NAME
Image::Leptonica::Func::numafunc1
VERSION
version 0.04
numafunc1.c
numafunc1.c
Arithmetic and logic
NUMA *numaArithOp()
NUMA *numaLogicalOp()
NUMA *numaInvert()
l_int32 numaSimilar()
l_int32 numaAddToNumber()
Simple extractions
l_int32 numaGetMin()
l_int32 numaGetMax()
l_int32 numaGetSum()
NUMA *numaGetPartialSums()
l_int32 numaGetSumOnInterval()
l_int32 numaHasOnlyIntegers()
NUMA *numaSubsample()
NUMA *numaMakeDelta()
NUMA *numaMakeSequence()
NUMA *numaMakeConstant()
NUMA *numaMakeAbsValue()
NUMA *numaAddBorder()
NUMA *numaAddSpecifiedBorder()
NUMA *numaRemoveBorder()
l_int32 numaGetNonzeroRange()
l_int32 numaGetCountRelativeToZero()
NUMA *numaClipToInterval()
NUMA *numaMakeThresholdIndicator()
NUMA *numaUniformSampling()
NUMA *numaReverse()
Signal feature extraction
NUMA *numaLowPassIntervals()
NUMA *numaThresholdEdges()
NUMA *numaGetSpanValues()
NUMA *numaGetEdgeValues()
Interpolation
l_int32 numaInterpolateEqxVal()
l_int32 numaInterpolateEqxInterval()
l_int32 numaInterpolateArbxVal()
l_int32 numaInterpolateArbxInterval()
Functions requiring interpolation
l_int32 numaFitMax()
l_int32 numaDifferentiateInterval()
l_int32 numaIntegrateInterval()
Sorting
NUMA *numaSortGeneral()
NUMA *numaSortAutoSelect()
NUMA *numaSortIndexAutoSelect()
l_int32 numaChooseSortType()
NUMA *numaSort()
NUMA *numaBinSort()
NUMA *numaGetSortIndex()
NUMA *numaGetBinSortIndex()
NUMA *numaSortByIndex()
l_int32 numaIsSorted()
l_int32 numaSortPair()
NUMA *numaInvertMap()
Random permutation
NUMA *numaPseudorandomSequence()
NUMA *numaRandomPermutation()
Functions requiring sorting
l_int32 numaGetRankValue()
l_int32 numaGetMedian()
l_int32 numaGetBinnedMedian()
l_int32 numaGetMode()
l_int32 numaGetMedianVariation()
Numa combination
l_int32 numaJoin()
l_int32 numaaJoin()
NUMA *numaaFlattenToNuma()
Things to remember when using the Numa:
(1) The numa is a struct, not an array. Always use accessors
(see numabasic.c), never the fields directly.
(2) The number array holds l_float32 values. It can also
be used to store l_int32 values. See numabasic.c for
details on using the accessors.
(3) If you use numaCreate(), no numbers are stored and the size is 0.
You have to add numbers to increase the size.
If you want to start with a numa of a fixed size, with each
entry initialized to the same value, use numaMakeConstant().
(4) Occasionally, in the comments we denote the i-th element of a
numa by na[i]. This is conceptual only -- the numa is not an array!FUNCTIONS
numaAddBorder
NUMA * numaAddBorder ( NUMA *nas, l_int32 left, l_int32 right, l_float32 val )
numaAddBorder()
Input: nas
left, right (number of elements to add on each side)
val (initialize border elements)
Return: nad (with added elements at left and right), or null on errornumaAddSpecifiedBorder
NUMA * numaAddSpecifiedBorder ( NUMA *nas, l_int32 left, l_int32 right, l_int32 type )
numaAddSpecifiedBorder()
Input: nas
left, right (number of elements to add on each side)
type (L_CONTINUED_BORDER, L_MIRRORED_BORDER)
Return: nad (with added elements at left and right), or null on errornumaAddToNumber
l_int32 numaAddToNumber ( NUMA *na, l_int32 index, l_float32 val )
numaAddToNumber()
Input: na
index (element to be changed)
val (new value to be added)
Return: 0 if OK, 1 on error
Notes:
(1) This is useful for accumulating sums, regardless of the index
order in which the values are made available.
