GALAHAD BGO package#
purpose#
The bgo package uses a multi-start trust-region method to find an
approximation to the global minimizer of a differentiable objective
function \(f(x)\) of n variables \(x\), subject to simple
bounds \(x^l <= x <= x^u\) on the variables. Here, any of the
components of the vectors of bounds \(x^l\) and \(x^u\)
may be infinite. The method offers the choice of direct and
iterative solution of the key trust-region subproblems, and
is suitable for large problems. First derivatives are required,
and if second derivatives can be calculated, they will be exploited -
if the product of second derivatives with a vector may be found but
not the derivatives themselves, that may also be exploited.
The package offers both random multi-start and local-minimize-and-probe methods to try to locate the global minimizer. There are no theoretical guarantees unless the sampling is huge, and realistically the success of the methods decreases as the dimension and nonconvexity increase.
See Section 4 of $GALAHAD/doc/bgo.pdf for additional details.
method#
A choice of two methods is available.
In the first, local-minimization-and-probe, approach, local minimization
and univariate global minimization are intermixed. Given a current
champion \(x^S_k\), a local minimizer \(x_k\) of \(f(x)\) within the
feasible box \(x^l \leq x \leq x^u\) is found using TRB.
Thereafter \(m\) random directions \(p\) are generated, and univariate
local minimizer of \(f(x_k + \alpha p)\) as a function of the scalar
\(\alpha\) along each \(p\) within the interval \([\alpha^L,\alpha^u]\),
where \(\alpha^L\) and \(\alpha^u\) are the smallest and largest \(\alpha\)
for which \(x^l \leq x_k + \alpha p \leq x^u\),
is performed using UGO. The point \(x_k + \alpha p\)
that gives the smallest value of \(f\) is then selected as the new champion
\(x^S_{k+1}\).
The random directions \(p\) are chosen in one of three ways. The simplest is to select the components as
LHS.
Each components of \(p\) is then selected in its sub-box, either uniformly
or pseudo randomly.
The other, random-multi-start, method provided selects \(m\) starting points
at random, either componentwise pseudo randomly in the feasible box,
or by partitioning each component into \(m\) equal segments, assigning each to
a sub-box using Latin hypercube sampling, and finally choosing the
values either uniformly or pseudo randomly. Local minimizers within the
feasible box are then computed by TRB, and
the best is assigned as the current champion. This process is then
repeated until evaluation limits are achieved.
If \(n=1\), UGO is called directly.
We reiterate that there are no theoretical guarantees unless the sampling is huge, and realistically the success of the methods decreases as the dimension and nonconvexity increase. Thus the methods used should best be viewed as heuristics.
references#
The generic bound-constrained trust-region method is described in detail in
A. R. Conn, N. I. M. Gould and Ph. L. Toint, Trust-region methods. SIAM/MPS Series on Optimization (2000),
the univariate global minimization method employed is an extension of that due to
D. Lera and Ya. D. Sergeyev, ``Acceleration of univariate global optimization algorithms working with Lipschitz functions and Lipschitz first derivatives’’ SIAM J. Optimization 23(1) (2013) 508–529,
while the Latin-hypercube sampling method employed is that of
B. Beachkofski and R. Grandhi, ``Improved Distributed Hypercube Sampling’’, 43rd AIAA structures, structural dynamics, and materials conference, (2002) 2002-1274.
matrix storage#
The symmetric \(n\) by \(n\) matrix \(H = \nabla^2_{xx}f\) may be presented and stored in a variety of formats. But crucially symmetry is exploited by only storing values from the lower triangular part (i.e, those entries that lie on or below the leading diagonal).
Dense storage format: The matrix \(H\) is stored as a compact dense matrix by rows, that is, the values of the entries of each row in turn are stored in order within an appropriate real one-dimensional array. Since \(H\) is symmetric, only the lower triangular part (that is the part \(H_{ij}\) for \(0 <= j <= i <= n-1\)) need be held. In this case the lower triangle should be stored by rows, that is component \(i * i / 2 + j\) of the storage array H_val will hold the value \(H_{ij}\) (and, by symmetry, \(H_{ji}\)) for \(0 <= j <= i <= n-1\).
Sparse co-ordinate storage format: Only the nonzero entries of the matrices are stored. For the \(l\)-th entry, \(0 <= l <= ne-1\), of \(H\), its row index i, column index j and value \(H_{ij}\), \(0 <= j <= i <= n-1\), are stored as the \(l\)-th components of the integer arrays H_row and H_col and real array H_val, respectively, while the number of nonzeros is recorded as H_ne = \(ne\). Note that only the entries in the lower triangle should be stored.
Sparse row-wise storage format: Again only the nonzero entries are stored, but this time they are ordered so that those in row i appear directly before those in row i+1. For the i-th row of \(H\) the i-th component of the integer array H_ptr holds the position of the first entry in this row, while H_ptr(n) holds the total number of entries. The column indices j, \(0 <= j <= i\), and values \(H_{ij}\) of the entries in the i-th row are stored in components l = H_ptr(i), …, H_ptr(i+1)-1 of the integer array H_col, and real array H_val, respectively. Note that as before only the entries in the lower triangle should be stored. For sparse matrices, this scheme almost always requires less storage than its predecessor.
introduction to function calls#
To solve a given problem, functions from the bgo package must be called in the following order:
bgo_initialize - provide default control parameters and set up initial data structures
bgo_read_specfile (optional) - override control values by reading replacement values from a file
bgo_import - set up problem data structures and fixed values
bgo_reset_control (optional) - possibly change control parameters if a sequence of problems are being solved
solve the problem by calling one of
bgo_solve_with_mat - solve using function calls to evaluate function, gradient and Hessian values
bgo_solve_without_mat - solve using function calls to evaluate function and gradient values and Hessian-vector products
bgo_solve_reverse_with_mat - solve returning to the calling program to obtain function, gradient and Hessian values, or
bgo_solve_reverse_without_mat - solve returning to the calling prorgram to obtain function and gradient values and Hessian-vector products
bgo_information (optional) - recover information about the solution and solution process
bgo_terminate - deallocate data structures
See the examples section for illustrations of use.
callable functions#
overview of functions provided#
// typedefs typedef float spc_; typedef double rpc_; typedef int ipc_; // structs struct bgo_control_type; struct bgo_inform_type; struct bgo_time_type; // function calls void bgo_initialize(void **data, struct bgo_control_type* control, ipc_ *status); void bgo_read_specfile(struct bgo_control_type* control, const char specfile[]); void bgo_import( struct bgo_control_type* control, void **data, ipc_ *status, ipc_ n, const rpc_ x_l[], const rpc_ x_u[], const char H_type[], ipc_ ne, const ipc_ H_row[], const ipc_ H_col[], const ipc_ H_ptr[] ); void bgo_reset_control( struct bgo_control_type* control, void **data, ipc_ *status ); void bgo_solve_with_mat( void **data, void *userdata, ipc_ *status, ipc_ n, rpc_ x[], rpc_ g[], ipc_ ne, ipc_(*)(ipc_, const rpc_[], rpc_*, const void*) eval_f, ipc_(*)(ipc_, const rpc_[], rpc_[], const void*) eval_g, ipc_(*)(ipc_, ipc_, const rpc_[], rpc_[], const void*) eval_h, ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], bool, const void*) eval_hprod, ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], const void*) eval_prec ); void bgo_solve_without_mat( void **data, void *userdata, ipc_ *status, ipc_ n, rpc_ x[], rpc_ g[], ipc_(*)(ipc_, const rpc_[], rpc_*, const void*) eval_f, ipc_(*)(ipc_, const rpc_[], rpc_[], const void*) eval_g, ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], bool, const void*) eval_hprod, ipc_(*)(ipc_, const rpc_[], ipc_, const int[], const rpc_[], int*, int[], rpc_[], bool, const void*) eval_shprod, ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], const void*) eval_prec ); void bgo_solve_reverse_with_mat( void **data, ipc_ *status, ipc_ *eval_status, ipc_ n, rpc_ x[], rpc_ f, rpc_ g[], ipc_ ne, rpc_ H_val[], const rpc_ u[], rpc_ v[] ); void bgo_solve_reverse_without_mat( void **data, ipc_ *status, ipc_ *eval_status, ipc_ n, rpc_ x[], rpc_ f, rpc_ g[], rpc_ u[], rpc_ v[], ipc_ index_nz_v[], ipc_ *nnz_v, const ipc_ index_nz_u[], ipc_ nnz_u ); void bgo_information(void **data, struct bgo_inform_type* inform, ipc_ *status); void bgo_terminate( void **data, struct bgo_control_type* control, struct bgo_inform_type* inform );
typedefs#
typedef float spc_
spc_ is real single precision
typedef double rpc_
rpc_ is the real working precision used, but may be changed to float by
defining the preprocessor variable REAL_32 or (if supported) to
__real128 using the variable REAL_128.
typedef int ipc_
ipc_ is the default integer word length used, but may be changed to
int64_t by defining the preprocessor variable INTEGER_64.
function calls#
void bgo_initialize(void **data, struct bgo_control_type* control, ipc_ *status)
Set default control values and initialize private data
Parameters:
data |
holds private internal data |
control |
is a struct containing control information (see bgo_control_type) |
status |
is a scalar variable of type ipc_, that gives the exit status from the package. Possible values are (currently):
|
void bgo_read_specfile(struct bgo_control_type* control, const char specfile[])
Read the content of a specification file, and assign values associated with given keywords to the corresponding control parameters. An in-depth discussion of specification files is available, and a detailed list of keywords with associated default values is provided in $GALAHAD/src/bgo/BGO.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/bgo.pdf for a list of how these keywords relate to the components of the control structure.
