Python2/PyMuPDF: mupdf-source/thirdparty/leptonica/src/numafunc1.c comparison

comparison mupdf-source/thirdparty/leptonica/src/numafunc1.c @ 2:b50eed0cc0ef upstream

ADD: MuPDF v1.26.7: the MuPDF source as downloaded by a default build of PyMuPDF 1.26.4. The directory name has changed: no version number in the expanded directory now.

author	Franz Glasner <fzglas.hg@dom66.de>
date	Mon, 15 Sep 2025 11:43:07 +0200
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-:1d09e1dec1d9
+:b50eed0cc0ef
+/*====================================================================*
+-  Copyright (C) 2001 Leptonica.  All rights reserved.
+-
+-  Redistribution and use in source and binary forms, with or without
+-  modification, are permitted provided that the following conditions
+-  are met:
+-  1. Redistributions of source code must retain the above copyright
+-     notice, this list of conditions and the following disclaimer.
+-  2. Redistributions in binary form must reproduce the above
+-     copyright notice, this list of conditions and the following
+-     disclaimer in the documentation and/or other materials
+-     provided with the distribution.
+-
+-  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+-  ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+-  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+-  A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL ANY
+-  CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+-  EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+-  PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+-  PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
+-  OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+-  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+-  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*====================================================================*/
+/*!
+* \file  numafunc1.c
+* <pre>
+*
+*      --------------------------------------
+*      This file has these Numa utilities:
+*         - arithmetic operations
+*         - simple data analysis
+*         - generation of special sequences
+*         - permutations
+*         - interpolation
+*         - sorting
+*         - data analysis requiring sorting
+*         - joins and rearrangements
+*      --------------------------------------
+*
+*      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()
+*          l_int32      numaGetMean()
+*          l_int32      numaGetMeanAbsval()
+*          NUMA        *numaSubsample()
+*          NUMA        *numaMakeDelta()
+*          NUMA        *numaMakeSequence()
+*          NUMA        *numaMakeConstant()
+*          NUMA        *numaMakeAbsval()
+*          NUMA        *numaAddBorder()
+*          NUMA        *numaAddSpecifiedBorder()
+*          NUMA        *numaRemoveBorder()
+*          l_int32      numaCountNonzeroRuns()
+*          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()
+*          l_int32      numaAddSorted()
+*          l_int32      numaFindSortedLoc()
+*
+*      Random permutation
+*          NUMA        *numaPseudorandomSequence()
+*          NUMA        *numaRandomPermutation()
+*
+*      Functions requiring sorting
+*          l_int32      numaGetRankValue()
+*          l_int32      numaGetMedian()
+*          l_int32      numaGetBinnedMedian()
+*          l_int32      numaGetMeanDevFromMedian()
+*          l_int32      numaGetMedianDevFromMedian()
+*          l_int32      numaGetMode()
+*
+*      Rearrangements
+*          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!
+* </pre>
+*/
+#ifdef HAVE_CONFIG_H
+#include <config_auto.h>
+#endif  /* HAVE_CONFIG_H */
+#include <math.h>
+#include "allheaders.h"
+#include "array_internal.h"
+/*----------------------------------------------------------------------*
+*                Arithmetic and logical ops on Numas                   *
+*----------------------------------------------------------------------*/
+/*!
+* \brief   numaArithOp()
+*
+* \param[in]    nad     [optional] can be null or equal to na1 (in-place
+* \param[in]    na1
+* \param[in]    na2
+* \param[in]    op      L_ARITH_ADD, L_ARITH_SUBTRACT,
+*                       L_ARITH_MULTIPLY, L_ARITH_DIVIDE
+* \return  nad always: operation applied to na1 and na2
+*
+* <pre>
+* 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 multiply a numa by
+*          a constant, use numaTransform().
+* </pre>
+*/
+NUMA *
+numaArithOp(NUMA    *nad,
+NUMA    *na1,
+NUMA    *na2,
+l_int32  op)
+{
+l_int32    i, n;
+l_float32  val1, val2;
+if (!na1 || !na2)
+return (NUMA *)ERROR_PTR("na1, na2 not both defined", __func__, nad);
+n = numaGetCount(na1);
+if (n != numaGetCount(na2))
+return (NUMA *)ERROR_PTR("na1, na2 sizes differ", __func__, nad);
+if (nad && nad != na1)
+return (NUMA *)ERROR_PTR("nad defined but not in-place", __func__, nad);
+if (op != L_ARITH_ADD && op != L_ARITH_SUBTRACT &&
+op != L_ARITH_MULTIPLY && op != L_ARITH_DIVIDE)
+return (NUMA *)ERROR_PTR("invalid op", __func__, nad);
+if (op == L_ARITH_DIVIDE) {
+for (i = 0; i < n; i++) {
+numaGetFValue(na2, i, &val2);
+if (val2 == 0.0)
+return (NUMA *)ERROR_PTR("na2 has 0 element", __func__, nad);
+}
+}
+/* If nad is not identical to na1, make it an identical copy */
+if (!nad)
+nad = numaCopy(na1);
+for (i = 0; i < n; i++) {
+numaGetFValue(nad, i, &val1);
+numaGetFValue(na2, i, &val2);
+switch (op) {
+case L_ARITH_ADD:
+numaSetValue(nad, i, val1 + val2);
+break;
+case L_ARITH_SUBTRACT:
+numaSetValue(nad, i, val1 - val2);
+break;
+case L_ARITH_MULTIPLY:
+numaSetValue(nad, i, val1 * val2);
+break;
+case L_ARITH_DIVIDE:
+numaSetValue(nad, i, val1 / val2);
+break;
+default:
+lept_stderr(" Unknown arith op: %d\n", op);
+return nad;
+}
+}
+return nad;
+}
+/*!
+* \brief   numaLogicalOp()
+*
+* \param[in]    nad     [optional] can be null or equal to na1 (in-place
+* \param[in]    na1
+* \param[in]    na2
+* \param[in]    op      L_UNION, L_INTERSECTION, L_SUBTRACTION, L_EXCLUSIVE_OR
+* \return  nad always: operation applied to na1 and na2
+*
+* <pre>
+* Notes:
+*      (1) The sizes of na1 and na2 must be equal.
+*      (2) nad can only be 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).
+* </pre>
+*/
+NUMA *
+numaLogicalOp(NUMA    *nad,
+NUMA    *na1,
+NUMA    *na2,
+l_int32  op)
+{
+l_int32  i, n, val1, val2, val;
+if (!na1 || !na2)
+return (NUMA *)ERROR_PTR("na1, na2 not both defined", __func__, nad);
+n = numaGetCount(na1);
+if (n != numaGetCount(na2))
+return (NUMA *)ERROR_PTR("na1, na2 sizes differ", __func__, nad);
+if (nad && nad != na1)
+return (NUMA *)ERROR_PTR("nad defined; not in-place", __func__, nad);
+if (op != L_UNION && op != L_INTERSECTION &&
+op != L_SUBTRACTION && op != L_EXCLUSIVE_OR)
+return (NUMA *)ERROR_PTR("invalid op", __func__, nad);
+/* If nad is not identical to na1, make it an identical copy */
+if (!nad)
+nad = numaCopy(na1);
+for (i = 0; i < n; i++) {
+numaGetIValue(nad, i, &val1);
+numaGetIValue(na2, i, &val2);
+val1 = (val1 == 0) ? 0 : 1;
+val2 = (val2 == 0) ? 0 : 1;
+switch (op) {
+case L_UNION:
+val = (val1 || val2) ? 1 : 0;
+numaSetValue(nad, i, val);
+break;
+case L_INTERSECTION:
+val = (val1 && val2) ? 1 : 0;
+numaSetValue(nad, i, val);
+break;
+case L_SUBTRACTION:
+val = (val1 && !val2) ? 1 : 0;
+numaSetValue(nad, i, val);
+break;
+case L_EXCLUSIVE_OR:
+val = (val1 != val2) ? 1 : 0;
+numaSetValue(nad, i, val);
+break;
+default:
+lept_stderr(" Unknown logical op: %d\n", op);
+return nad;
+}
+}
+return nad;
+}
+/*!
+* \brief   numaInvert()
+*
+* \param[in]    nad    [optional] can be null or equal to nas (in-place
+* \param[in]    nas
+* \return  nad always: 'inverts' nas
+*
+* <pre>
+* 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
+* </pre>
+*/
+NUMA *
+numaInvert(NUMA  *nad,
+NUMA  *nas)
+{
+l_int32  i, n, val;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, nad);
+if (nad && nad != nas)
+return (NUMA *)ERROR_PTR("nad defined; not in-place", __func__, nad);
+if (!nad)
+nad = numaCopy(nas);
+n = numaGetCount(nad);
+for (i = 0; i < n; i++) {
+numaGetIValue(nad, i, &val);
+if (!val)
+val = 1;
+else
+val = 0;
+numaSetValue(nad, i, val);
+}
+return nad;
+}
+/*!
+* \brief   numaSimilar()
+*
+* \param[in]    na1
+* \param[in]    na2
+* \param[in]    maxdiff    use 0.0 for exact equality
+* \param[out]   psimilar   1 if similar; 0 if different
+* \return  0 if OK, 1 on error
+*
+* <pre>
+* Notes:
+*      (1) Float values can differ slightly due to roundoff and
+*          accumulated errors.  Using %maxdiff > 0.0 allows similar
+*          arrays to be identified.
+* </pre>
+*/
+l_int32
+numaSimilar(NUMA      *na1,
+NUMA      *na2,
+l_float32  maxdiff,
+l_int32   *psimilar)
+{
+l_int32    i, n;
+l_float32  val1, val2;
+if (!psimilar)
+return ERROR_INT("&similar not defined", __func__, 1);
+*psimilar = 0;
+if (!na1 || !na2)
+return ERROR_INT("na1 and na2 not both defined", __func__, 1);
+maxdiff = L_ABS(maxdiff);
+n = numaGetCount(na1);
+if (n != numaGetCount(na2)) return 0;
+for (i = 0; i < n; i++) {
+numaGetFValue(na1, i, &val1);
+numaGetFValue(na2, i, &val2);
+if (L_ABS(val1 - val2) > maxdiff) return 0;
+}
+*psimilar = 1;
+return 0;
+}
+/*!
+* \brief   numaAddToNumber()
+*
+* \param[in]    na       source numa
+* \param[in]    index    element to be changed
+* \param[in]    val      new value to be added
+* \return  0 if OK, 1 on error
+*
+* <pre>
+* 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().
+* </pre>
+*/
+l_ok
+numaAddToNumber(NUMA      *na,
+l_int32    index,
+l_float32  val)
+{
+l_int32  n;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+if (index < 0 || index >= n) {
+L_ERROR("index %d not in [0,...,%d]\n", __func__, index, n - 1);
+return 1;
+}
+na->array[index] += val;
+return 0;
+}
+/*----------------------------------------------------------------------*
+*                         Simple extractions                           *
+*----------------------------------------------------------------------*/
+/*!
+* \brief   numaGetMin()
+*
+* \param[in]    na        source numa
+* \param[out]   pminval   [optional] min value
+* \param[out]   piminloc  [optional] index of min location
+* \return  0 if OK; 1 on error
+*/
+l_ok
+numaGetMin(NUMA       *na,
+l_float32  *pminval,
+l_int32    *piminloc)
+{
+l_int32    i, n, iminloc;
+l_float32  val, minval;
+if (!pminval && !piminloc)
+return ERROR_INT("nothing to do", __func__, 1);
+if (pminval) *pminval = 0.0;
+if (piminloc) *piminloc = 0;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+minval = +1000000000.;
+iminloc = 0;
+for (i = 0; i < n; i++) {
+numaGetFValue(na, i, &val);
+if (val < minval) {
+minval = val;
+iminloc = i;
+}
+}
+if (pminval) *pminval = minval;
+if (piminloc) *piminloc = iminloc;
+return 0;
+}
+/*!
+* \brief   numaGetMax()
+*
+* \param[in]    na        source numa
+* \param[out]   pmaxval   [optional] max value
+* \param[out]   pimaxloc  [optional] index of max location
+* \return  0 if OK; 1 on error
+*/
+l_ok
+numaGetMax(NUMA       *na,
+l_float32  *pmaxval,
+l_int32    *pimaxloc)
+{
+l_int32    i, n, imaxloc;
+l_float32  val, maxval;
+if (!pmaxval && !pimaxloc)
+return ERROR_INT("nothing to do", __func__, 1);
+if (pmaxval) *pmaxval = 0.0;
+if (pimaxloc) *pimaxloc = 0;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+maxval = -1000000000.;
+imaxloc = 0;
+for (i = 0; i < n; i++) {
+numaGetFValue(na, i, &val);
+if (val > maxval) {
+maxval = val;
+imaxloc = i;
+}
+}
+if (pmaxval) *pmaxval = maxval;
+if (pimaxloc) *pimaxloc = imaxloc;
+return 0;
+}
+/*!
