Leptonica
1.54
|
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 error
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 error
NUMA* numaaFlattenToNuma | ( | NUMAA * | naa | ) |
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().
NUMA* numaBinSort | ( | NUMA * | nas, |
l_int32 | sortorder | ||
) |
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().
NUMA* numaClipToInterval | ( | NUMA * | nas, |
l_int32 | first, | ||
l_int32 | last | ||
) |
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.
l_int32 numaDifferentiateInterval | ( | NUMA * | nax, |
NUMA * | nay, | ||
l_float32 | x0, | ||
l_float32 | x1, | ||
l_int32 | npts, | ||
NUMA ** | pnadx, | ||
NUMA ** | pnady | ||
) |
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.
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) = 0
l_int32 numaGetBinnedMedian | ( | NUMA * | na, |
l_int32 * | pval | ||
) |
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().
NUMA* numaGetBinSortIndex | ( | NUMA * | nas, |
l_int32 | sortorder | ||
) |
Input: na (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) This creates an array (or lookup table) that gives 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().
l_int32 numaGetCountRelativeToZero | ( | NUMA * | na, |
l_int32 | type, | ||
l_int32 * | pcount | ||
) |
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 error
l_int32 numaGetEdgeValues | ( | NUMA * | na, |
l_int32 | edge, | ||
l_int32 * | pstart, | ||
l_int32 * | pend, | ||
l_int32 * | psign | ||
) |
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 error
l_int32 numaGetMax | ( | NUMA * | na, |
l_float32 * | pmaxval, | ||
l_int32 * | pimaxloc | ||
) |
Input: na &maxval (<optional return>=""> max value) &imaxloc (<optional return>=""> index of max location) Return: 0 if OK; 1 on error
l_int32 numaGetMedian | ( | NUMA * | na, |
l_float32 * | pval | ||
) |
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.
l_int32 numaGetMedianVariation | ( | NUMA * | na, |
l_float32 * | pmedval, | ||
l_float32 * | pmedvar | ||
) |
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 variation from the median value in the array.
l_int32 numaGetMin | ( | NUMA * | na, |
l_float32 * | pminval, | ||
l_int32 * | piminloc | ||
) |
Input: na &minval (<optional return>=""> min value) &iminloc (<optional return>=""> index of min location) Return: 0 if OK; 1 on error
l_int32 numaGetMode | ( | NUMA * | na, |
l_float32 * | pval, | ||
l_int32 * | pcount | ||
) |
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.
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.
NUMA* numaGetPartialSums | ( | NUMA * | na | ) |
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.
l_int32 numaGetRankValue | ( | NUMA * | na, |
l_float32 | fract, | ||
NUMA * | nasort, | ||
l_int32 | usebins, | ||
l_float32 * | pval | ||
) |
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 , which is the number that is a fraction from the small end of the sorted version of . (2) If you do this multiple times for different rank values, sort the array in advance and use that for ; if you're only calling this once, input == NULL. (3) If == 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.
NUMA* numaGetSortIndex | ( | NUMA * | na, |
l_int32 | sortorder | ||
) |
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 error
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 error
l_int32 numaGetSum | ( | NUMA * | na, |
l_float32 * | psum | ||
) |
Input: na &sum (<return> sum of values) Return: 0 if OK, 1 on error
Input: na first (beginning index) last (final index) &sum (<return> sum of values in the index interval range) Return: 0 if OK, 1 on error
l_int32 numaHasOnlyIntegers | ( | NUMA * | na, |
l_int32 | maxsamples, | ||
l_int32 * | pallints | ||
) |
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 == 0 to check every integer in na. Otherwise, this samples no more than .
l_int32 numaIntegrateInterval | ( | NUMA * | nax, |
NUMA * | nay, | ||
l_float32 | x0, | ||
l_float32 | x1, | ||
l_int32 | npts, | ||
l_float32 * | psum | ||
) |
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.
l_int32 numaInterpolateArbxInterval | ( | NUMA * | nax, |
NUMA * | nay, | ||
l_int32 | type, | ||
l_float32 | x0, | ||
l_float32 | x1, | ||
l_int32 | npts, | ||
NUMA ** | pnadx, | ||
NUMA ** | pnady | ||
) |
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.
l_int32 numaInterpolateArbxVal | ( | NUMA * | nax, |
NUMA * | nay, | ||
l_int32 | type, | ||
l_float32 | xval, | ||
l_float32 * | pyval | ||
) |
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.
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 | ||
) |
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.
l_int32 numaInterpolateEqxVal | ( | l_float32 | startx, |
l_float32 | deltax, | ||
NUMA * | nay, | ||
l_int32 | type, | ||
l_float32 | xval, | ||
l_float32 * | pyval | ||
) |
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))
NUMA* numaInvert | ( | NUMA * | nad, |
NUMA * | nas | ||
) |
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 --> 0
l_int32 numaIsSorted | ( | NUMA * | nas, |
l_int32 | sortorder, | ||
l_int32 * | psorted | ||
) |
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.
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 0 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-op
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).
NUMA* numaLowPassIntervals | ( | NUMA * | nas, |
l_float32 | thresh, | ||
l_float32 | maxn | ||
) |
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.
NUMA* numaMakeAbsValue | ( | NUMA * | nad, |
NUMA * | nas | ||
) |
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 error
NUMA* numaMakeConstant | ( | l_float32 | val, |
l_int32 | size | ||
) |
Input: val size (of numa) Return: numa (of given size with all entries equal to 'val'), or null on error
NUMA* numaMakeDelta | ( | NUMA * | nas | ) |
Input: nas (input numa) Return: numa (of difference values val[i+1] - val[i]), or null on error
NUMA* numaMakeSequence | ( | l_float32 | startval, |
l_float32 | increment, | ||
l_int32 | size | ||
) |
Input: startval increment size (of sequence) Return: numa of sequence of evenly spaced values, or null on error
NUMA* numaMakeThresholdIndicator | ( | NUMA * | nas, |
l_float32 | thresh, | ||
l_int32 | type | ||
) |
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.
NUMA* numaPseudorandomSequence | ( | l_int32 | size, |
l_int32 | seed | ||
) |
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.
NUMA* numaRandomPermutation | ( | NUMA * | nas, |
l_int32 | seed | ||
) |
Input: nas (input array) seed (for random number generation) Return: nas (randomly shuffled array), or null on error
NUMA* numaRemoveBorder | ( | NUMA * | nas, |
l_int32 | left, | ||
l_int32 | right | ||
) |
Input: nas left, right (number of elements to remove from each side) Return: nad (with removed elements at left and right), or null on error
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.
NUMA* numaSortByIndex | ( | NUMA * | nas, |
NUMA * | naindex | ||
) |
Input: nas naindex (na that maps from the new numa to the input numa) Return: nad (sorted), or null on error
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.
NUMA* numaSubsample | ( | NUMA * | nas, |
l_int32 | subfactor | ||
) |
Input: nas subfactor (subsample factor, >= 1) Return: nad (evenly sampled values from nas), or null on error
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 on one side, greater than 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.
NUMA* numaUniformSampling | ( | NUMA * | nas, |
l_int32 | nsamp | ||
) |
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 equal divisions.