Parameters:
control |
is a struct containing control information (see bgo_control_type) |
specfile |
is a character string containing the name of the specification file |
void bgo_import( struct bgo_control_type* control, void **data, ipc_ *status, ipc_ n, const rpc_ x_l[], const rpc_ x_u[], const char H_type[], ipc_ ne, const ipc_ H_row[], const ipc_ H_col[], const ipc_ H_ptr[] )
Import problem data into internal storage prior to solution.
Parameters:
control |
is a struct whose members provide control paramters for the remaining prcedures (see bgo_control_type) |
data |
holds private internal data |
status |
is a scalar variable of type ipc_, that gives the exit status from the package. Possible values are:
|
n |
is a scalar variable of type ipc_, that holds the number of variables. |
x_l |
is a one-dimensional array of size n and type rpc_, that holds the values \(x^l\) of the lower bounds on the optimization variables \(x\). The j-th component of x_l, \(j = 0, \ldots, n-1\), contains \(x^l_j\). |
x_u |
is a one-dimensional array of size n and type rpc_, that holds the values \(x^u\) of the upper bounds on the optimization variables \(x\). The j-th component of x_u, \(j = 0, \ldots, n-1\), contains \(x^u_j\). |
H_type |
is a one-dimensional array of type char that specifies the symmetric storage scheme used for the Hessian. It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’, ‘diagonal’ or ‘absent’, the latter if access to the Hessian is via matrix-vector products; lower or upper case variants are allowed. |
ne |
is a scalar variable of type ipc_, that holds the number of entries in the lower triangular part of H in the sparse co-ordinate storage scheme. It need not be set for any of the other three schemes. |
H_row |
is a one-dimensional array of size ne and type ipc_, that holds the row indices of the lower triangular part of H in the sparse co-ordinate storage scheme. It need not be set for any of the other three schemes, and in this case can be NULL |
H_col |
is a one-dimensional array of size ne and type ipc_, that holds the column indices of the lower triangular part of H in either the sparse co-ordinate, or the sparse row-wise storage scheme. It need not be set when the dense or diagonal storage schemes are used, and in this case can be NULL |
H_ptr |
is a one-dimensional array of size n+1 and type ipc_, that holds the starting position of each row of the lower triangular part of H, as well as the total number of entries, in the sparse row-wise storage scheme. It need not be set when the other schemes are used, and in this case can be NULL |
void bgo_reset_control( struct bgo_control_type* control, void **data, ipc_ *status )
Reset control parameters after import if required.
Parameters:
control |
is a struct whose members provide control paramters for the remaining prcedures (see bgo_control_type) |
data |
holds private internal data |
status |
is a scalar variable of type ipc_, that gives the exit status from the package. Possible values are:
|
void bgo_solve_with_mat( void **data, void *userdata, ipc_ *status, ipc_ n, rpc_ x[], rpc_ g[], ipc_ ne, ipc_(*)(ipc_, const rpc_[], rpc_*, const void*) eval_f, ipc_(*)(ipc_, const rpc_[], rpc_[], const void*) eval_g, ipc_(*)(ipc_, ipc_, const rpc_[], rpc_[], const void*) eval_h, ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], bool, const void*) eval_hprod, ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], const void*) eval_prec )
Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a multistart trust-region method.
This call is for the case where \(H = \nabla_{xx}f(x)\) is provided specifically, and all function/derivative information is available by function calls.
Parameters:
data |
holds private internal data |
userdata |
is a structure that allows data to be passed into the function and derivative evaluation programs. |
status |
is a scalar variable of type ipc_, that gives the entry and exit status from the package. On initial entry, status must be set to 1. Possible exit values are:
|
n |
is a scalar variable of type ipc_, that holds the number of variables |
x |
is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\). |
g |
is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\). |
ne |
is a scalar variable of type ipc_, that holds the number of entries in the lower triangular part of the Hessian matrix \(H\). |
eval_f |
is a user-supplied function that must have the following signature: ipc_ eval_f( ipc_ n, const rpc_ x[], rpc_ *f, const void *userdata ) The value of the objective function \(f(x)\) evaluated at x= \(x\) must be assigned to f, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into |
eval_g |
is a user-supplied function that must have the following signature: ipc_ eval_g( ipc_ n, const rpc_ x[], rpc_ g[], const void *userdata ) The components of the gradient \(g = \nabla_x f(x\)) of the objective function evaluated at x= \(x\) must be assigned to g, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into |
eval_h |
is a user-supplied function that must have the following signature: ipc_ eval_h( ipc_ n, ipc_ ne, const rpc_ x[], rpc_ h[], const void *userdata ) The nonzeros of the Hessian \(H = \nabla_{xx}f(x)\) of the objective function evaluated at x= \(x\) must be assigned to h in the same order as presented to bgo_import, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into |
eval_prec |
is an optional user-supplied function that may be NULL. If non-NULL, it must have the following signature: ipc_ eval_prec( ipc_ n, const rpc_ x[], rpc_ u[], const rpc_ v[], const void *userdata ) The product \(u = P(x) v\) of the user’s preconditioner \(P(x)\) evaluated at \(x\) with the vector v = \(v\), the result \(u\) must be retured in u, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into |
void bgo_solve_without_mat( void **data, void *userdata, ipc_ *status, ipc_ n, rpc_ x[], rpc_ g[], ipc_(*)(ipc_, const rpc_[], rpc_*, const void*) eval_f, ipc_(*)(ipc_, const rpc_[], rpc_[], const void*) eval_g, ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], bool, const void*) eval_hprod, ipc_(*)(ipc_, const rpc_[], ipc_, const int[], const rpc_[], int*, int[], rpc_[], bool, const void*) eval_shprod, ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], const void*) eval_prec )
Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a multistart trust-region method.
This call is for the case where access to \(H = \nabla_{xx}f(x)\) is provided by Hessian-vector products, and all function/derivative information is available by function calls.
Parameters:
data |
holds private internal data |
userdata |
is a structure that allows data to be passed into the function and derivative evaluation programs. |
status |
is a scalar variable of type ipc_, that gives the entry and exit status from the package. On initial entry, status must be set to 1. Possible exit values are:
|
n |
is a scalar variable of type ipc_, that holds the number of variables |
x |
is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\). |
g |
is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\). |
eval_f |
is a user-supplied function that must have the following signature: ipc_ eval_f( ipc_ n, const rpc_ x[], rpc_ *f, const void *userdata ) The value of the objective function \(f(x)\) evaluated at x= \(x\) must be assigned to f, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into |
eval_g |
is a user-supplied function that must have the following signature: ipc_ eval_g( ipc_ n, const rpc_ x[], rpc_ g[], const void *userdata ) The components of the gradient \(g = \nabla_x f(x\)) of the objective function evaluated at x= \(x\) must be assigned to g, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into |
eval_hprod |
is a user-supplied function that must have the following signature: ipc_ eval_hprod( ipc_ n, const rpc_ x[], rpc_ u[], const rpc_ v[], bool got_h, const void *userdata ) The sum \(u + \nabla_{xx}f(x) v\) of the product of the Hessian \(\nabla_{xx}f(x)\) of the objective function evaluated at x= \(x\) with the vector v= \(v\) and the vector $ \(u\) must be returned in u, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. The Hessian has already been evaluated or used at x if got_h is true. Data may be passed into |
eval_shprod |
is a user-supplied function that must have the following signature: ipc_ eval_shprod( ipc_ n, const rpc_ x[], ipc_ nnz_v, const ipc_ index_nz_v[], const rpc_ v[], ipc_ *nnz_u, ipc_ index_nz_u[], rpc_ u[], bool got_h, const void *userdata ) The product \(u = \nabla_{xx}f(x) v\) of the Hessian \(\nabla_{xx}f(x)\) of the objective function evaluated at \(x\) with the sparse vector v= \(v\) must be returned in u, and the function return value set to 0. Only the components index_nz_v[0:nnz_v-1] of v are nonzero, and the remaining components may not have been be set. On exit, the user must indicate the nnz_u indices of u that are nonzero in index_nz_u[0:nnz_u-1], and only these components of u need be set. If the evaluation is impossible at x, return should be set to a nonzero value. The Hessian has already been evaluated or used at x if got_h is true. Data may be passed into |
eval_prec |
is an optional user-supplied function that may be NULL. If non-NULL, it must have the following signature: ipc_ eval_prec( ipc_ n, const rpc_ x[], rpc_ u[], const rpc_ v[], const void *userdata ) The product \(u = P(x) v\) of the user’s preconditioner \(P(x)\) evaluated at \(x\) with the vector v = \(v\), the result \(u\) must be retured in u, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into |
void bgo_solve_reverse_with_mat( void **data, ipc_ *status, ipc_ *eval_status, ipc_ n, rpc_ x[], rpc_ f, rpc_ g[], ipc_ ne, rpc_ H_val[], const rpc_ u[], rpc_ v[] )
Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a multistart trust-region method.