+* \brief   numaGetSum()
+*
+* \param[in]    na     source numa
+* \param[out]   psum   sum of values
+* \return  0 if OK, 1 on error
+*/
+l_ok
+numaGetSum(NUMA       *na,
+l_float32  *psum)
+{
+l_int32    i, n;
+l_float32  val, sum;
+if (!psum)
+return ERROR_INT("&sum not defined", __func__, 1);
+*psum = 0;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+sum = 0.0;
+for (i = 0; i < n; i++) {
+numaGetFValue(na, i, &val);
+sum += val;
+}
+*psum = sum;
+return 0;
+}
+/*!
+* \brief   numaGetPartialSums()
+*
+* \param[in]    na    source numa
+* \return  nasum, or NULL on error
+*
+* <pre>
+* 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.
+* </pre>
+*/
+NUMA *
+numaGetPartialSums(NUMA  *na)
+{
+l_int32    i, n;
+l_float32  val, sum;
+NUMA      *nasum;
+if (!na)
+return (NUMA *)ERROR_PTR("na not defined", __func__, NULL);
+if ((n = numaGetCount(na)) == 0)
+L_WARNING("na is empty\n", __func__);
+nasum = numaCreate(n);
+sum = 0.0;
+for (i = 0; i < n; i++) {
+numaGetFValue(na, i, &val);
+sum += val;
+numaAddNumber(nasum, sum);
+}
+return nasum;
+}
+/*!
+* \brief   numaGetSumOnInterval()
+*
+* \param[in]    na      source numa
+* \param[in]    first   beginning index
+* \param[in]    last    final index; use -1 to go to the end
+* \param[out]   psum    sum of values in the index interval range
+* \return  0 if OK, 1 on error
+*/
+l_ok
+numaGetSumOnInterval(NUMA       *na,
+l_int32     first,
+l_int32     last,
+l_float32  *psum)
+{
+l_int32    i, n;
+l_float32  val, sum;
+if (!psum)
+return ERROR_INT("&sum not defined", __func__, 1);
+*psum = 0.0;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+sum = 0.0;
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+if (first < 0) first = 0;
+if (first >= n || last < -1)  /* not an error */
+return 0;
+if (last == -1)
+last = n - 1;
+last = L_MIN(last, n - 1);
+for (i = first; i <= last; i++) {
+numaGetFValue(na, i, &val);
+sum += val;
+}
+*psum = sum;
+return 0;
+}
+/*!
+* \brief   numaHasOnlyIntegers()
+*
+* \param[in]    na           source numa
+* \param[out]   pallints     1 if all sampled values are ints; else 0
+* \return  0 if OK, 1 on error
+*/
+l_ok
+numaHasOnlyIntegers(NUMA     *na,
+l_int32  *pallints)
+{
+l_int32    i, n;
+l_float32  val;
+if (!pallints)
+return ERROR_INT("&allints not defined", __func__, 1);
+*pallints = TRUE;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+for (i = 0; i < n; i ++) {
+numaGetFValue(na, i, &val);
+if (val != (l_int32)val) {
+*pallints = FALSE;
+return 0;
+}
+}
+return 0;
+}
+/*!
+* \brief   numaGetMean()
+*
+* \param[in]    na     source numa
+* \param[out]   pave   average of values
+* \return  0 if OK, 1 on error
+*/
+l_ok
+numaGetMean(NUMA       *na,
+l_float32  *pave)
+{
+l_int32    n;
+l_float32  sum;
+if (!pave)
+return ERROR_INT("&ave not defined", __func__, 1);
+*pave = 0;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+numaGetSum(na, &sum);
+*pave = sum / n;
+return 0;
+}
+/*!
+* \brief   numaGetMeanAbsval()
+*
+* \param[in]    na         source numa
+* \param[out]   paveabs    average of absolute values
+* \return  0 if OK, 1 on error
+*/
+l_ok
+numaGetMeanAbsval(NUMA       *na,
+l_float32  *paveabs)
+{
+l_int32  n;
+NUMA    *na1;
+if (!paveabs)
+return ERROR_INT("&aveabs not defined", __func__, 1);
+*paveabs = 0;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+na1 = numaMakeAbsval(NULL, na);
+numaGetMean(na1, paveabs);
+numaDestroy(&na1);
+return 0;
+}
+/*!
+* \brief   numaSubsample()
+*
+* \param[in]    nas
+* \param[in]    subfactor    subsample factor, >= 1
+* \return  nad evenly sampled values from nas, or NULL on error
+*/
+NUMA *
+numaSubsample(NUMA    *nas,
+l_int32  subfactor)
+{
+l_int32    i, n;
+l_float32  val;
+NUMA      *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if (subfactor < 1)
+return (NUMA *)ERROR_PTR("subfactor < 1", __func__, NULL);
+nad = numaCreate(0);
+if ((n = numaGetCount(nas)) == 0)
+L_WARNING("nas is empty\n", __func__);
+for (i = 0; i < n; i++) {
+if (i % subfactor != 0) continue;
+numaGetFValue(nas, i, &val);
+numaAddNumber(nad, val);
+}
+return nad;
+}
+/*!
+* \brief   numaMakeDelta()
+*
+* \param[in]    nas    input numa
+* \return  numa of difference values val[i+1] - val[i],
+*                    or NULL on error
+*/
+NUMA *
+numaMakeDelta(NUMA  *nas)
+{
+l_int32    i, n;
+l_float32  prev, cur;
+NUMA      *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if ((n = numaGetCount(nas)) < 2) {
+L_WARNING("n < 2; returning empty numa\n", __func__);
+return numaCreate(1);
+}
+nad = numaCreate(n - 1);
+numaGetFValue(nas, 0, &prev);
+for (i = 1; i < n; i++) {
+numaGetFValue(nas, i, &cur);
+numaAddNumber(nad, cur - prev);
+prev = cur;
+}
+return nad;
+}
+/*!
+* \brief   numaMakeSequence()
+*
+* \param[in]    startval
+* \param[in]    increment
+* \param[in]    size        of sequence
+* \return  numa of sequence of evenly spaced values, or NULL on error
+*/
+NUMA *
+numaMakeSequence(l_float32  startval,
+l_float32  increment,
+l_int32    size)
+{
+l_int32    i;
+l_float32  val;
+NUMA      *na;
+if ((na = numaCreate(size)) == NULL)
+return (NUMA *)ERROR_PTR("na not made", __func__, NULL);
+for (i = 0; i < size; i++) {
+val = startval + i * increment;
+numaAddNumber(na, val);
+}
+return na;
+}
+/*!
+* \brief   numaMakeConstant()
+*
+* \param[in]    val
+* \param[in]    size     of numa
+* \return  numa of given size with all entries equal to 'val',
+*              or NULL on error
+*/
+NUMA *
+numaMakeConstant(l_float32  val,
+l_int32    size)
+{
+return numaMakeSequence(val, 0.0, size);
+}
+/*!
+* \brief   numaMakeAbsval()
+*
+* \param[in]    nad   can be null for new array, or the same as nas for inplace
+* \param[in]    nas   input numa
+* \return  nad with all numbers being the absval of the input,
+*              or NULL on error
+*/
+NUMA *
+numaMakeAbsval(NUMA  *nad,
+NUMA  *nas)
+{
+l_int32    i, n;
+l_float32  val;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if (nad && nad != nas)
+return (NUMA *)ERROR_PTR("nad and not in-place", __func__, NULL);
+if (!nad)
+nad = numaCopy(nas);
+n = numaGetCount(nad);
+for (i = 0; i < n; i++) {
+val = nad->array[i];
+nad->array[i] = L_ABS(val);
+}
+return nad;
+}
+/*!
+* \brief   numaAddBorder()
+*
+* \param[in]    nas
+* \param[in]    left    number of elements to add before the start
+* \param[in]    right   number of elements to add after the end
+* \param[in]    val     initialize border elements
+* \return  nad with added elements at left and right, or NULL on error
+*/
+NUMA *
+numaAddBorder(NUMA      *nas,
+l_int32    left,
+l_int32    right,
+l_float32  val)
+{
+l_int32     i, n, len;
+l_float32   startx, delx;
+l_float32  *fas, *fad;
+NUMA       *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if (left < 0) left = 0;
+if (right < 0) right = 0;
+if (left == 0 && right == 0)
+return numaCopy(nas);
+n = numaGetCount(nas);
+len = n + left + right;
+nad = numaMakeConstant(val, len);
+numaGetParameters(nas, &startx, &delx);
+numaSetParameters(nad, startx - delx * left, delx);
+fas = numaGetFArray(nas, L_NOCOPY);
+fad = numaGetFArray(nad, L_NOCOPY);
+for (i = 0; i < n; i++)
+fad[left + i] = fas[i];
+return nad;
+}
+/*!
+* \brief   numaAddSpecifiedBorder()
+*
+* \param[in]    nas
+* \param[in]    left    number of elements to add before the start
+* \param[in]    right   number of elements to add after the end
+* \param[in]    type    L_CONTINUED_BORDER, L_MIRRORED_BORDER
+* \return  nad with added elements at left and right, or NULL on error
+*/
+NUMA *
+numaAddSpecifiedBorder(NUMA    *nas,
+l_int32  left,
+l_int32  right,
+l_int32  type)
+{
+l_int32     i, n;
+l_float32  *fa;
+NUMA       *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if (left < 0) left = 0;
+if (right < 0) right = 0;
+if (left == 0 && right == 0)
+return numaCopy(nas);
+if (type != L_CONTINUED_BORDER && type != L_MIRRORED_BORDER)
+return (NUMA *)ERROR_PTR("invalid type", __func__, NULL);
+n = numaGetCount(nas);
+if (type == L_MIRRORED_BORDER && (left > n || right > n))
+return (NUMA *)ERROR_PTR("border too large", __func__, NULL);
+nad = numaAddBorder(nas, left, right, 0);
+n = numaGetCount(nad);
+fa = numaGetFArray(nad, L_NOCOPY);
+if (type == L_CONTINUED_BORDER) {
+for (i = 0; i < left; i++)
+fa[i] = fa[left];
+for (i = n - right; i < n; i++)
+fa[i] = fa[n - right - 1];
+} else {  /* type == L_MIRRORED_BORDER */
+for (i = 0; i < left; i++)
+fa[i] = fa[2 * left - 1 - i];
+for (i = 0; i < right; i++)
+fa[n - right + i] = fa[n - right - i - 1];
+}
+return nad;
+}
+/*!
+* \brief   numaRemoveBorder()
+*
+* \param[in]    nas
+* \param[in]    left    number of elements to remove from the start
+* \param[in]    right   number of elements to remove up to the end
+* \return  nad with removed elements at left and right, or NULL on error
+*/
+NUMA *
+numaRemoveBorder(NUMA      *nas,
+l_int32    left,
+l_int32    right)
+{
+l_int32     i, n, len;
+l_float32   startx, delx;
+l_float32  *fas, *fad;
+NUMA       *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if (left < 0) left = 0;
+if (right < 0) right = 0;
+if (left == 0 && right == 0)
+return numaCopy(nas);
+n = numaGetCount(nas);
+if ((len = n - left - right) < 0)
+return (NUMA *)ERROR_PTR("len < 0 after removal", __func__, NULL);
+nad = numaMakeConstant(0, len);
+numaGetParameters(nas, &startx, &delx);
+numaSetParameters(nad, startx + delx * left, delx);
+fas = numaGetFArray(nas, L_NOCOPY);
+fad = numaGetFArray(nad, L_NOCOPY);
+for (i = 0; i < len; i++)
+fad[i] = fas[left + i];
+return nad;
+}
+/*!
+* \brief   numaCountNonzeroRuns()
+*
+* \param[in]    na      e.g., of pixel counts in rows or columns
+* \param[out]   pcount  number of nonzero runs
+* \return  0 if OK, 1 on error
+*/
+l_ok
+numaCountNonzeroRuns(NUMA     *na,
+l_int32  *pcount)
+{
+l_int32  n, i, val, count, inrun;
+if (!pcount)
+return ERROR_INT("&count not defined", __func__, 1);
+*pcount = 0;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+count = 0;
+inrun = FALSE;
+for (i = 0; i < n; i++) {
+numaGetIValue(na, i, &val);
+if (!inrun && val > 0) {
+count++;
+inrun = TRUE;
+} else if (inrun && val == 0) {
+inrun = FALSE;
+}
+}
+*pcount = count;
+return 0;
+}
+/*!
