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+/* */
+/* Little cms - profiler construction set */
+/* Copyright (C) 1998-2001 Marti Maria <[email protected]> */
+/* */
+/* THIS SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND, */
+/* EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY */
+/* WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. */
+/* */
+/* IN NO EVENT SHALL MARTI MARIA BE LIABLE FOR ANY SPECIAL, INCIDENTAL, */
+/* INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, */
+/* OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, */
+/* WHETHER OR NOT ADVISED OF THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF */
+/* LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE */
+/* OF THIS SOFTWARE. */
+/* */
+/* This file is free software; you can redistribute it and/or modify it */
+/* under the terms of the GNU General Public License as published by */
+/* the Free Software Foundation; either version 2 of the License, or */
+/* (at your option) any later version. */
+/* */
+/* This program is distributed in the hope that it will be useful, but */
+/* WITHOUT ANY WARRANTY; without even the implied warranty of */
+/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU */
+/* General Public License for more details. */
+/* */
+/* You should have received a copy of the GNU General Public License */
+/* along with this program; if not, write to the Free Software */
+/* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */
+/* */
+/* As a special exception to the GNU General Public License, if you */
+/* distribute this file as part of a program that contains a */
+/* configuration script generated by Autoconf, you may include it under */
+/* the same distribution terms that you use for the rest of that program. */
+/* */
+/* Version 1.09a */
+
+
+#include "lcmsprf.h"
+
+
+/* There are three kinds of lies: */
+/* */
+/* * lies */
+/* * damn lies */
+/* * statistics */
+/* */
+/* -Some Wag */
+/* */
+/* */
+/* This module handles multiple linear regression stuff */
+
+
+
+/* A measurement of error
+
+typedef struct {
+
+ double SSE; // The error sum of squares
+ double MSE; // The error mean sum of squares
+ double SSR; // The regression sum of squares
+ double MSR; // The regression mean sum of squares
+ double SSTO; // Total sum of squares
+ double F; // The Fisher-F value (MSR / MSE)
+ double R2; // Proportion of variability explained by the regression
+ // (root is Pearson correlation coefficient)
+
+ double R2adj; // The adjusted coefficient of multiple determination.
+ // R2-adjusted or R2adj. This is calculated as
+ // R2adj = 1 - (1-R2)(N-n-1)/(N-1)
+ // and used as multiple correlation coefficient
+ // (really, it should be square root)
+
+ } MLRSTATISTICS, FAR* LPMLRSTATISTICS;
+
+*/
+
+
+int cdecl cmsxRegressionCreateMatrix(LPMEASUREMENT m, SETOFPATCHES Allowed, int nterms,