This call is for the case where \(H = \nabla_{xx}f(x)\) is provided specifically, but function/derivative information is only available by returning to the calling procedure
Parameters:
data |
holds private internal data |
status |
is a scalar variable of type ipc_, that gives the entry and exit status from the package. On initial entry, status must be set to 1. Possible exit values are:
|
eval_status |
is a scalar variable of type ipc_, that is used to indicate if objective function/gradient/Hessian values can be provided (see above) |
n |
is a scalar variable of type ipc_, that holds the number of variables |
x |
is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\). |
f |
is a scalar variable pointer of type rpc_, that holds the value of the objective function. |
g |
is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\). |
ne |
is a scalar variable of type ipc_, that holds the number of entries in the lower triangular part of the Hessian matrix \(H\). |
H_val |
is a one-dimensional array of size ne and type rpc_, that holds the values of the entries of the lower triangular part of the Hessian matrix \(H\) in any of the available storage schemes. |
u |
is a one-dimensional array of size n and type rpc_, that is used for reverse communication (see above for details) |
v |
is a one-dimensional array of size n and type rpc_, that is used for reverse communication (see above for details) |
void bgo_solve_reverse_without_mat( void **data, ipc_ *status, ipc_ *eval_status, ipc_ n, rpc_ x[], rpc_ f, rpc_ g[], rpc_ u[], rpc_ v[], ipc_ index_nz_v[], ipc_ *nnz_v, const ipc_ index_nz_u[], ipc_ nnz_u )
Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a multistart trust-region method.
This call is for the case where access to \(H = \nabla_{xx}f(x)\) is provided by Hessian-vector products, but function/derivative information is only available by returning to the calling procedure.
Parameters:
data |
holds private internal data |
status |
is a scalar variable of type ipc_, that gives the entry and exit status from the package. On initial entry, status must be set to 1. Possible exit values are:
|
eval_status |
is a scalar variable of type ipc_, that is used to indicate if objective function/gradient/Hessian values can be provided (see above) |
n |
is a scalar variable of type ipc_, that holds the number of variables |
x |
is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\). |
f |
is a scalar variable pointer of type rpc_, that holds the value of the objective function. |
g |
is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\). |
u |
is a one-dimensional array of size n and type rpc_, that is used for reverse communication (see status=5,6,7 above for details) |
v |
is a one-dimensional array of size n and type rpc_, that is used for reverse communication (see status=5,6,7 above for details) |
index_nz_v |
is a one-dimensional array of size n and type ipc_, that is used for reverse communication (see status=7 above for details) |
nnz_v |
is a scalar variable of type ipc_, that is used for reverse communication (see status=7 above for details) |
index_nz_u |
s a one-dimensional array of size n and type ipc_, that is used for reverse communication (see status=7 above for details) |
nnz_u |
is a scalar variable of type ipc_, that is used for reverse communication (see status=7 above for details). On initial (status=1) entry, nnz_u should be set to an (arbitrary) nonzero value, and nnz_u=0 is recommended |
void bgo_information(void **data, struct bgo_inform_type* inform, ipc_ *status)
Provides output information
Parameters:
data |
holds private internal data |
inform |
is a struct containing output information (see bgo_inform_type) |
status |
is a scalar variable of type ipc_, that gives the exit status from the package. Possible values are (currently):
|
void bgo_terminate( void **data, struct bgo_control_type* control, struct bgo_inform_type* inform )
Deallocate all internal private storage
Parameters:
data |
holds private internal data |
control |
is a struct containing control information (see bgo_control_type) |
inform |
is a struct containing output information (see bgo_inform_type) |
available structures#
bgo_control_type structure#
#include <galahad_bgo.h> struct bgo_control_type { // components bool f_indexing; ipc_ error; ipc_ out; ipc_ print_level; ipc_ attempts_max; ipc_ max_evals; ipc_ sampling_strategy; ipc_ hypercube_discretization; ipc_ alive_unit; char alive_file[31]; rpc_ infinity; rpc_ obj_unbounded; rpc_ cpu_time_limit; rpc_ clock_time_limit; bool random_multistart; bool hessian_available; bool space_critical; bool deallocate_error_fatal; char prefix[31]; struct ugo_control_type ugo_control; struct lhs_control_type lhs_control; struct trb_control_type trb_control; };
detailed documentation#
control derived type as a C struct
components#
bool f_indexing
use C or Fortran sparse matrix indexing
ipc_ error
error and warning diagnostics occur on stream error
ipc_ out
general output occurs on stream out
ipc_ print_level
the level of output required. Possible values are:
\(\leq\) 0 no output,
1 a one-line summary for every improvement
2 a summary of each iteration
\(\geq\) 3 increasingly verbose (debugging) output
ipc_ attempts_max
the maximum number of random searches from the best point found so far
ipc_ max_evals
the maximum number of function evaluations made
ipc_ sampling_strategy
sampling strategy used. Possible values are
1 uniformly spread
2 Latin hypercube sampling
3 niformly spread within a Latin hypercube
ipc_ hypercube_discretization
hyper-cube discretization (for sampling stategies 2 and 3)
ipc_ alive_unit
removal of the file alive_file from unit alive_unit terminates execution
char alive_file[31]
see alive_unit
rpc_ infinity
any bound larger than infinity in modulus will be regarded as infinite
rpc_ obj_unbounded
the smallest value the objective function may take before the problem is marked as unbounded
rpc_ cpu_time_limit
the maximum CPU time allowed (-ve means infinite)
rpc_ clock_time_limit
the maximum elapsed clock time allowed (-ve means infinite)
bool random_multistart
perform random-multistart as opposed to local minimize and probe
bool hessian_available
is the Hessian matrix of second derivatives available or is access only via matrix-vector products?
bool space_critical
if .space_critical true, every effort will be made to use as little space as possible. This may result in longer computation time
bool deallocate_error_fatal
if .deallocate_error_fatal is true, any array/pointer deallocation error will terminate execution. Otherwise, computation will continue
char prefix[31]
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’
struct ugo_control_type ugo_control
control parameters for UGO
struct lhs_control_type lhs_control
control parameters for LHS
struct trb_control_type trb_control
control parameters for TRB
bgo_time_type structure#
#include <galahad_bgo.h> struct bgo_time_type { // components spc_ total; spc_ univariate_global; spc_ multivariate_local; rpc_ clock_total; rpc_ clock_univariate_global; rpc_ clock_multivariate_local; };
detailed documentation#
time derived type as a C struct
components#
spc_ total
the total CPU time spent in the package
spc_ univariate_global
the CPU time spent performing univariate global optimization
spc_ multivariate_local
the CPU time spent performing multivariate local optimization
rpc_ clock_total
the total clock time spent in the package
rpc_ clock_univariate_global
the clock time spent performing univariate global optimization
rpc_ clock_multivariate_local
the clock time spent performing multivariate local optimization
bgo_inform_type structure#
#include <galahad_bgo.h> struct bgo_inform_type { // components ipc_ status; ipc_ alloc_status; char bad_alloc[81]; ipc_ f_eval; ipc_ g_eval; ipc_ h_eval; rpc_ obj; rpc_ norm_pg; struct bgo_time_type time; struct ugo_inform_type ugo_inform; struct lhs_inform_type lhs_inform; struct trb_inform_type trb_inform; };
detailed documentation#
inform derived type as a C struct
components#
ipc_ status
return status. See BGO_solve for details
ipc_ alloc_status
the status of the last attempted allocation/deallocation
char bad_alloc[81]
the name of the array for which an allocation/deallocation error occurred
ipc_ f_eval
the total number of evaluations of the objective function
ipc_ g_eval
the total number of evaluations of the gradient of the objective function
ipc_ h_eval
the total number of evaluations of the Hessian of the objective function
rpc_ obj
the value of the objective function at the best estimate of the solution determined by BGO_solve
rpc_ norm_pg
the norm of the projected gradient of the objective function at the best estimate of the solution determined by BGO_solve
struct bgo_time_type time
timings (see above)
struct ugo_inform_type ugo_inform
inform parameters for UGO
struct lhs_inform_type lhs_inform
inform parameters for LHS
struct trb_inform_type trb_inform
inform parameters for TRB
example calls#
This is an example of how to use the package to minimize a multi-dimensional objective within a box; the code is available in $GALAHAD/src/bgo/C/bgot.c . A variety of supported Hessian and constraint matrix storage formats are shown.