+* \brief   numaGetNonzeroRange()
+*
+* \param[in]    na              source numa
+* \param[in]    eps             largest value considered to be zero
+* \param[out]   pfirst, plast   interval of array indices
+*                               where values are nonzero
+* \return  0 if OK, 1 on error or if no nonzero range is found.
+*/
+l_ok
+numaGetNonzeroRange(NUMA      *na,
+l_float32  eps,
+l_int32   *pfirst,
+l_int32   *plast)
+{
+l_int32    n, i, found;
+l_float32  val;
+if (pfirst) *pfirst = 0;
+if (plast) *plast = 0;
+if (!pfirst || !plast)
+return ERROR_INT("pfirst and plast not both defined", __func__, 1);
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+found = FALSE;
+for (i = 0; i < n; i++) {
+numaGetFValue(na, i, &val);
+if (val > eps) {
+found = TRUE;
+break;
+}
+}
+if (!found) {
+*pfirst = n - 1;
+*plast = 0;
+return 1;
+}
+*pfirst = i;
+for (i = n - 1; i >= 0; i--) {
+numaGetFValue(na, i, &val);
+if (val > eps)
+break;
+}
+*plast = i;
+return 0;
+}
+/*!
+* \brief   numaGetCountRelativeToZero()
+*
+* \param[in]    na      source numa
+* \param[in]    type    L_LESS_THAN_ZERO, L_EQUAL_TO_ZERO, L_GREATER_THAN_ZERO
+* \param[out]   pcount  count of values of given type
+* \return  0 if OK, 1 on error
+*/
+l_ok
+numaGetCountRelativeToZero(NUMA     *na,
+l_int32   type,
+l_int32  *pcount)
+{
+l_int32    n, i, count;
+l_float32  val;
+if (!pcount)
+return ERROR_INT("&count not defined", __func__, 1);
+*pcount = 0;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+for (i = 0, count = 0; i < n; i++) {
+numaGetFValue(na, i, &val);
+if (type == L_LESS_THAN_ZERO && val < 0.0)
+count++;
+else if (type == L_EQUAL_TO_ZERO && val == 0.0)
+count++;
+else if (type == L_GREATER_THAN_ZERO && val > 0.0)
+count++;
+}
+*pcount = count;
+return 0;
+}
+/*!
+* \brief   numaClipToInterval()
+*
+* \param[in]    nas
+* \param[in]    first    >= 0; <= last
+* \param[in]    last
+* \return  numa with the same values as the input, but clipped
+*              to the specified interval
+*
+* <pre>
+* Notes:
+*        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.
+* </pre>
+*/
+NUMA *
+numaClipToInterval(NUMA    *nas,
+l_int32  first,
+l_int32  last)
+{
+l_int32    n, i;
+l_float32  val, startx, delx;
+NUMA      *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if ((n = numaGetCount(nas)) == 0)
+return (NUMA *)ERROR_PTR("nas is empty", __func__, NULL);
+if (first < 0 || first > last)
+return (NUMA *)ERROR_PTR("range not valid", __func__, NULL);
+if (first >= n)
+return (NUMA *)ERROR_PTR("no elements in range", __func__, NULL);
+last = L_MIN(last, n - 1);
+if ((nad = numaCreate(last - first + 1)) == NULL)
+return (NUMA *)ERROR_PTR("nad not made", __func__, NULL);
+for (i = first; i <= last; i++) {
+numaGetFValue(nas, i, &val);
+numaAddNumber(nad, val);
+}
+numaGetParameters(nas, &startx, &delx);
+numaSetParameters(nad, startx + first * delx, delx);
+return nad;
+}
+/*!
+* \brief   numaMakeThresholdIndicator()
+*
+* \param[in]    nas      input numa
+* \param[in]    thresh   threshold value
+* \param[in]    type     L_SELECT_IF_LT, L_SELECT_IF_GT,
+*                        L_SELECT_IF_LTE, L_SELECT_IF_GTE
+* \return   nad : indicator array: values are 0 and 1
+*
+* <pre>
+* 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.
+* </pre>
+*/
+NUMA *
+numaMakeThresholdIndicator(NUMA      *nas,
+l_float32  thresh,
+l_int32    type)
+{
+l_int32    n, i, ival;
+l_float32  fval;
+NUMA      *nai;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if ((n = numaGetCount(nas)) == 0)
+return (NUMA *)ERROR_PTR("nas is empty", __func__, NULL);
+nai = numaCreate(n);
+for (i = 0; i < n; i++) {
+numaGetFValue(nas, i, &fval);
+ival = 0;
+switch (type)
+{
+case L_SELECT_IF_LT:
+if (fval < thresh) ival = 1;
+break;
+case L_SELECT_IF_GT:
+if (fval > thresh) ival = 1;
+break;
+case L_SELECT_IF_LTE:
+if (fval <= thresh) ival = 1;
+break;
+case L_SELECT_IF_GTE:
+if (fval >= thresh) ival = 1;
+break;
+default:
+numaDestroy(&nai);
+return (NUMA *)ERROR_PTR("invalid type", __func__, NULL);
+}
+numaAddNumber(nai, ival);
+}
+return nai;
+}
+/*!
+* \brief   numaUniformSampling()
+*
+* \param[in]    nas     input numa
+* \param[in]    nsamp   number of samples
+* \return  nad : resampled array, or NULL on error
+*
+* <pre>
+* Notes:
+*      (1) This resamples the values in the array, using %nsamp
+*          equal divisions.
+* </pre>
+*/
+NUMA *
+numaUniformSampling(NUMA    *nas,
+l_int32  nsamp)
+{
+l_int32     n, i, j, ileft, iright;
+l_float32   left, right, binsize, lfract, rfract, sum, startx, delx;
+l_float32  *array;
+NUMA       *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if ((n = numaGetCount(nas)) == 0)
+return (NUMA *)ERROR_PTR("nas is empty", __func__, NULL);
+if (nsamp <= 0)
+return (NUMA *)ERROR_PTR("nsamp must be > 0", __func__, NULL);
+nad = numaCreate(nsamp);
+array = numaGetFArray(nas, L_NOCOPY);
+binsize = (l_float32)n / (l_float32)nsamp;
+numaGetParameters(nas, &startx, &delx);
+numaSetParameters(nad, startx, binsize * delx);
+left = 0.0;
+for (i = 0; i < nsamp; i++) {
+sum = 0.0;
+right = left + binsize;
+ileft = (l_int32)left;
+lfract = 1.0f - left + ileft;
+if (lfract >= 1.0)  /* on left bin boundary */
+lfract = 0.0;
+iright = (l_int32)right;
+rfract = right - iright;
+iright = L_MIN(iright, n - 1);
+if (ileft == iright) {  /* both are within the same original sample */
+sum += (lfract + rfract - 1.0f) * array[ileft];
+} else {
+if (lfract > 0.0001)  /* left fraction */
+sum += lfract * array[ileft];
+if (rfract > 0.0001)  /* right fraction */
+sum += rfract * array[iright];
+for (j = ileft + 1; j < iright; j++)  /* entire pixels */
+sum += array[j];
+}
+numaAddNumber(nad, sum);
+left = right;
+}
+return nad;
+}
+/*!
+* \brief   numaReverse()
+*
+* \param[in]    nad    [optional] can be null or equal to nas
+* \param[in]    nas    input numa
+* \return  nad : reversed, or NULL on error
+*
+* <pre>
+* Notes:
+*      (1) Usage:
+*            numaReverse(nas, nas);   // in-place
+*            nad = numaReverse(NULL, nas);  // makes a new one
+* </pre>
+*/
+NUMA *
+numaReverse(NUMA  *nad,
+NUMA  *nas)
+{
+l_int32    n, i;
+l_float32  val1, val2;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if (nad && nas != nad)
+return (NUMA *)ERROR_PTR("nad defined but != nas", __func__, NULL);
+n = numaGetCount(nas);
+if (nad) {  /* in-place */
+for (i = 0; i < n / 2; i++) {
+numaGetFValue(nad, i, &val1);
+numaGetFValue(nad, n - i - 1, &val2);
+numaSetValue(nad, i, val2);
+numaSetValue(nad, n - i - 1, val1);
+}
+} else {
+nad = numaCreate(n);
+for (i = n - 1; i >= 0; i--) {
+numaGetFValue(nas, i, &val1);
+numaAddNumber(nad, val1);
+}
+}
+/* Reverse the startx and delx fields */
+nad->startx = nas->startx + (n - 1) * nas->delx;
+nad->delx = -nas->delx;
+return nad;
+}
+/*----------------------------------------------------------------------*
+*                       Signal feature extraction                      *
+*----------------------------------------------------------------------*/
+/*!
+* \brief   numaLowPassIntervals()
+*
+* \param[in]    nas      input numa
+* \param[in]    thresh   threshold fraction of max; in [0.0 ... 1.0]
+* \param[in]    maxn     for normalizing; set maxn = 0.0 to use the max in nas
+* \return  nad : interval abscissa pairs, or NULL on error
+*
+* <pre>
+* 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.
+* </pre>
+*/
+NUMA *
+numaLowPassIntervals(NUMA      *nas,
+l_float32  thresh,
+l_float32  maxn)
+{
+l_int32    n, i, inrun;
+l_float32  maxval, threshval, fval, startx, delx, x0, x1;
+NUMA      *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if ((n = numaGetCount(nas)) == 0)
+return (NUMA *)ERROR_PTR("nas is empty", __func__, NULL);
+if (thresh < 0.0 || thresh > 1.0)
+return (NUMA *)ERROR_PTR("invalid thresh", __func__, NULL);
+/* The input threshold is a fraction of the max.
+* The first entry in nad is the value of the max. */
+if (maxn == 0.0)
+numaGetMax(nas, &maxval, NULL);
+else
+maxval = maxn;
+numaGetParameters(nas, &startx, &delx);
+threshval = thresh * maxval;
+nad = numaCreate(0);
+numaAddNumber(nad, maxval);
+/* Write pairs of pts (x0, x1) for the intervals */
+inrun = FALSE;
+for (i = 0; i < n; i++) {
+numaGetFValue(nas, i, &fval);
+if (fval < threshval && inrun == FALSE) {  /* start a new run */
+inrun = TRUE;
+x0 = startx + i * delx;
+} else if (fval > threshval && inrun == TRUE) {  /* end the run */
+inrun = FALSE;
+x1 = startx + i * delx;
+numaAddNumber(nad, x0);
+numaAddNumber(nad, x1);
+}
+}
+if (inrun == TRUE) {  /* must end the last run */
+x1 = startx + (n - 1) * delx;
+numaAddNumber(nad, x0);
+numaAddNumber(nad, x1);
+}
+return nad;
+}
+/*!
+* \brief   numaThresholdEdges()
+*
+* \param[in]    nas      input numa
+* \param[in]    thresh1  low threshold as fraction of max; in [0.0 ... 1.0]
+* \param[in]    thresh2  high threshold as fraction of max; in [0.0 ... 1.0]
+* \param[in]    maxn     for normalizing; set maxn = 0.0 to use the max in nas
+* \return  nad   edge interval triplets, or NULL on error
+*
+* <pre>
+* Notes:
+*      (1) For each edge interval, 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.
+* </pre>
+*/
+NUMA *
+numaThresholdEdges(NUMA      *nas,
+l_float32  thresh1,
+l_float32  thresh2,
+l_float32  maxn)
+{
+l_int32    n, i, istart, inband, output, sign;
+l_int32    startbelow, below, above, belowlast, abovelast;
+l_float32  maxval, threshval1, threshval2, fval, startx, delx, x0, x1;
+NUMA      *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if ((n = numaGetCount(nas)) == 0)
+return (NUMA *)ERROR_PTR("nas is empty", __func__, NULL);
+if (thresh1 < 0.0 || thresh1 > 1.0 || thresh2 < 0.0 || thresh2 > 1.0)
+return (NUMA *)ERROR_PTR("invalid thresholds", __func__, NULL);
+if (thresh2 < thresh1)
+return (NUMA *)ERROR_PTR("thresh2 < thresh1", __func__, NULL);
+/* The input thresholds are fractions of the max.
+* The first entry in nad is the value of the max used
+* here for normalization. */
+if (maxn == 0.0)
+numaGetMax(nas, &maxval, NULL);
+else
+maxval = maxn;
+numaGetMax(nas, &maxval, NULL);
+numaGetParameters(nas, &startx, &delx);
+threshval1 = thresh1 * maxval;
+threshval2 = thresh2 * maxval;
+nad = numaCreate(0);
+numaAddNumber(nad, maxval);
+/* Write triplets of pts (x0, x1, sign) for the edges.
+* First make sure we start search from outside the band.
