GORegressionFunction ()

GORegressionResult
(*GORegressionFunction) (double *x,
                         double *params,
                         double *f);

GORegressionFunctionl ()

GORegressionResult
(*GORegressionFunctionl) (long double *x,
                          long double *params,
                          long double *f);

GORegressionFunctionD ()

GORegressionResult
(*GORegressionFunctionD) (_Decimal64 *x,
                          _Decimal64 *params,
                          _Decimal64 *f);

go_exponential_regression ()

GORegressionResult
go_exponential_regression (double **xss,
                           int dim,
                           const double *ys,
                           int n,
                           gboolean affine,
                           double *res,
                           go_regression_stat_t *stat_);

Performs one-dimensional linear regressions on the input points. Fits to "y = b * m1^x1 * ... * md^xd " or equivalently to "log y = log b + x1 * log m1 + ... + xd * log md".

go_exponential_regressionl ()

GORegressionResult
go_exponential_regressionl (long double **xss,
                            int dim,
                            const long double *ys,
                            int n,
                            gboolean affine,
                            long double *res,
                            go_regression_stat_tl *stat_);

Performs one-dimensional linear regressions on the input points. Fits to "y = b * m1^x1 * ... * md^xd " or equivalently to "log y = log b + x1 * log m1 + ... + xd * log md".

go_exponential_regressionD ()

GORegressionResult
go_exponential_regressionD (_Decimal64 **xss,
                            int dim,
                            const _Decimal64 *ys,
                            int n,
                            gboolean affine,
                            _Decimal64 *res,
                            go_regression_stat_tD *stat_);

Performs one-dimensional linear regressions on the input points. Fits to "y = b * m1^x1 * ... * md^xd " or equivalently to "log y = log b + x1 * log m1 + ... + xd * log md".

go_exponential_regression_as_log ()

GORegressionResult
go_exponential_regression_as_log (double **xss,
                                  int dim,
                                  const double *ys,
                                  int n,
                                  gboolean affine,
                                  double *res,
                                  go_regression_stat_t *stat_);

Performs one-dimensional linear regressions on the input points as go_exponential_regression, but returns the logarithm of the coefficients instead or the coefficients themselves. Fits to "y = b * exp (m1*x1) * ... * exp (md*xd) " or equivalently to "ln y = ln b + x1 * m1 + ... + xd * md".

go_exponential_regression_as_logl ()

GORegressionResult
go_exponential_regression_as_logl (long double **xss,
                                   int dim,
                                   const long double *ys,
                                   int n,
                                   gboolean affine,
                                   long double *res,
                                   go_regression_stat_tl *stat_);

Performs one-dimensional linear regressions on the input points as go_exponential_regression, but returns the logarithm of the coefficients instead or the coefficients themselves. Fits to "y = b * exp (m1*x1) * ... * exp (md*xd) " or equivalently to "ln y = ln b + x1 * m1 + ... + xd * md".

go_exponential_regression_as_logD ()

GORegressionResult
go_exponential_regression_as_logD (_Decimal64 **xss,
                                   int dim,
                                   const _Decimal64 *ys,
                                   int n,
                                   gboolean affine,
                                   _Decimal64 *res,
                                   go_regression_stat_tD *stat_);

Performs one-dimensional linear regressions on the input points as go_exponential_regression, but returns the logarithm of the coefficients instead or the coefficients themselves. Fits to "y = b * exp (m1*x1) * ... * exp (md*xd) " or equivalently to "ln y = ln b + x1 * m1 + ... + xd * md".

go_linear_regression ()

GORegressionResult
go_linear_regression (double **xss,
                      int dim,
                      const double *ys,
                      int n,
                      gboolean affine,
                      double *res,
                      go_regression_stat_t *stat_);

Performs multi-dimensional linear regressions on the input points. Fits to "y = b + a1 * x1 + ... ad * xd".

go_linear_regressionl ()

GORegressionResult
go_linear_regressionl (long double **xss,
                       int dim,
                       const long double *ys,
                       int n,
                       gboolean affine,
                       long double *res,
                       go_regression_stat_tl *stat_);

Performs multi-dimensional linear regressions on the input points. Fits to "y = b + a1 * x1 + ... ad * xd".

go_linear_regressionD ()

GORegressionResult
go_linear_regressionD (_Decimal64 **xss,
                       int dim,
                       const _Decimal64 *ys,
                       int n,
                       gboolean affine,
                       _Decimal64 *res,
                       go_regression_stat_tD *stat_);