(2) Before use, the numa has to be filled up to @index. This would
typically be used by creating the numa with the full sized
array, initialized to 0.0, using numaMakeConstant().numaArithOp
NUMA * numaArithOp ( NUMA *nad, NUMA *na1, NUMA *na2, l_int32 op )
numaArithOp()
Input: nad (<optional> can be null or equal to na1 (in-place)
na1
na2
op (L_ARITH_ADD, L_ARITH_SUBTRACT,
L_ARITH_MULTIPLY, L_ARITH_DIVIDE)
Return: nad (always: operation applied to na1 and na2)
Notes:
(1) The sizes of na1 and na2 must be equal.
(2) nad can only null or equal to na1.
(3) To add a constant to a numa, or to multipy a numa by
a constant, use numaTransform().numaBinSort
NUMA * numaBinSort ( NUMA *nas, l_int32 sortorder )
numaBinSort()
Input: nas (of non-negative integers with a max that is
typically less than 50,000)
sortorder (L_SORT_INCREASING or L_SORT_DECREASING)
Return: na (sorted), or null on error
Notes:
(1) Because this uses a bin sort with buckets of size 1, it
is not appropriate for sorting either small arrays or
arrays containing very large integer values. For such
arrays, use a standard general sort function like
numaSort().numaChooseSortType
l_int32 numaChooseSortType ( NUMA *nas )
numaChooseSortType()
Input: na (to be sorted)
Return: sorttype (L_SHELL_SORT or L_BIN_SORT), or UNDEF on error.
Notes:
(1) This selects either a shell sort or a bin sort, depending on
the number of elements in nas and the dynamic range.
(2) If there are negative values in nas, it selects shell sort.numaClipToInterval
NUMA * numaClipToInterval ( NUMA *nas, l_int32 first, l_int32 last )
numaClipToInterval()
Input: numa
first, last (clipping interval)
Return: numa with the same values as the input, but clipped
to the specified interval
Note: If you want the indices of the array values to be unchanged,
use first = 0.
Usage: This is useful to clip a histogram that has a few nonzero
values to its nonzero range.numaDifferentiateInterval
l_int32 numaDifferentiateInterval ( NUMA *nax, NUMA *nay, l_float32 x0, l_float32 x1, l_int32 npts, NUMA **pnadx, NUMA **pnady )
numaDifferentiateInterval()
Input: nax (numa of abscissa values)
nay (numa of ordinate values, corresponding to nax)
x0 (start value of interval)
x1 (end value of interval)
npts (number of points to evaluate function in interval)
&nadx (<optional return> array of x values in interval)
&nady (<return> array of derivatives in interval)
Return: 0 if OK, 1 on error (e.g., if x0 or x1 is outside range)
Notes:
(1) The values in nax must be sorted in increasing order.
If they are not sorted, it is done in the interpolation
step, and a warning is issued.
(2) Caller should check for valid return.numaFitMax
l_int32 numaFitMax ( NUMA *na, l_float32 *pmaxval, NUMA *naloc, l_float32 *pmaxloc )
numaFitMax()
Input: na (numa of ordinate values, to fit a max to)
&maxval (<return> max value)
naloc (<optional> associated numa of abscissa values)
&maxloc (<return> abscissa value that gives max value in na;
if naloc == null, this is given as an interpolated
index value)
Return: 0 if OK; 1 on error
Note: if naloc is given, there is no requirement that the
data points are evenly spaced. Lagrangian interpolation
handles that. The only requirement is that the
data points are ordered so that the values in naloc
are either increasing or decreasing. We test to make
sure that the sizes of na and naloc are equal, and it
is assumed that the correspondences na[i] as a function
of naloc[i] are properly arranged for all i.