Notice that C-style indexing is used, and that this is flagged by setting
control.f_indexing to false. The floating-point type rpc_
is set in galahad_precision.h to double by default, but to float
if the preprocessor variable SINGLE is defined. Similarly, the integer
type ipc_ from galahad_precision.h is set to int by default,
but to int64_t if the preprocessor variable INTEGER_64 is defined.
/* bgot.c */
/* Full test for the BGO C interface using C sparse matrix indexing */
#include <stdio.h>
#include <math.h>
#include <string.h>
#include "galahad_precision.h"
#include "galahad_cfunctions.h"
#include "galahad_bgo.h"
#ifdef REAL_128
#include <quadmath.h>
#endif
// Custom userdata struct
struct userdata_type {
rpc_ p;
rpc_ freq;
rpc_ mag;
};
// Function prototypes
ipc_ fun( ipc_ n, const rpc_ x[], rpc_ *f, const void * );
ipc_ grad( ipc_ n, const rpc_ x[], rpc_ g[], const void * );
ipc_ hess( ipc_ n, ipc_ ne, const rpc_ x[], rpc_ hval[], const void * );
ipc_ hess_dense( ipc_ n, ipc_ ne, const rpc_ x[], rpc_ hval[],
const void * );
ipc_ hessprod( ipc_ n, const rpc_ x[], rpc_ u[], const rpc_ v[],
bool got_h, const void * );
ipc_ shessprod( ipc_ n, const rpc_ x[], ipc_ nnz_v, const ipc_ index_nz_v[],
const rpc_ v[], ipc_ *nnz_u, ipc_ index_nz_u[], rpc_ u[],
bool got_h, const void * );
ipc_ prec(ipc_ n, const rpc_ x[], rpc_ u[], const rpc_ v[],
const void * );
ipc_ fun_diag(ipc_ n, const rpc_ x[], rpc_ *f, const void * );
ipc_ grad_diag(ipc_ n, const rpc_ x[], rpc_ g[], const void * );
ipc_ hess_diag(ipc_ n, ipc_ ne, const rpc_ x[], rpc_ hval[],
const void * );
ipc_ hessprod_diag( ipc_ n, const rpc_ x[], rpc_ u[],
const rpc_ v[], bool got_h, const void * );
ipc_ shessprod_diag( ipc_ n, const rpc_ x[], ipc_ nnz_v,
const ipc_ index_nz_v[], const rpc_ v[], ipc_ *nnz_u,
ipc_ index_nz_u[], rpc_ u[], bool got_h, const void * );
int main(void) {
// Derived types
void *data;
struct bgo_control_type control;
struct bgo_inform_type inform;
// Set user data
struct userdata_type userdata;
userdata.p = 4.0;
userdata.freq = 10;
userdata.mag = 1000;
// Set problem data
ipc_ n = 3; // dimension
ipc_ ne = 5; // Hesssian elements
rpc_ x_l[] = {-10,-10,-10};
rpc_ x_u[] = {0.5,0.5,0.5};
ipc_ H_row[] = {0, 1, 2, 2, 2}; // Hessian H
ipc_ H_col[] = {0, 1, 0, 1, 2}; // NB lower triangle
ipc_ H_ptr[] = {0, 1, 2, 5}; // row pointers
// Set storage
rpc_ g[n]; // gradient
char st = ' ';
ipc_ status;
printf(" C sparse matrix indexing\n\n");
printf(" tests options for all-in-one storage format\n\n");
for(ipc_ d=1; d <= 5; d++){
// Initialize BGO
bgo_initialize( &data, &control, &status );
strcpy(control.trb_control.trs_control.symmetric_linear_solver,"sytr ");
strcpy(control.trb_control.trs_control.definite_linear_solver,"potr ");
strcpy(control.trb_control.psls_control.definite_linear_solver,"potr ");
// Set user-defined control options
control.f_indexing = false; // C sparse matrix indexing
control.attempts_max = 10000;
control.max_evals = 20000;
control.sampling_strategy = 3;
control.trb_control.maxit = 100;
//control.print_level = 1;
// Start from 0
rpc_ x[] = {0,0,0};
switch(d){
case 1: // sparse co-ordinate storage
st = 'C';
bgo_import( &control, &data, &status, n, x_l, x_u,
"coordinate", ne, H_row, H_col, NULL );
bgo_solve_with_mat( &data, &userdata, &status, n, x, g,
ne, fun, grad, hess, hessprod, prec );
break;
case 2: // sparse by rows
st = 'R';
bgo_import( &control, &data, &status, n, x_l, x_u,
"sparse_by_rows", ne, NULL, H_col, H_ptr );
bgo_solve_with_mat( &data, &userdata, &status, n, x, g,
ne, fun, grad, hess, hessprod, prec );
break;
case 3: // dense
st = 'D';
bgo_import( &control, &data, &status, n, x_l, x_u,
"dense", ne, NULL, NULL, NULL );
bgo_solve_with_mat( &data, &userdata, &status, n, x, g,
ne, fun, grad, hess_dense, hessprod, prec );
break;
case 4: // diagonal
st = 'I';
bgo_import( &control, &data, &status, n, x_l, x_u,
"diagonal", ne, NULL, NULL, NULL );
bgo_solve_with_mat( &data, &userdata, &status, n, x, g,
ne, fun_diag, grad_diag, hess_diag,
hessprod_diag, prec );
break;
case 5: // access by products
st = 'P';
bgo_import( &control, &data, &status, n, x_l, x_u,
"absent", ne, NULL, NULL, NULL );
bgo_solve_without_mat( &data, &userdata, &status, n, x, g,
fun, grad, hessprod, shessprod, prec );
break;
}
// Record solution information
bgo_information( &data, &inform, &status );
if(inform.status == 0){
#ifdef REAL_128
// interim replacement for quad output: $GALAHAD/include/galahad_pquad_of.h
#include "galahad_pquad_of.h"
#else
printf("%c:%6" i_ipc_ " evaluations. Optimal objective "
"value = %.2f status = %1" i_ipc_ "\n",
st, inform.f_eval, inform.obj, inform.status);
#endif
}else{
printf("%c: BGO_solve exit status = %1" i_ipc_ "\n",
st, inform.status);
}
//printf("x: ");
//for(ipc_ i = 0; i < n; i++) printf("%f ", x[i]);
//printf("\n");
//printf("gradient: ");
//for(ipc_ i = 0; i < n; i++) printf("%f ", g[i]);
//printf("\n");
// Delete internal workspace
bgo_terminate( &data, &control, &inform );
}
printf("\n tests reverse-communication options\n\n");
// reverse-communication input/output
ipc_ eval_status, nnz_u, nnz_v;
rpc_ f = 0.0;
rpc_ u[n], v[n];
ipc_ index_nz_u[n], index_nz_v[n];
rpc_ H_val[ne], H_dense[n*(n+1)/2], H_diag[n];
for(ipc_ d=1; d <= 5; d++){
// Initialize BGO
bgo_initialize( &data, &control, &status );
strcpy(control.trb_control.trs_control.symmetric_linear_solver,"sytr ");
strcpy(control.trb_control.trs_control.definite_linear_solver,"potr ");
strcpy(control.trb_control.psls_control.definite_linear_solver,"potr ");
// Set user-defined control options
control.f_indexing = false; // C sparse matrix indexing
control.attempts_max = 10000;
control.max_evals = 20000;
control.sampling_strategy = 3;
control.trb_control.maxit = 100;
//control.print_level = 1;
// Start from 0
rpc_ x[] = {0,0,0};
switch(d){
case 1: // sparse co-ordinate storage
st = 'C';
bgo_import( &control, &data, &status, n, x_l, x_u,
"coordinate", ne, H_row, H_col, NULL );
while(true){ // reverse-communication loop
bgo_solve_reverse_with_mat( &data, &status, &eval_status,
n, x, f, g, ne, H_val, u, v );
if(status == 0){ // successful termination
break;
}else if(status < 0){ // error exit
break;
}else if(status == 2){ // evaluate f
eval_status = fun( n, x, &f, &userdata );
}else if(status == 3){ // evaluate g
eval_status = grad( n, x, g, &userdata );
}else if(status == 4){ // evaluate H
eval_status = hess( n, ne, x, H_val, &userdata );
}else if(status == 5){ // evaluate Hv product
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 6){ // evaluate the product with P
eval_status = prec( n, x, u, v, &userdata );
}else if(status == 23){ // evaluate f and g
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
}else if(status == 25){ // evaluate f and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 35){ // evaluate g and Hv product
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 235){ // evaluate f, g and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else{
printf(" the value %1" i_ipc_ " of status should not occur\n",