+* Only one of {belowlast, abovelast} is true. */
+for (i = 0; i < n; i++) {
+istart = i;
+numaGetFValue(nas, i, &fval);
+belowlast = (fval < threshval1) ? TRUE : FALSE;
+abovelast = (fval > threshval2) ? TRUE : FALSE;
+if (belowlast == TRUE || abovelast == TRUE)
+break;
+}
+if (istart == n)  /* no intervals found */
+return nad;
+/* x0 and x1 can only be set from outside the edge.
+* They are the values just before entering the band,
+* and just after entering the band.  We can jump through
+* the band, in which case they differ by one index in nas. */
+inband = FALSE;
+startbelow = belowlast; /* one of these is true */
+output = FALSE;
+x0 = startx + istart * delx;
+for (i = istart + 1; i < n; i++) {
+numaGetFValue(nas, i, &fval);
+below = (fval < threshval1) ? TRUE : FALSE;
+above = (fval > threshval2) ? TRUE : FALSE;
+if (!inband && belowlast && above) {  /* full jump up */
+x1 = startx + i * delx;
+sign = 1;
+startbelow = FALSE;  /* for the next transition */
+output = TRUE;
+} else if (!inband && abovelast && below) {  /* full jump down */
+x1 = startx + i * delx;
+sign = -1;
+startbelow = TRUE;  /* for the next transition */
+output = TRUE;
+} else if (inband && startbelow && above) {  /* exit rising; success */
+x1 = startx + i * delx;
+sign = 1;
+inband = FALSE;
+startbelow = FALSE;  /* for the next transition */
+output = TRUE;
+} else if (inband && !startbelow && below) {
+/* exit falling; success */
+x1 = startx + i * delx;
+sign = -1;
+inband = FALSE;
+startbelow = TRUE;  /* for the next transition */
+output = TRUE;
+} else if (inband && !startbelow && above) {  /* exit rising; failure */
+x0 = startx + i * delx;
+inband = FALSE;
+} else if (inband && startbelow && below) {  /* exit falling; failure */
+x0 = startx + i * delx;
+inband = FALSE;
+} else if (!inband && !above && !below) {  /* enter */
+inband = TRUE;
+startbelow = belowlast;
+} else if (!inband && (above || below)) {  /* outside and remaining */
+x0 = startx + i * delx;  /* update position */
+}
+belowlast = below;
+abovelast = above;
+if (output) {  /* we have exited; save new x0 */
+numaAddNumber(nad, x0);
+numaAddNumber(nad, x1);
+numaAddNumber(nad, sign);
+output = FALSE;
+x0 = startx + i * delx;
+}
+}
+return nad;
+}
+/*!
+* \brief   numaGetSpanValues()
+*
+* \param[in]    na       numa that is output of numaLowPassIntervals()
+* \param[in]    span     span number, zero-based
+* \param[out]   pstart   [optional] location of start of transition
+* \param[out]   pend     [optional] location of end of transition
+* \return  0 if OK, 1 on error
+*/
+l_int32
+numaGetSpanValues(NUMA    *na,
+l_int32  span,
+l_int32 *pstart,
+l_int32 *pend)
+{
+l_int32  n, nspans;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+if (n % 2 != 1)
+return ERROR_INT("n is not odd", __func__, 1);
+nspans = n / 2;
+if (nspans < 0 || span >= nspans)
+return ERROR_INT("invalid span", __func__, 1);
+if (pstart) numaGetIValue(na, 2 * span + 1, pstart);
+if (pend) numaGetIValue(na, 2 * span + 2, pend);
+return 0;
+}
+/*!
+* \brief   numaGetEdgeValues()
+*
+* \param[in]    na       numa that is output of numaThresholdEdges()
+* \param[in]    edge     edge number, zero-based
+* \param[out]   pstart   [optional] location of start of transition
+* \param[out]   pend     [optional] location of end of transition
+* \param[out]   psign    [optional] transition sign: +1 is rising,
+*                        -1 is falling
+* \return  0 if OK, 1 on error
+*/
+l_int32
+numaGetEdgeValues(NUMA    *na,
+l_int32  edge,
+l_int32 *pstart,
+l_int32 *pend,
+l_int32 *psign)
+{
+l_int32  n, nedges;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+if (n % 3 != 1)
+return ERROR_INT("n % 3 is not 1", __func__, 1);
+nedges = (n - 1) / 3;
+if (edge < 0 || edge >= nedges)
+return ERROR_INT("invalid edge", __func__, 1);
+if (pstart) numaGetIValue(na, 3 * edge + 1, pstart);
+if (pend) numaGetIValue(na, 3 * edge + 2, pend);
+if (psign) numaGetIValue(na, 3 * edge + 3, psign);
+return 0;
+}
+/*----------------------------------------------------------------------*
+*                             Interpolation                            *
+*----------------------------------------------------------------------*/
+/*!
+* \brief   numaInterpolateEqxVal()
+*
+* \param[in]    startx   xval corresponding to first element in array
+* \param[in]    deltax   x increment between array elements
+* \param[in]    nay      numa of ordinate values, assumed equally spaced
+* \param[in]    type     L_LINEAR_INTERP, L_QUADRATIC_INTERP
+* \param[in]    xval
+* \param[out]   pyval    interpolated value
+* \return  0 if OK, 1 on error e.g., if xval is outside range
+*
+* <pre>
+* 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))
+*
+* </pre>
+*/
+l_ok
+numaInterpolateEqxVal(l_float32   startx,
+l_float32   deltax,
+NUMA       *nay,
+l_int32     type,
+l_float32   xval,
+l_float32  *pyval)
+{
+l_int32     i, n, i1, i2, i3;
+l_float32   x1, x2, x3, fy1, fy2, fy3, d1, d2, d3, del, fi, maxx;
+l_float32  *fa;
+if (!pyval)
+return ERROR_INT("&yval not defined", __func__, 1);
+*pyval = 0.0;
+if (!nay)
+return ERROR_INT("nay not defined", __func__, 1);
+if (deltax <= 0.0)
+return ERROR_INT("deltax not > 0", __func__, 1);
+if (type != L_LINEAR_INTERP && type != L_QUADRATIC_INTERP)
+return ERROR_INT("invalid interp type", __func__, 1);
+if ((n = numaGetCount(nay)) < 2)
+return ERROR_INT("not enough points", __func__, 1);
+if (type == L_QUADRATIC_INTERP && n == 2) {
+type = L_LINEAR_INTERP;
+L_WARNING("only 2 points; using linear interp\n", __func__);
+}
+maxx = startx + deltax * (n - 1);
+if (xval < startx || xval > maxx)
+return ERROR_INT("xval is out of bounds", __func__, 1);
+fa = numaGetFArray(nay, L_NOCOPY);
+fi = (xval - startx) / deltax;
+i = (l_int32)fi;
+del = fi - i;
+if (del == 0.0) {  /* no interpolation required */
+*pyval = fa[i];
+return 0;
+}
+if (type == L_LINEAR_INTERP) {
+*pyval = fa[i] + del * (fa[i + 1] - fa[i]);
+return 0;
+}
+/* Quadratic interpolation */
+d1 = d3 = 0.5f / (deltax * deltax);
+d2 = -2.f * d1;
+if (i == 0) {
+i1 = i;
+i2 = i + 1;
+i3 = i + 2;
+} else {
+i1 = i - 1;
+i2 = i;
+i3 = i + 1;
+}
+x1 = startx + i1 * deltax;
+x2 = startx + i2 * deltax;
+x3 = startx + i3 * deltax;
+fy1 = d1 * fa[i1];
+fy2 = d2 * fa[i2];
+fy3 = d3 * fa[i3];
+*pyval = fy1 * (xval - x2) * (xval - x3) +
+fy2 * (xval - x1) * (xval - x3) +
+fy3 * (xval - x1) * (xval - x2);
+return 0;
+}
+/*!
+* \brief   numaInterpolateArbxVal()
+*
+* \param[in]    nax    numa of abscissa values
+* \param[in]    nay    numa of ordinate values, corresponding to nax
+* \param[in]    type   L_LINEAR_INTERP, L_QUADRATIC_INTERP
+* \param[in]    xval
+* \param[out]   pyval  interpolated value
+* \return  0 if OK, 1 on error e.g., if xval is outside range
+*
+* <pre>
+* 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.
+* </pre>
+*/
+l_ok
+numaInterpolateArbxVal(NUMA       *nax,
+NUMA       *nay,
+l_int32     type,
+l_float32   xval,
+l_float32  *pyval)
+{
+l_int32     i, im, nx, ny, i1, i2, i3;
+l_float32   delu, dell, fract, d1, d2, d3;
+l_float32   minx, maxx;
+l_float32  *fax, *fay;
+if (!pyval)
+return ERROR_INT("&yval not defined", __func__, 1);
+*pyval = 0.0;
+if (!nax)
+return ERROR_INT("nax not defined", __func__, 1);
+if (!nay)
+return ERROR_INT("nay not defined", __func__, 1);
+if (type != L_LINEAR_INTERP && type != L_QUADRATIC_INTERP)
+return ERROR_INT("invalid interp type", __func__, 1);
+ny = numaGetCount(nay);
+nx = numaGetCount(nax);
+if (nx != ny)
+return ERROR_INT("nax and nay not same size arrays", __func__, 1);
+if (ny < 2)
+return ERROR_INT("not enough points", __func__, 1);
+if (type == L_QUADRATIC_INTERP && ny == 2) {
+type = L_LINEAR_INTERP;
+L_WARNING("only 2 points; using linear interp\n", __func__);
+}
+numaGetFValue(nax, 0, &minx);
+numaGetFValue(nax, nx - 1, &maxx);
+if (xval < minx || xval > maxx)
+return ERROR_INT("xval is out of bounds", __func__, 1);
+fax = numaGetFArray(nax, L_NOCOPY);
+fay = numaGetFArray(nay, L_NOCOPY);
+/* Linear search for interval.  We are guaranteed
+* to either return or break out of the loop.
+* In addition, we are assured that fax[i] - fax[im] > 0.0 */
+if (xval == fax[0]) {
+*pyval = fay[0];
+return 0;
+}
+im = 0;
+dell = 0.0;
+for (i = 1; i < nx; i++) {
+delu = fax[i] - xval;
+if (delu >= 0.0) {  /* we've passed it */
+if (delu == 0.0) {
+*pyval = fay[i];
+return 0;
+}
+im = i - 1;
+dell = xval - fax[im];  /* >= 0 */
+break;
+}
+}
+fract = dell / (fax[i] - fax[im]);
+if (type == L_LINEAR_INTERP) {
+*pyval = fay[i] + fract * (fay[i + 1] - fay[i]);
+return 0;
+}
+/* Quadratic interpolation */
+if (im == 0) {
+i1 = im;
+i2 = im + 1;
+i3 = im + 2;
+} else {
+i1 = im - 1;
+i2 = im;
+i3 = im + 1;
+}
+d1 = (fax[i1] - fax[i2]) * (fax[i1] - fax[i3]);
+d2 = (fax[i2] - fax[i1]) * (fax[i2] - fax[i3]);
+d3 = (fax[i3] - fax[i1]) * (fax[i3] - fax[i2]);
+*pyval = fay[i1] * (xval - fax[i2]) * (xval - fax[i3]) / d1 +
+fay[i2] * (xval - fax[i1]) * (xval - fax[i3]) / d2 +
+fay[i3] * (xval - fax[i1]) * (xval - fax[i2]) / d3;
+return 0;
+}
+/*!
+* \brief   numaInterpolateEqxInterval()
+*
+* \param[in]    startx    xval corresponding to first element in nas
+* \param[in]    deltax    x increment between array elements in nas
+* \param[in]    nasy      numa of ordinate values, assumed equally spaced
+* \param[in]    type      L_LINEAR_INTERP, L_QUADRATIC_INTERP
+* \param[in]    x0        start value of interval
+* \param[in]    x1        end value of interval
+* \param[in]    npts      number of points to evaluate function in interval
+* \param[out]   pnax      [optional] array of x values in interval
+* \param[out]   pnay      array of y values in interval
+* \return  0 if OK, 1 on error
+*
+* <pre>
+* 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.
