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Ford-modules part 3
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!----------------------------------------------------------------------------
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MODULE bfgs_module
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!----------------------------------------------------------------------------
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!! Ionic relaxation through the Newton-Raphson optimization scheme
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!! based on the Broyden-Fletcher-Goldfarb-Shanno algorithm for the
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!! estimate of the inverse Hessian matrix.
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!! The ionic relaxation is performed converting cartesian (and cell)
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!! positions into internal coordinates.
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!! The algorithm uses a "trust radius" line search based on Wolfe
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!! conditions. Steps are rejected until the first Wolfe condition
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!! (sufficient energy decrease) is satisfied. Updated step length
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!! is estimated from quadratic interpolation.
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!! When the step is accepted inverse hessian is updated according to
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!! BFGS scheme and a new search direction is obtained from NR or GDIIS
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!! method. The corresponding step length is limited by trust_radius_max
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!! and can't be larger than the previous step multiplied by a certain
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!! factor determined by Wolfe and other convergence conditions.
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!
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! ... Ionic relaxation through the Newton-Raphson optimization scheme
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! ... based on the Broyden-Fletcher-Goldfarb-Shanno algorithm for the
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! ... estimate of the inverse Hessian matrix.
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! ... The ionic relaxation is performed converting cartesian (and cell)
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! ... positions into internal coordinates.
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! ... The algorithm uses a "trust radius" line search based on Wolfe
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! ... conditions. Steps are rejected until the first Wolfe condition
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! ... (sufficient energy decrease) is satisfied. Updated step length
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! ... is estimated from quadratic interpolation.
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! ... When the step is accepted inverse hessian is updated according to
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! ... BFGS scheme and a new search direction is obtained from NR or GDIIS
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! ... method. The corresponding step length is limited by trust_radius_max
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! ... and can't be larger than the previous step multiplied by a certain
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! ... factor determined by Wolfe and other convergence conditions.
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!
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! ... Originally written ( 5/12/2003 ) and maintained ( 2003-2007 ) by
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! ... Carlo Sbraccia
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! ... Modified for variable-cell-shape relaxation ( 2007-2008 ) by
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! ... Javier Antonio Montoya, Lorenzo Paulatto and Stefano de Gironcoli
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! ... Re-analyzed by Stefano de Gironcoli ( 2010 )
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! ... FCP case added by Minoru Otani and collaborators (2020)
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!
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! ... references :
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!
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! ... 1) Roger Fletcher, Practical Methods of Optimization, John Wiley and
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! ... Sons, Chichester, 2nd edn, 1987.
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! ... 2) Salomon R. Billeter, Alexander J. Turner, Walter Thiel,
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! ... Phys. Chem. Chem. Phys. 2, 2177 (2000).
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! ... 3) Salomon R. Billeter, Alessandro Curioni, Wanda Andreoni,
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! ... Comput. Mat. Science 27, 437, (2003).
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! ... 4) Ren Weiqing, PhD Thesis: Numerical Methods for the Study of Energy
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! ... Landscapes and Rare Events.
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!! Originally written (5/12/2003) and maintained (2003-2007) by
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!! Carlo Sbraccia.
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!! Modified for variable-cell-shape relaxation (2007-2008) by
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!! Javier Antonio Montoya, Lorenzo Paulatto and Stefano de Gironcoli.
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!! Re-analyzed by Stefano de Gironcoli (2010).
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!! FCP case added by Minoru Otani and collaborators (2020).
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!
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!! References:
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!! 1) Roger Fletcher, Practical Methods of Optimization, John Wiley and
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!! Sons, Chichester, 2nd edn, 1987.
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!! 2) Salomon R. Billeter, Alexander J. Turner, Walter Thiel,
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!! Phys. Chem. Chem. Phys. 2, 2177 (2000).
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!! 3) Salomon R. Billeter, Alessandro Curioni, Wanda Andreoni,
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!! Comput. Mat. Science 27, 437, (2003).
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!! 4) Ren Weiqing, PhD Thesis: Numerical Methods for the Study of Energy
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!! Landscapes and Rare Events.
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!