status );
break;
}
}
break;
case 2: // sparse by rows
st = 'R';
bgo_import( &control, &data, &status, n, x_l, x_u,
"sparse_by_rows", ne, NULL, H_col, H_ptr );
while(true){ // reverse-communication loop
bgo_solve_reverse_with_mat( &data, &status, &eval_status,
n, x, f, g, ne, H_val, u, v );
if(status == 0){ // successful termination
break;
}else if(status < 0){ // error exit
break;
}else if(status == 2){ // evaluate f
eval_status = fun( n, x, &f, &userdata );
}else if(status == 3){ // evaluate g
eval_status = grad( n, x, g, &userdata );
}else if(status == 4){ // evaluate H
eval_status = hess( n, ne, x, H_val, &userdata );
}else if(status == 5){ // evaluate Hv product
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 6){ // evaluate the product with P
eval_status = prec( n, x, u, v, &userdata );
}else if(status == 23){ // evaluate f and g
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
}else if(status == 25){ // evaluate f and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 35){ // evaluate g and Hv product
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 235){ // evaluate f, g and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else{
printf(" the value %1" i_ipc_ " of status should not occur\n",
status);
break;
}
}
break;
case 3: // dense
st = 'D';
bgo_import( &control, &data, &status, n, x_l, x_u,
"dense", ne, NULL, NULL, NULL );
while(true){ // reverse-communication loop
bgo_solve_reverse_with_mat( &data, &status, &eval_status,
n, x, f, g, n*(n+1)/2,
H_dense, u, v );
if(status == 0){ // successful termination
break;
}else if(status < 0){ // error exit
break;
}else if(status == 2){ // evaluate f
eval_status = fun( n, x, &f, &userdata );
}else if(status == 3){ // evaluate g
eval_status = grad( n, x, g, &userdata );
}else if(status == 4){ // evaluate H
eval_status = hess_dense( n, n*(n+1)/2, x, H_dense,
&userdata );
}else if(status == 5){ // evaluate Hv product
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 6){ // evaluate the product with P
eval_status = prec( n, x, u, v, &userdata );
}else if(status == 23){ // evaluate f and g
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
}else if(status == 25){ // evaluate f and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 35){ // evaluate g and Hv product
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 235){ // evaluate f, g and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else{
printf(" the value %1" i_ipc_ " of status should not occur\n",
status);
break;
}
}
break;
case 4: // diagonal
st = 'I';
bgo_import( &control, &data, &status, n, x_l, x_u,
"diagonal", ne, NULL, NULL, NULL );
while(true){ // reverse-communication loop
bgo_solve_reverse_with_mat( &data, &status, &eval_status,
n, x, f, g, n, H_diag, u, v );
if(status == 0){ // successful termination
break;
}else if(status < 0){ // error exit
break;
}else if(status == 2){ // evaluate f
eval_status = fun_diag( n, x, &f, &userdata );
}else if(status == 3){ // evaluate g
eval_status = grad_diag( n, x, g, &userdata );
}else if(status == 4){ // evaluate H
eval_status = hess_diag( n, n, x, H_diag, &userdata );
}else if(status == 5){ // evaluate Hv product
eval_status = hessprod_diag( n, x, u, v, false,
&userdata );
}else if(status == 6){ // evaluate the product with P
eval_status = prec( n, x, u, v, &userdata );
}else if(status == 23){ // evaluate f and g
eval_status = fun_diag( n, x, &f, &userdata );
eval_status = grad_diag( n, x, g, &userdata );
}else if(status == 25){ // evaluate f and Hv product
eval_status = fun_diag( n, x, &f, &userdata );
eval_status = hessprod_diag( n, x, u, v, false,
&userdata );
}else if(status == 35){ // evaluate g and Hv product
eval_status = grad_diag( n, x, g, &userdata );
eval_status = hessprod_diag( n, x, u, v, false,
&userdata );
}else if(status == 235){ // evaluate f, g and Hv product
eval_status = fun_diag( n, x, &f, &userdata );
eval_status = grad_diag( n, x, g, &userdata );
eval_status = hessprod_diag( n, x, u, v, false,
&userdata );
}else{
printf(" the value %1" i_ipc_ " of status should not occur\n",
status);
break;
}
}
break;
case 5: // access by products
st = 'P';
bgo_import( &control, &data, &status, n, x_l, x_u,
"absent", ne, NULL, NULL, NULL );
nnz_u = 0;
while(true){ // reverse-communication loop
bgo_solve_reverse_without_mat( &data, &status, &eval_status,
n, x, f, g, u, v, index_nz_v,
&nnz_v, index_nz_u, nnz_u );
if(status == 0){ // successful termination
break;
}else if(status < 0){ // error exit
break;
}else if(status == 2){ // evaluate f
eval_status = fun( n, x, &f, &userdata );
}else if(status == 3){ // evaluate g
eval_status = grad( n, x, g, &userdata );
}else if(status == 5){ // evaluate Hv product
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 6){ // evaluate the product with P
eval_status = prec( n, x, u, v, &userdata );
}else if(status == 7){ // evaluate sparse Hess-vect product
eval_status = shessprod( n, x, nnz_v, index_nz_v, v,
&nnz_u, index_nz_u, u,
false, &userdata );
}else if(status == 23){ // evaluate f and g
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
}else if(status == 25){ // evaluate f and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 35){ // evaluate g and Hv product
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 235){ // evaluate f, g and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else{
printf(" the value %1" i_ipc_ " of status should not occur\n",
status);
break;
}
}
break;
}
// Record solution information
bgo_information( &data, &inform, &status );
if(inform.status == 0){
#ifdef REAL_128
// interim replacement for quad output: $GALAHAD/include/galahad_pquad_of.h
#include "galahad_pquad_of.h"
#else
printf("%c:%6" i_ipc_ " evaluations. Optimal objective "
"value = %.2f status = %1" i_ipc_ "\n",
st, inform.f_eval, inform.obj, inform.status);
#endif
}else{
printf("%c: BGO_solve exit status = %1" i_ipc_ "\n",
st, inform.status);
}
//printf("x: ");
//for(ipc_ i = 0; i < n; i++) printf("%f ", x[i]);
//printf("\n");
//printf("gradient: ");
//for(ipc_ i = 0; i < n; i++) printf("%f ", g[i]);
//printf("\n");
// Delete internal workspace
bgo_terminate( &data, &control, &inform );
}
}
// Objective function
ipc_ fun( ipc_ n,
const rpc_ x[],
rpc_ *f,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ p = myuserdata->p;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
*f = pow(x[0] + x[2] + p, 2) + pow(x[1] + x[2], 2) + mag * cos(freq*x[0])
+ x[0] + x[1] + x[2];
return 0;
}
// Gradient of the objective
ipc_ grad( ipc_ n,
const rpc_ x[],
rpc_ g[],
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ p = myuserdata->p;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
g[0] = 2.0 * ( x[0] + x[2] + p ) - mag * freq * sin(freq*x[0]) + 1;
g[1] = 2.0 * ( x[1] + x[2] ) + 1;
g[2] = 2.0 * ( x[0] + x[2] + p ) + 2.0 * ( x[1] + x[2] ) + 1;
return 0;
}
// Hessian of the objective
ipc_ hess( ipc_ n,
ipc_ ne,
const rpc_ x[],
rpc_ hval[],
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
hval[0] = 2.0 - mag * freq * freq * cos(freq*x[0]);
hval[1] = 2.0;
hval[2] = 2.0;
