm: If true, Func(Time,Psi,DtPsi) = -i H\|Psi>, else * Func(Time,Psi,DtPsi) = H\|Psi>. * Steps: Number of steps made so far (Steps is passed to * "WriteStep"). * Krylov: Matrix with minimum size PsiDim(IntOrder-1) with columns containing the Krylov vectors H^2\|psi> to * H^TrueOrder\|psi>. * TrueOrder: On input: the minimal order to be used. * ortho: if .true., then a full re-orthogonalisation of the * Krylov vectors is performed. * Output parameters: * Psi: Computed eigenvector. The number of the eigenvector * to be chosen is specified by rlaxnum. * DtPsi: Normalised first Krylov vector, i. e. (H-<H>)\|Psi>. * Krylov: Matrix with minimum size PsiDim(IntOrder-1) with columns containing the Krylov vectors H^2\|psi> to * H^TrueOrder\|psi>. * TrueOrder: The order that has actually been used (may be less * than IntOrder). * Steps: Same as on entry. * ErrorCode: Error code having the following meaning: * 0: everything was o. k., * 1: illegal integration order, * 3: diagonalization failed, * External routines: * Func: Computes the action of the Hamiltonian on Psi. * Called as * Func(AbsTime,Psi,DtPsi,CData,RData,IData,LData). * Some new Variables: * rlaxnum : This is the argument of the keyword relaxation. * If relaxation has no argument, rlaxnum=-1 . * V8.3 10/03 HDM * More...

Detailed Description

In this module the Short Iterative Lanczos routines are collected.

Todo:: make the Krylov basis arrays allocatables

Member Function/Subroutine Documentation

subroutine sil_integrators::sildiag	(	complex*16, dimension(psidim)	Psi,
		complex*16, dimension(psidim)	DtPsi,
		integer	PsiDim,
		integer	IntOrder,
		real*8	TolError,
		logical	StdForm,
		integer	Steps,
		integer	ErrorCode,
		integer	rlaxnum,
		real*8	Time,
		logical	ortho,
		external	Func,
		integer	minorder
	)

SUBROUTINE SILDIAG *
Diagonalises a (complex) Hermitian matrix by Lanczos-iterations. * This routine is used for improved relaxation and for meigenf. *
Input parameters: * Psi: The (complex) initial-value vector. * DtPsi: Action of Hamiltonian on the initial-value vector, * i.e. H|Psi> or -i H|Psi>, depending on "StdForm". * PsiDim Length of Psi and DtPsi vectors. * IntPeriod: Lenght of time interval to be integrated. * IntOrder: Maximum integration order. * TolError: Maximum error that is tolerated. * StdForm: If true, Func(Time,Psi,DtPsi) = -i H|Psi>, else * Func(Time,Psi,DtPsi) = H|Psi>. * Steps: Number of steps made so far (Steps is passed to * "WriteStep"). * Krylov: Matrix with minimum size PsiDim*(IntOrder-1) with * columns containing the Krylov vectors H^2|psi> to * H^TrueOrder|psi>. * TrueOrder: On input: the minimal order to be used. * ortho: if .true., then a full re-orthogonalisation of the * Krylov vectors is performed. *
Output parameters: * Psi: Computed eigenvector. The number of the eigenvector * to be chosen is specified by rlaxnum. * DtPsi: Normalised first Krylov vector, i. e. (H-<H>)|Psi>. * Krylov: Matrix with minimum size PsiDim*(IntOrder-1) with * columns containing the Krylov vectors H^2|psi> to * H^TrueOrder|psi>. * TrueOrder: The order that has actually been used (may be less * than IntOrder). * Steps: Same as on entry. * ErrorCode: Error code having the following meaning: * 0: everything was o. k., * 1: illegal integration order, * 3: diagonalization failed, *
External routines: * Func: Computes the action of the Hamiltonian on Psi. * Called as * Func(AbsTime,Psi,DtPsi,CData,RData,IData,LData). *
Some new Variables: * rlaxnum : This is the argument of the keyword relaxation. * If relaxation has no argument, rlaxnum=-1 . *
V8.3 10/03 HDM *

References function_library::beta(), function_library::cpvxd(), and orbital_equationofmotion::func().