+* </pre>
+*/
+l_ok
+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)
+{
+l_int32     i, n;
+l_float32   x, yval, maxx, delx;
+NUMA       *nax = NULL, *nay;
+if (pnax) *pnax = NULL;
+if (!pnay)
+return ERROR_INT("&nay not defined", __func__, 1);
+*pnay = NULL;
+if (!nasy)
+return ERROR_INT("nasy not defined", __func__, 1);
+if ((n = numaGetCount(nasy)) < 2)
+return ERROR_INT("n < 2", __func__, 1);
+if (deltax <= 0.0)
+return ERROR_INT("deltax not > 0", __func__, 1);
+if (type != L_LINEAR_INTERP && type != L_QUADRATIC_INTERP)
+return ERROR_INT("invalid interp type", __func__, 1);
+if (type == L_QUADRATIC_INTERP && n == 2) {
+type = L_LINEAR_INTERP;
+L_WARNING("only 2 points; using linear interp\n", __func__);
+}
+maxx = startx + deltax * (n - 1);
+if (x0 < startx || x1 > maxx || x1 <= x0)
+return ERROR_INT("[x0 ... x1] is not valid", __func__, 1);
+if (npts < 3)
+return ERROR_INT("npts < 3", __func__, 1);
+delx = (x1 - x0) / (l_float32)(npts - 1);  /* delx is for output nay */
+if ((nay = numaCreate(npts)) == NULL)
+return ERROR_INT("nay not made", __func__, 1);
+numaSetParameters(nay, x0, delx);
+*pnay = nay;
+if (pnax) {
+nax = numaCreate(npts);
+*pnax = nax;
+}
+for (i = 0; i < npts; i++) {
+x = x0 + i * delx;
+if (pnax)
+numaAddNumber(nax, x);
+numaInterpolateEqxVal(startx, deltax, nasy, type, x, &yval);
+numaAddNumber(nay, yval);
+}
+return 0;
+}
+/*!
+* \brief   numaInterpolateArbxInterval()
+*
+* \param[in]    nax     numa of abscissa values
+* \param[in]    nay     numa of ordinate values, corresponding to nax
+* \param[in]    type    L_LINEAR_INTERP, L_QUADRATIC_INTERP
+* \param[in]    x0      start value of interval
+* \param[in]    x1      end value of interval
+* \param[in]    npts    number of points to evaluate function in interval
+* \param[out]   pnadx   [optional] array of x values in interval
+* \param[out]   pnady   array of y values in interval
+* \return  0 if OK, 1 on error e.g., if x0 or x1 is outside range
+*
+* <pre>
+* 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.
+* </pre>
+*/
+l_ok
+numaInterpolateArbxInterval(NUMA       *nax,
+NUMA       *nay,
+l_int32     type,
+l_float32   x0,
+l_float32   x1,
+l_int32     npts,
+NUMA      **pnadx,
+NUMA      **pnady)
+{
+l_int32     i, im, j, nx, ny, i1, i2, i3, sorted;
+l_int32    *index;
+l_float32   del, xval, yval, excess, fract, minx, maxx, d1, d2, d3;
+l_float32  *fax, *fay;
+NUMA       *nasx, *nasy, *nadx = NULL, *nady;
+if (pnadx) *pnadx = NULL;
+if (!pnady)
+return ERROR_INT("&nady not defined", __func__, 1);
+*pnady = NULL;
+if (!nay)
+return ERROR_INT("nay not defined", __func__, 1);
+if (!nax)
+return ERROR_INT("nax not defined", __func__, 1);
+if (type != L_LINEAR_INTERP && type != L_QUADRATIC_INTERP)
+return ERROR_INT("invalid interp type", __func__, 1);
+if (x0 > x1)
+return ERROR_INT("x0 > x1", __func__, 1);
+ny = numaGetCount(nay);
+nx = numaGetCount(nax);
+if (nx != ny)
+return ERROR_INT("nax and nay not same size arrays", __func__, 1);
+if (ny < 2)
+return ERROR_INT("not enough points", __func__, 1);
+if (type == L_QUADRATIC_INTERP && ny == 2) {
+type = L_LINEAR_INTERP;
+L_WARNING("only 2 points; using linear interp\n", __func__);
+}
+numaGetMin(nax, &minx, NULL);
+numaGetMax(nax, &maxx, NULL);
+if (x0 < minx || x1 > maxx)
+return ERROR_INT("xval is out of bounds", __func__, 1);
+/* Make sure that nax is sorted in increasing order */
+numaIsSorted(nax, L_SORT_INCREASING, &sorted);
+if (!sorted) {
+L_WARNING("we are sorting nax in increasing order\n", __func__);
+numaSortPair(nax, nay, L_SORT_INCREASING, &nasx, &nasy);
+} else {
+nasx = numaClone(nax);
+nasy = numaClone(nay);
+}
+fax = numaGetFArray(nasx, L_NOCOPY);
+fay = numaGetFArray(nasy, L_NOCOPY);
+/* Get array of indices into fax for interpolated locations */
+if ((index = (l_int32 *)LEPT_CALLOC(npts, sizeof(l_int32))) == NULL) {
+numaDestroy(&nasx);
+numaDestroy(&nasy);
+return ERROR_INT("ind not made", __func__, 1);
+}
+del = (x1 - x0) / (npts - 1.0f);
+for (i = 0, j = 0; j < nx && i < npts; i++) {
+xval = x0 + i * del;
+while (j < nx - 1 && xval > fax[j])
+j++;
+if (xval == fax[j])
+index[i] = L_MIN(j, nx - 1);
+else    /* the index of fax[] is just below xval */
+index[i] = L_MAX(j - 1, 0);
+}
+/* For each point to be interpolated, get the y value */
+nady = numaCreate(npts);
+*pnady = nady;
+if (pnadx) {
+nadx = numaCreate(npts);
+*pnadx = nadx;
+}
+for (i = 0; i < npts; i++) {
+xval = x0 + i * del;
+if (pnadx)
+numaAddNumber(nadx, xval);
+im = index[i];
+excess = xval - fax[im];
+if (excess == 0.0) {
+numaAddNumber(nady, fay[im]);
+continue;
+}
+fract = excess / (fax[im + 1] - fax[im]);
+if (type == L_LINEAR_INTERP) {
+yval = fay[im] + fract * (fay[im + 1] - fay[im]);
+numaAddNumber(nady, yval);
+continue;
+}
+/* Quadratic interpolation */
+if (im == 0) {
+i1 = im;
+i2 = im + 1;
+i3 = im + 2;
+} else {
+i1 = im - 1;
+i2 = im;
+i3 = im + 1;
+}
+d1 = (fax[i1] - fax[i2]) * (fax[i1] - fax[i3]);
+d2 = (fax[i2] - fax[i1]) * (fax[i2] - fax[i3]);
+d3 = (fax[i3] - fax[i1]) * (fax[i3] - fax[i2]);
+yval = fay[i1] * (xval - fax[i2]) * (xval - fax[i3]) / d1 +
+fay[i2] * (xval - fax[i1]) * (xval - fax[i3]) / d2 +
+fay[i3] * (xval - fax[i1]) * (xval - fax[i2]) / d3;
+numaAddNumber(nady, yval);
+}
+LEPT_FREE(index);
+numaDestroy(&nasx);
+numaDestroy(&nasy);
+return 0;
+}
+/*----------------------------------------------------------------------*
+*                     Functions requiring interpolation                *
+*----------------------------------------------------------------------*/
+/*!
+* \brief   numaFitMax()
+*
+* \param[in]    na       numa of ordinate values, to fit a max to
+* \param[out]   pmaxval  max value
+* \param[in]    naloc    [optional] associated numa of abscissa values
+* \param[out]   pmaxloc  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
+*
+* <pre>
+* Notes:
+*        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
+* </pre>
+*/
+l_ok
+numaFitMax(NUMA       *na,
+l_float32  *pmaxval,
+NUMA       *naloc,
+l_float32  *pmaxloc)
+{
+l_float32  val;
+l_float32  smaxval;  /* start value of maximum sample, before interpolating */
+l_int32    n, imaxloc;
+l_float32  x1, x2, x3, y1, y2, y3, c1, c2, c3, a, b, xmax, ymax;
+if (pmaxval) *pmaxval = 0.0;
+if (pmaxloc) *pmaxloc = 0.0;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+if (!pmaxval)
+return ERROR_INT("&maxval not defined", __func__, 1);
+if (!pmaxloc)
+return ERROR_INT("&maxloc not defined", __func__, 1);
+if (naloc) {
+if (n != numaGetCount(naloc))
+return ERROR_INT("na and naloc of unequal size", __func__, 1);
+}
+numaGetMax(na, &smaxval, &imaxloc);
+/* Simple case: max is at end point */
+if (imaxloc == 0 || imaxloc == n - 1) {
+*pmaxval = smaxval;
+if (naloc) {
+numaGetFValue(naloc, imaxloc, &val);
+*pmaxloc = val;
+} else {
+*pmaxloc = imaxloc;
+}
+return 0;
+}
+/* Interior point; use quadratic interpolation */
+y2 = smaxval;
+numaGetFValue(na, imaxloc - 1, &val);
+y1 = val;
+numaGetFValue(na, imaxloc + 1, &val);
+y3 = val;
+if (naloc) {
+numaGetFValue(naloc, imaxloc - 1, &val);
+x1 = val;
+numaGetFValue(naloc, imaxloc, &val);
+x2 = val;
+numaGetFValue(naloc, imaxloc + 1, &val);
+x3 = val;
+} else {
+x1 = imaxloc - 1;
+x2 = imaxloc;
+x3 = imaxloc + 1;
+}
+/* Can't interpolate; just use the max val in na
+* and the corresponding one in naloc */
+if (x1 == x2 || x1 == x3 || x2 == x3) {
+*pmaxval = y2;
+*pmaxloc = x2;
+return 0;
+}
+/* Use lagrangian interpolation; set dy/dx = 0 */
+c1 = y1 / ((x1 - x2) * (x1 - x3));
+c2 = y2 / ((x2 - x1) * (x2 - x3));
+c3 = y3 / ((x3 - x1) * (x3 - x2));
+a = c1 + c2 + c3;
+b = c1 * (x2 + x3) + c2 * (x1 + x3) + c3 * (x1 + x2);
+xmax = b / (2 * a);
+ymax = c1 * (xmax - x2) * (xmax - x3) +
+c2 * (xmax - x1) * (xmax - x3) +
+c3 * (xmax - x1) * (xmax - x2);
+*pmaxval = ymax;
+*pmaxloc = xmax;
+return 0;
+}
+/*!
+* \brief   numaDifferentiateInterval()
+*
+* \param[in]    nax     numa of abscissa values
+* \param[in]    nay     numa of ordinate values, corresponding to nax
+* \param[in]    x0      start value of interval
+* \param[in]    x1      end value of interval
+* \param[in]    npts    number of points to evaluate function in interval
+* \param[out]   pnadx   [optional] array of x values in interval
+* \param[out]   pnady   array of derivatives in interval
+* \return  0 if OK, 1 on error e.g., if x0 or x1 is outside range
+*
+* <pre>
+* 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.
+* </pre>
+*/
+l_ok
+numaDifferentiateInterval(NUMA       *nax,
+NUMA       *nay,
+l_float32   x0,
+l_float32   x1,
+l_int32     npts,
+NUMA      **pnadx,
+NUMA      **pnady)
+{
+l_int32     i, nx, ny;
+l_float32   minx, maxx, der, invdel;
+l_float32  *fay;
+NUMA       *nady, *naiy;
+if (pnadx) *pnadx = NULL;
+if (!pnady)
+return ERROR_INT("&nady not defined", __func__, 1);
+*pnady = NULL;
+if (!nay)
+return ERROR_INT("nay not defined", __func__, 1);
+if (!nax)
+return ERROR_INT("nax not defined", __func__, 1);
+if (x0 > x1)
+return ERROR_INT("x0 > x1", __func__, 1);
+ny = numaGetCount(nay);
+nx = numaGetCount(nax);
+if (nx != ny)
+return ERROR_INT("nax and nay not same size arrays", __func__, 1);
+if (ny < 2)
+return ERROR_INT("not enough points", __func__, 1);
+numaGetMin(nax, &minx, NULL);
+numaGetMax(nax, &maxx, NULL);
+if (x0 < minx || x1 > maxx)
+return ERROR_INT("xval is out of bounds", __func__, 1);
+if (npts < 2)
+return ERROR_INT("npts < 2", __func__, 1);
+/* Generate interpolated array over specified interval */
+if (numaInterpolateArbxInterval(nax, nay, L_LINEAR_INTERP, x0, x1,
+npts, pnadx, &naiy))
+return ERROR_INT("interpolation failed", __func__, 1);
+nady = numaCreate(npts);
+*pnady = nady;
+invdel = 0.5f * ((l_float32)npts - 1.0f) / (x1 - x0);
+fay = numaGetFArray(naiy, L_NOCOPY);
+/* Compute and save derivatives */
+der = 0.5f * invdel * (fay[1] - fay[0]);
+numaAddNumber(nady, der);
+for (i = 1; i < npts - 1; i++)  {
+der = invdel * (fay[i + 1] - fay[i - 1]);
+numaAddNumber(nady, der);
+}
+der = 0.5f * invdel * (fay[npts - 1] - fay[npts - 2]);
+numaAddNumber(nady, der);
+numaDestroy(&naiy);
+return 0;
+}
+/*!