hval[3] = 2.0;
hval[4] = 4.0;
return 0;
}
// Dense Hessian
ipc_ hess_dense( ipc_ n,
ipc_ ne,
const rpc_ x[],
rpc_ hval[],
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
hval[0] = 2.0 - mag * freq * freq * cos(freq*x[0]);
hval[1] = 0.0;
hval[2] = 2.0;
hval[3] = 2.0;
hval[4] = 2.0;
hval[5] = 4.0;
return 0;
}
// Hessian-vector product
ipc_ hessprod( ipc_ n,
const rpc_ x[],
rpc_ u[],
const rpc_ v[],
bool got_h,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
u[0] = u[0] + 2.0 * ( v[0] + v[2] )
- mag * freq * freq * cos(freq*x[0]) * v[0];
u[1] = u[1] + 2.0 * ( v[1] + v[2] );
u[2] = u[2] + 2.0 * ( v[0] + v[1] + 2.0 * v[2] );
return 0;
}
// Sparse Hessian-vector product
ipc_ shessprod( ipc_ n,
const rpc_ x[],
ipc_ nnz_v,
const ipc_ index_nz_v[],
const rpc_ v[],
ipc_ *nnz_u,
ipc_ index_nz_u[],
rpc_ u[],
bool got_h,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
rpc_ p[] = {0., 0., 0.};
bool used[] = {false, false, false};
for(ipc_ i = 0; i < nnz_v; i++){
ipc_ j = index_nz_v[i];
switch(j){
case 0:
p[0] = p[0] + 2.0 * v[0] - mag * freq * freq * cos(freq*x[0]) * v[0];
used[0] = true;
p[2] = p[2] + 2.0 * v[0];
used[2] = true;
break;
case 1:
p[1] = p[1] + 2.0 * v[1];
used[1] = true;
p[2] = p[2] + 2.0 * v[1];
used[2] = true;
break;
case 2:
p[0] = p[0] + 2.0 * v[2];
used[0] = true;
p[1] = p[1] + 2.0 * v[2];
used[1] = true;
p[2] = p[2] + 4.0 * v[2];
used[2] = true;
break;
}
}
*nnz_u = 0;
for(ipc_ j = 0; j < 3; j++){
if(used[j]){
u[j] = p[j];
*nnz_u = *nnz_u + 1;
index_nz_u[*nnz_u-1] = j;
}
}
return 0;
}
// Apply preconditioner
ipc_ prec( ipc_ n,
const rpc_ x[],
rpc_ u[],
const rpc_ v[],
const void *userdata ){
u[0] = 0.5 * v[0];
u[1] = 0.5 * v[1];
u[2] = 0.25 * v[2];
return 0;
}
// Objective function
ipc_ fun_diag( ipc_ n,
const rpc_ x[],
rpc_ *f,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ p = myuserdata->p;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
*f = pow(x[2] + p, 2) + pow(x[1], 2) + mag * cos(freq*x[0])
+ x[0] + x[1] + x[2];
return 0;
}
// Gradient of the objective
ipc_ grad_diag( ipc_ n,
const rpc_ x[],
rpc_ g[],
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ p = myuserdata->p;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
g[0] = -mag * freq * sin(freq*x[0]) + 1;
g[1] = 2.0 * x[1] + 1;
g[2] = 2.0 * ( x[2] + p ) + 1;
return 0;
}
// Hessian of the objective
ipc_ hess_diag( ipc_ n,
ipc_ ne,
const rpc_ x[],
rpc_ hval[],
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
hval[0] = -mag * freq * freq * cos(freq*x[0]);
hval[1] = 2.0;
hval[2] = 2.0;
return 0;
}
// Hessian-vector product
ipc_ hessprod_diag( ipc_ n,
const rpc_ x[],
rpc_ u[],
const rpc_ v[],
bool got_h,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
u[0] = u[0] + -mag * freq * freq * cos(freq*x[0]) * v[0];
u[1] = u[1] + 2.0 * v[1];
u[2] = u[2] + 2.0 * v[2];
return 0;
}
// Sparse Hessian-vector product
ipc_ shessprod_diag( ipc_ n,
const rpc_ x[],
ipc_ nnz_v,
const ipc_ index_nz_v[],
const rpc_ v[],
ipc_ *nnz_u,
ipc_ index_nz_u[],
rpc_ u[],
bool got_h,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
rpc_ p[] = {0., 0., 0.};
bool used[] = {false, false, false};
for(ipc_ i = 0; i < nnz_v; i++){
ipc_ j = index_nz_v[i];
switch(j){
case 0:
p[0] = p[0] - mag * freq * freq * cos(freq*x[0]) * v[0];
used[0] = true;
break;
case 1:
p[1] = p[1] + 2.0 * v[1];
used[1] = true;
break;
case 2:
p[2] = p[2] + 2.0 * v[2];
used[2] = true;
break;
}
}
*nnz_u = 0;
for(ipc_ j = 0; j < 3; j++){
if(used[j]){
u[j] = p[j];
*nnz_u = *nnz_u + 1;
index_nz_u[*nnz_u-1] = j;
}
}
return 0;
}
This is the same example, but now fortran-style indexing is used; the code is available in $GALAHAD/src/bgo/C/bgotf.c .
/* bgotf.c */
/* Full test for the BGO C interface using Fortran sparse matrix indexing */
#include <stdio.h>
#include <math.h>
#include <string.h>
#include "galahad_precision.h"
#include "galahad_cfunctions.h"
#include "galahad_bgo.h"
#ifdef REAL_128
#include <quadmath.h>
#endif
// Custom userdata struct
struct userdata_type {
rpc_ p;
rpc_ freq;
rpc_ mag;
};
// Function prototypes
ipc_ fun( ipc_ n, const rpc_ x[], rpc_ *f, const void * );
ipc_ grad( ipc_ n, const rpc_ x[], rpc_ g[], const void * );
ipc_ hess( ipc_ n, ipc_ ne, const rpc_ x[], rpc_ hval[], const void * );
ipc_ hess_dense( ipc_ n, ipc_ ne, const rpc_ x[], rpc_ hval[],
const void * );
ipc_ hessprod( ipc_ n, const rpc_ x[], rpc_ u[], const rpc_ v[],
bool got_h, const void * );
ipc_ shessprod( ipc_ n, const rpc_ x[], ipc_ nnz_v, const ipc_ index_nz_v[],
const rpc_ v[], ipc_ *nnz_u, ipc_ index_nz_u[], rpc_ u[],
bool got_h, const void * );
ipc_ prec( ipc_ n, const rpc_ x[], rpc_ u[], const rpc_ v[],
const void * );
ipc_ fun_diag( ipc_ n, const rpc_ x[], rpc_ *f, const void * );
ipc_ grad_diag( ipc_ n, const rpc_ x[], rpc_ g[], const void * );
ipc_ hess_diag( ipc_ n, ipc_ ne, const rpc_ x[], rpc_ hval[],
const void * );
ipc_ hessprod_diag( ipc_ n, const rpc_ x[], rpc_ u[],
const rpc_ v[], bool got_h, const void * );
ipc_ shessprod_diag( ipc_ n, const rpc_ x[], ipc_ nnz_v,
const ipc_ index_nz_v[],
const rpc_ v[], ipc_ *nnz_u, ipc_ index_nz_u[],
rpc_ u[], bool got_h, const void * );
int main(void) {
// Derived types
void *data;
struct bgo_control_type control;
struct bgo_inform_type inform;
// Set user data
struct userdata_type userdata;
userdata.p = 4.0;
userdata.freq = 10;
userdata.mag = 1000;
// Set problem data
ipc_ n = 3; // dimension
ipc_ ne = 5; // Hesssian elements
rpc_ x_l[] = {-10,-10,-10};
rpc_ x_u[] = {0.5,0.5,0.5};
ipc_ H_row[] = {1, 2, 3, 3, 3}; // Hessian H
ipc_ H_col[] = {1, 2, 1, 2, 3}; // NB lower triangle
ipc_ H_ptr[] = {1, 2, 3, 6}; // row pointers
// Set storage
rpc_ g[n]; // gradient
char st = ' ';
ipc_ status;
printf(" Fortran sparse matrix indexing\n\n");
printf(" tests options for all-in-one storage format\n\n");
for(ipc_ d=1; d <= 5; d++){
// Initialize BGO
bgo_initialize( &data, &control, &status );
strcpy(control.trb_control.trs_control.symmetric_linear_solver,"sytr ");
strcpy(control.trb_control.trs_control.definite_linear_solver,"potr ");
strcpy(control.trb_control.psls_control.definite_linear_solver,"potr ");
// Set user-defined control options
control.f_indexing = true; // Fortran sparse matrix indexing
control.attempts_max = 10000;
control.max_evals = 20000;
control.sampling_strategy = 3;
control.trb_control.maxit = 100;
//control.print_level = 1;
// Start from 0
rpc_ x[] = {0,0,0};
switch(d){
case 1: // sparse co-ordinate storage
st = 'C';
bgo_import( &control, &data, &status, n, x_l, x_u,
"coordinate", ne, H_row, H_col, NULL );
bgo_solve_with_mat( &data, &userdata, &status, n, x, g,
ne, fun, grad, hess, hessprod, prec );
break;
case 2: // sparse by rows
st = 'R';
bgo_import( &control, &data, &status, n, x_l, x_u,
"sparse_by_rows", ne, NULL, H_col, H_ptr );
bgo_solve_with_mat( &data, &userdata, &status, n, x, g,
ne, fun, grad, hess, hessprod, prec );
break;
case 3: // dense
st = 'D';
bgo_import( &control, &data, &status, n, x_l, x_u,
"dense", ne, NULL, NULL, NULL );
bgo_solve_with_mat( &data, &userdata, &status, n, x, g,
