NAME
Image::Leptonica::Func::ptafunc1
VERSION
version 0.04
ptafunc1.c
ptafunc1.c
Pta and Ptaa rearrangements
PTA *ptaSubsample()
l_int32 ptaJoin()
l_int32 ptaaJoin()
PTA *ptaReverse()
PTA *ptaTranspose()
PTA *ptaCyclicPerm()
PTA *ptaSort()
l_int32 ptaGetSortIndex()
PTA *ptaSortByIndex()
PTA *ptaRemoveDuplicates()
PTAA *ptaaSortByIndex()
Geometric
BOX *ptaGetBoundingRegion()
l_int32 *ptaGetRange()
PTA *ptaGetInsideBox()
PTA *pixFindCornerPixels()
l_int32 ptaContainsPt()
l_int32 ptaTestIntersection()
PTA *ptaTransform()
l_int32 ptaPtInsidePolygon()
l_float32 l_angleBetweenVectors()
Least Squares Fit
l_int32 ptaGetLinearLSF()
l_int32 ptaGetQuadraticLSF()
l_int32 ptaGetCubicLSF()
l_int32 ptaGetQuarticLSF()
l_int32 ptaNoisyLinearLSF()
l_int32 ptaNoisyQuadraticLSF()
l_int32 applyLinearFit()
l_int32 applyQuadraticFit()
l_int32 applyCubicFit()
l_int32 applyQuarticFit()
Interconversions with Pix
l_int32 pixPlotAlongPta()
PTA *ptaGetPixelsFromPix()
PIX *pixGenerateFromPta()
PTA *ptaGetBoundaryPixels()
PTAA *ptaaGetBoundaryPixels()
Display Pta and Ptaa
PIX *pixDisplayPta()
PIX *pixDisplayPtaaPattern()
PIX *pixDisplayPtaPattern()
PTA *ptaReplicatePattern()
PIX *pixDisplayPtaa()FUNCTIONS
applyCubicFit
l_int32 applyCubicFit ( l_float32 a, l_float32 b, l_float32 c, l_float32 d, l_float32 x, l_float32 *py )
applyCubicFit()
Input: a, b, c, d (cubic fit coefficients)
x
&y (<return> y = a * x^3 + b * x^2 + c * x + d)
Return: 0 if OK, 1 on errorapplyLinearFit
l_int32 applyLinearFit ( l_float32 a, l_float32 b, l_float32 x, l_float32 *py )
applyLinearFit()
Input: a, b (linear fit coefficients)
x
&y (<return> y = a * x + b)
Return: 0 if OK, 1 on errorapplyQuadraticFit
l_int32 applyQuadraticFit ( l_float32 a, l_float32 b, l_float32 c, l_float32 x, l_float32 *py )
applyQuadraticFit()
Input: a, b, c (quadratic fit coefficients)
x
&y (<return> y = a * x^2 + b * x + c)
Return: 0 if OK, 1 on errorapplyQuarticFit
l_int32 applyQuarticFit ( l_float32 a, l_float32 b, l_float32 c, l_float32 d, l_float32 e, l_float32 x, l_float32 *py )
applyQuarticFit()
Input: a, b, c, d, e (quartic fit coefficients)
x
&y (<return> y = a * x^4 + b * x^3 + c * x^2 + d * x + e)
Return: 0 if OK, 1 on errorl_angleBetweenVectors
l_float32 l_angleBetweenVectors ( l_float32 x1, l_float32 y1, l_float32 x2, l_float32 y2 )
l_angleBetweenVectors()
Input: x1, y1 (end point of first vector)
x2, y2 (end point of second vector)
Return: angle (radians), or 0.0 on error
Notes:
(1) This gives the angle between two vectors, going between
vector1 (x1,y1) and vector2 (x2,y2). The angle is swept
out from 1 --> 2. If this is clockwise, the angle is
positive, but the result is folded into the interval [-pi, pi].pixDisplayPta
PIX * pixDisplayPta ( PIX *pixd, PIX *pixs, PTA *pta )
pixDisplayPta()
Input: pixd (can be same as pixs or null; 32 bpp if in-place)
pixs (1, 2, 4, 8, 16 or 32 bpp)
pta (of path to be plotted)
Return: pixd (32 bpp RGB version of pixs, with path in green).
