ドキュメントはあまり用意されていない模様。 関数の仕様についてはコード内のコメントが充実している。

Getting start 

• ライブラリは順に依存していくので生成された*.aファイルは/usr/libあたりにln -sする

• gfortranをインストール

  • http://gcc.gnu.org/wiki/GFortranBinaries#MacOS

  • brewのが手軽で良いかも

• blasをmake -> blas_LINUX.a

  • http://www.netlib.org/blas/blas.tgz

• lapackをmake -> lapack_LINUX.a

  • http://www.netlib.org/lapack/lapack-3.3.1.tgz

• libf2cをmake -> libf2c.a

  • http://www.netlib.org/f2c/libf2c.zip

• levmarをmake -> liblevmar.a

  • http://www.ics.forth.gr/~lourakis/levmar/levmar-2.5.tgz

• 2021/11追記

  • それぞれ新しいverが出ているので必要に応じて差し替える。特にlapackは古いコードと新しいgccの相性の問題があるので差し替え推奨。

  • リンカオプションに-lgfortranが必要なことが多い。

  • gccはXCodeのを使うと何かとうまく行かないのでgfortranについてきたgccを使う。

↑

Example 

• サンプルコード

  • 3点の2次元データを線形近似

  • g++ main.cpp -llevmar -llapack -lblas -lgfortran

#include <stdio.h>

#include <stdlib.h>

#include <levmar.h>

void func(double *p, double *hx, int m, int n, void *adata);

int main()

{

       double*     p;          p = (double*)malloc(2*sizeof(double));  p[0]=0.0; p[1]=0.0;

       double*     x;          x = NULL;

       int         m;          m = 2;          //num of parameter

       int         n;          n = 3;          //num of equation

       int         itmax;      itmax = 300;    //iteration max

       double*     opts;       opts = NULL;

       double*     info;       info = NULL;

       double*     work;       work = NULL;

       double*     covar;      covar = NULL;

       void*       adata;      adata = NULL;

       dlevmar_dif(func, p, x, m, n, itmax, opts, info, work, covar, adata);

       printf("x = %f\ny = %f\n", p[0], p[1]);

       return 0;

}

void func(double *p, double *hx, int m, int n, void *adata)     //p:parameter vector, hx:objective function vector

{

       double  datax[3] = {1.0, 2.0, 3.0};

       double  datay[3] = {5.0, 8.0, 11.0};

       hx[0] = (-datay[0] + p[0] * datax[0] + p[1]) * (-datay[0] + p[0] * datax[0] + p[1]);

       hx[1] = (-datay[1] + p[0] * datax[1] + p[1]) * (-datay[1] + p[0] * datax[1] + p[1]);

       hx[2] = (-datay[2] + p[0] * datax[2] + p[1]) * (-datay[2] + p[0] * datax[2] + p[1]);

       return;

}

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xlevmar_bc_dif 

バウンダリの制約をかける。p[i]の値の範囲の下限がlb[i]、上限がub[i]に設定される。

/* No Jacobian version of the LEVMAR_BC_DER() function above: the Jacobian is approximated with 

* the aid of finite differences (forward or central, see the comment for the opts argument)

* Ideally, this function should be implemented with a secant approach. Currently, it just calls

* LEVMAR_BC_DER()

*/

int LEVMAR_BC_DIF(

 void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata), /* functional relation describing measurements. A p \in R^m yields a \hat{x} \in  R^n */

 LM_REAL *p,         /* I/O: initial parameter estimates. On output has the estimated solution */

 LM_REAL *x,         /* I: measurement vector. NULL implies a zero vector */

 int m,              /* I: parameter vector dimension (i.e. #unknowns) */

 int n,              /* I: measurement vector dimension */

 LM_REAL *lb,        /* I: vector of lower bounds. If NULL, no lower bounds apply */

 LM_REAL *ub,        /* I: vector of upper bounds. If NULL, no upper bounds apply */

 int itmax,          /* I: maximum number of iterations */

 LM_REAL opts[5],    /* I: opts[0-4] = minim. options [\mu, \epsilon1, \epsilon2, \epsilon3, \delta]. Respectively the

                      * scale factor for initial \mu, stopping thresholds for ||J^T e||_inf, ||Dp||_2 and ||e||_2 and

                      * the step used in difference approximation to the Jacobian. Set to NULL for defaults to be used.

                      * If \delta<0, the Jacobian is approximated with central differences which are more accurate

                      * (but slower!) compared to the forward differences employed by default. 

                      */

 LM_REAL info[LM_INFO_SZ],

                     /* O: information regarding the minimization. Set to NULL if don't care

                     * info[0]= ||e||_2 at initial p.

                     * info[1-4]=[ ||e||_2, ||J^T e||_inf,  ||Dp||_2, mu/max[J^T J]_ii ], all computed at estimated p.

                     * info[5]= # iterations,

                     * info[6]=reason for terminating: 1 - stopped by small gradient J^T e

                     *                                 2 - stopped by small Dp

                     *                                 3 - stopped by itmax

                     *                                 4 - singular matrix. Restart from current p with increased mu 

                     *                                 5 - no further error reduction is possible. Restart with increased mu

                     *                                 6 - stopped by small ||e||_2

                     *                                 7 - stopped by invalid (i.e. NaN or Inf) "func" values. This is a user error

                     * info[7]= # function evaluations

                     * info[8]= # Jacobian evaluations

                     * info[9]= # linear systems solved, i.e. # attempts for reducing error

                     */

 LM_REAL *work,     /* working memory at least LM_BC_DIF_WORKSZ() reals large, allocated if NULL */

 LM_REAL *covar,    /* O: Covariance matrix corresponding to LS solution; mxm. Set to NULL if not needed. */

 void *adata)       /* pointer to possibly additional data, passed uninterpreted to func.

                     * Set to NULL if not needed

                     */