+ int ColorSpace,
+ LPMATN* lpMat, LPMLRSTATISTICS Stat);
+
+BOOL cdecl cmsxRegressionRGB2Lab(double r, double g, double b,
+ LPMATN tfm, LPcmsCIELab Lab);
+
+BOOL cdecl cmsxRegressionRGB2XYZ(double r, double g, double b,
+ LPMATN tfm, LPcmsCIEXYZ XYZ);
+
+
+/* -------------------------------------------------------------- Implementation */
+
+/* #define DEBUG 1 */
+
+
+/* Multiple linear regression. Also keep track of error. */
+/* Returns false if something goes wrong, or true if all Ok. */
+
+static
+BOOL MultipleLinearRegression(const LPMATN xi, /* Dependent variable */
+ const LPMATN y, /* Independent variable */
+ int nvar, /* Number of samples */
+ int npar, /* Number of parameters (terms) */
+ double* coeff, /* Returned coefficients */
+ LPMATN vcb, /* Variance-covariance array */
+ double *tvl, /* T-Values */
+ LPMLRSTATISTICS ans) /* The returned statistics */
+{
+ LPMATN bt, xt, a, xy, yt, b;
+ double sum;
+ LPMATN temp1, temp2;
+ int i;
+
+
+ /* |xt| = |xi| T */
+ xt = MATNtranspose(xi);
+ if (xt == NULL) return false;
+
+
+ /* |a| = |xt|* |xi| */
+ a = MATNmult(xt, xi);
+ if (a == NULL) return false;
+
+
+ /* |xy| = |xy| * |y| */
+ xy = MATNmult (xt, y);
+ if (xy == NULL) return false;
+
+
+ /* solve system |a|*|xy| = 0 */
+ if (!MATNsolve(a, xy)) return false;
+
+ /* b will hold coefficients */
+ b = MATNalloc (xy->Rows, 1);
+ if (b == NULL) return false;
+
+ for (i = 0; i < npar; i++)
+ b->Values[i][0] = xy->Values[i][0];
+
+ /* Store a copy for later user */
+ for (i = 0; i < npar; i++)
+ coeff[i] = b->Values[i][0];
+
+ /* Error analysis. */
+
+ /* SSE and MSE. */
+ temp1 = MATNalloc (1,1);
+ if ((temp1->Values[0][0] = MATNcross(y)) == 0) return false;
+
+ /* |bt| = |b| T */
+ bt = MATNtranspose (b);
+ if (bt == NULL) return false;
+
+ /* |yt| = |bt| * |xt| */
+ yt = MATNmult (bt, xt);
+ if (yt == NULL) return false;
+
+
+ /* |temp2| = |yt|* |y| */
+ temp2 = MATNmult (yt, y);
+ if (temp2 == NULL) return false;
+
+ /* SSE, MSE */
+ ans->SSE = temp1 -> Values[0][0] - temp2 -> Values[0][0];
+ ans->MSE = ans->SSE / (double) (nvar - npar);
+
+ /* SSTO */
+ sum = 0;
+ for (i=0; i < nvar; i++)
+ sum += y->Values[i][0];
+
+ sum *= sum / (double) nvar;
+ ans->SSTO = temp1->Values[0][0] - sum;
+
+ /* SSR, MSR, and Fisher-F */
+ ans->SSR = temp2->Values[0][0] - sum;
+ ans->MSR = ans->SSR / (double) (npar - 1);
+ ans->F = ans->MSR / ans->MSE;
+
+ /* Correlation coefficients. */
+ ans->R2 = ans->SSR/ans->SSTO;
+ ans->R2adj = 1.0 - (ans->SSE/ans->SSTO)*((nvar-1.)/(nvar-npar));
+
+ /* Variance-covariance matrix */
+ /* */
+ /* In RGB->Lab, for example: */
+ /* */
+ /* Var(R) Cov(R,G) Cov(R,B) */
+ /* |vcb| = Cov(R,G) Var(G) Cov(G,B) */
+ /* Cov(R,B) Cov(G,B) Var(B) */
+ /* */
+
+ MATNscalar(a, ans->MSE, vcb);
+
+ /* Determine the T-values */
+
+ for (i=0; i < npar; i++) {
+
+ temp1->Values[0][0] = fabs(vcb->Values[i][0]);