Notes:
(1) To write on an existing pixs, pixs must be 32 bpp and
call with pixd == pixs:
pixDisplayPta(pixs, pixs, pta);
To write to a new pix, use pixd == NULL and call:
pixd = pixDisplayPta(NULL, pixs, pta);
(2) On error, returns pixd to avoid losing pixs if called as
pixs = pixDisplayPta(pixs, pixs, pta);pixDisplayPtaPattern
PIX * pixDisplayPtaPattern ( PIX *pixd, PIX *pixs, PTA *pta, PIX *pixp, l_int32 cx, l_int32 cy, l_uint32 color )
pixDisplayPtaPattern()
Input: pixd (can be same as pixs or null; 32 bpp if in-place)
pixs (1, 2, 4, 8, 16 or 32 bpp)
pta (giving locations at which the pattern is displayed)
pixp (1 bpp pattern to be placed such that its reference
point co-locates with each point in pta)
cx, cy (reference point in pattern)
color (in 0xrrggbb00 format)
Return: pixd (32 bpp RGB version of pixs).
Notes:
(1) To write on an existing pixs, pixs must be 32 bpp and
call with pixd == pixs:
pixDisplayPtaPattern(pixs, pixs, pta, ...);
To write to a new pix, use pixd == NULL and call:
pixd = pixDisplayPtaPattern(NULL, pixs, pta, ...);
(2) On error, returns pixd to avoid losing pixs if called as
pixs = pixDisplayPtaPattern(pixs, pixs, pta, ...);
(3) A typical pattern to be used is a circle, generated with
generatePtaFilledCircle()pixDisplayPtaa
PIX * pixDisplayPtaa ( PIX *pixs, PTAA *ptaa )
pixDisplayPtaa()
Input: pixs (1, 2, 4, 8, 16 or 32 bpp)
ptaa (array of paths to be plotted)
Return: pixd (32 bpp RGB version of pixs, with paths plotted
in different colors), or null on errorpixDisplayPtaaPattern
PIX * pixDisplayPtaaPattern ( PIX *pixd, PIX *pixs, PTAA *ptaa, PIX *pixp, l_int32 cx, l_int32 cy )
pixDisplayPtaaPattern()
Input: pixd (32 bpp)
pixs (1, 2, 4, 8, 16 or 32 bpp; 32 bpp if in place)
ptaa (giving locations at which the pattern is displayed)
pixp (1 bpp pattern to be placed such that its reference
point co-locates with each point in pta)
cx, cy (reference point in pattern)
Return: pixd (32 bpp RGB version of pixs).
Notes:
(1) To write on an existing pixs, pixs must be 32 bpp and
call with pixd == pixs:
pixDisplayPtaPattern(pixs, pixs, pta, ...);
To write to a new pix, use pixd == NULL and call:
pixd = pixDisplayPtaPattern(NULL, pixs, pta, ...);
(2) Puts a random color on each pattern associated with a pta.
(3) On error, returns pixd to avoid losing pixs if called as
pixs = pixDisplayPtaPattern(pixs, pixs, pta, ...);
(4) A typical pattern to be used is a circle, generated with
generatePtaFilledCircle()pixFindCornerPixels
PTA * pixFindCornerPixels ( PIX *pixs )
pixFindCornerPixels()
Input: pixs (1 bpp)
Return: pta, or null on error
Notes:
(1) Finds the 4 corner-most pixels, as defined by a search
inward from each corner, using a 45 degree line.pixGenerateFromPta
PIX * pixGenerateFromPta ( PTA *pta, l_int32 w, l_int32 h )
pixGenerateFromPta()
Input: pta
w, h (of pix)
Return: pix (1 bpp), or null on error
Notes:
(1) Points are rounded to nearest ints.
(2) Any points outside (w,h) are silently discarded.
(3) Output 1 bpp pix has values 1 for each point in the pta.pixPlotAlongPta
l_int32 pixPlotAlongPta ( PIX *pixs, PTA *pta, l_int32 outformat, const char *title )
pixPlotAlongPta()
Input: pixs (any depth)
pta (set of points on which to plot)
outformat (GPLOT_PNG, GPLOT_PS, GPLOT_EPS, GPLOT_X11,
GPLOT_LATEX)
title (<optional> for plot; can be null)
Return: 0 if OK, 1 on error
Notes:
(1) We remove any existing colormap and clip the pta to the input pixs.