+* \brief   numaIntegrateInterval()
+*
+* \param[in]    nax     numa of abscissa values
+* \param[in]    nay     numa of ordinate values, corresponding to nax
+* \param[in]    x0      start value of interval
+* \param[in]    x1      end value of interval
+* \param[in]    npts    number of points to evaluate function in interval
+* \param[out]   psum    integral of function over interval
+* \return  0 if OK, 1 on error e.g., if x0 or x1 is outside range
+*
+* <pre>
+* 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.
+* </pre>
+*/
+l_ok
+numaIntegrateInterval(NUMA       *nax,
+NUMA       *nay,
+l_float32   x0,
+l_float32   x1,
+l_int32     npts,
+l_float32  *psum)
+{
+l_int32     i, nx, ny;
+l_float32   minx, maxx, sum, del;
+l_float32  *fay;
+NUMA       *naiy;
+if (!psum)
+return ERROR_INT("&sum not defined", __func__, 1);
+*psum = 0.0;
+if (!nay)
+return ERROR_INT("nay not defined", __func__, 1);
+if (!nax)
+return ERROR_INT("nax not defined", __func__, 1);
+if (x0 > x1)
+return ERROR_INT("x0 > x1", __func__, 1);
+if (npts < 2)
+return ERROR_INT("npts < 2", __func__, 1);
+ny = numaGetCount(nay);
+nx = numaGetCount(nax);
+if (nx != ny)
+return ERROR_INT("nax and nay not same size arrays", __func__, 1);
+if (ny < 2)
+return ERROR_INT("not enough points", __func__, 1);
+numaGetMin(nax, &minx, NULL);
+numaGetMax(nax, &maxx, NULL);
+if (x0 < minx || x1 > maxx)
+return ERROR_INT("xval is out of bounds", __func__, 1);
+/* Generate interpolated array over specified interval */
+if (numaInterpolateArbxInterval(nax, nay, L_LINEAR_INTERP, x0, x1,
+npts, NULL, &naiy))
+return ERROR_INT("interpolation failed", __func__, 1);
+del = (x1 - x0) / ((l_float32)npts - 1.0f);
+fay = numaGetFArray(naiy, L_NOCOPY);
+/* Compute integral (simple trapezoid) */
+sum = 0.5f * (fay[0] + fay[npts - 1]);
+for (i = 1; i < npts - 1; i++)
+sum += fay[i];
+*psum = del * sum;
+numaDestroy(&naiy);
+return 0;
+}
+/*----------------------------------------------------------------------*
+*                                Sorting                               *
+*----------------------------------------------------------------------*/
+/*!
+* \brief   numaSortGeneral()
+*
+* \param[in]    na          source numa
+* \param[out]   pnasort     [optional] sorted numa
+* \param[out]   pnaindex    [optional] index of elements in na associated
+*                           with each element of nasort
+* \param[out]   pnainvert   [optional] index of elements in nasort associated
+*                           with each element of na
+* \param[in]    sortorder   L_SORT_INCREASING or L_SORT_DECREASING
+* \param[in]    sorttype    L_SHELL_SORT or L_BIN_SORT
+* \return  0 if OK, 1 on error
+*
+* <pre>
+* 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]]
+* </pre>
+*/
+l_ok
+numaSortGeneral(NUMA    *na,
+NUMA   **pnasort,
+NUMA   **pnaindex,
+NUMA   **pnainvert,
+l_int32  sortorder,
+l_int32  sorttype)
+{
+l_int32    isize;
+l_float32  size;
+NUMA      *naindex = NULL;
+if (pnasort) *pnasort = NULL;
+if (pnaindex) *pnaindex = NULL;
+if (pnainvert) *pnainvert = NULL;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if (sortorder != L_SORT_INCREASING && sortorder != L_SORT_DECREASING)
+return ERROR_INT("invalid sort order", __func__, 1);
+if (sorttype != L_SHELL_SORT && sorttype != L_BIN_SORT)
+return ERROR_INT("invalid sort type", __func__, 1);
+if (!pnasort && !pnaindex && !pnainvert)
+return ERROR_INT("nothing to do", __func__, 1);
+if (sorttype == L_BIN_SORT) {
+numaGetMax(na, &size, NULL);
+isize = (l_int32)size;
+if (isize > MaxInitPtraSize - 1) {
+L_WARNING("array too large; using shell sort\n", __func__);
+sorttype = L_SHELL_SORT;
+} else {
+naindex = numaGetBinSortIndex(na, sortorder);
+}
+}
+if (sorttype == L_SHELL_SORT)
+naindex = numaGetSortIndex(na, sortorder);
+if (pnasort)
+*pnasort = numaSortByIndex(na, naindex);
+if (pnainvert)
+*pnainvert = numaInvertMap(naindex);
+if (pnaindex)
+*pnaindex = naindex;
+else
+numaDestroy(&naindex);
+return 0;
+}
+/*!
+* \brief   numaSortAutoSelect()
+*
+* \param[in]    nas
+* \param[in]    sortorder   L_SORT_INCREASING or L_SORT_DECREASING
+* \return  naout output sorted numa, or NULL on error
+*
+* <pre>
+* Notes:
+*      (1) This does either a shell sort or a bin sort, depending on
+*          the number of elements in nas and the dynamic range.
+* </pre>
+*/
+NUMA *
+numaSortAutoSelect(NUMA    *nas,
+l_int32  sortorder)
+{
+l_int32  type;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if (numaGetCount(nas) == 0) {
+L_WARNING("nas is empty; returning copy\n", __func__);
+return numaCopy(nas);
+}
+if (sortorder != L_SORT_INCREASING && sortorder != L_SORT_DECREASING)
+return (NUMA *)ERROR_PTR("invalid sort order", __func__, NULL);
+type = numaChooseSortType(nas);
+if (type != L_SHELL_SORT && type != L_BIN_SORT)
+return (NUMA *)ERROR_PTR("invalid sort type", __func__, NULL);
+if (type == L_BIN_SORT)
+return numaBinSort(nas, sortorder);
+else  /* shell sort */
+return numaSort(NULL, nas, sortorder);
+}
+/*!
+* \brief   numaSortIndexAutoSelect()
+*
+* \param[in]    nas
+* \param[in]    sortorder     L_SORT_INCREASING or L_SORT_DECREASING
+* \return  nad indices of nas, sorted by value in nas, or NULL on error
+*
+* <pre>
+* Notes:
+*      (1) This does either a shell sort or a bin sort, depending on
+*          the number of elements in nas and the dynamic range.
+* </pre>
+*/
+NUMA *
+numaSortIndexAutoSelect(NUMA    *nas,
+l_int32  sortorder)
+{
+l_int32  type;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if (numaGetCount(nas) == 0) {
+L_WARNING("nas is empty; returning copy\n", __func__);
+return numaCopy(nas);
+}
+if (sortorder != L_SORT_INCREASING && sortorder != L_SORT_DECREASING)
+return (NUMA *)ERROR_PTR("invalid sort order", __func__, NULL);
+type = numaChooseSortType(nas);
+if (type != L_SHELL_SORT && type != L_BIN_SORT)
+return (NUMA *)ERROR_PTR("invalid sort type", __func__, NULL);
+if (type == L_BIN_SORT)
+return numaGetBinSortIndex(nas, sortorder);
+else  /* shell sort */
+return numaGetSortIndex(nas, sortorder);
+}
+/*!
+* \brief   numaChooseSortType()
+*
+* \param[in]    nas     to be sorted
+* \return  sorttype  L_SHELL_SORT or L_BIN_SORT, or UNDEF on error.
+*
+* <pre>
+* 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.
+* </pre>
+*/
+l_int32
+numaChooseSortType(NUMA  *nas)
+{
+l_int32    n;
+l_float32  minval, maxval;
+if (!nas)
+return ERROR_INT("nas not defined", __func__, UNDEF);
+/* If small histogram or negative values; use shell sort */
+numaGetMin(nas, &minval, NULL);
+n = numaGetCount(nas);
+if (minval < 0.0 || n < 200)
+return L_SHELL_SORT;
+/* If large maxval, use shell sort */
+numaGetMax(nas, &maxval, NULL);
+if (maxval > MaxInitPtraSize - 1)
+return L_SHELL_SORT;
+/* Otherwise, need to compare nlog(n) with maxval.
+* The factor of 0.003 was determined by comparing times for
+* different histogram sizes and maxval.  It is very small
+* because binsort is fast and shell sort gets slow for large n. */
+if (n * log((l_float32)n) < 0.003 * maxval)
+return L_SHELL_SORT;
+else
+return L_BIN_SORT;
+}
+/*!
+* \brief   numaSort()
+*
+* \param[in]    naout       output numa; can be NULL or equal to nain
+* \param[in]    nain        input numa
+* \param[in]    sortorder   L_SORT_INCREASING or L_SORT_DECREASING
+* \return  naout   output sorted numa, or NULL on error
+*
+* <pre>
+* 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.
+* </pre>
+*/
+NUMA *
+numaSort(NUMA    *naout,
+NUMA    *nain,
+l_int32  sortorder)
+{
+l_int32     i, n, gap, j;
+l_float32   tmp;
+l_float32  *array;
+if (!nain)
+return (NUMA *)ERROR_PTR("nain not defined", __func__, NULL);
+if (sortorder != L_SORT_INCREASING && sortorder != L_SORT_DECREASING)
+return (NUMA *)ERROR_PTR("invalid sort order", __func__, NULL);
+/* Make naout if necessary; otherwise do in-place */
+if (!naout)
+naout = numaCopy(nain);
+else if (nain != naout)
+return (NUMA *)ERROR_PTR("invalid: not in-place", __func__, NULL);
+if ((n = numaGetCount(naout)) == 0) {
+L_WARNING("naout is empty\n", __func__);
+return naout;
+}
+array = naout->array;  /* operate directly on the array */
+n = numaGetCount(naout);
+/* Shell sort */
+for (gap = n/2; gap > 0; gap = gap / 2) {
+for (i = gap; i < n; i++) {
+for (j = i - gap; j >= 0; j -= gap) {
+if ((sortorder == L_SORT_INCREASING &&
+array[j] > array[j + gap]) ||
+(sortorder == L_SORT_DECREASING &&
+array[j] < array[j + gap]))
+{
+tmp = array[j];
+array[j] = array[j + gap];
+array[j + gap] = tmp;
+}
+}
+}
+}
+return naout;
+}
+/*!
+* \brief   numaBinSort()
+*
+* \param[in]    nas         of non-negative integers with a max that can
+*                           not exceed (MaxInitPtraSize - 1)
+* \param[in]    sortorder   L_SORT_INCREASING or L_SORT_DECREASING
+* \return  na   sorted, or NULL on error
+*
+* <pre>
+* 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().
+*      (2) You can use numaSortAutoSelect() to decide which sorting
+*          method to use.
+* </pre>
+*/
+NUMA *
+numaBinSort(NUMA    *nas,
+l_int32  sortorder)
+{
+NUMA  *nat, *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if (numaGetCount(nas) == 0) {
+L_WARNING("nas is empty; returning copy\n", __func__);
+return numaCopy(nas);
+}
+if (sortorder != L_SORT_INCREASING && sortorder != L_SORT_DECREASING)
+return (NUMA *)ERROR_PTR("invalid sort order", __func__, NULL);
+if ((nat = numaGetBinSortIndex(nas, sortorder)) == NULL)
+return (NUMA *)ERROR_PTR("bin sort failed", __func__, NULL);
+nad = numaSortByIndex(nas, nat);
+numaDestroy(&nat);
+return nad;
+}
+/*!
+* \brief   numaGetSortIndex()
+*
+* \param[in]    na          source numa
+* \param[in]    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
+*/
+NUMA *
+numaGetSortIndex(NUMA    *na,
+l_int32  sortorder)
+{
+l_int32     i, n, gap, j;
+l_float32   tmp;
+l_float32  *array;   /* copy of input array */
+l_float32  *iarray;  /* array of indices */
+NUMA       *naisort;
+if (!na)
+return (NUMA *)ERROR_PTR("na not defined", __func__, NULL);
+if (numaGetCount(na) == 0) {
+L_WARNING("na is empty\n", __func__);
+return numaCreate(1);
+}
+if (sortorder != L_SORT_INCREASING && sortorder != L_SORT_DECREASING)
+return (NUMA *)ERROR_PTR("invalid sortorder", __func__, NULL);
+n = numaGetCount(na);
+if ((array = numaGetFArray(na, L_COPY)) == NULL)
+return (NUMA *)ERROR_PTR("array not made", __func__, NULL);
+if ((iarray = (l_float32 *)LEPT_CALLOC(n, sizeof(l_float32))) == NULL) {
+LEPT_FREE(array);
+return (NUMA *)ERROR_PTR("iarray not made", __func__, NULL);
+}
+for (i = 0; i < n; i++)
+iarray[i] = i;
+/* Shell sort */
+for (gap = n/2; gap > 0; gap = gap / 2) {
+for (i = gap; i < n; i++) {
+for (j = i - gap; j >= 0; j -= gap) {
+if ((sortorder == L_SORT_INCREASING &&
+array[j] > array[j + gap]) ||
+(sortorder == L_SORT_DECREASING &&
+array[j] < array[j + gap]))
+{
+tmp = array[j];
+array[j] = array[j + gap];
+array[j + gap] = tmp;
+tmp = iarray[j];
+iarray[j] = iarray[j + gap];
+iarray[j + gap] = tmp;
+}
+}
+}
+}
+naisort = numaCreate(n);
+for (i = 0; i < n; i++)
+numaAddNumber(naisort, iarray[i]);
+LEPT_FREE(array);
+LEPT_FREE(iarray);
+return naisort;
+}
+/*!