The formula for Lagrangian interpolation through 3 data pts is:
y(x) = y1(x-x2)(x-x3)/((x1-x2)(x1-x3)) +
y2(x-x1)(x-x3)/((x2-x1)(x2-x3)) +
y3(x-x1)(x-x2)/((x3-x1)(x3-x2))
Then the derivative, using the constants (c1,c2,c3) defined below,
is set to 0:
y'(x) = 2x(c1+c2+c3) - c1(x2+x3) - c2(x1+x3) - c3(x1+x2) = 0numaGetBinSortIndex
NUMA * numaGetBinSortIndex ( NUMA *nas, l_int32 sortorder )
numaGetBinSortIndex()
Input: na (of non-negative integers with a max that is typically
less than 1,000,000)
sortorder (L_SORT_INCREASING or L_SORT_DECREASING)
Return: na (sorted), or null on error
Notes:
(1) This creates an array (or lookup table) that contains
the sorted position of the elements in the input Numa.
(2) Because it uses a bin sort with buckets of size 1, it
is not appropriate for sorting either small arrays or
arrays containing very large integer values. For such
arrays, use a standard general sort function like
numaGetSortIndex().numaGetBinnedMedian
l_int32 numaGetBinnedMedian ( NUMA *na, l_int32 *pval )
numaGetBinnedMedian()
Input: na
&val (<return> integer median value)
Return: 0 if OK; 1 on error
Notes:
(1) Computes the median value of the numbers in the numa,
using bin sort and finding the middle value in the sorted array.
(2) See numaGetRankValue() for conditions on na for which
this should be used. Otherwise, use numaGetMedian().numaGetCountRelativeToZero
l_int32 numaGetCountRelativeToZero ( NUMA *na, l_int32 type, l_int32 *pcount )
numaGetCountRelativeToZero()
Input: numa
type (L_LESS_THAN_ZERO, L_EQUAL_TO_ZERO, L_GREATER_THAN_ZERO)
&count (<return> count of values of given type)
Return: 0 if OK, 1 on errornumaGetEdgeValues
l_int32 numaGetEdgeValues ( NUMA *na, l_int32 edge, l_int32 *pstart, l_int32 *pend, l_int32 *psign )
numaGetEdgeValues()
Input: na (numa that is output of numaThresholdEdges())
edge (edge number, zero-based)
&start (<optional return> location of start of transition)
&end (<optional return> location of end of transition)
&sign (<optional return> transition sign: +1 is rising,
-1 is falling)
Output: 0 if OK, 1 on errornumaGetMax
l_int32 numaGetMax ( NUMA *na, l_float32 *pmaxval, l_int32 *pimaxloc )
numaGetMax()
Input: na
&maxval (<optional return> max value)
&imaxloc (<optional return> index of max location)
Return: 0 if OK; 1 on errornumaGetMedian
l_int32 numaGetMedian ( NUMA *na, l_float32 *pval )
numaGetMedian()
Input: na
&val (<return> median value)
Return: 0 if OK; 1 on error
Notes:
(1) Computes the median value of the numbers in the numa, by
sorting and finding the middle value in the sorted array.numaGetMedianVariation
l_int32 numaGetMedianVariation ( NUMA *na, l_float32 *pmedval, l_float32 *pmedvar )
numaGetMedianVariation()
Input: na
&medval (<optional return> median value)
&medvar (<return> median variation from median val)
Return: 0 if OK; 1 on error
Notes:
(1) Finds the median of the absolute value of the variation from
the median value in the array. Why take the absolute value?
Consider the case where you have values equally distributed
about both sides of a median value. Without taking the absolute
value of the differences, you will get 0 for the variation,
and this is not useful.numaGetMin
l_int32 numaGetMin ( NUMA *na, l_float32 *pminval, l_int32 *piminloc )
numaGetMin()
Input: na
&minval (<optional return> min value)
&iminloc (<optional return> index of min location)
Return: 0 if OK; 1 on errornumaGetMode
l_int32 numaGetMode ( NUMA *na, l_float32 *pval, l_int32 *pcount )
numaGetMode()
Input: na
&val (<return> mode val)
&count (<optional return> mode count)
Return: 0 if OK; 1 on error
Notes:
(1) Computes the mode value of the numbers in the numa, by
sorting and finding the value of the number with the
largest count.