(2) This is a debugging function, and does not remove temporary
plotting files that it generates.
(3) If the image is RGB, three separate plots are generated.ptaContainsPt
l_int32 ptaContainsPt ( PTA *pta, l_int32 x, l_int32 y )
ptaContainsPt()
Input: pta
x, y (point)
Return: 1 if contained, 0 otherwise or on errorptaCyclicPerm
PTA * ptaCyclicPerm ( PTA *ptas, l_int32 xs, l_int32 ys )
ptaCyclicPerm()
Input: ptas
xs, ys (start point; must be in ptas)
Return: ptad (cyclic permutation, starting and ending at (xs, ys),
or null on error
Notes:
(1) Check to insure that (a) ptas is a closed path where
the first and last points are identical, and (b) the
resulting pta also starts and ends on the same point
(which in this case is (xs, ys).ptaGetBoundaryPixels
PTA * ptaGetBoundaryPixels ( PIX *pixs, l_int32 type )
ptaGetBoundaryPixels()
Input: pixs (1 bpp)
type (L_BOUNDARY_FG, L_BOUNDARY_BG)
Return: pta, or null on error
Notes:
(1) This generates a pta of either fg or bg boundary pixels.ptaGetBoundingRegion
BOX * ptaGetBoundingRegion ( PTA *pta )
ptaGetBoundingRegion()
Input: pta
Return: box, or null on error
Notes:
(1) This is used when the pta represents a set of points in
a two-dimensional image. It returns the box of minimum
size containing the pts in the pta.ptaGetCubicLSF
l_int32 ptaGetCubicLSF ( PTA *pta, l_float32 *pa, l_float32 *pb, l_float32 *pc, l_float32 *pd, NUMA **pnafit )
ptaGetCubicLSF()
Input: pta
&a (<optional return> coeff a of LSF: y = ax^3 + bx^2 + cx + d)
&b (<optional return> coeff b of LSF)
&c (<optional return> coeff c of LSF)
&d (<optional return> coeff d of LSF)
&nafit (<optional return> numa of least square fit)
Return: 0 if OK, 1 on error
Notes:
(1) This does a cubic least square fit to the set of points
in @pta. That is, it finds coefficients a, b, c and d
that minimize:
sum (yi - a*xi*xi*xi -b*xi*xi -c*xi - d)^2
i
Differentiate this expression w/rt a, b, c and d, and solve
the resulting four equations for these coefficients in
terms of various sums over the input data (xi, yi).
The four equations are in the form:
f[0][0]a + f[0][1]b + f[0][2]c + f[0][3] = g[0]
f[1][0]a + f[1][1]b + f[1][2]c + f[1][3] = g[1]
f[2][0]a + f[2][1]b + f[2][2]c + f[2][3] = g[2]
f[3][0]a + f[3][1]b + f[3][2]c + f[3][3] = g[3]
(2) If @nafit is defined, this returns an array of fitted values,
corresponding to the two implicit Numa arrays (nax and nay) in pta.
Thus, just as you can plot the data in pta as nay vs. nax,
you can plot the linear least square fit as nafit vs. nax.ptaGetInsideBox
PTA * ptaGetInsideBox ( PTA *ptas, BOX *box )
ptaGetInsideBox()
Input: ptas (input pts)
box
Return: ptad (of pts in ptas that are inside the box), or null on errorptaGetLinearLSF
l_int32 ptaGetLinearLSF ( PTA *pta, l_float32 *pa, l_float32 *pb, NUMA **pnafit )
ptaGetLinearLSF()
Input: pta
&a (<optional return> slope a of least square fit: y = ax + b)
&b (<optional return> intercept b of least square fit)
&nafit (<optional return> numa of least square fit)
Return: 0 if OK, 1 on error
Notes:
(1) Either or both &a and &b must be input. They determine the
type of line that is fit.
(2) If both &a and &b are defined, this returns a and b that minimize:
sum (yi - axi -b)^2
i
The method is simple: differentiate this expression w/rt a and b,
and solve the resulting two equations for a and b in terms of
various sums over the input data (xi, yi).
(3) We also allow two special cases, where either a = 0 or b = 0:
(a) If &a is given and &b = null, find the linear LSF that
goes through the origin (b = 0).
(b) If &b is given and &a = null, find the linear LSF with
zero slope (a = 0).