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USE kinds, ONLY : DP
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USE constants, ONLY : eps4, eps8, eps16, RYTOEV
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@ -66,56 +63,77 @@ MODULE bfgs_module
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CHARACTER (len=320):: bfgs_file=" "
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!! name of file (with path) used to store and retrieve the status
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!
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REAL(DP), ALLOCATABLE :: &
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pos(:), &! positions + cell
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grad(:), &! gradients + cell_force
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pos_p(:), &! positions at the previous accepted iteration
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grad_p(:), &! gradients at the previous accepted iteration
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inv_hess(:,:), &! inverse hessian matrix (updated using BFGS formula)
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metric(:,:), &
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inv_metric(:,:), &
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h_block(:,:), &
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hinv_block(:,:), &
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step(:), &! the (new) search direction (normalized NR step)
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step_old(:), &! the previous search direction (normalized NR step)
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pos_old(:,:), &! list of m old positions - used only by gdiis
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grad_old(:,:), &! list of m old gradients - used only by gdiis
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pos_best(:) ! best extrapolated positions - used only by gdiis
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REAL(DP) :: &
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nr_step_length, &! length of (new) Newton-Raphson step
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nr_step_length_old,&! length of previous Newton-Raphson step
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trust_radius, &! new displacement along the search direction
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trust_radius_old, &! old displacement along the search direction
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energy_p ! energy at previous accepted iteration
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INTEGER :: &
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scf_iter, &! number of scf iterations
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bfgs_iter, &! number of bfgs iterations
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gdiis_iter, &! number of gdiis iterations
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tr_min_hit = 0 ! set to 1 if the trust_radius has already been
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! set to the minimum value at the previous step
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! set to 2 if trust_radius is reset again: exit
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LOGICAL :: &
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conv_bfgs = .FALSE. ! .TRUE. when bfgs convergence has been achieved
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REAL(DP), ALLOCATABLE :: pos(:)
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!! positions + cell
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REAL(DP), ALLOCATABLE :: grad(:)
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!! gradients + cell_force
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REAL(DP), ALLOCATABLE :: pos_p(:)
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!! positions at the previous accepted iteration
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REAL(DP), ALLOCATABLE :: grad_p(:)
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!! gradients at the previous accepted iteration
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REAL(DP), ALLOCATABLE :: inv_hess(:,:)
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!! inverse hessian matrix (updated using BFGS formula)
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REAL(DP), ALLOCATABLE :: metric(:,:)
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REAL(DP), ALLOCATABLE :: inv_metric(:,:)
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REAL(DP), ALLOCATABLE :: h_block(:,:)
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REAL(DP), ALLOCATABLE :: hinv_block(:,:)
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REAL(DP), ALLOCATABLE :: step(:)
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!! the (new) search direction (normalized NR step)
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REAL(DP), ALLOCATABLE :: step_old(:)
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!! the previous search direction (normalized NR step)
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REAL(DP), ALLOCATABLE :: pos_old(:,:)
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!! list of m old positions - used only by gdiis
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REAL(DP), ALLOCATABLE :: grad_old(:,:)
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!! list of m old gradients - used only by gdiis
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REAL(DP), ALLOCATABLE :: pos_best(:)
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!! best extrapolated positions - used only by gdiis
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!
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REAL(DP) :: nr_step_length
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!! length of (new) Newton-Raphson step
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REAL(DP) :: nr_step_length_old
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!! length of previous Newton-Raphson step
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REAL(DP) :: trust_radius
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!! new displacement along the search direction
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REAL(DP) :: trust_radius_old
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!! old displacement along the search direction
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REAL(DP) :: energy_p
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!! energy at previous accepted iteration
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!
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INTEGER :: scf_iter
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!! number of scf iterations
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INTEGER :: bfgs_iter
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!! number of bfgs iterations
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INTEGER :: gdiis_iter
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!! number of gdiis iterations
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INTEGER :: tr_min_hit = 0
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!! set to 1 if the trust_radius has already been set to the minimum value
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!! at the previous step. Set to 2 if trust_radius is reset again: exit.
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LOGICAL :: conv_bfgs = .FALSE.
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!! .TRUE. when bfgs convergence has been achieved
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!
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! ... default values for bfgs_ndim, trust_radius_max, trust_radius_min,
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! ... trust_radius_ini, w_1, w_2, are set in Modules/read_namelist.f90
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! ... (SUBROUTINE ions_defaults) and can be assigned in the input
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!