Performs multi-dimensional linear regressions on the input points. Fits to "y = b + a1 * x1 + ... ad * xd".

go_linear_regression_leverage ()

GORegressionResult
go_linear_regression_leverage (double **A,
                               double *d,
                               int m,
                               int n);

go_linear_regression_leveragel ()

GORegressionResult
go_linear_regression_leveragel (long double **A,
                                long double *d,
                                int m,
                                int n);

go_linear_regression_leverageD ()

GORegressionResult
go_linear_regression_leverageD (_Decimal64 **A,
                                _Decimal64 *d,
                                int m,
                                int n);

go_linear_solve_multiple ()

GORegressionResult
go_linear_solve_multiple (double *const *const A,
                          double **B,
                          int n,
                          int bn);

go_linear_solve_multiplel ()

GORegressionResult
go_linear_solve_multiplel (long double *const *const A,
                           long double **B,
                           int n,
                           int bn);

go_linear_solve_multipleD ()

GORegressionResult
go_linear_solve_multipleD (_Decimal64 *const *const A,
                           _Decimal64 **B,
                           int n,
                           int bn);

go_linear_solve ()

GORegressionResult
go_linear_solve (double *const *const A,
                 const double *b,
                 int n,
                 double *res);

go_linear_solvel ()

GORegressionResult
go_linear_solvel (long double *const *const A,
                  const long double *b,
                  int n,
                  long double *res);

go_linear_solveD ()

GORegressionResult
go_linear_solveD (_Decimal64 *const *const A,
                  const _Decimal64 *b,
                  int n,
                  _Decimal64 *res);

go_logarithmic_fit ()

GORegressionResult
go_logarithmic_fit (double *xs,
                    const double *ys,
                    int n,
                    double *res);

Performs a two-dimensional non-linear fitting on the input points. Fits to "y = a + b * ln (sign * (x - c))", with sign in {-1, +1}. The graph is a logarithmic curve moved horizontally by c and possibly mirrored across the y-axis (if sign = -1).

Fits c (and sign) by iterative trials, but seems to be fast enough even for automatic recomputation.

Adapts c until a local minimum of squared residuals is reached. For each new c tried out the corresponding a and b are calculated by linear regression. If no local minimum is found, an error is returned. If there is more than one local minimum, the one found is not necessarily the smallest (i.e., there might be cases in which the returned fit is not the best possible). If the shape of the point cloud is to different from ``logarithmic'', either sign can not be determined (error returned) or no local minimum will be found.

(Requires: at least 3 different x values, at least 3 different y values.)

go_logarithmic_fitl ()

GORegressionResult
go_logarithmic_fitl (long double *xs,
                     const long double *ys,
                     int n,
                     long double *res);

Performs a two-dimensional non-linear fitting on the input points. Fits to "y = a + b * ln (sign * (x - c))", with sign in {-1, +1}. The graph is a logarithmic curve moved horizontally by c and possibly mirrored across the y-axis (if sign = -1).

Fits c (and sign) by iterative trials, but seems to be fast enough even for automatic recomputation.

Adapts c until a local minimum of squared residuals is reached. For each new c tried out the corresponding a and b are calculated by linear regression. If no local minimum is found, an error is returned. If there is more than one local minimum, the one found is not necessarily the smallest (i.e., there might be cases in which the returned fit is not the best possible). If the shape of the point cloud is to different from ``logarithmic'', either sign can not be determined (error returned) or no local minimum will be found.

(Requires: at least 3 different x values, at least 3 different y values.)

go_logarithmic_fitD ()

GORegressionResult
go_logarithmic_fitD (_Decimal64 *xs,
                     const _Decimal64 *ys,
                     int n,
                     _Decimal64 *res);

Performs a two-dimensional non-linear fitting on the input points. Fits to "y = a + b * ln (sign * (x - c))", with sign in {-1, +1}. The graph is a logarithmic curve moved horizontally by c and possibly mirrored across the y-axis (if sign = -1).

Fits c (and sign) by iterative trials, but seems to be fast enough even for automatic recomputation.

Adapts c until a local minimum of squared residuals is reached. For each new c tried out the corresponding a and b are calculated by linear regression. If no local minimum is found, an error is returned. If there is more than one local minimum, the one found is not necessarily the smallest (i.e., there might be cases in which the returned fit is not the best possible). If the shape of the point cloud is to different from ``logarithmic'', either sign can not be determined (error returned) or no local minimum will be found.