(4) If @nafit is defined, this returns an array of fitted values,
corresponding to the two implicit Numa arrays (nax and nay) in pta.
Thus, just as you can plot the data in pta as nay vs. nax,
you can plot the linear least square fit as nafit vs. nax.ptaGetPixelsFromPix
PTA * ptaGetPixelsFromPix ( PIX *pixs, BOX *box )
ptaGetPixelsFromPix()
Input: pixs (1 bpp)
box (<optional> can be null)
Return: pta, or null on error
Notes:
(1) Generates a pta of fg pixels in the pix, within the box.
If box == NULL, it uses the entire pix.ptaGetQuadraticLSF
l_int32 ptaGetQuadraticLSF ( PTA *pta, l_float32 *pa, l_float32 *pb, l_float32 *pc, NUMA **pnafit )
ptaGetQuadraticLSF()
Input: pta
&a (<optional return> coeff a of LSF: y = ax^2 + bx + c)
&b (<optional return> coeff b of LSF: y = ax^2 + bx + c)
&c (<optional return> coeff c of LSF: y = ax^2 + bx + c)
&nafit (<optional return> numa of least square fit)
Return: 0 if OK, 1 on error
Notes:
(1) This does a quadratic least square fit to the set of points
in @pta. That is, it finds coefficients a, b and c that minimize:
sum (yi - a*xi*xi -b*xi -c)^2
i
The method is simple: differentiate this expression w/rt
a, b and c, and solve the resulting three equations for these
coefficients in terms of various sums over the input data (xi, yi).
The three equations are in the form:
f[0][0]a + f[0][1]b + f[0][2]c = g[0]
f[1][0]a + f[1][1]b + f[1][2]c = g[1]
f[2][0]a + f[2][1]b + f[2][2]c = g[2]
(2) If @nafit is defined, this returns an array of fitted values,
corresponding to the two implicit Numa arrays (nax and nay) in pta.
Thus, just as you can plot the data in pta as nay vs. nax,
you can plot the linear least square fit as nafit vs. nax.ptaGetQuarticLSF
l_int32 ptaGetQuarticLSF ( PTA *pta, l_float32 *pa, l_float32 *pb, l_float32 *pc, l_float32 *pd, l_float32 *pe, NUMA **pnafit )
ptaGetQuarticLSF()
Input: pta
&a (<optional return> coeff a of LSF:
y = ax^4 + bx^3 + cx^2 + dx + e)
&b (<optional return> coeff b of LSF)
&c (<optional return> coeff c of LSF)
&d (<optional return> coeff d of LSF)
&e (<optional return> coeff e of LSF)
&nafit (<optional return> numa of least square fit)
Return: 0 if OK, 1 on error
Notes:
(1) This does a quartic least square fit to the set of points
in @pta. That is, it finds coefficients a, b, c, d and 3
that minimize:
sum (yi - a*xi*xi*xi*xi -b*xi*xi*xi -c*xi*xi - d*xi - e)^2
i
Differentiate this expression w/rt a, b, c, d and e, and solve
the resulting five equations for these coefficients in
terms of various sums over the input data (xi, yi).
The five equations are in the form:
f[0][0]a + f[0][1]b + f[0][2]c + f[0][3] + f[0][4] = g[0]
f[1][0]a + f[1][1]b + f[1][2]c + f[1][3] + f[1][4] = g[1]
f[2][0]a + f[2][1]b + f[2][2]c + f[2][3] + f[2][4] = g[2]
f[3][0]a + f[3][1]b + f[3][2]c + f[3][3] + f[3][4] = g[3]
f[4][0]a + f[4][1]b + f[4][2]c + f[4][3] + f[4][4] = g[4]
(2) If @nafit is defined, this returns an array of fitted values,
corresponding to the two implicit Numa arrays (nax and nay) in pta.
