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Gwyddion Library Reference Manual | ![]() |
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#define ROUND (x) #define GWY_SQRT3 #define GWY_SQRT_PI gdouble gwy_math_humanize_numbers (gdouble unit, gdouble maximum, gint *precision); gint gwy_math_find_nearest_line (gdouble x, gdouble y, gdouble *d2min, gint n, const gdouble *coords, const gdouble *metric); gint gwy_math_find_nearest_point (gdouble x, gdouble y, gdouble *d2min, gint n, const gdouble *coords, const gdouble *metric); gdouble* gwy_math_lin_solve (gint n, const gdouble *matrix, const gdouble *rhs, gdouble *result); gdouble* gwy_math_lin_solve_rewrite (gint n, gdouble *matrix, gdouble *rhs, gdouble *result); gboolean gwy_math_tridiag_solve_rewrite (gint n, gdouble *d, const gdouble *a, const gdouble *b, gdouble *rhs); gdouble* gwy_math_fit_polynom (gint ndata, const gdouble *xdata, const gdouble *ydata, gint n, gdouble *coeffs); gboolean gwy_math_choleski_decompose (gint n, gdouble *matrix); void gwy_math_choleski_solve (gint n, const gdouble *decomp, gdouble *rhs); gdouble gwy_math_median (gsize n, gdouble *array); void gwy_math_sort (gsize n, gdouble *array);
Functions gwy_math_SI_prefix()
and gwy_math_humanize_numbers()
deal with
number representation.
Nearest object finding functions gwy_math_find_nearest_line()
and
gwy_math_find_nearest_point()
can be useful in widget and vector layer
implementation.
And gwy_math_lin_solve()
, gwy_math_lin_solve_rewrite()
, and
gwy_math_fit_polynom()
are general purpose numeric methods.
#define ROUND(x) ((gint)floor((x) + 0.5))
Rounds a number to nearest integer.
x : |
A double value. |
#define GWY_SQRT3 1.73205080756887729352744634150587236694280525381038
The square root of 3.
#define GWY_SQRT_PI 1.77245385090551602729816748334114518279754945612237
The square root of π.
gdouble gwy_math_humanize_numbers (gdouble unit, gdouble maximum, gint *precision);
Finds a human-friendly representation for a range of numbers.
unit : |
The smallest possible step. |
maximum : |
The maximum possible value. |
precision : |
A location to store printf() precession, if not NULL .
|
Returns : | The magnitude i.e., a power of 1000. |
gint gwy_math_find_nearest_line (gdouble x, gdouble y, gdouble *d2min, gint n, const gdouble *coords, const gdouble *metric);
Finds the line from coords
nearest to the point (x
, y
).
x : |
X-coordinate of the point to search. |
y : |
Y-coordinate of the point to search. |
d2min : |
Where to store the squared minimal distance, or NULL .
|
n : |
The number of lines (i.e. coords has 4n items).
|
coords : |
Line coordinates stored as x00, y00, x01, y01, x10, y10, etc. |
metric : |
Metric matrix (2x2, but stored sequentially by rows: m11, m12,
m21, m22), it must be positive definite. Vector norm is then
calculated as m11*x*x + (m12 + m21)*x*y + m22*y*y.
It can be NULL , standard Euclidean metric is then used.
|
Returns : | The line number. It may return -1 if (x , y ) doesn't lie
in the orthogonal stripe of any of the lines.
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gint gwy_math_find_nearest_point (gdouble x, gdouble y, gdouble *d2min, gint n, const gdouble *coords, const gdouble *metric);
Finds the point from coords
nearest to the point (x
, y
).
x : |
X-coordinate of the point to search. |
y : |
Y-coordinate of the point to search. |
d2min : |
Location to store the squared minimal distance to, or NULL .
|
n : |
The number of points (i.e. coords has 2n items).
|
coords : |
Point coordinates stored as x0, y0, x1, y1, x2, y2, etc. |
metric : |
Metric matrix (2x2, but stored sequentially by rows: m11, m12,
m21, m22). Vector norm is then calculated as
m11*x*x + (m12 + m21)*x*y + m22*y*y.