(2) Optionally, also returns that count.numaGetNonzeroRange
l_int32 numaGetNonzeroRange ( NUMA *na, l_float32 eps, l_int32 *pfirst, l_int32 *plast )
numaGetNonzeroRange()
Input: numa
eps (largest value considered to be zero)
&first, &last (<return> interval of array indices
where values are nonzero)
Return: 0 if OK, 1 on error or if no nonzero range is found.numaGetPartialSums
NUMA * numaGetPartialSums ( NUMA *na )
numaGetPartialSums()
Input: na
Return: nasum, or null on error
Notes:
(1) nasum[i] is the sum for all j <= i of na[j].
So nasum[0] = na[0].
(2) If you want to generate a rank function, where rank[0] - 0.0,
insert a 0.0 at the beginning of the nasum array.numaGetRankValue
l_int32 numaGetRankValue ( NUMA *na, l_float32 fract, NUMA *nasort, l_int32 usebins, l_float32 *pval )
numaGetRankValue()
Input: na
fract (use 0.0 for smallest, 1.0 for largest)
nasort (<optional> increasing sorted version of na)
usebins (0 for general sort; 1 for bin sort)
&val (<return> rank val)
Return: 0 if OK; 1 on error
Notes:
(1) Computes the rank value of a number in the @na, which is
the number that is a fraction @fract from the small
end of the sorted version of @na.
(2) If you do this multiple times for different rank values,
sort the array in advance and use that for @nasort;
if you're only calling this once, input @nasort == NULL.
(3) If @usebins == 1, this uses a bin sorting method.
Use this only where:
* the numbers are non-negative integers
* there are over 100 numbers
* the maximum value is less than about 50,000
(4) The advantage of using a bin sort is that it is O(n),
instead of O(nlogn) for general sort routines.numaGetSortIndex
NUMA * numaGetSortIndex ( NUMA *na, l_int32 sortorder )
numaGetSortIndex()
Input: na
sortorder (L_SORT_INCREASING or L_SORT_DECREASING)
Return: na giving an array of indices that would sort
the input array, or null on errornumaGetSpanValues
l_int32 numaGetSpanValues ( NUMA *na, l_int32 span, l_int32 *pstart, l_int32 *pend )
numaGetSpanValues()
Input: na (numa that is output of numaLowPassIntervals())
span (span number, zero-based)
&start (<optional return> location of start of transition)
&end (<optional return> location of end of transition)
Output: 0 if OK, 1 on errornumaGetSum
l_int32 numaGetSum ( NUMA *na, l_float32 *psum )
numaGetSum()
Input: na
&sum (<return> sum of values)
Return: 0 if OK, 1 on errornumaGetSumOnInterval
l_int32 numaGetSumOnInterval ( NUMA *na, l_int32 first, l_int32 last, l_float32 *psum )
numaGetSumOnInterval()
Input: na
first (beginning index)
last (final index)
&sum (<return> sum of values in the index interval range)
Return: 0 if OK, 1 on errornumaHasOnlyIntegers
l_int32 numaHasOnlyIntegers ( NUMA *na, l_int32 maxsamples, l_int32 *pallints )
numaHasOnlyIntegers()
Input: na
maxsamples (maximum number of samples to check)
&allints (<return> 1 if all sampled values are ints; else 0)
Return: 0 if OK, 1 on error
Notes:
(1) Set @maxsamples == 0 to check every integer in na. Otherwise,
this samples no more than @maxsamples.numaIntegrateInterval
l_int32 numaIntegrateInterval ( NUMA *nax, NUMA *nay, l_float32 x0, l_float32 x1, l_int32 npts, l_float32 *psum )
numaIntegrateInterval()
Input: nax (numa of abscissa values)
nay (numa of ordinate values, corresponding to nax)
x0 (start value of interval)
x1 (end value of interval)
npts (number of points to evaluate function in interval)
&sum (<return> integral of function over interval)
Return: 0 if OK, 1 on error (e.g., if x0 or x1 is outside range)
Notes:
(1) The values in nax must be sorted in increasing order.
If they are not sorted, it is done in the interpolation
step, and a warning is issued.