Thus, just as you can plot the data in pta as nay vs. nax,
you can plot the linear least square fit as nafit vs. nax.ptaGetRange
l_int32 ptaGetRange ( PTA *pta, l_float32 *pminx, l_float32 *pmaxx, l_float32 *pminy, l_float32 *pmaxy )
ptaGetRange()
Input: pta
&minx (<optional return> min value of x)
&maxx (<optional return> max value of x)
&miny (<optional return> min value of y)
&maxy (<optional return> max value of y)
Return: 0 if OK, 1 on error
Notes:
(1) We can use pts to represent pairs of floating values, that
are not necessarily tied to a two-dimension region. For
example, the pts can represent a general function y(x).ptaGetSortIndex
l_int32 ptaGetSortIndex ( PTA *ptas, l_int32 sorttype, l_int32 sortorder, NUMA **pnaindex )
ptaGetSortIndex()
Input: ptas
sorttype (L_SORT_BY_X, L_SORT_BY_Y)
sortorder (L_SORT_INCREASING, L_SORT_DECREASING)
&naindex (<return> index of sorted order into
original array)
Return: 0 if OK, 1 on errorptaJoin
l_int32 ptaJoin ( PTA *ptad, PTA *ptas, l_int32 istart, l_int32 iend )
ptaJoin()
Input: ptad (dest pta; add to this one)
ptas (source pta; add from this one)
istart (starting index in ptas)
iend (ending index in ptas; use -1 to cat all)
Return: 0 if OK, 1 on error
Notes:
(1) istart < 0 is taken to mean 'read from the start' (istart = 0)
(2) iend < 0 means 'read to the end'
(3) if ptas == NULL, this is a no-opptaNoisyLinearLSF
l_int32 ptaNoisyLinearLSF ( PTA *pta, l_float32 factor, PTA **pptad, l_float32 *pa, l_float32 *pb, l_float32 *pmederr, NUMA **pnafit )
ptaNoisyLinearLSF()
Input: pta
factor (reject outliers with error greater than this
number of medians; typically ~ 3)
&ptad (<optional return> with outliers removed)
&a (<optional return> slope a of least square fit: y = ax + b)
&b (<optional return> intercept b of least square fit)
&mederr (<optional return> median error)
&nafit (<optional return> numa of least square fit to ptad)
Return: 0 if OK, 1 on error
Notes:
(1) This does a linear least square fit to the set of points
in @pta. It then evaluates the errors and removes points
whose error is >= factor * median_error. It then re-runs
the linear LSF on the resulting points.
(2) Either or both &a and &b must be input. They determine the
type of line that is fit.
(3) The median error can give an indication of how good the fit
is likely to be.ptaNoisyQuadraticLSF
l_int32 ptaNoisyQuadraticLSF ( PTA *pta, l_float32 factor, PTA **pptad, l_float32 *pa, l_float32 *pb, l_float32 *pc, l_float32 *pmederr, NUMA **pnafit )
ptaNoisyQuadraticLSF()
Input: pta
factor (reject outliers with error greater than this
number of medians; typically ~ 3)
&ptad (<optional return> with outliers removed)
&a (<optional return> coeff a of LSF: y = ax^2 + bx + c)
&b (<optional return> coeff b of LSF: y = ax^2 + bx + c)
&c (<optional return> coeff c of LSF: y = ax^2 + bx + c)
&mederr (<optional return> median error)
&nafit (<optional return> numa of least square fit to ptad)
Return: 0 if OK, 1 on error
Notes:
(1) This does a quadratic least square fit to the set of points
in @pta. It then evaluates the errors and removes points
whose error is >= factor * median_error. It then re-runs
a quadratic LSF on the resulting points.ptaPtInsidePolygon
l_int32 ptaPtInsidePolygon ( PTA *pta, l_float32 x, l_float32 y, l_int32 *pinside )
ptaPtInsidePolygon()
Input: pta (vertices of a polygon)
x, y (point to be tested)
&inside (<return> 1 if inside; 0 if outside or on boundary)
Return: 1 if OK, 0 on error
The abs value of the sum of the angles subtended from a point by
the sides of a polygon, when taken in order traversing the polygon,
is 0 if the point is outside the polygon and 2*pi if inside.
The sign will be positive if traversed cw and negative if ccw.ptaRemoveDuplicates
PTA * ptaRemoveDuplicates ( PTA *ptas, l_uint32 factor )
ptaRemoveDuplicates()
Input: ptas (assumed to be integer values)
factor (should be larger than the largest point value;
use 0 for default)
Return: ptad (with duplicates removed), or null on errorptaReplicatePattern
PTA * ptaReplicatePattern ( PTA *ptas, PIX *pixp, PTA *ptap, l_int32 cx, l_int32 cy, l_int32 w, l_int32 h )
ptaReplicatePattern()
Input: ptas ("sparse" input pta)
pixp (<optional> 1 bpp pattern, to be replicated in output pta)
ptap (<optional> set of pts, to be replicated in output pta)
cx, cy (reference point in pattern)
w, h (clipping sizes for output pta)
Return: ptad (with all points of replicated pattern), or null on error
Notes:
(1) You can use either the image @pixp or the set of pts @ptap.