Referenced by integration::integrator_ci().

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subroutine sil_integrators::silerrormsg	(	integer	Error,
		character()	Msg
	)

SUBROUTINE SILERRORMSG *

Generates for a given error number returned by "SILStep/SILStep2/ * SILStep3" a corresponding error message. *

Input parameters: * Error: Error code returned by SILStep/SILStep2. *
Output parameters: * Msg: Error message. *
V7.0 MB *

subroutine sil_integrators::silstep	(	complex*16, dimension(psidim)	Psi,
		complex*16, dimension(psidim)	DtPsi,
		integer	PsiDim,
		real*8	IntPeriod,
		integer	IntOrder,
		real*8	TolError,
		logical	Relax,
		logical	Restart,
		logical	StdForm,
		real*8	Stepsize,
		integer	ErrorCode,
		real*8	Time,
		external	Func,
		integer	STATE,
		logical	Also_BackProp,
		integer	MinOrder
	)

SHORT ITERATIVE LANCZOS (sillib.f) *

Library module containing a short iterative Lanczos integrator. *

Contains: * SILStep: The (real) Lanczos integration routine. * SILErrorMsg: Returns for a given error number a corresponding * error message. * SILDiag: The (real) Lanczos diagonalisation routine. *

SUBROUTINE SILSTEP *
Integrates a system of complex linear first order differential * equations with constant and Hermitian Hamiltonian employing the * short iterative Lanczos method. The routine runs with both * variable step size and order. (First it increases the order to * achieve the desired accuracy. If this failes within the maximum * order, the stepsize is reduced.) SILStep makes only one single * integration step, so it has to be imbedded into a loop that calls * SILStep until the desired time interval is integrated. The ODE is * of the form i dPsi/dt = H|Psi> = Func(Time,Psi,DtPsi) =: DtPsi or * dPsi/dt = -i H|Psi> = Func(Time,Psi,DtPsi) =: DtPsi, depending on * the flag "StdForm". All computations are performed with double * precision. *
Input parameters: * Psi: The (complex) initial-value vector. * DtPsi: Action of Hamiltonian on the initial-value vector, * i.e. H|Psi> or -i H|Psi>, depending on "StdForm". * PsiDim Length of Psi and DtPsi vectors. * IntPeriod: Lenght of time interval to be integrated. * IntOrder: Maximum integration order. * TolError: Maximum error that is tolerated. * Relax: Flag for relaxation calculation. If true, Psi is * relaxated, else propagated. * Restart: Flag for restarting the integrator. If true, the * Krylov space is built up before propagation, else the * old Krylov vectors are used. * StdForm: If true, Func(Time,Psi,DtPsi) = -i H|Psi>, else * Func(Time,Psi,DtPsi) = H|Psi>. * Steps: Number of steps made so far (Steps is passed to * "WriteStep"). * Krylov: Matrix with minimum size PsiDim*(IntOrder-1) with * columns containing the Krylov vectors H^2|psi> to * H^TrueOrder|psi>. The Krylov vectors are needed on * entry only when Restart is false. * Also_BackProp: Logical that decides if the constructed Krylov * vectors are used also to propagate Psi back in * time. If Also_BackProp it .true. then Psi is the * propagated and DtPsi the backpropagated function * on output. * Output parameters: * Psi: Propagated Psi. * DtPsi: If Also_BackProp is .true. then DtPsi contains the * backpropagated Psi and otherwise the * Normalised first Krylov vector, i. e. (H-<H>)|Psi>. * Krylov: Matrix with minimum size PsiDim*(IntOrder-1) with * columns containing the Krylov vectors H^2|psi> to * H^TrueOrder|psi>. * Stepsize: Time interval that actually has been integrated (can * be lower than IntPeriod). * TrueOrder: The order that has actually been used (may be less * than IntOrder). * Steps: Same as on entry. *
External routines: * Func: Computes the action of the Hamiltonian on Psi. * Called as * Func(AbsTime,Psi,DtPsi,CData,RData,IData,LData). * Some new Variables: * Relax : logical set true for a relaxation run. *
V6.0 MB * V8.2 05/01 HDM Addition of 'relaxation' to exited states. * Eigenvector-space now dynamically allocated. *