+* \brief   numaGetBinSortIndex()
+*
+* \param[in]    nas         of non-negative integers with a max that can
+*                           not exceed (MaxInitPtraSize - 1)
+* \param[in]    sortorder   L_SORT_INCREASING or L_SORT_DECREASING
+* \return  na  sorted, or NULL on error
+*
+* <pre>
+* 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().
+*      (3) You can use numaSortIndexAutoSelect() to decide which
+*          sorting method to use.
+* </pre>
+*/
+NUMA *
+numaGetBinSortIndex(NUMA    *nas,
+l_int32  sortorder)
+{
+l_int32    i, n, isize, ival, imax;
+l_float32  minsize, size;
+NUMA      *na, *nai, *nad;
+L_PTRA    *paindex;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if (numaGetCount(nas) == 0) {
+L_WARNING("nas is empty\n", __func__);
+return numaCreate(1);
+}
+if (sortorder != L_SORT_INCREASING && sortorder != L_SORT_DECREASING)
+return (NUMA *)ERROR_PTR("invalid sort order", __func__, NULL);
+numaGetMin(nas, &minsize, NULL);
+if (minsize < 0)
+return (NUMA *)ERROR_PTR("nas has negative numbers", __func__, NULL);
+numaGetMax(nas, &size, NULL);
+isize = (l_int32)size;
+if (isize > MaxInitPtraSize - 1) {
+L_ERROR("array too large: %d elements > max size = %d\n",
+__func__, isize, MaxInitPtraSize - 1);
+return NULL;
+}
+/* Set up a ptra holding numa at indices for which there
+* are values in nas.  Suppose nas has the value 230 at index
+* 7355.  A numa holding the index 7355 is created and stored
+* at the ptra index 230.  If there is another value of 230
+* in nas, its index is added to the same numa (at index 230
+* in the ptra).  When finished, the ptra can be scanned for numa,
+* and the original indices in the nas can be read out.  In this
+* way, the ptra effectively sorts the input numbers in the nas. */
+paindex = ptraCreate(isize + 1);
+n = numaGetCount(nas);
+for (i = 0; i < n; i++) {
+numaGetIValue(nas, i, &ival);
+nai = (NUMA *)ptraGetPtrToItem(paindex, ival);
+if (!nai) {  /* make it; no shifting will occur */
+nai = numaCreate(1);
+ptraInsert(paindex, ival, nai, L_MIN_DOWNSHIFT);
+}
+numaAddNumber(nai, i);
+}
+/* Sort by scanning the ptra, extracting numas and pulling
+* the (index into nas) numbers out of each numa, taken
+* successively in requested order. */
+ptraGetMaxIndex(paindex, &imax);
+nad = numaCreate(0);
+if (sortorder == L_SORT_INCREASING) {
+for (i = 0; i <= imax; i++) {
+na = (NUMA *)ptraRemove(paindex, i, L_NO_COMPACTION);
+if (!na) continue;
+numaJoin(nad, na, 0, -1);
+numaDestroy(&na);
+}
+} else {  /* L_SORT_DECREASING */
+for (i = imax; i >= 0; i--) {
+na = (NUMA *)ptraRemoveLast(paindex);
+if (!na) break;  /* they've all been removed */
+numaJoin(nad, na, 0, -1);
+numaDestroy(&na);
+}
+}
+ptraDestroy(&paindex, FALSE, FALSE);
+return nad;
+}
+/*!
+* \brief   numaSortByIndex()
+*
+* \param[in]    nas
+* \param[in]    naindex     na that maps from the new numa to the input numa
+* \return  nad  sorted, or NULL on error
+*/
+NUMA *
+numaSortByIndex(NUMA  *nas,
+NUMA  *naindex)
+{
+l_int32    i, n, ni, index;
+l_float32  val;
+NUMA      *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if (!naindex)
+return (NUMA *)ERROR_PTR("naindex not defined", __func__, NULL);
+n = numaGetCount(nas);
+ni = numaGetCount(naindex);
+if (n != ni)
+return (NUMA *)ERROR_PTR("numa sizes differ", __func__, NULL);
+if (n == 0) {
+L_WARNING("nas is empty\n", __func__);
+return numaCopy(nas);
+}
+nad = numaCreate(n);
+for (i = 0; i < n; i++) {
+numaGetIValue(naindex, i, &index);
+numaGetFValue(nas, index, &val);
+numaAddNumber(nad, val);
+}
+return nad;
+}
+/*!
+* \brief   numaIsSorted()
+*
+* \param[in]    nas
+* \param[in]    sortorder   L_SORT_INCREASING or L_SORT_DECREASING
+* \param[out]   psorted     1 if sorted; 0 if not
+* \return  1 if OK; 0 on error
+*
+* <pre>
+* 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.
+* </pre>
+*/
+l_int32
+numaIsSorted(NUMA     *nas,
+l_int32   sortorder,
+l_int32  *psorted)
+{
+l_int32    i, n;
+l_float32  prevval, val;
+if (!psorted)
+return ERROR_INT("&sorted not defined", __func__, 1);
+*psorted = FALSE;
+if (!nas)
+return ERROR_INT("nas not defined", __func__, 1);
+if ((n = numaGetCount(nas))== 0) {
+L_WARNING("nas is empty\n", __func__);
+*psorted = TRUE;
+return 0;
+}
+if (sortorder != L_SORT_INCREASING && sortorder != L_SORT_DECREASING)
+return ERROR_INT("invalid sortorder", __func__, 1);
+n = numaGetCount(nas);
+numaGetFValue(nas, 0, &prevval);
+for (i = 1; i < n; i++) {
+numaGetFValue(nas, i, &val);
+if ((sortorder == L_SORT_INCREASING && val < prevval) ||
+(sortorder == L_SORT_DECREASING && val > prevval))
+return 0;
+}
+*psorted = TRUE;
+return 0;
+}
+/*!
+* \brief   numaSortPair()
+*
+* \param[in]    nax, nay     input arrays
+* \param[in]    sortorder    L_SORT_INCREASING or L_SORT_DECREASING
+* \param[out]   pnasx        sorted
+* \param[out]   pnasy        sorted exactly in order of nasx
+* \return  0 if OK, 1 on error
+*
+* <pre>
+* Notes:
+*      (1) This function sorts the two input arrays, nax and nay,
+*          together, using nax as the key for sorting.
+* </pre>
+*/
+l_ok
+numaSortPair(NUMA    *nax,
+NUMA    *nay,
+l_int32  sortorder,
+NUMA   **pnasx,
+NUMA   **pnasy)
+{
+l_int32  sorted;
+NUMA    *naindex;
+if (pnasx) *pnasx = NULL;
+if (pnasy) *pnasy = NULL;
+if (!pnasx || !pnasy)
+return ERROR_INT("&nasx and/or &nasy not defined", __func__, 1);
+if (!nax)
+return ERROR_INT("nax not defined", __func__, 1);
+if (!nay)
+return ERROR_INT("nay not defined", __func__, 1);
+if (sortorder != L_SORT_INCREASING && sortorder != L_SORT_DECREASING)
+return ERROR_INT("invalid sortorder", __func__, 1);
+numaIsSorted(nax, sortorder, &sorted);
+if (sorted == TRUE) {
+*pnasx = numaCopy(nax);
+*pnasy = numaCopy(nay);
+} else {
+naindex = numaGetSortIndex(nax, sortorder);
+*pnasx = numaSortByIndex(nax, naindex);
+*pnasy = numaSortByIndex(nay, naindex);
+numaDestroy(&naindex);
+}
+return 0;
+}
+/*!
+* \brief   numaInvertMap()
+*
+* \param[in]    nas
+* \return  nad  the inverted map, or NULL on error or if not invertible
+*
+* <pre>
+* 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.
+* </pre>
+*/
+NUMA *
+numaInvertMap(NUMA  *nas)
+{
+l_int32   i, n, val, error;
+l_int32  *test;
+NUMA     *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if ((n = numaGetCount(nas)) == 0) {
+L_WARNING("nas is empty\n", __func__);
+return numaCopy(nas);
+}
+nad = numaMakeConstant(0.0, n);
+test = (l_int32 *)LEPT_CALLOC(n, sizeof(l_int32));
+error = 0;
+for (i = 0; i < n; i++) {
+numaGetIValue(nas, i, &val);
+if (val >= n) {
+error = 1;
+break;
+}
+numaReplaceNumber(nad, val, i);
+if (test[val] == 0) {
+test[val] = 1;
+} else {
+error = 1;
+break;
+}
+}
+LEPT_FREE(test);
+if (error) {
+numaDestroy(&nad);
+return (NUMA *)ERROR_PTR("nas not invertible", __func__, NULL);
+}
+return nad;
+}
+/*!
+* \brief   numaAddSorted()
+*
+* \param[in]    na     sorted input
+* \param[in]    val    value to be inserted in sorted order
+* \return  0 if OK, 1 on error
+*
+* <pre>
+* Notes:
+*      (1) The input %na is sorted.  This function determines the
+*          sort order of %na and inserts %val into the array.
+* </pre>
+*/
+l_ok
+numaAddSorted(NUMA      *na,
+l_float32  val)
+{
+l_int32  index;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if (numaFindSortedLoc(na, val, &index) == 1)
+return ERROR_INT("insert failure", __func__, 1);
+numaInsertNumber(na, index, val);
+return 0;
+}
+/*!
+* \brief   numaFindSortedLoc()
+*
+* \param[in]    na     sorted input
+* \param[in]    val    value to be inserted in sorted order
+* \param[out]  *ploc   index location to insert @val
+* \return  0 if OK, 1 on error
+*
+* <pre>
+* Notes:
+*      (1) The input %na is sorted.  This determines the sort order of @na,
+*          either increasing or decreasing, and does a binary search for the
+*          location to insert %val into the array.  The search is O(log n).
+*      (2) The index returned is the location to insert into the array.
+*          The value at the index, and all values to the right, are
+*          moved to the right (increasing their index location by 1).
+*      (3) If n is the size of %na, *ploc can be anything in [0 ... n].
+*          if *ploc == 0, the value is inserted at the beginning of the
+*          array; if *ploc == n, it is inserted at the end.
+*      (4) If the size of %na is 1, insert with an increasing sort.
+* </pre>
+*/
+l_ok
+numaFindSortedLoc(NUMA      *na,
+l_float32  val,
+l_int32   *pindex)
+{
+l_int32    n, increasing, lindex, rindex, midindex;
+l_float32  val0, valn, valmid;
+if (!pindex)
+return ERROR_INT("&index not defined", __func__, 1);
+*pindex = 0;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+n = numaGetCount(na);
+if (n == 0) return 0;
+numaGetFValue(na, 0, &val0);
+if (n == 1) {  /* use increasing sort order */
+if (val >= val0)
+*pindex = 1;
+return 0;
+}
+/* -----------------  n >= 2 ----------------- */
+numaGetFValue(na, n - 1, &valn);
+increasing = (valn >= val0) ? 1 : 0;  /* sort order */
+/* Check if outside bounds of existing array */
+if (increasing) {
+if (val < val0) {
+*pindex = 0;
+return 0;
+} else if (val > valn) {
+*pindex = n;
+return 0;
+}
+} else {  /* decreasing */
+if (val > val0) {
+*pindex = 0;
+return 0;
+} else if (val < valn) {
+*pindex = n;
+return 0;
+}
+}
+/* Within bounds of existing array; search */
+lindex = 0;
+rindex = n - 1;
+while (1) {
+midindex = (lindex + rindex) / 2;
+if (midindex == lindex || midindex == rindex) break;
+numaGetFValue(na, midindex, &valmid);
+if (increasing) {
+if (val > valmid)
+lindex = midindex;
+else
+rindex = midindex;
+} else {  /* decreasing */
+if (val > valmid)
+rindex = midindex;
+else
+lindex = midindex;
+}
+}
+*pindex = rindex;
+return 0;
+}
+/*----------------------------------------------------------------------*
+*                          Random permutation                          *
+*----------------------------------------------------------------------*/
+/*!
