minimization_mod

link to source code

Dependency Diagrams:

minimization_mod.svg

Direct Dependency Diagram

minimization_mod_rev.svg

Reverse Dependency Diagram

Description

MODULE minimization_mod (prefix=’min’ category=’1. High-level functionality’)

Purpose

Minimization for variational assimilation, including the subroutine that evaluates the cost function and its gradient.

Quick access

Variables

min_niter, min_nsim

Routines

dcanab(), dcanonb(), dscalqn(), grtest2(), hessianio(), min_minimize(), min_setup(), min_writehessian(), prscal(), quasinewtonminimization(), simvar()

Needed modules

  • codeprecision_mod: MODULE codePrecision_mod (prefix=’pre’ category=’8. Low-level utilities and constants’)

  • timecoord_mod: MODULE timeCoord_mod (prefix=’tim’ category=’7. Low-level data objects’)

  • obstimeinterp_mod: MODULE obsTimeInterp_mod (prefix=’oti’ category=’4. Data Object transformations’)

  • verticalcoord_mod: MODULE verticalCoord_mod (prefix=’vco’ category=’7. Low-level data objects’)

  • columndata_mod: MODULE columnData_mod (prefix=’col’ category=’6. High-level data objects’)

  • obsspacedata_mod: MODULE obsSpaceData_mod (prefix=’obs’ category=’6. High-level data objects’)

  • controlvector_mod: MODULE controlVector_mod (prefix=’cvm’ category=’6. High-level data objects’)

  • midasmpi_mod: MODULE midasMpi_mod (prefix=’mmpi’ category=’8. Low-level utilities and constants’)

  • horizontalcoord_mod: MODULE horizontalCoord_mod (prefix=’hco’ category=’7. Low-level data objects’)

  • gridstatevector_mod: MODULE gridStateVector_mod (prefix=’gsv’ category=’6. High-level data objects’)

  • gridstatevectorfileio_mod: MODULE gridStateVectorFileIO_mod (prefix=’gio’ category=’4. Data Object transformations’)

  • bmatrix_mod: MODULE bMatrix_mod (prefix=’bmat’ category=’2. B and R matrices’)

  • bmatrix1dvar_mod: MODULE bMatrix1DVar_mod (prefix=’bmat1D’ category=’2. B and R matrices’)

  • statetocolumn_mod: MODULE stateToColumn_mod (prefix=’s2c’ category=’4. Data Object transformations’)

  • varqc_mod: MODULE varQC_mod (prefix=’vqc’ category=’1. High-level functionality’)

  • rmatrix_mod: MODULE rMatrix_mod (prefix=’rmat’ category=’2. B and R matrices’)

  • costfunction_mod: MODULE costFunction_mod, (prefix=’cfn’ category=’5. Observation operators’)

  • residual_mod: MODULE residual_mod (prefix=’res’ category=’1. High-level functionality’)

  • obsoperators_mod: MODULE obsOperators_mod (prefix=’oop’ category=’5. Observation operators’)

  • quasinewton_mod: MODULE quasiNewton_mod (prefix=’qna’ category=’1. High-level functionality’)

  • utilities_mod: MODULE utilities_mod (prefix=’utl’ category=’8. Low-level utilities and constants’)

  • biascorrectionsat_mod: MODULE biasCorrectionSat_mod (prefix=’bcs’ category=’1. High-level functionality’)

  • columnvariabletransforms_mod: MODULE columnVariableTransforms_mod (prefix=’cvt’ category=’4. Data Object transformations’)

Variables

  • minimization_mod/min_niter [integer,public]
  • minimization_mod/min_nsim [integer,public]

Subroutines and functions

subroutine  minimization_mod/min_setup(nvadim_mpilocal_in, hco_anl_in[, onedvarmode_opt[, varqc_opt[, nwoqcv_opt]]])
Purpose

Reading NAMMIN namelist to setup variables for minimization.

Arguments

  • nvadim_mpilocal_in [integer ,in]

  • hco_anl_in [struct_hco ,in,pointer]

Options

  • onedvarmode_opt [logical ,in,]

  • varqc_opt [logical ,out,]

  • nwoqcv_opt [integer ,out,]

Called from

midas_var, midas_var1d

Call to

utl_tmg_start(), utl_abort(), utl_tmg_stop()

subroutine  minimization_mod/min_minimize(outerloopindex_in, columntrlonanlinclev, obsspacedata, controlvectorincrsum, vazx, numitermaxinnerloop[, deallochessian_opt[, isminimizationfinalcall_opt[, numitermaxinnerloopused_opt]]])
Purpose

Minimizing cost function to get the increments. The maximum number of inner-loop iterations is set to nitermax if the namelist variable nitermax is provided. Otherwise, it is set to the numIterMaxInnerLoop supplied by the calling subroutine/program. numIterMaxInnerLoopUsed_opt is passing the maximum number of inner-loop iterations to the calling subroutine/program.