+ if ( temp1->Values[0][0] == 0)
+ tvl[i] = 0; /* This should never happen */
+ else
+ tvl[i] = b->Values[i][0] / sqrt(temp1->Values[0][0]);
+ }
+
+
+ /* Ok, done */
+
+ MATNfree(a); MATNfree(xy); MATNfree(yt); MATNfree(b);
+ MATNfree(temp1); MATNfree(temp2); MATNfree(bt); MATNfree(xt);
+
+
+ return true;
+}
+
+
+
+/* Does create (so, it allocates) the regression matrix, */
+/* keeping track of error as well. */
+
+static
+BOOL CreateRegressionMatrix(const LPMATN Input, const LPMATN Output,
+ LPMATN* ptrMatrix, LPMLRSTATISTICS maxErrorMeas)
+{
+ double* coef;
+ double* tval;
+ LPMATN ivar, dvar, vcov;
+ MLRSTATISTICS ErrorMeas, PeakErrorMeas;
+ int i, j, nIn, nOut, NumOfPatches;
+
+ nIn = Input -> Cols;
+ nOut = Output -> Cols;
+ NumOfPatches = Input -> Rows;
+
+ /* Checkpoint */
+ if (Output -> Rows != NumOfPatches) {
+
+ cmsSignalError(LCMS_ERRC_ABORTED, "(internal) Regression matrix mismatch");
+ return false;
+ }
+
+ coef = (double*) malloc(nIn * sizeof(double));
+ if (coef == NULL) return false;
+
+ tval = (double*) malloc(nIn * sizeof(double));
+ if (tval == NULL) {
+ free(coef);
+ return false;
+ }
+
+ ivar = MATNalloc(NumOfPatches, nIn);
+ dvar = MATNalloc(NumOfPatches, 1);
+
+ /* Copy In to ivar, */
+ for (i = 0; i < NumOfPatches; i++) {
+
+ for (j = 0; j < nIn; j++)
+ ivar->Values[i][j] = Input->Values[i][j];
+ }
+
+ /* This is the (symmetric) Covariance matrix */
+ vcov = MATNalloc(nIn, nIn);
+
+ /* This is the regression matrix */
+ *ptrMatrix = MATNalloc(nIn, nOut);
+
+ PeakErrorMeas.R2adj = 0;
+ for (j = 0; j < nOut; ++j)
+ {
+ for (i = 0; i < NumOfPatches; ++i)
+ dvar->Values[i][0] = Output->Values[i][j];
+
+ if (MultipleLinearRegression(ivar, dvar, NumOfPatches, nIn, coef, vcov, tval, &ErrorMeas)) {
+
+ /* Ok so far... store values */
+ for (i = 0; i < nIn; i++)
+ (*ptrMatrix)->Values[i][j] = coef[i];
+ }
+ else {
+ /* Boo... got error. Discard whole point. */
+ MATNfree(ivar); MATNfree(dvar); MATNfree(vcov);
+ if (coef) free(coef);
+ if (tval) free(tval);
+ MATNfree(*ptrMatrix); *ptrMatrix = NULL;
+ return false;
+ }
+
+ /* Did this colorant got higer error? If so, this is */
+ /* the peak of all pixel */
+
+ if(fabs(ErrorMeas.R2adj) > fabs(PeakErrorMeas.R2adj))
+ PeakErrorMeas = ErrorMeas;
+ }
+
+ /* This is the peak error on all components */
+ *maxErrorMeas = PeakErrorMeas;
+
+
+#ifdef DEBUG
+ MATNprintf("Variance-Covariance", vcov);
+ printf("R2adj: %g, F: %g\n", PeakErrorMeas.R2adj, PeakErrorMeas.F);
+#endif
+
+ /* Free stuff. */
+ MATNfree(ivar); MATNfree(dvar); MATNfree(vcov);
+ if (coef) free(coef);
+ if (tval) free(tval);
+
+ return true;
+}
+
+
+/* Does compute the term of regression based on inputs. */
+
+static
+double Term(int n, double r, double g, double b)
+{
+
+ switch (n) {
+
+ /* 0 */
+ case 0 : return 255.0; /* 0 0 0 */
+
+ /* 1 */
+ case 1 : return r; /* 1 0 0 */