+* \brief   numaPseudorandomSequence()
+*
+* \param[in]    size     of sequence
+* \param[in]    seed     for random number generation
+* \return  na  pseudorandom on [0,...,size - 1], or NULL on error
+*
+* <pre>
+* 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.
+* </pre>
+*/
+NUMA *
+numaPseudorandomSequence(l_int32  size,
+l_int32  seed)
+{
+l_int32   i, index, temp;
+l_int32  *array;
+NUMA     *na;
+if (size <= 0)
+return (NUMA *)ERROR_PTR("size <= 0", __func__, NULL);
+if ((array = (l_int32 *)LEPT_CALLOC(size, sizeof(l_int32))) == NULL)
+return (NUMA *)ERROR_PTR("array not made", __func__, NULL);
+for (i = 0; i < size; i++)
+array[i] = i;
+srand(seed);
+for (i = size - 1; i > 0; i--) {
+index = (l_int32)((i + 1) * ((l_float64)rand() / (l_float64)RAND_MAX));
+index = L_MIN(index, i);
+temp = array[i];
+array[i] = array[index];
+array[index] = temp;
+}
+na = numaCreateFromIArray(array, size);
+LEPT_FREE(array);
+return na;
+}
+/*!
+* \brief   numaRandomPermutation()
+*
+* \param[in]    nas    input array
+* \param[in]    seed   for random number generation
+* \return  nas  randomly shuffled array, or NULL on error
+*/
+NUMA *
+numaRandomPermutation(NUMA    *nas,
+l_int32  seed)
+{
+l_int32    i, index, size;
+l_float32  val;
+NUMA      *naindex, *nad;
+if (!nas)
+return (NUMA *)ERROR_PTR("nas not defined", __func__, NULL);
+if ((size = numaGetCount(nas)) == 0) {
+L_WARNING("nas is empty\n", __func__);
+return numaCopy(nas);
+}
+naindex = numaPseudorandomSequence(size, seed);
+nad = numaCreate(size);
+for (i = 0; i < size; i++) {
+numaGetIValue(naindex, i, &index);
+numaGetFValue(nas, index, &val);
+numaAddNumber(nad, val);
+}
+numaDestroy(&naindex);
+return nad;
+}
+/*----------------------------------------------------------------------*
+*                     Functions requiring sorting                      *
+*----------------------------------------------------------------------*/
+/*!
+* \brief   numaGetRankValue()
+*
+* \param[in]    na        source numa
+* \param[in]    fract     use 0.0 for smallest, 1.0 for largest
+* \param[in]    nasort    [optional] increasing sorted version of na
+* \param[in]    usebins   0 for general sort; 1 for bin sort
+* \param[out]   pval      rank val
+* \return  0 if OK; 1 on error
+*
+* <pre>
+* 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.
+* </pre>
+*/
+l_ok
+numaGetRankValue(NUMA       *na,
+l_float32   fract,
+NUMA       *nasort,
+l_int32     usebins,
+l_float32  *pval)
+{
+l_int32  n, index;
+NUMA    *nas;
+if (!pval)
+return ERROR_INT("&val not defined", __func__, 1);
+*pval = 0.0;  /* init */
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na empty", __func__, 1);
+if (fract < 0.0 || fract > 1.0)
+return ERROR_INT("fract not in [0.0 ... 1.0]", __func__, 1);
+if (nasort) {
+nas = nasort;
+} else {
+if (usebins == 0)
+nas = numaSort(NULL, na, L_SORT_INCREASING);
+else
+nas = numaBinSort(na, L_SORT_INCREASING);
+if (!nas)
+return ERROR_INT("nas not made", __func__, 1);
+}
+index = (l_int32)(fract * (l_float32)(n - 1) + 0.5);
+numaGetFValue(nas, index, pval);
+if (!nasort) numaDestroy(&nas);
+return 0;
+}
+/*!
+* \brief   numaGetMedian()
+*
+* \param[in]    na     source numa
+* \param[out]   pval   median value
+* \return  0 if OK; 1 on error
+*
+* <pre>
+* Notes:
+*      (1) Computes the median value of the numbers in the numa, by
+*          sorting and finding the middle value in the sorted array.
+* </pre>
+*/
+l_ok
+numaGetMedian(NUMA       *na,
+l_float32  *pval)
+{
+if (!pval)
+return ERROR_INT("&val not defined", __func__, 1);
+*pval = 0.0;  /* init */
+if (!na || numaGetCount(na) == 0)
+return ERROR_INT("na not defined or empty", __func__, 1);
+return numaGetRankValue(na, 0.5, NULL, 0, pval);
+}
+/*!
+* \brief   numaGetBinnedMedian()
+*
+* \param[in]    na      source numa
+* \param[out]   pval    integer median value
+* \return  0 if OK; 1 on error
+*
+* <pre>
+* 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().
+* </pre>
+*/
+l_ok
+numaGetBinnedMedian(NUMA     *na,
+l_int32  *pval)
+{
+l_int32    ret;
+l_float32  fval;
+if (!pval)
+return ERROR_INT("&val not defined", __func__, 1);
+*pval = 0;  /* init */
+if (!na || numaGetCount(na) == 0)
+return ERROR_INT("na not defined or empty", __func__, 1);
+ret = numaGetRankValue(na, 0.5, NULL, 1, &fval);
+*pval = lept_roundftoi(fval);
+return ret;
+}
+/*!
+* \brief   numaGetMeanDevFromMedian()
+*
+* \param[in]      na     source numa
+* \param[in]      med    median value
+* \param[out]     pdev   average absolute value deviation from median value
+* \return  0 if OK; 1 on error
+*/
+l_ok
+numaGetMeanDevFromMedian(NUMA       *na,
+l_float32   med,
+l_float32  *pdev)
+{
+l_int32    i, n;
+l_float32  val, dev;
+if (!pdev)
+return ERROR_INT("&dev not defined", __func__, 1);
+*pdev = 0.0;  /* init */
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+dev = 0.0;
+for (i = 0; i < n; i++) {
+numaGetFValue(na, i, &val);
+dev += L_ABS(val - med);
+}
+*pdev = dev / (l_float32)n;
+return 0;
+}
+/*!
+* \brief   numaGetMedianDevFromMedian()
+*
+* \param[in]    na        source numa
+* \param[out]   pmed      [optional] median value
+* \param[out]   pdev      median deviation from median val
+* \return  0 if OK; 1 on error
+*
+* <pre>
+* Notes:
+*      (1) Finds the median of the absolute value of the deviation 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 deviation,
+*          and this is not useful.
+* </pre>
+*/
+l_ok
+numaGetMedianDevFromMedian(NUMA       *na,
+l_float32  *pmed,
+l_float32  *pdev)
+{
+l_int32    n, i;
+l_float32  val, med;
+NUMA      *nadev;
+if (pmed) *pmed = 0.0;
+if (!pdev)
+return ERROR_INT("&dev not defined", __func__, 1);
+*pdev = 0.0;
+if (!na || numaGetCount(na) == 0)
+return ERROR_INT("na not defined or empty", __func__, 1);
+numaGetMedian(na, &med);
+if (pmed) *pmed = med;
+n = numaGetCount(na);
+nadev = numaCreate(n);
+for (i = 0; i < n; i++) {
+numaGetFValue(na, i, &val);
+numaAddNumber(nadev, L_ABS(val - med));
+}
+numaGetMedian(nadev, pdev);
+numaDestroy(&nadev);
+return 0;
+}
+/*!
+* \brief   numaGetMode()
+*
+* \param[in]    na      source numa
+* \param[out]   pval    mode val
+* \param[out]   pcount  [optional] mode count
+* \return  0 if OK; 1 on error
+*
+* <pre>
+* 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.
+* </pre>
+*/
+l_ok
+numaGetMode(NUMA       *na,
+l_float32  *pval,
+l_int32    *pcount)
+{
+l_int32     i, n, maxcount, prevcount;
+l_float32   val, maxval, prevval;
+l_float32  *array;
+NUMA       *nasort;
+if (pcount) *pcount = 0;
+if (!pval)
+return ERROR_INT("&val not defined", __func__, 1);
+*pval = 0.0;
+if (!na)
+return ERROR_INT("na not defined", __func__, 1);
+if ((n = numaGetCount(na)) == 0)
+return ERROR_INT("na is empty", __func__, 1);
+if ((nasort = numaSort(NULL, na, L_SORT_DECREASING)) == NULL)
+return ERROR_INT("nas not made", __func__, 1);
+array = numaGetFArray(nasort, L_NOCOPY);
+/* Initialize with array[0] */
+prevval = array[0];
+prevcount = 1;
+maxval = prevval;
+maxcount = prevcount;
+/* Scan the sorted array, aggregating duplicates */
+for (i = 1; i < n; i++) {
+val = array[i];
+if (val == prevval) {
+prevcount++;
+} else {  /* new value */
+if (prevcount > maxcount) {  /* new max */
+maxcount = prevcount;
+maxval = prevval;
+}
+prevval = val;
+prevcount = 1;
+}
+}
+/* Was the mode the last run of elements? */
+if (prevcount > maxcount) {
+maxcount = prevcount;
+maxval = prevval;
+}
+*pval = maxval;
+if (pcount)
+*pcount = maxcount;
+numaDestroy(&nasort);
+return 0;
+}
+/*----------------------------------------------------------------------*
+*                            Rearrangements                            *
+*----------------------------------------------------------------------*/
+/*!
+* \brief   numaJoin()
+*
+* \param[in]    nad      dest numa; add to this one
+* \param[in]    nas      [optional] source numa; add from this one
+* \param[in]    istart   starting index in nas
+* \param[in]    iend     ending index in nas; use -1 to cat all
+* \return  0 if OK, 1 on error
+*
+* <pre>
+* 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
+* </pre>
+*/
+l_ok
+numaJoin(NUMA    *nad,
+NUMA    *nas,
+l_int32  istart,
+l_int32  iend)
+{
+l_int32    n, i;
+l_float32  val;
+if (!nad)
+return ERROR_INT("nad not defined", __func__, 1);
+if (!nas)
+return 0;
+if (istart < 0)
+istart = 0;
+n = numaGetCount(nas);
+if (iend < 0 || iend >= n)
+iend = n - 1;
+if (istart > iend)
+return ERROR_INT("istart > iend; nothing to add", __func__, 1);
+for (i = istart; i <= iend; i++) {
+numaGetFValue(nas, i, &val);
+numaAddNumber(nad, val);
+}
+return 0;
+}
+/*!
+* \brief   numaaJoin()
+*
+* \param[in]    naad     dest naa; add to this one
+* \param[in]    naas     [optional] source naa; add from this one
+* \param[in]    istart   starting index in nas
+* \param[in]    iend     ending index in naas; use -1 to cat all
+* \return  0 if OK, 1 on error
+*
+* <pre>
+* 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-op
+* </pre>
+*/
+l_ok
+numaaJoin(NUMAA   *naad,
+NUMAA   *naas,
+l_int32  istart,
+l_int32  iend)
+{
+l_int32  n, i;
+NUMA    *na;
+if (!naad)
+return ERROR_INT("naad not defined", __func__, 1);
+if (!naas)
+return 0;
+if (istart < 0)
+istart = 0;
+n = numaaGetCount(naas);
+if (iend < 0 || iend >= n)
+iend = n - 1;
+if (istart > iend)
+return ERROR_INT("istart > iend; nothing to add", __func__, 1);
+for (i = istart; i <= iend; i++) {
+na = numaaGetNuma(naas, i, L_CLONE);
+numaaAddNuma(naad, na, L_INSERT);
+}
+return 0;
+}
+/*!
+* \brief   numaaFlattenToNuma()
+*
+* \param[in]    naa
+* \return  numa, or NULL on error
+*
+* <pre>
+* 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.
+* </pre>
+*/
+NUMA *
+numaaFlattenToNuma(NUMAA  *naa)
+{
+l_int32  i, nalloc;
+NUMA    *na, *nad;
+NUMA   **array;
+if (!naa)
+return (NUMA *)ERROR_PTR("naa not defined", __func__, NULL);
+nalloc = naa->nalloc;
+array = numaaGetPtrArray(naa);
+nad = numaCreate(0);
+for (i = 0; i < nalloc; i++) {
+na = array[i];
+if (!na) continue;
+numaJoin(nad, na, 0, -1);
+}
+return nad;
+}

Mercurial > hgrepos > Python2 > PyMuPDF

comparison mupdf-source/thirdparty/leptonica/src/numafunc1.c @ 2:b50eed0cc0ef upstream