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LOGICAL :: &
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bfgs_initialized = .FALSE.
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INTEGER :: &
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stdout ! standard output for writing
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INTEGER :: &
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bfgs_ndim ! dimension of the subspace for GDIIS
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! for standard BFGS algorithm, bfgs_ndim=1
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REAL(DP) :: &
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trust_radius_ini, &! suggested initial displacement
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trust_radius_min, &! minimum allowed displacement
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trust_radius_max ! maximum allowed displacement
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REAL(DP) :: &! parameters for Wolfe conditions
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w_1, &! 1st Wolfe condition: sufficient energy decrease
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w_2 ! 2nd Wolfe condition: sufficient gradient decrease
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LOGICAL :: bfgs_initialized = .FALSE.
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INTEGER :: stdout
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!! standard output for writing
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INTEGER :: bfgs_ndim
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!! dimension of the subspace for GDIIS for standard BFGS algorithm,
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!! \(\text{bfgs_ndim}=1\)
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REAL(DP) :: trust_radius_ini
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!! suggested initial displacement
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REAL(DP) :: trust_radius_min
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!! minimum allowed displacement
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REAL(DP) :: trust_radius_max
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!! maximum allowed displacement
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!
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! ... parameters for Wolfe conditions
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!
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REAL(DP) :: w_1
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!! 1st Wolfe condition: sufficient energy decrease
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REAL(DP) :: w_2
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!! 2nd Wolfe condition: sufficient gradient decrease
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!
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CONTAINS
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!
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@ -123,8 +141,7 @@ CONTAINS
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SUBROUTINE init_bfgs( stdout_, bfgs_ndim_, trust_radius_max_, &
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trust_radius_min_, trust_radius_ini_, w_1_, w_2_)
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!------------------------------------------------------------------------
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!
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! ... set values for several parameters of the algorithm
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!! set values for several parameters of the algorithm
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!
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INTEGER, INTENT(IN) :: &
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stdout_, &
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@ -146,58 +163,69 @@ CONTAINS
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bfgs_initialized = .true.
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!
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END SUBROUTINE init_bfgs
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!------------------------------------------------------------------------
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!
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!------------------------------------------------------------------------
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SUBROUTINE bfgs( filebfgs, pos_in, h, nelec, energy, &
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grad_in, fcell, iforceh, felec, &
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energy_thr, grad_thr, cell_thr, fcp_thr, &
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energy_error, grad_error, cell_error, fcp_error, &
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lmovecell, lfcp, fcp_cap, fcp_hess, step_accepted, stop_bfgs, istep )
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!------------------------------------------------------------------------
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!
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! ... list of input/output arguments :
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!
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! filebfgs : file name for storing and retrieving data
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! pos_in : vector containing 3N coordinates of the system ( x )
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! h : 3x3 matrix of the primitive lattice vectors
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! nelec : number of elecrons (for FCP)
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! energy : energy of the system ( V(x) )
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! grad : vector containing 3N components of grad( V(x) )
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! fcell : 3x3 matrix containing the stress tensor
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! iforceh : 3x3 matrix containing cell constraints
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! energy_thr : threshold on energy difference for BFGS convergence
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! grad_thr : threshold on grad difference for BFGS convergence
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! the largest component of grad( V(x) ) is considered
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! cell_thr : threshold on grad of cell for BFGS convergence
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! fcp_thr : treshold on grad of FCP for BFGS convergence
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! energy_error : energy difference | V(x_i) - V(x_i-1) |
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! grad_error : the largest component of
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! | grad(V(x_i)) - grad(V(x_i-1)) |
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! cell_error : the largest component of: omega*(stress-press*I)
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! fcp_error : | grad(V(x_FCP)) |
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! step_accepted : .TRUE. if a new BFGS step is done
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! stop_bfgs : .TRUE. if BFGS convergence has been achieved
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!! BFGS algorithm.
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!
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IMPLICIT NONE
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!