(2) The pattern is placed with its reference point at each point
in ptas, and all the fg pixels are colleced into ptad.
For @pixp, this is equivalent to blitting pixp at each point
in ptas, and then converting the resulting pix to a pta.ptaReverse
PTA * ptaReverse ( PTA *ptas, l_int32 type )
ptaReverse()
Input: ptas
type (0 for float values; 1 for integer values)
Return: ptad (reversed pta), or null on errorptaSort
PTA * ptaSort ( PTA *ptas, l_int32 sorttype, l_int32 sortorder, NUMA **pnaindex )
ptaSort()
Input: ptas
sorttype (L_SORT_BY_X, L_SORT_BY_Y)
sortorder (L_SORT_INCREASING, L_SORT_DECREASING)
&naindex (<optional return> index of sorted order into
original array)
Return: ptad (sorted version of ptas), or null on errorptaSortByIndex
PTA * ptaSortByIndex ( PTA *ptas, NUMA *naindex )
ptaSortByIndex()
Input: ptas
naindex (na that maps from the new pta to the input pta)
Return: ptad (sorted), or null on errorptaSubsample
PTA * ptaSubsample ( PTA *ptas, l_int32 subfactor )
ptaSubsample()
Input: ptas
subfactor (subsample factor, >= 1)
Return: ptad (evenly sampled pt values from ptas, or null on errorptaTestIntersection
l_int32 ptaTestIntersection ( PTA *pta1, PTA *pta2 )
ptaTestIntersection()
Input: pta1, pta2
Return: bval which is 1 if they have any elements in common;
0 otherwise or on error.ptaTransform
PTA * ptaTransform ( PTA *ptas, l_int32 shiftx, l_int32 shifty, l_float32 scalex, l_float32 scaley )
ptaTransform()
Input: pta
shiftx, shifty
scalex, scaley
Return: pta, or null on error
Notes:
(1) Shift first, then scale.ptaTranspose
PTA * ptaTranspose ( PTA *ptas )
ptaTranspose()
Input: ptas
Return: ptad (with x and y values swapped), or null on errorptaaGetBoundaryPixels
PTAA * ptaaGetBoundaryPixels ( PIX *pixs, l_int32 type, l_int32 connectivity, BOXA **pboxa, PIXA **ppixa )
ptaaGetBoundaryPixels()
Input: pixs (1 bpp)
type (L_BOUNDARY_FG, L_BOUNDARY_BG)
connectivity (4 or 8)
&boxa (<optional return> bounding boxes of the c.c.)
&pixa (<optional return> pixa of the c.c.)
Return: ptaa, or null on error
Notes:
(1) This generates a ptaa of either fg or bg boundary pixels,
where each pta has the boundary pixels for a connected
component.
(2) We can't simply find all the boundary pixels and then select
those within the bounding box of each component, because
bounding boxes can overlap. It is necessary to extract and
dilate or erode each component separately. Note also that
special handling is required for bg pixels when the
component touches the pix boundary.ptaaJoin
l_int32 ptaaJoin ( PTAA *ptaad, PTAA *ptaas, l_int32 istart, l_int32 iend )
ptaaJoin()
Input: ptaad (dest ptaa; add to this one)
ptaas (source ptaa; add from this one)
istart (starting index in ptaas)
iend (ending index in ptaas; use -1 to cat all)
Return: 0 if OK, 1 on error
Notes:
(1) istart < 0 is taken to mean 'read from the start' (istart = 0)
(2) iend < 0 means 'read to the end'
(3) if ptas == NULL, this is a no-opptaaSortByIndex
PTAA * ptaaSortByIndex ( PTAA *ptaas, NUMA *naindex )
ptaaSortByIndex()
Input: ptaas
naindex (na that maps from the new ptaa to the input ptaa)
Return: ptaad (sorted), or null on errorAUTHOR
Zakariyya Mughal <zmughal@cpan.org>
COPYRIGHT AND LICENSE
This software is copyright (c) 2014 by Zakariyya Mughal.
This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.