GALAHAD SEC package

purpose

The sec package builds and updates dense BFGS and SR1 secant approximations to a Hessian so that the approximation \(B\) satisfies the secant condition \(B s = y\) for given vectors \(s\) and \(y\).

Currently only the options and inform dictionaries are exposed; these are provided and used by other GALAHAD packages with Python interfaces. Please contact us if you would like full functionality!

See Section 4 of $GALAHAD/doc/sec.pdf for a brief description of the method employed and other details.

parametric real type T and integer type INT

Below, the symbol T refers to a parametric real type that may be Float32 (single precision), Float64 (double precision) or, if supported, Float128 (quadruple precision). The symbol INT refers to a parametric integer type that may be Int32 (32-bit integer) or Int64 (64-bit integer).

callable functions

    function sec_initialize(T, INT, control, status)

Set default control values and initialize private data

Parameters:

control	is a structure containing control information (see sec_control_type)
status	is a scalar variable of type INT that gives the exit status from the package. Possible values are (currently): 0 The initialization was successful.

    function sec_information(T, INT, data, inform, status)

Provides output information

Parameters:

data	holds private internal data
inform	is a structure containing output information (see sec_inform_type)
status	is a scalar variable of type INT that gives the exit status from the package. Possible values are (currently): 0 The values were recorded successfully

    function sec_terminate(T, INT, data, control, inform)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a structure containing control information (see sec_control_type)
inform	is a structure containing output information (see sec_inform_type)

available structures

sec_control_type structure

    struct sec_control_type{T,INT}
      f_indexing::Bool
      error::INT
      out::INT
      print_level::INT
      h_initial::T
      update_skip_tol::T
      prefix::NTuple{31,Cchar}

detailed documentation

control derived type as a Julia structure

components

Bool f_indexing

use C or Fortran sparse matrix indexing

INT error

error and warning diagnostics occur on stream error

INT out

general output occurs on stream out

INT print_level

the level of output required. <= 0 gives no output, >= 1 warning message

T h_initial

the initial Hessian approximation will be h_initial \* \(I\)

T update_skip_tol

an update is skipped if the resulting matrix would have grown too much; specifically it is skipped when y^T s / y^T y <= update_skip_tol.

NTuple{31,Cchar} prefix

all output lines will be prefixed by .prefix(2:LEN(TRIM(.prefix))-1) where .prefix contains the required string enclosed in quotes, e.g. “string” or ‘string’

sec_inform_type structure

    struct sec_inform_type{INT}
      status::INT

detailed documentation

inform derived type as a Julia structure

components

INT status

return status. Possible values are:

• 0

  A successful return

• -85

  An update is inappropriate and has been skipped

Index