(2) Caller should check for valid return.numaInterpolateArbxInterval
l_int32 numaInterpolateArbxInterval ( NUMA *nax, NUMA *nay, l_int32 type, l_float32 x0, l_float32 x1, l_int32 npts, NUMA **pnadx, NUMA **pnady )
numaInterpolateArbxInterval()
Input: nax (numa of abscissa values)
nay (numa of ordinate values, corresponding to nax)
type (L_LINEAR_INTERP, L_QUADRATIC_INTERP)
x0 (start value of interval)
x1 (end value of interval)
npts (number of points to evaluate function in interval)
&nadx (<optional return> array of x values in interval)
&nady (<return> array of y values in interval)
Return: 0 if OK, 1 on error (e.g., if x0 or x1 is outside range)
Notes:
(1) The values in nax must be sorted in increasing order.
If they are not sorted, we do it here, and complain.
(2) If the values in nax are equally spaced, you can use
numaInterpolateEqxInterval().
(3) Caller should check for valid return.
(4) We don't call numaInterpolateArbxVal() for each output
point, because that requires an O(n) search for
each point. Instead, we do a single O(n) pass through
nax, saving the indices to be used for each output yval.
(5) Uses lagrangian interpolation. See numaInterpolateEqxVal()
for formulas.numaInterpolateArbxVal
l_int32 numaInterpolateArbxVal ( NUMA *nax, NUMA *nay, l_int32 type, l_float32 xval, l_float32 *pyval )
numaInterpolateArbxVal()
Input: nax (numa of abscissa values)
nay (numa of ordinate values, corresponding to nax)
type (L_LINEAR_INTERP, L_QUADRATIC_INTERP)
xval
&yval (<return> interpolated value)
Return: 0 if OK, 1 on error (e.g., if xval is outside range)
Notes:
(1) The values in nax must be sorted in increasing order.
If, additionally, they are equally spaced, you can use
numaInterpolateEqxVal().
(2) Caller should check for valid return.
(3) Uses lagrangian interpolation. See numaInterpolateEqxVal()
for formulas.numaInterpolateEqxInterval
l_int32 numaInterpolateEqxInterval ( l_float32 startx, l_float32 deltax, NUMA *nasy, l_int32 type, l_float32 x0, l_float32 x1, l_int32 npts, NUMA **pnax, NUMA **pnay )
numaInterpolateEqxInterval()
Input: startx (xval corresponding to first element in nas)
deltax (x increment between array elements in nas)
nasy (numa of ordinate values, assumed equally spaced)
type (L_LINEAR_INTERP, L_QUADRATIC_INTERP)
x0 (start value of interval)
x1 (end value of interval)
npts (number of points to evaluate function in interval)
&nax (<optional return> array of x values in interval)
&nay (<return> array of y values in interval)
Return: 0 if OK, 1 on error
Notes:
(1) Considering nasy as a function of x, the x values
are equally spaced.
(2) This creates nay (and optionally nax) of interpolated
values over the specified interval (x0, x1).
(3) If the interval (x0, x1) lies partially outside the array
nasy (as interpreted by startx and deltax), it is an
error and returns 1.
(4) Note that deltax is the intrinsic x-increment for the input
array nasy, whereas delx is the intrinsic x-increment for the
output interpolated array nay.numaInterpolateEqxVal
l_int32 numaInterpolateEqxVal ( l_float32 startx, l_float32 deltax, NUMA *nay, l_int32 type, l_float32 xval, l_float32 *pyval )
numaInterpolateEqxVal()
Input: startx (xval corresponding to first element in array)
deltax (x increment between array elements)
nay (numa of ordinate values, assumed equally spaced)
type (L_LINEAR_INTERP, L_QUADRATIC_INTERP)
xval
&yval (<return> interpolated value)
Return: 0 if OK, 1 on error (e.g., if xval is outside range)
Notes:
(1) Considering nay as a function of x, the x values
are equally spaced
(2) Caller should check for valid return.