Arguments

  • outerloopindex_in [integer ,in]

  • columntrlonanlinclev [struct_columndata ,inout]

  • obsspacedata [struct_obs ,inout]

  • controlvectorincrsum (*) [real ,inout,target]

  • vazx (*) [real ,inout]

  • numitermaxinnerloop [integer ,in]

Options

  • deallochessian_opt [logical ,in,]

  • isminimizationfinalcall_opt [logical ,in,]

  • numitermaxinnerloopused_opt [integer ,out,]

Called from

midas_var, midas_var1d

Call to

utl_tmg_start(), utl_abort(), col_setvco(), col_getvco(), col_allocate(), col_getnumcol(), oti_timebinning(), quasinewtonminimization(), col_deallocate(), utl_tmg_stop()

subroutine  minimization_mod/quasinewtonminimization(columnanlinc, columntrlonanlinclev, obsspacedata, vazx)
Purpose

3D/En-VAR minimization

Arguments

  • columnanlinc [struct_columndata ,in,target]

  • columntrlonanlinclev [struct_columndata ,in,target]

  • obsspacedata [struct_obs ,inout,target]

  • vazx (*) [real ,out]

Called from

min_minimize()

Call to

vqc_setup(), utl_abort(), tim_getdatestamp(), hessianio(), utl_tmg_start(), grtest2(), utl_tmg_stop(), simvar(), prscal(), qna_n1qn3(), obs_numheader(), obs_prnthdr(), obs_prntbdy()

subroutine  minimization_mod/min_writehessian(vazx)
Arguments

vazx (*) [real ,inout]

Called from

midas_var, midas_var1d

Call to

utl_tmg_start(), tim_getdatestamp(), hessianio(), utl_tmg_stop()

subroutine  minimization_mod/simvar(na_indic, na_dim, da_v, da_j, da_gradj)
Purpose

To implement the Variational solver as described in Courtier, 1997, Dual Formulation of Four-Dimentional Variational Assimilation, Q.J.R., pp2449-2461.

Arguments

Arguments

  • na_indic [integer ,in] ::

    =1 No action taken

    =2 Same as 4 (compute J and gradJ) but do not interrupt

    timer of the minimizer.

    =3 Compute Jo and gradJo only.

    =4 Both J(u) and its gradient are computed.

    Note

    1 and 4 are reserved values for call back from m1qn3. For direct calls, use a value other than 1 and 4.

  • na_dim [integer ,in,] :: Control-vector dimension, forecast-error covariance space

  • da_v (na_dim) [real ,in] :: Control variable, forecast-error covariance space

  • da_j [real ,out] :: Cost function of the Variational algorithm

  • da_gradj (na_dim) [real ,out] :: Gradient of the Variational Cost funtion

Called from

minimize(), quasinewtonminimization()

Call to

utl_tmg_stop(), mmpi_allreduce_sumreal8scalar(), bmat1d_sqrtb(), cvt_transform(), gsv_isallocated(), col_getvco(), gsv_allocate(), gio_readmaskfromfile(), bmat_sqrtb(), s2c_tl(), utl_tmg_start(), oop_htl(), res_compute(), bcs_calcbias_tl(), rmat_rsqrtinverseallobs(), cfn_calcjo(), vqc_nltl(), cfn_sumjo(), vqc_ad(), res_computead(), col_zero(), oop_had(), s2c_ad(), bcs_calcbias_ad(), bmat1d_sqrtbt(), bmat_sqrtbt()

subroutine  minimization_mod/dscalqn(kdim, px, py, ddsc)
Purpose

Interface for the inner product to be used by the minimization subroutines QNA_N1QN3.