+ case 2 : return g; /* 0 1 0 */
+ case 3 : return b; /* 0 0 1 */
+
+ /* 2 */
+ case 4 : return r * g; /* 1 1 0 */
+ case 5 : return r * b; /* 1 0 1 */
+ case 6 : return g * b; /* 0 1 1 */
+ case 7 : return r * r; /* 2 0 0 */
+ case 8 : return g * g; /* 0 2 0 */
+ case 9 : return b * b; /* 0 0 2 */
+
+ /* 3 */
+ case 10: return r * g * b; /* 1 1 1 */
+ case 11: return r * r * r; /* 3 0 0 */
+ case 12: return g * g * g; /* 0 3 0 */
+ case 13: return b * b * b; /* 0 0 3 */
+ case 14: return r * g * g; /* 1 2 0 */
+ case 15: return r * r * g; /* 2 1 0 */
+ case 16: return g * g * b; /* 0 2 1 */
+ case 17: return b * r * r; /* 2 0 1 */
+ case 18: return b * b * r; /* 1 0 2 */
+
+ /* 4 */
+
+ case 19: return r * r * g * g; /* 2 2 0 */
+ case 20: return g * g * b * b; /* 0 2 2 */
+ case 21: return r * r * b * b; /* 2 0 2 */
+ case 22: return r * r * g * b; /* 2 1 1 */
+ case 23: return r * g * g * b; /* 1 2 1 */
+ case 24: return r * g * b * b; /* 1 1 2 */
+ case 25: return r * r * r * g; /* 3 1 0 */
+ case 26: return r * r * r * b; /* 3 0 1 */
+ case 27: return r * g * g * g; /* 1 3 0 */
+ case 28: return g * g * g * b; /* 0 3 1 */
+ case 29: return r * b * b * b; /* 1 0 3 */
+ case 30: return g * b * b * b; /* 0 1 3 */
+ case 31: return r * r * r * r; /* 4 0 0 */
+ case 32: return g * g * g * g; /* 0 4 0 */
+ case 33: return b * b * b * b; /* 0 0 4 */
+
+ /* 5 */
+
+ case 34: return r * r * g * g * b; /* 2 2 1 */
+ case 35: return r * g * g * b * b; /* 1 2 2 */
+ case 36: return r * r * g * b * b; /* 2 1 2 */
+ case 37: return r * r * r * g * g; /* 3 2 0 */
+ case 38: return r * r * r * g * b; /* 3 1 1 */
+ case 39: return r * r * r * b * b; /* 3 0 2 */
+ case 40: return g * g * g * b * b; /* 0 3 2 */
+ case 41: return r * r * g * g * g; /* 2 3 0 */
+ case 42: return r * g * g * g * b; /* 1 3 1 */
+ case 43: return r * r * b * b * b; /* 2 0 3 */
+ case 44: return g * g * b * b * b; /* 0 2 3 */
+ case 45: return r * g * b * b * b; /* 1 1 3 */
+ case 46: return r * r * r * r * g; /* 4 1 0 */
+ case 47: return r * r * r * r * b; /* 4 0 1 */
+ case 48: return r * g * g * g * g; /* 1 4 0 */
+ case 49: return g * g * g * g * b; /* 0 4 1 */
+ case 50: return r * b * b * b * b; /* 1 0 4 */
+ case 51: return g * b * b * b * b; /* 0 1 4 */
+ case 52: return r * r * r * r * r; /* 5 0 0 */
+ case 53: return g * g * g * g * g; /* 0 5 0 */
+ case 54: return b * b * b * b * b; /* 0 0 5 */
+
+
+ default: return 0;
+ }
+}
+
+
+
+int cmsxRegressionCreateMatrix(LPMEASUREMENT m, SETOFPATCHES Allowed, int nterms,
+ int ColorSpace,
+ LPMATN* lpMat, LPMLRSTATISTICS Stat)
+{
+ LPMATN Input, Output;
+ int nCollected = cmsxPCollCountSet(m, Allowed);
+ int i, j, n, rc;
+
+ /* We are going always 3 -> 3 for now.... */
+
+ Input = MATNalloc(nCollected, nterms);
+ Output = MATNalloc(nCollected, 3);
+
+ /* Set independent terms */
+
+ for (n = i = 0; i < m -> nPatches; i++)