ne, fun, grad, hess_dense, hessprod, prec );
break;
case 4: // diagonal
st = 'I';
bgo_import( &control, &data, &status, n, x_l, x_u,
"diagonal", ne, NULL, NULL, NULL );
bgo_solve_with_mat( &data, &userdata, &status, n, x, g,
ne, fun_diag, grad_diag, hess_diag,
hessprod_diag, prec );
break;
case 5: // access by products
st = 'P';
bgo_import( &control, &data, &status, n, x_l, x_u,
"absent", ne, NULL, NULL, NULL );
bgo_solve_without_mat( &data, &userdata, &status, n, x, g,
fun, grad, hessprod, shessprod, prec );
break;
}
// Record solution information
bgo_information( &data, &inform, &status );
if(inform.status == 0){
#ifdef REAL_128
// interim replacement for quad output: $GALAHAD/include/galahad_pquad_of.h
#include "galahad_pquad_of.h"
#else
printf("%c:%6" i_ipc_ " evaluations. Optimal objective "
"value = %.2f status = %1" i_ipc_ "\n",
st, inform.f_eval, inform.obj, inform.status);
#endif
}else{
printf("%c: BGO_solve exit status = %1" i_ipc_ "\n",
st, inform.status);
}
//printf("x: ");
//for(ipc_ i = 0; i < n; i++) printf("%f ", x[i]);
//printf("\n");
//printf("gradient: ");
//for(ipc_ i = 0; i < n; i++) printf("%f ", g[i]);
//printf("\n");
// Delete internal workspace
bgo_terminate( &data, &control, &inform );
}
printf("\n tests reverse-communication options\n\n");
// reverse-communication input/output
ipc_ eval_status, nnz_u, nnz_v;
rpc_ f = 0.0;
rpc_ u[n], v[n];
ipc_ index_nz_u[n], index_nz_v[n];
rpc_ H_val[ne], H_dense[n*(n+1)/2], H_diag[n];
for(ipc_ d=1; d <= 5; d++){
// Initialize BGO
bgo_initialize( &data, &control, &status );
strcpy(control.trb_control.trs_control.symmetric_linear_solver,"sytr ");
strcpy(control.trb_control.trs_control.definite_linear_solver,"potr ");
strcpy(control.trb_control.psls_control.definite_linear_solver,"potr ");
// Set user-defined control options
control.f_indexing = true; // Fortran sparse matrix indexing
control.attempts_max = 10000;
control.max_evals = 20000;
control.sampling_strategy = 3;
control.trb_control.maxit = 100;
//control.print_level = 1;
// Start from 0
rpc_ x[] = {0,0,0};
switch(d){
case 1: // sparse co-ordinate storage
st = 'C';
bgo_import( &control, &data, &status, n, x_l, x_u,
"coordinate", ne, H_row, H_col, NULL );
while(true){ // reverse-communication loop
bgo_solve_reverse_with_mat( &data, &status, &eval_status,
n, x, f, g, ne, H_val, u, v );
if(status == 0){ // successful termination
break;
}else if(status < 0){ // error exit
break;
}else if(status == 2){ // evaluate f
eval_status = fun( n, x, &f, &userdata );
}else if(status == 3){ // evaluate g
eval_status = grad( n, x, g, &userdata );
}else if(status == 4){ // evaluate H
eval_status = hess( n, ne, x, H_val, &userdata );
}else if(status == 5){ // evaluate Hv product
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 6){ // evaluate the product with P
eval_status = prec( n, x, u, v, &userdata );
}else if(status == 23){ // evaluate f and g
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
}else if(status == 25){ // evaluate f and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 35){ // evaluate g and Hv product
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 235){ // evaluate f, g and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else{
printf(" the value %1" i_ipc_ " of status should not occur\n",
status );
break;
}
}
break;
case 2: // sparse by rows
st = 'R';
bgo_import( &control, &data, &status, n, x_l, x_u,
"sparse_by_rows", ne, NULL, H_col, H_ptr );
while(true){ // reverse-communication loop
bgo_solve_reverse_with_mat( &data, &status, &eval_status,
n, x, f, g, ne, H_val, u, v );
if(status == 0){ // successful termination
break;
}else if(status < 0){ // error exit
break;
}else if(status == 2){ // evaluate f
eval_status = fun( n, x, &f, &userdata );
}else if(status == 3){ // evaluate g
eval_status = grad( n, x, g, &userdata );
}else if(status == 4){ // evaluate H
eval_status = hess( n, ne, x, H_val, &userdata );
}else if(status == 5){ // evaluate Hv product
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 6){ // evaluate the product with P
eval_status = prec( n, x, u, v, &userdata );
}else if(status == 23){ // evaluate f and g
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
}else if(status == 25){ // evaluate f and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 35){ // evaluate g and Hv product
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 235){ // evaluate f, g and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else{
printf(" the value %1" i_ipc_ " of status should not occur\n",
status);
break;
}
}
break;
case 3: // dense
st = 'D';
bgo_import( &control, &data, &status, n, x_l, x_u,
"dense", ne, NULL, NULL, NULL );
while(true){ // reverse-communication loop
bgo_solve_reverse_with_mat( &data, &status, &eval_status,
n, x, f, g, n*(n+1)/2,
H_dense, u, v );
if(status == 0){ // successful termination
break;
}else if(status < 0){ // error exit
break;
}else if(status == 2){ // evaluate f
eval_status = fun( n, x, &f, &userdata );
}else if(status == 3){ // evaluate g
eval_status = grad( n, x, g, &userdata );
}else if(status == 4){ // evaluate H
eval_status = hess_dense( n, n*(n+1)/2, x, H_dense,
&userdata );
}else if(status == 5){ // evaluate Hv product
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 6){ // evaluate the product with P
eval_status = prec( n, x, u, v, &userdata );
}else if(status == 23){ // evaluate f and g
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
}else if(status == 25){ // evaluate f and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 35){ // evaluate g and Hv product
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 235){ // evaluate f, g and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else{
printf(" the value %1" i_ipc_ " of status should not occur\n",
status);
break;
}
}
break;
case 4: // diagonal
st = 'I';
bgo_import( &control, &data, &status, n, x_l, x_u,
"diagonal", ne, NULL, NULL, NULL );
while(true){ // reverse-communication loop
bgo_solve_reverse_with_mat( &data, &status, &eval_status,
n, x, f, g, n, H_diag, u, v );
if(status == 0){ // successful termination
break;
}else if(status < 0){ // error exit
break;
}else if(status == 2){ // evaluate f
eval_status = fun_diag( n, x, &f, &userdata );
}else if(status == 3){ // evaluate g
eval_status = grad_diag( n, x, g, &userdata );
}else if(status == 4){ // evaluate H
eval_status = hess_diag( n, n, x, H_diag, &userdata );
}else if(status == 5){ // evaluate Hv product
eval_status = hessprod_diag( n, x, u, v, false,
&userdata );
}else if(status == 6){ // evaluate the product with P
eval_status = prec( n, x, u, v, &userdata );
}else if(status == 23){ // evaluate f and g
eval_status = fun_diag( n, x, &f, &userdata );
eval_status = grad_diag( n, x, g, &userdata );
}else if(status == 25){ // evaluate f and Hv product
eval_status = fun_diag( n, x, &f, &userdata );
eval_status = hessprod_diag( n, x, u, v, false,
&userdata );
}else if(status == 35){ // evaluate g and Hv product
eval_status = grad_diag( n, x, g, &userdata );
eval_status = hessprod_diag( n, x, u, v, false,