Arguments

i : kdim i : px,py o : ddsc i : kzs i : pzs i : ddzs

Arguments

  • kdim [integer ,in,] :: dimension of the vectors

  • px (kdim) [real ,in] :: vector for which <PX,PY> is being calculated

  • py (kdim) [real ,in] :: vector for which <PX,PY> is being calculated

  • ddsc [real ,out] :: result of the inner product

Call to

prscal()

subroutine  minimization_mod/prscal(kdim, px, py, ddsc)
Purpose

To evaluate the inner product used in the minimization

Arguments

  • kdim [integer ,in,] :: dimension of the vectors

  • px (kdim) [real ,in] :: vector for which <PX,PY> is being calculated

  • py (kdim) [real ,in] :: vector for which <PX,PY> is being calculated

  • ddsc [real ,out] :: result of the inner product

Called from

minimize(), quasinewtonminimization(), dscalqn()

Call to

mmpi_allreduce_sumreal8scalar()

subroutine  minimization_mod/dcanab(kdim, py, px)
Purpose

Change of variable associated with the canonical inner product:

  • PX = L^-1 * Py with L related to the inner product

  • <PX,PY> = PX^t L^t L PY

  • (see the modulopt documentation aboutn DTCAB)

  • NOTE: L is assumed to be the identity!

Arguments

  • kdim [integer ,in,]

  • py (kdim) [real ,in]

  • px (kdim) [real ,out]

subroutine  minimization_mod/dcanonb(kdim, px, py)
Purpose

Change of variable associated with the canonical inner product:

  • PY = L * PX with L related to the inner product

  • <PX,PY> = PX^t L^t L PY

  • (see the modulopt documentation about DTONB)

Arguments

  • kdim [integer ,in,]

  • px (kdim) [real ,in]

  • py (kdim) [real ,out]

subroutine  minimization_mod/hessianio(cfname, status, nsim, kbrpstamp, zeps1, zdf1, itertot, isimtot, iztrl, vatra, vazxbar, vazx, llxbar, llvazx, k1gc, imode)
Purpose

Read-Write Hessian and increment (possibly for outer loop) on a file

Arguments

  • i cfname

  • i status

  • i nsim

  • io kbrpstamp

  • i zeps1

  • i zdf1

  • i itertot

  • i isimtot

  • i iztrl

  • i vatra

  • i vazxbar

  • i vazx

  • i llxbar

  • i llvazx

  • i k1gc

  • o imode

Arguments

  • cfname [character ,in] :: precon file

  • status [integer ,in] :: = 0 if READ, = 1 if WRITE

  • nsim [integer ,inout] :: Number of simulations in QNA_N1QN3

  • kbrpstamp [integer ,inout] :: Date

  • zeps1 [real ,inout] :: Parameter in QNA_N1QN3

  • zdf1 [real ,inout] :: Parameter in QNA_N1QN3

  • itertot [integer ,inout] :: Parameter in QNA_N1QN3

  • isimtot [integer ,inout] :: Parameter in QNA_N1QN3

  • iztrl (5) [integer ,inout,target] :: Localisation parameters for Hessian

  • vatra (nmtra) [real ,inout,target] :: Hessian

  • vazxbar (nvadim_mpilocal) [real ,inout,target] :: Vazx of previous loop

  • vazx (nvadim_mpilocal) [real ,inout,target] :: Current state of the minimization

  • llxbar [logical ,in] :: read in vaxzbar if dates are compatible

  • llvazx [logical ,in] :: Logical to read vazx

  • k1gc [integer ,in] :: Minimizer ID (2: m1qn2, 3: m1qn3)

  • imode [integer ,out] :: If status=0, set imode=0 (no prec) or 2 (prec)

Called from

quasinewtonminimization(), min_writehessian()

Call to

utl_tmg_start(), utl_abort(), bmat_reducetompilocal_r4(), bmat_reducetompilocal(), bmat_expandtompiglobal_r4(), bmat_expandtompiglobal(), utl_tmg_stop()

subroutine  minimization_mod/grtest2(simul, na_dim, da_x0, na_range)
Purpose

To compare the variation of the functional against what the gradient gives for small changes in the control variable. This test should be accurate for values as small as DLALPHA = SQRT(machine precision). (see Courtier, 1987)

Arguments

Arguments

  • na_range [integer ,in] :: the test will be carried over values of ALPHA ranging between 10**(-NA_RANGE) < ALPHA < 0.1

  • simul [external] :: simulator: return cost function estimate and its gradient

  • na_dim [integer ,in,] :: Size of the control vector

  • da_x0 (na_dim) [real ,in] :: Control vector

Needed modules

  • grtest2__user__routines

Called from

quasinewtonminimization()

Call to

mmpi_allreduce_sumreal8scalar()