For linear Lagrangian interpolation (through 2 data pts):
y(x) = y1(x-x2)/(x1-x2) + y2(x-x1)/(x2-x1)
For quadratic Lagrangian interpolation (through 3 data pts):
y(x) = y1(x-x2)(x-x3)/((x1-x2)(x1-x3)) +
y2(x-x1)(x-x3)/((x2-x1)(x2-x3)) +
y3(x-x1)(x-x2)/((x3-x1)(x3-x2))numaInvert
NUMA * numaInvert ( NUMA *nad, NUMA *nas )
numaInvert()
Input: nad (<optional> can be null or equal to nas (in-place)
nas
Return: nad (always: 'inverts' nas)
Notes:
(1) This is intended for use with indicator arrays (0s and 1s).
It gives a boolean-type output, taking the input as
an integer and inverting it:
0 --> 1
anything else --> 0numaInvertMap
NUMA * numaInvertMap ( NUMA *nas )
numaInvertMap()
Input: nas
Return: nad (the inverted map), or null on error or if not invertible
Notes:
(1) This requires that nas contain each integer from 0 to n-1.
The array is typically an index array into a sort or permutation
of another array.numaIsSorted
l_int32 numaIsSorted ( NUMA *nas, l_int32 sortorder, l_int32 *psorted )
numaIsSorted()
Input: nas
sortorder (L_SORT_INCREASING or L_SORT_DECREASING)
&sorted (<return> 1 if sorted; 0 if not)
Return: 1 if OK; 0 on error
Notes:
(1) This is a quick O(n) test if nas is sorted. It is useful
in situations where the array is likely to be already
sorted, and a sort operation can be avoided.numaJoin
l_int32 numaJoin ( NUMA *nad, NUMA *nas, l_int32 istart, l_int32 iend )
numaJoin()
Input: nad (dest numa; add to this one)
nas (<optional> source numa; add from this one)
istart (starting index in nas)
iend (ending index in nas; 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 nas == NULL, this is a no-opnumaLogicalOp
NUMA * numaLogicalOp ( NUMA *nad, NUMA *na1, NUMA *na2, l_int32 op )
numaLogicalOp()
Input: nad (<optional> can be null or equal to na1 (in-place)
na1
na2
op (L_UNION, L_INTERSECTION, L_SUBTRACTION, L_EXCLUSIVE_OR)
Return: nad (always: operation applied to na1 and na2)
Notes:
(1) The sizes of na1 and na2 must be equal.
(2) nad can only null or equal to na1.
(3) This is intended for use with indicator arrays (0s and 1s).
Input data is extracted as integers (0 == false, anything
else == true); output results are 0 and 1.
(4) L_SUBTRACTION is subtraction of val2 from val1. For bit logical
arithmetic this is (val1 & ~val2), but because these values
are integers, we use (val1 && !val2).numaLowPassIntervals
NUMA * numaLowPassIntervals ( NUMA *nas, l_float32 thresh, l_float32 maxn )
numaLowPassIntervals()
Input: nas (input numa)
thresh (threshold fraction of max; in [0.0 ... 1.0])
maxn (for normalizing; set maxn = 0.0 to use the max in nas)
Output: nad (interval abscissa pairs), or null on error
Notes:
(1) For each interval where the value is less than a specified
fraction of the maximum, this records the left and right "x"
value.numaMakeAbsValue
NUMA * numaMakeAbsValue ( NUMA *nad, NUMA *nas )
numaMakeAbsValue()
Input: nad (can be null for new array, or the same as nas for inplace)
nas (input numa)
Return: nad (with all numbers being the absval of the input),
or null on errornumaMakeConstant
NUMA * numaMakeConstant ( l_float32 val, l_int32 size )
numaMakeConstant()
Input: val
size (of numa)
Return: numa (of given size with all entries equal to 'val'),
or null on errornumaMakeDelta
NUMA * numaMakeDelta ( NUMA *nas )
numaMakeDelta()
Input: nas (input numa)
Return: numa (of difference values val[i+1] - val[i]),
or null on errornumaMakeSequence
NUMA * numaMakeSequence ( l_float32 startval, l_float32 increment, l_int32 size )
numaMakeSequence()
Input: startval
increment
size (of sequence)
Return: numa of sequence of evenly spaced values, or null on errornumaMakeThresholdIndicator
NUMA * numaMakeThresholdIndicator ( NUMA *nas, l_float32 thresh, l_int32 type )
numaMakeThresholdIndicator()
Input: nas (input numa)
thresh (threshold value)
type (L_SELECT_IF_LT, L_SELECT_IF_GT,
L_SELECT_IF_LTE, L_SELECT_IF_GTE)
Output: nad (indicator array: values are 0 and 1)
Notes:
(1) For each element in nas, if the constraint given by 'type'
correctly specifies its relation to thresh, a value of 1
is recorded in nad.numaPseudorandomSequence
NUMA * numaPseudorandomSequence ( l_int32 size, l_int32 seed )
numaPseudorandomSequence()
Input: size (of sequence)
seed (for random number generation)
Return: na (pseudorandom on {0,...,size - 1}), or null on error
Notes:
(1) This uses the Durstenfeld shuffle.