&userdata );
}else if(status == 235){ // evaluate f, g and Hv product
eval_status = fun_diag( n, x, &f, &userdata );
eval_status = grad_diag( n, x, g, &userdata );
eval_status = hessprod_diag( n, x, u, v, false,
&userdata );
}else{
printf(" the value %1" i_ipc_ " of status should not occur\n",
status);
break;
}
}
break;
case 5: // access by products
st = 'P';
bgo_import( &control, &data, &status, n, x_l, x_u,
"absent", ne, NULL, NULL, NULL );
nnz_u = 0;
while(true){ // reverse-communication loop
bgo_solve_reverse_without_mat( &data, &status, &eval_status,
n, x, f, g, u, v, index_nz_v,
&nnz_v, index_nz_u, nnz_u );
if(status == 0){ // successful termination
break;
}else if(status < 0){ // error exit
break;
}else if(status == 2){ // evaluate f
eval_status = fun( n, x, &f, &userdata );
}else if(status == 3){ // evaluate g
eval_status = grad( n, x, g, &userdata );
}else if(status == 5){ // evaluate Hv product
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 6){ // evaluate the product with P
eval_status = prec( n, x, u, v, &userdata );
}else if(status == 7){ // evaluate sparse Hess-vect product
eval_status = shessprod( n, x, nnz_v, index_nz_v, v,
&nnz_u, index_nz_u, u,
false, &userdata );
}else if(status == 23){ // evaluate f and g
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
}else if(status == 25){ // evaluate f and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 35){ // evaluate g and Hv product
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else if(status == 235){ // evaluate f, g and Hv product
eval_status = fun( n, x, &f, &userdata );
eval_status = grad( n, x, g, &userdata );
eval_status = hessprod( n, x, u, v, false, &userdata );
}else{
printf(" the value %1" i_ipc_ " of status should not occur\n",
status);
break;
}
}
break;
}
// Record solution information
bgo_information( &data, &inform, &status );
if(inform.status == 0){
#ifdef REAL_128
// interim replacement for quad output: $GALAHAD/include/galahad_pquad_of.h
#include "galahad_pquad_of.h"
#else
printf("%c:%6" i_ipc_ " evaluations. Optimal objective "
"value = %.2f status = %1" i_ipc_ "\n",
st, inform.f_eval, inform.obj, inform.status);
#endif
}else{
printf("%c: BGO_solve exit status = %1" i_ipc_ "\n",
st, inform.status);
}
//printf("x: ");
//for(ipc_ i = 0; i < n; i++) printf("%f ", x[i]);
//printf("\n");
//printf("gradient: ");
//for(ipc_ i = 0; i < n; i++) printf("%f ", g[i]);
//printf("\n");
// Delete internal workspace
bgo_terminate( &data, &control, &inform );
}
}
// Objective function
ipc_ fun( ipc_ n,
const rpc_ x[],
rpc_ *f,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ p = myuserdata->p;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
*f = pow(x[0] + x[2] + p, 2) + pow(x[1] + x[2], 2) + mag * cos(freq*x[0])
+ x[0] + x[1] + x[2];
return 0;
}
// Gradient of the objective
ipc_ grad( ipc_ n,
const rpc_ x[],
rpc_ g[],
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ p = myuserdata->p;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
g[0] = 2.0 * ( x[0] + x[2] + p ) - mag * freq * sin(freq*x[0]) + 1;
g[1] = 2.0 * ( x[1] + x[2] ) + 1;
g[2] = 2.0 * ( x[0] + x[2] + p ) + 2.0 * ( x[1] + x[2] ) + 1;
return 0;
}
// Hessian of the objective
ipc_ hess( ipc_ n,
ipc_ ne,
const rpc_ x[],
rpc_ hval[],
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
hval[0] = 2.0 - mag * freq * freq * cos(freq*x[0]);
hval[1] = 2.0;
hval[2] = 2.0;
hval[3] = 2.0;
hval[4] = 4.0;
return 0;
}
// Dense Hessian
ipc_ hess_dense( ipc_ n,
ipc_ ne,
const rpc_ x[],
rpc_ hval[],
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
hval[0] = 2.0 - mag * freq * freq * cos(freq*x[0]);
hval[1] = 0.0;
hval[2] = 2.0;
hval[3] = 2.0;
hval[4] = 2.0;
hval[5] = 4.0;
return 0;
}
// Hessian-vector product
ipc_ hessprod( ipc_ n,
const rpc_ x[],
rpc_ u[],
const rpc_ v[],
bool got_h,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
u[0] = u[0] + 2.0 * ( v[0] + v[2] )
- mag * freq * freq * cos(freq*x[0]) * v[0];
u[1] = u[1] + 2.0 * ( v[1] + v[2] );
u[2] = u[2] + 2.0 * ( v[0] + v[1] + 2.0 * v[2] );
return 0;
}
// Sparse Hessian-vector product
ipc_ shessprod( ipc_ n,
const rpc_ x[],
ipc_ nnz_v,
const ipc_ index_nz_v[],
const rpc_ v[],
ipc_ *nnz_u,
ipc_ index_nz_u[],
rpc_ u[],
bool got_h,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
rpc_ p[] = {0., 0., 0.};
bool used[] = {false, false, false};
for(ipc_ i = 0; i < nnz_v; i++){
ipc_ j = index_nz_v[i];
switch(j){
case 1:
p[0] = p[0] + 2.0 * v[0]
- mag * freq * freq * cos(freq*x[0]) * v[0];
used[0] = true;
p[2] = p[2] + 2.0 * v[0];
used[2] = true;
break;
case 2:
p[1] = p[1] + 2.0 * v[1];
used[1] = true;
p[2] = p[2] + 2.0 * v[1];
used[2] = true;
break;
case 3:
p[0] = p[0] + 2.0 * v[2];
used[0] = true;
p[1] = p[1] + 2.0 * v[2];
used[1] = true;
p[2] = p[2] + 4.0 * v[2];
used[2] = true;
break;
}
}
*nnz_u = 0;
for(ipc_ j = 0; j < 3; j++){
if(used[j]){
u[j] = p[j];
*nnz_u = *nnz_u + 1;
index_nz_u[*nnz_u-1] = j+1;
}
}
return 0;
}
// Apply preconditioner
ipc_ prec( ipc_ n,
const rpc_ x[],
rpc_ u[],
const rpc_ v[],
const void *userdata ){
u[0] = 0.5 * v[0];
u[1] = 0.5 * v[1];
u[2] = 0.25 * v[2];
return 0;
}
// Objective function
ipc_ fun_diag( ipc_ n,
const rpc_ x[],
rpc_ *f,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ p = myuserdata->p;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
*f = pow(x[2] + p, 2) + pow(x[1], 2) + mag * cos(freq*x[0])
+ x[0] + x[1] + x[2];
return 0;
}
// Gradient of the objective
ipc_ grad_diag( ipc_ n,
const rpc_ x[],
rpc_ g[],
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ p = myuserdata->p;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
g[0] = -mag * freq * sin(freq*x[0]) + 1;
g[1] = 2.0 * x[1] + 1;
g[2] = 2.0 * ( x[2] + p ) + 1;
return 0;
}
// Hessian of the objective
ipc_ hess_diag( ipc_ n,
ipc_ ne,
const rpc_ x[],
rpc_ hval[],
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
hval[0] = -mag * freq * freq * cos(freq*x[0]);
hval[1] = 2.0;
hval[2] = 2.0;
return 0;
}
// Hessian-vector product
ipc_ hessprod_diag( ipc_ n,
const rpc_ x[],
rpc_ u[],
const rpc_ v[],
bool got_h,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
u[0] = u[0] + -mag * freq * freq * cos(freq*x[0]) * v[0];
u[1] = u[1] + 2.0 * v[1];
u[2] = u[2] + 2.0 * v[2];
return 0;
}
// Sparse Hessian-vector product
ipc_ shessprod_diag( ipc_ n,
const rpc_ x[],
ipc_ nnz_v,
const ipc_ index_nz_v[],
const rpc_ v[],
ipc_ *nnz_u,
ipc_ index_nz_u[],
rpc_ u[],
bool got_h,
const void *userdata ){
struct userdata_type *myuserdata = (struct userdata_type *) userdata;
rpc_ freq = myuserdata->freq;
rpc_ mag = myuserdata->mag;
rpc_ p[] = {0., 0., 0.};
bool used[] = {false, false, false};
for(ipc_ i = 0; i < nnz_v; i++){
ipc_ j = index_nz_v[i];
switch(j){
case 1:
p[0] = p[0] - mag * freq * freq * cos(freq*x[0]) * v[0];
used[0] = true;
break;
case 2:
p[1] = p[1] + 2.0 * v[1];
used[1] = true;
break;
case 3:
p[2] = p[2] + 2.0 * v[2];
used[2] = true;
break;
}
}
*nnz_u = 0;
for(ipc_ j = 0; j < 3; j++){
if(used[j]){
u[j] = p[j];
*nnz_u = *nnz_u + 1;
index_nz_u[*nnz_u-1] = j+1;
}
}
return 0;
}