+ {
+ if (Allowed[i]) {
+
+ LPPATCH p = m -> Patches + i;
+
+ for (j=0; j < nterms; j++)
+ Input -> Values[n][j] = Term(j, p -> Colorant.RGB[0], p -> Colorant.RGB[1], p->Colorant.RGB[2]);
+
+ switch (ColorSpace) {
+
+ case PT_Lab:
+
+ Output-> Values[n][0] = p -> Lab.L;
+ Output-> Values[n][1] = p -> Lab.a;
+ Output-> Values[n][2] = p -> Lab.b;
+ break;
+
+ case PT_XYZ:
+ Output-> Values[n][0] = p -> XYZ.X;
+ Output-> Values[n][1] = p -> XYZ.Y;
+ Output-> Values[n][2] = p -> XYZ.Z;
+ break;
+
+
+ default:
+ cmsSignalError(LCMS_ERRC_ABORTED, "Invalid colorspace");
+ }
+
+ n++;
+ }
+ }
+
+
+ /* Apply multiple linear regression */
+
+ if (*lpMat) MATNfree(*lpMat);
+ rc = CreateRegressionMatrix(Input, Output, lpMat, Stat);
+
+ /* Free variables */
+
+ MATNfree(Input);
+ MATNfree(Output);
+
+
+#ifdef DEBUG
+ if (rc == true)
+ MATNprintf("tfm", *lpMat);
+#endif
+
+ return rc;
+}
+
+
+/* Convert a RGB triplet to Lab by using regression matrix */
+
+BOOL cmsxRegressionRGB2Lab(double r, double g, double b, LPMATN tfm, LPcmsCIELab Lab)
+{
+ LPMATN inVec, outVec;
+ int i;
+
+ inVec = MATNalloc(1, tfm->Rows);
+ if (inVec == NULL)
+ return false;
+
+ /* Put terms */
+ for (i=0; i < tfm->Rows; i++)
+ inVec -> Values[0][i] = Term(i, r, g, b);
+
+ /* Across regression matrix */
+ outVec = MATNmult(inVec, tfm);
+
+ /* Store result */
+ if (outVec != NULL) {
+
+ Lab->L = outVec->Values[0][0];
+ Lab->a = outVec->Values[0][1];
+ Lab->b = outVec->Values[0][2];
+ MATNfree(outVec);
+ }
+
+ MATNfree(inVec);
+ return true;
+}
+
+
+/* Convert a RGB triplet to XYX by using regression matrix */
+
+BOOL cmsxRegressionRGB2XYZ(double r, double g, double b, LPMATN tfm, LPcmsCIEXYZ XYZ)
+{
+ LPMATN inVec, outVec;
+ int i;
+
+ inVec = MATNalloc(1, tfm->Rows);
+ if (inVec == NULL)
+ return false;
+
+ /* Put terms */
+ for (i=0; i < tfm->Rows; i++)
+ inVec -> Values[0][i] = Term(i, r, g, b);
+
+ /* Across regression matrix */
+ outVec = MATNmult(inVec, tfm);
+
+ /* Store result */
+ if (outVec != NULL) {
+
+ XYZ->X = outVec->Values[0][0];
+ XYZ->Y = outVec->Values[0][1];
+ XYZ->Z = outVec->Values[0][2];
+ MATNfree(outVec);
+ }
+
+ MATNfree(inVec);
+ return true;
+}
+
+
+/* Convert a RGB triplet to XYX by using regression matrix */
+
+BOOL cmsxRegressionXYZ2RGB(LPcmsCIEXYZ XYZ, LPMATN tfm, double RGB[3])
+{
+ LPMATN inVec, outVec;
+ int i;
+
+ inVec = MATNalloc(1, tfm->Rows);
+ if (inVec == NULL)
+ return false;
+
+ /* Put terms */
+ for (i=0; i < tfm->Rows; i++)
+ inVec -> Values[0][i] = Term(i, XYZ->X, XYZ->Y, XYZ->Z);
+
+ /* Across regression matrix */
+ outVec = MATNmult(inVec, tfm);
+
+ /* Store result */
+ if (outVec != NULL) {
+
+ RGB[0] = outVec->Values[0][0];
+ RGB[1] = outVec->Values[0][1];
+ RGB[2] = outVec->Values[0][2];
+ MATNfree(outVec);
+ }
+
+ MATNfree(inVec);
+ return true;
+}
+
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