(Requires: at least 3 different x values, at least 3 different y values.)

go_logarithmic_regression ()

GORegressionResult
go_logarithmic_regression (double **xss,
                           int dim,
                           const double *ys,
                           int n,
                           gboolean affine,
                           double *res,
                           go_regression_stat_t *stat_);

This is almost a copy of linear_regression and produces multi-dimensional linear regressions on the input points after transforming xss to ln(xss). Fits to "y = b + a1 * z1 + ... ad * zd" with "zi = ln (xi)". Problems with arrays in the calling function: see comment to gnumeric_linest, which is also valid for gnumeric_logreg.

(Errors: less than two points, all points on a vertical line, non-positive x data.)

go_logarithmic_regressionl ()

GORegressionResult
go_logarithmic_regressionl (long double **xss,
                            int dim,
                            const long double *ys,
                            int n,
                            gboolean affine,
                            long double *res,
                            go_regression_stat_tl *stat_);

This is almost a copy of linear_regression and produces multi-dimensional linear regressions on the input points after transforming xss to ln(xss). Fits to "y = b + a1 * z1 + ... ad * zd" with "zi = ln (xi)". Problems with arrays in the calling function: see comment to gnumeric_linest, which is also valid for gnumeric_logreg.

(Errors: less than two points, all points on a vertical line, non-positive x data.)

go_logarithmic_regressionD ()

GORegressionResult
go_logarithmic_regressionD (_Decimal64 **xss,
                            int dim,
                            const _Decimal64 *ys,
                            int n,
                            gboolean affine,
                            _Decimal64 *res,
                            go_regression_stat_tD *stat_);

This is almost a copy of linear_regression and produces multi-dimensional linear regressions on the input points after transforming xss to ln(xss). Fits to "y = b + a1 * z1 + ... ad * zd" with "zi = ln (xi)". Problems with arrays in the calling function: see comment to gnumeric_linest, which is also valid for gnumeric_logreg.

(Errors: less than two points, all points on a vertical line, non-positive x data.)

go_matrix_determinant ()

double
go_matrix_determinant (double *const *const A,
                       int n);

go_matrix_determinantl ()

long double
go_matrix_determinantl (long double *const * const A,
                        int n);

go_matrix_determinantD ()

_Decimal64
go_matrix_determinantD (_Decimal64 *const * const A,
                        int n);

go_matrix_invert ()

gboolean
go_matrix_invert (double **A,
                  int n);

go_matrix_invertl ()

gboolean
go_matrix_invertl (long double **A,
                   int n);

go_matrix_invertD ()

gboolean
go_matrix_invertD (_Decimal64 **A,
                   int n);

go_matrix_pseudo_inverse ()

void
go_matrix_pseudo_inverse (double *const * const A,
                          int m,
                          int n,
                          double threshold,
                          double **B);

go_matrix_pseudo_inversel ()

void
go_matrix_pseudo_inversel (long double *const * const A,
                           int m,
                           int n,
                           long double threshold,
                           long double **B);

go_matrix_pseudo_inverseD ()

void
go_matrix_pseudo_inverseD (_Decimal64 *const * const A,
                           int m,
                           int n,
                           _Decimal64 threshold,
                           _Decimal64 **B);

go_non_linear_regression ()

GORegressionResult
go_non_linear_regression (GORegressionFunction f,
                          double **xvals,
                          double *par,
                          double *yvals,
                          double *sigmas,
                          int x_dim,
                          int p_dim,
                          double *chi,
                          double *errors);

SYNOPSIS: result = non_linear_regression (f, xvals, par, yvals, sigmas, x_dim, p_dim, &chi, errors) Non linear regression.

go_non_linear_regressionl ()

GORegressionResult
go_non_linear_regressionl (GORegressionFunctionl f,
                           long double **xvals,
                           long double *par,
                           long double *yvals,
                           long double *sigmas,
                           int x_dim,
                           int p_dim,
                           long double *chi,
                           long double *errors);

SYNOPSIS: result = non_linear_regression (f, xvals, par, yvals, sigmas, x_dim, p_dim, &chi, errors) Non linear regression.

go_non_linear_regressionD ()

GORegressionResult
go_non_linear_regressionD (GORegressionFunctionD f,
                           _Decimal64 **xvals,
                           _Decimal64 *par,
                           _Decimal64 *yvals,
                           _Decimal64 *sigmas,
                           int x_dim,
                           int p_dim,
                           _Decimal64 *chi,
                           _Decimal64 *errors);

SYNOPSIS: result = non_linear_regression (f, xvals, par, yvals, sigmas, x_dim, p_dim, &chi, errors) Non linear regression.

go_power_regression ()