See: http://en.wikipedia.org/wiki/Fisher–Yates_shuffle.
Result is a pseudorandom permutation of the sequence of integers
from 0 to size - 1.numaRandomPermutation
NUMA * numaRandomPermutation ( NUMA *nas, l_int32 seed )
numaRandomPermutation()
Input: nas (input array)
seed (for random number generation)
Return: nas (randomly shuffled array), or null on errornumaRemoveBorder
NUMA * numaRemoveBorder ( NUMA *nas, l_int32 left, l_int32 right )
numaRemoveBorder()
Input: nas
left, right (number of elements to remove from each side)
Return: nad (with removed elements at left and right), or null on errornumaReverse
NUMA * numaReverse ( NUMA *nad, NUMA *nas )
numaReverse()
Input: nad (<optional> can be null or equal to nas)
nas (input numa)
Output: nad (reversed), or null on error
Notes:
(1) Usage:
numaReverse(nas, nas); // in-place
nad = numaReverse(NULL, nas); // makes a new onenumaSimilar
l_int32 numaSimilar ( NUMA *na1, NUMA *na2, l_float32 maxdiff, l_int32 *psimilar )
numaSimilar()
Input: na1
na2
maxdiff (use 0.0 for exact equality)
&similar (<return> 1 if similar; 0 if different)
Return: 0 if OK, 1 on error
Notes:
(1) Float values can differ slightly due to roundoff and
accumulated errors. Using @maxdiff > 0.0 allows similar
arrays to be identified.numaSort
NUMA * numaSort ( NUMA *naout, NUMA *nain, l_int32 sortorder )
numaSort()
Input: naout (output numa; can be NULL or equal to nain)
nain (input numa)
sortorder (L_SORT_INCREASING or L_SORT_DECREASING)
Return: naout (output sorted numa), or null on error
Notes:
(1) Set naout = nain for in-place; otherwise, set naout = NULL.
(2) Source: Shell sort, modified from K&R, 2nd edition, p.62.
Slow but simple O(n logn) sort.numaSortAutoSelect
NUMA * numaSortAutoSelect ( NUMA *nas, l_int32 sortorder )
numaSortAutoSelect()
Input: nas (input numa)
sortorder (L_SORT_INCREASING or L_SORT_DECREASING)
Return: naout (output sorted numa), or null on error
Notes:
(1) This does either a shell sort or a bin sort, depending on
the number of elements in nas and the dynamic range.numaSortByIndex
NUMA * numaSortByIndex ( NUMA *nas, NUMA *naindex )
numaSortByIndex()
Input: nas
naindex (na that maps from the new numa to the input numa)
Return: nad (sorted), or null on errornumaSortGeneral
l_int32 numaSortGeneral ( NUMA *na, NUMA **pnasort, NUMA **pnaindex, NUMA **pnainvert, l_int32 sortorder, l_int32 sorttype )
numaSortGeneral()
Input: na (source numa)
nasort (<optional> sorted numa)
naindex (<optional> index of elements in na associated
with each element of nasort)
nainvert (<optional> index of elements in nasort associated
with each element of na)
sortorder (L_SORT_INCREASING or L_SORT_DECREASING)
sorttype (L_SHELL_SORT or L_BIN_SORT)
Return: 0 if OK, 1 on error
Notes:
(1) Sorting can be confusing. Here's an array of five values with
the results shown for the 3 output arrays.