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REAL(DP), INTENT(INOUT) :: pos_in(:)
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!! vector containing 3N coordinates of the system ( x )
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REAL(DP), INTENT(INOUT) :: h(3,3)
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REAL(DP), INTENT(INOUT) :: nelec ! number of electrons
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!! 3x3 matrix of the primitive lattice vectors
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REAL(DP), INTENT(INOUT) :: nelec
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!! number of electrons (for FCP)
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REAL(DP), INTENT(INOUT) :: energy
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!! energy of the system ( V(x) )
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REAL(DP), INTENT(INOUT) :: grad_in(:)
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!! vector containing 3N components of grad( V(x) )
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REAL(DP), INTENT(INOUT) :: fcell(3,3)
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REAL(DP), INTENT(INOUT) :: felec ! force on FCP
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!! 3x3 matrix containing the stress tensor
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REAL(DP), INTENT(INOUT) :: felec
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!! force on FCP
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CHARACTER(LEN=*), INTENT(IN) :: filebfgs
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REAL(DP), INTENT(IN) :: energy_thr, grad_thr, cell_thr, fcp_thr
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!! file name for storing and retrieving data
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REAL(DP), INTENT(IN) :: energy_thr
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!! threshold on energy difference for BFGS convergence
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REAL(DP), INTENT(IN) :: grad_thr
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!! threshold on grad difference for BFGS convergence
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!! the largest component of grad( V(x) ) is considered
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REAL(DP), INTENT(IN) :: cell_thr
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!! threshold on grad of cell for BFGS convergence
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REAL(DP), INTENT(IN) :: fcp_thr
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!! treshold on grad of FCP for BFGS convergence
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INTEGER, INTENT(IN) :: iforceh(3,3)
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!! 3x3 matrix containing cell constraints
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LOGICAL, INTENT(IN) :: lmovecell
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LOGICAL, INTENT(IN) :: lfcp ! include FCP, or not ?
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REAL(DP), INTENT(IN) :: fcp_cap ! capacitance for FCP
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REAL(DP), INTENT(IN) :: fcp_hess ! hessian for FCP
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REAL(DP), INTENT(OUT) :: energy_error, grad_error, cell_error, fcp_error
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LOGICAL, INTENT(OUT) :: step_accepted, stop_bfgs
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LOGICAL, INTENT(IN) :: lfcp
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!! include FCP, or not ?
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REAL(DP), INTENT(IN) :: fcp_cap
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!! capacitance for FCP
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REAL(DP), INTENT(IN) :: fcp_hess
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!! hessian for FCP
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REAL(DP), INTENT(OUT) :: energy_error
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!! energy difference \(\| V(x_i) - V(x_{i-1}) \|\)
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REAL(DP), INTENT(OUT) :: grad_error
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!! the largest component of \(\|\text{grad}(V(x_i)) -
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!! \text{grad}(V(x_{i-1}))\|\)
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REAL(DP), INTENT(OUT) :: cell_error
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!! the largest component of: omega*(stress-press*I)
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REAL(DP), INTENT(OUT) :: fcp_error
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!! \(\| \text{grad}(V(x_{FCP})) \|\)
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LOGICAL, INTENT(OUT) :: step_accepted
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!! .TRUE. if a new BFGS step is done
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LOGICAL, INTENT(OUT) :: stop_bfgs
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!! .TRUE. if BFGS convergence has been achieved
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INTEGER, INTENT(OUT) :: istep
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!
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! ... local variables
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!
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INTEGER :: n, i, j, k, nat
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LOGICAL :: lwolfe
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REAL(DP) :: dE0s, den
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@ -552,6 +580,8 @@ CONTAINS
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!--------------------------------------------------------------------
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SUBROUTINE gdiis_step()
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!--------------------------------------------------------------------
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!! GDIIS extrapolation
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!
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USE basic_algebra_routines
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IMPLICIT NONE
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!
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@ -651,8 +681,8 @@ CONTAINS
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!------------------------------------------------------------------------
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SUBROUTINE reset_bfgs( n, lfcp, fcp_hess )
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!------------------------------------------------------------------------
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! ... inv_hess in re-initialized to the initial guess
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! ... defined as the inverse metric
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!! \(\text{inv_hess}\) in re-initialized to the initial guess
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!! defined as the inverse metric.
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!
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INTEGER, INTENT(IN) :: n
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LOGICAL, INTENT(IN) :: lfcp
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