It can be NULL , standard Euclidean metric is then used.
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Returns : | The point number. |
gdouble* gwy_math_lin_solve (gint n, const gdouble *matrix, const gdouble *rhs, gdouble *result);
Solve a regular system of linear equations.
n : |
The size of the system. |
matrix : |
The matrix of the system (n times n ), ordered by row, then
column.
|
rhs : |
The right hand side of the sytem. |
result : |
Where the result should be stored. May be NULL to allocate
a fresh array for the result.
|
Returns : | The solution (result if it wasn't NULL ), may be NULL if the
matrix is singular.
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gdouble* gwy_math_lin_solve_rewrite (gint n, gdouble *matrix, gdouble *rhs, gdouble *result);
Solves a regular system of linear equations.
This is a memory-conservative version of gwy_math_lin_solve()
overwriting
matrix
and rhs
with intermediate results.
n : |
The size of the system. |
matrix : |
The matrix of the system (n times n ), ordered by row, then
column.
|
rhs : |
The right hand side of the sytem. |
result : |
Where the result should be stored. May be NULL to allocate
a fresh array for the result.
|
Returns : | The solution (result if it wasn't NULL ), may be NULL if the
matrix is singular.
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gboolean gwy_math_tridiag_solve_rewrite (gint n, gdouble *d, const gdouble *a, const gdouble *b, gdouble *rhs);
Solves a tridiagonal system of linear equations.
n : |
The dimension of d .
|
d : |
The diagonal of a tridiagonal matrix, its contents will be overwritten. |
a : |
The above-diagonal stripe (it has n -1 elements).
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b : |
The below-diagonal stripe (it has n -1 elements).
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rhs : |
The right hand side of the system, upon return it will contain the solution. |
Returns : | TRUE if the elimination suceeded, FALSE if the system is
(numerically) singular. The contents of d and rhs may be
overwritten in the case of failure too, but not to any meaningful
values.
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gdouble* gwy_math_fit_polynom (gint ndata, const gdouble *xdata, const gdouble *ydata, gint n, gdouble *coeffs);
Fits a polynom through a general (x, y) data set.
ndata : |
The number of items in xdata , ydata .
|
xdata : |
Independent variable data (of size ndata ).
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ydata : |
Dependent variable data (of size ndata ).
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n : |
The degree of polynom to fit. |
coeffs : |
An array of size n +1 to store the coefficients to, or NULL
(a fresh array is allocated then).
|
Returns : | The coefficients of the polynom (coeffs when it was not NULL ,
otherwise a newly allocated array).
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gboolean gwy_math_choleski_decompose (gint n, gdouble *matrix);
Decomposes a symmetric positive definite matrix in place.
n : |
The dimension of a .
|
matrix : |
Lower triangular part of a symmetric matrix, stored by rows, i.e., matrix = [a_00 a_10 a_11 a_20 a_21 a_22 a_30 ...]. |
Returns : | Whether the matrix was really positive definite. If FALSE ,
the decomposition failed and a does not contain any meaningful
values.
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void gwy_math_choleski_solve (gint n, const gdouble *decomp, gdouble *rhs);
Solves a system of linear equations with predecomposed symmetric positive
definite matrix a
and right hand side b
.
n : |
The dimension of a .
|
decomp : |
Lower triangular part of Choleski decomposition as computed
by gwy_math_choleski_decompose() .
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rhs : |
Right hand side vector. Is is modified in place, on return it contains the solution. |
gdouble gwy_math_median (gsize n, gdouble *array);
Finds median of an array of values using Quick select algorithm.
n : |
Number of items in array .
|
array : |
Array of doubles. It is modified by this function. All values are kept, but their positions in the array change. |
Returns : | The median value of array .
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