na nasort naindex nainvert
-----------------------------------
3 9 2 3
4 6 3 2
9 4 1 0
6 3 0 1
1 1 4 4
Note that naindex is a LUT into na for the sorted array values,
and nainvert directly gives the sorted index values for the
input array. It is useful to view naindex is as a map:
0 --> 2
1 --> 3
2 --> 1
3 --> 0
4 --> 4
and nainvert, the inverse of this map:
0 --> 3
1 --> 2
2 --> 0
3 --> 1
4 --> 4
We can write these relations symbolically as:
nasort[i] = na[naindex[i]]
na[i] = nasort[nainvert[i]]numaSortIndexAutoSelect
NUMA * numaSortIndexAutoSelect ( NUMA *nas, l_int32 sortorder )
numaSortIndexAutoSelect()
Input: nas
sortorder (L_SORT_INCREASING or L_SORT_DECREASING)
Return: nad (indices of nas, sorted by value in nas), or null on error
Notes:
(1) This does either a shell sort or a bin sort, depending on
the number of elements in nas and the dynamic range.numaSortPair
l_int32 numaSortPair ( NUMA *nax, NUMA *nay, l_int32 sortorder, NUMA **pnasx, NUMA **pnasy )
numaSortPair()
Input: nax, nay (input arrays)
sortorder (L_SORT_INCREASING or L_SORT_DECREASING)
&nasx (<return> sorted)
&naxy (<return> sorted exactly in order of nasx)
Return: 0 if OK, 1 on error
Notes:
(1) This function sorts the two input arrays, nax and nay,
together, using nax as the key for sorting.numaSubsample
NUMA * numaSubsample ( NUMA *nas, l_int32 subfactor )
numaSubsample()
Input: nas
subfactor (subsample factor, >= 1)
Return: nad (evenly sampled values from nas), or null on errornumaThresholdEdges
NUMA * numaThresholdEdges ( NUMA *nas, l_float32 thresh1, l_float32 thresh2, l_float32 maxn )
numaThresholdEdges()
Input: nas (input numa)
thresh1 (low threshold as fraction of max; in [0.0 ... 1.0])
thresh2 (high threshold as fraction of max; in [0.0 ... 1.0])
maxn (for normalizing; set maxn = 0.0 to use the max in nas)
Output: nad (edge interval triplets), or null on error
Notes:
(1) For each edge interval, where where the value is less
than @thresh1 on one side, greater than @thresh2 on
the other, and between these thresholds throughout the
interval, this records a triplet of values: the
'left' and 'right' edges, and either +1 or -1, depending
on whether the edge is rising or falling.
(2) No assumption is made about the value outside the array,
so if the value at the array edge is between the threshold
values, it is not considered part of an edge. We start
looking for edge intervals only after leaving the thresholded
band.numaUniformSampling
NUMA * numaUniformSampling ( NUMA *nas, l_int32 nsamp )
numaUniformSampling()
Input: nas (input numa)
nsamp (number of samples)
Output: nad (resampled array), or null on error
Notes:
(1) This resamples the values in the array, using @nsamp
equal divisions.numaaFlattenToNuma
NUMA * numaaFlattenToNuma ( NUMAA *naa )
numaaFlattenToNuma()
Input: numaa
Return: numa, or null on error
Notes:
(1) This 'flattens' the Numaa to a Numa, by joining successively
each Numa in the Numaa.
(2) It doesn't make any assumptions about the location of the
Numas in the Numaa array, unlike most Numaa functions.
(3) It leaves the input Numaa unchanged.numaaJoin
l_int32 numaaJoin ( NUMAA *naad, NUMAA *naas, l_int32 istart, l_int32 iend )
numaaJoin()
Input: naad (dest naa; add to this one)
naas (<optional> source naa; add from this one)
istart (starting index in nas)
iend (ending index in naas; 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 naas == NULL, this is a no-opAUTHOR
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.