GORegressionResult
go_power_regression (double **xss,
                     int dim,
                     const double *ys,
                     int n,
                     gboolean affine,
                     double *res,
                     go_regression_stat_t *stat_);

Performs one-dimensional linear regressions on the input points. Fits to "y = b * x1^m1 * ... * xd^md " or equivalently to "log y = log b + m1 * log x1 + ... + md * log xd".

go_power_regressionl ()

GORegressionResult
go_power_regressionl (long double **xss,
                      int dim,
                      const long double *ys,
                      int n,
                      gboolean affine,
                      long double *res,
                      go_regression_stat_tl *stat_);

Performs one-dimensional linear regressions on the input points. Fits to "y = b * x1^m1 * ... * xd^md " or equivalently to "log y = log b + m1 * log x1 + ... + md * log xd".

go_power_regressionD ()

GORegressionResult
go_power_regressionD (_Decimal64 **xss,
                      int dim,
                      const _Decimal64 *ys,
                      int n,
                      gboolean affine,
                      _Decimal64 *res,
                      go_regression_stat_tD *stat_);

Performs one-dimensional linear regressions on the input points. Fits to "y = b * x1^m1 * ... * xd^md " or equivalently to "log y = log b + m1 * log x1 + ... + md * log xd".

go_regression_stat_destroy ()

void
go_regression_stat_destroy (go_regression_stat_t *stat_);

go_regression_stat_destroyl ()

void
go_regression_stat_destroyl (go_regression_stat_tl *stat_);

go_regression_stat_destroyD ()

void
go_regression_stat_destroyD (go_regression_stat_tD *stat_);

go_regression_stat_new ()

go_regression_stat_t *
go_regression_stat_new (void);

go_regression_stat_newl ()

go_regression_stat_tl *
go_regression_stat_newl (void);

go_regression_stat_newD ()

go_regression_stat_tD *
go_regression_stat_newD (void);

enum GORegressionResult

GORegressionStat

#define GORegressionStat go_regression_stat_t

GORegressionStatl

#define GORegressionStatl go_regression_stat_tl

GORegressionStatD

#define GORegressionStatD go_regression_stat_tD

GO_LOGFIT_C_ACCURACY

#define GO_LOGFIT_C_ACCURACY 0.000001

GO_LOGFIT_C_RANGE_FACTOR

#define GO_LOGFIT_C_RANGE_FACTOR 100

GO_LOGFIT_C_STEP_FACTOR

#define GO_LOGFIT_C_STEP_FACTOR 0.05

go_regression_stat_t

typedef struct {
        double *se;		/* SE for each parameter estimator */
        double *t;  		/* t values for each parameter estimator */
        double sqr_r;
	double adj_sqr_r;
        double se_y; 		/* The Standard Error of Y */
        double F;
        int    df_reg;
        int    df_resid;
        int    df_total;
        double ss_reg;
        double ss_resid;
        double ss_total;
        double ms_reg;
        double ms_resid;
	double ybar;
	double *xbar;
	double var; 		/* The variance of the entire regression: sum(errors^2)/(n-xdim) */
} go_regression_stat_t;

go_regression_stat_tl

typedef struct {
        long double *se; /*SE for each parameter estimator*/
        long double *t;  /*t values for each parameter estimator*/
        long double sqr_r;
	long double adj_sqr_r;
        long double se_y; /* The Standard Error of Y */
        long double F;
        int        df_reg;
        int        df_resid;
        int        df_total;
        long double ss_reg;
        long double ss_resid;
        long double ss_total;
        long double ms_reg;
        long double ms_resid;
	long double ybar;
	long double *xbar;
	long double var; /* The variance of the entire regression:
			sum(errors^2)/(n-xdim) */
} go_regression_stat_tl;

go_regression_stat_tD

typedef struct {
        _Decimal64 *se; /*SE for each parameter estimator*/
        _Decimal64 *t;  /*t values for each parameter estimator*/
        _Decimal64 sqr_r;
	_Decimal64 adj_sqr_r;
        _Decimal64 se_y; /* The Standard Error of Y */
        _Decimal64 F;
        int        df_reg;
        int        df_resid;
        int        df_total;
        _Decimal64 ss_reg;
        _Decimal64 ss_resid;
        _Decimal64 ss_total;
        _Decimal64 ms_reg;
        _Decimal64 ms_resid;
	_Decimal64 ybar;
	_Decimal64 *xbar;
	_Decimal64 var; /* The variance of the entire regression:
			sum(errors^2)/(n-xdim) */
} go_regression_stat_tD;