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/* |
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Teem: Tools to process and visualize scientific data and images . |
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Copyright (C) 2013, 2012, 2011, 2010, 2009 University of Chicago |
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Copyright (C) 2008, 2007, 2006, 2005 Gordon Kindlmann |
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Copyright (C) 2004, 2003, 2002, 2001, 2000, 1999, 1998 University of Utah |
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This library is free software; you can redistribute it and/or |
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modify it under the terms of the GNU Lesser General Public License |
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(LGPL) as published by the Free Software Foundation; either |
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version 2.1 of the License, or (at your option) any later version. |
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The terms of redistributing and/or modifying this software also |
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include exceptions to the LGPL that facilitate static linking. |
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This library is distributed in the hope that it will be useful, |
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but WITHOUT ANY WARRANTY; without even the implied warranty of |
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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Lesser General Public License for more details. |
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You should have received a copy of the GNU Lesser General Public License |
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along with this library; if not, write to Free Software Foundation, Inc., |
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51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA |
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*/ |
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#include "ten.h" |
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#include "privateTen.h" |
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double |
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tenBVecNonLinearFit_error(double *bb, double *ss, double *ww, int len, |
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double amp, double dec) { |
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int ii; |
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double err, tmp; |
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err = 0; |
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for (ii=0; ii<len; ii++) { |
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tmp = ww[ii]*(amp*exp(-dec*bb[ii]) - ss[ii]); |
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err += tmp*tmp; |
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} |
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return err; |
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} |
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void |
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tenBVecNonLinearFit_linear(double *amp, double *dec, |
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double *bb, double *ss, double *ww, int len) { |
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double x, y, wi=0, xi=0, yi=0, xiyi=0, xisq=0, det; |
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int ii; |
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for (ii=0; ii<len; ii++) { |
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x = bb[ii]; |
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y = log(AIR_MAX(ss[ii], 0.01)); |
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xi += ww[ii]*x; |
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yi += ww[ii]*y; |
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xiyi += ww[ii]*x*y; |
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xisq += ww[ii]*x*x; |
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wi += ww[ii]; |
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} |
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det = xisq*wi - xi*xi; |
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*dec = -(wi*xiyi - xi*yi)/det; /* negative sign assumed in model */ |
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*amp = exp((-xi*xiyi + xisq*yi)/det); |
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return; |
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} |
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void |
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tenBVecNonLinearFit_GNstep(double *d_amp, double *d_dec, |
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double *bb, double *ss, double *ww, int len, |
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double amp, double dec) { |
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double tmp, ff, dfdx1, dfdx2, AA=0, BB=0, CC=0, JTf[2], det; |
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int ii; |
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JTf[0] = JTf[1] = 0; |
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for (ii=0; ii<len; ii++) { |
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tmp = exp(-dec*bb[ii]); |
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ff = ww[ii]*(amp*tmp - ss[ii]); |
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dfdx1 = ww[ii]*tmp; |
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dfdx2 = -ww[ii]*amp*bb[ii]*tmp; |
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AA += dfdx1*dfdx1; |
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BB += dfdx1*dfdx2; |
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CC += dfdx2*dfdx2; |
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JTf[0] += dfdx1*ff; |
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JTf[1] += dfdx2*ff; |
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} |
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det = AA*CC - BB*BB; |
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*d_amp = -(CC*JTf[0] - BB*JTf[1])/det; |
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*d_dec = -(-BB*JTf[0] + AA*JTf[1])/det; |
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return; |
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} |
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/* |
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******** tenBVecNonLinearFit |
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** |
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** Assuming that axis 0 represents a sequence of DWI measurements at a |
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** range of b values (as described by bb[i]), do non-linear least-squares |
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** fitting of those measurements, governed by weights ww[i] (with at |
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** most iterMax interations, or terminated when L2 norm change < eps). |
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** |
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** Based on model fit amp*exp(-b*dec), output nrrd's axis 0 has three values: |
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** 0: amp |
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** 1: dec |
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** 2: error of fit |
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** and all other axes are unchanged from input. Output type is always double. |
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*/ |
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int |
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tenBVecNonLinearFit(Nrrd *nout, const Nrrd *nin, |
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double *bb, double *ww, int iterMax, double eps) { |
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static const char me[]="tenBVecNonLinearFit"; |
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int map[NRRD_DIM_MAX], vecSize, iter; |
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size_t ii, size[NRRD_DIM_MAX], vecI, vecNum; |
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char *vec; |
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double *out, ss[AIR_STRLEN_SMALL], amp, dec, d_amp, d_dec, error, diff, |
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(*vecLup)(const void *v, size_t I); |
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if (!( nout && nin && bb && ww )) { |
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biffAddf(TEN, "%s: got NULL pointer", me); |
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return 1; |
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} |
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if (!( nin->dim >= 2 )) { |
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biffAddf(TEN, "%s: nin->dim (%d) not >= 2", me, nin->dim); |
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return 1; |
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} |
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if (!( nin->axis[0].size < AIR_STRLEN_SMALL )) { |
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char stmp[AIR_STRLEN_SMALL]; |
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biffAddf(TEN, "%s: sorry need nin->axis[0].size (%s) < %d", me, |
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airSprintSize_t(stmp, nin->axis[0].size), AIR_STRLEN_SMALL); |
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return 1; |
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} |
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/* allocate/set-up output */ |
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nrrdAxisInfoGet_nva(nin, nrrdAxisInfoSize, size); |
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size[0] = 3; |
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if (nrrdMaybeAlloc_nva(nout, nrrdTypeDouble, nin->dim, size)) { |
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biffMovef(TEN, NRRD, "%s: couldn't allocate output", me); |
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return 1; |
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} |
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for (ii=1; ii<nin->dim; ii++) { |
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map[ii] = ii; |
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} |
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map[0] = -1; |
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if (nrrdAxisInfoCopy(nout, nin, map, NRRD_AXIS_INFO_NONE)) { |
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biffMovef(TEN, NRRD, "%s: couldn't copy axis info", me); |
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return 1; |
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} |
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/* process all b vectors */ |
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vecSize = nin->axis[0].size*nrrdTypeSize[nin->type]; |
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vecNum = nrrdElementNumber(nin)/nin->axis[0].size; |
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vecLup = nrrdDLookup[nin->type]; |
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vec = (char*)nin->data; |
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out = (double*)nout->data; |
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for (vecI=0; vecI<vecNum; vecI++) { |
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/* copy DWI signal values */ |
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for (ii=0; ii<nin->axis[0].size; ii++) { |
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ss[ii] = vecLup(vec, ii); |
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} |
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/* start with linear fit */ |
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tenBVecNonLinearFit_linear(&, &dec, bb, ss, ww, nin->axis[0].size); |
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error = tenBVecNonLinearFit_error(bb, ss, ww, nin->axis[0].size, amp, dec); |
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/* possibly refine with gauss-newton */ |
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if (iterMax > 0) { |
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iter = 0; |
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do { |
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iter++; |
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tenBVecNonLinearFit_GNstep(&d_amp, &d_dec, |
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bb, ss, ww, nin->axis[0].size, amp, dec); |
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amp += 0.3*d_amp; |
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dec += 0.3*d_dec; |
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diff = d_amp*d_amp + d_dec*d_dec; |
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} while (iter < iterMax && diff > eps); |
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} |
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error = tenBVecNonLinearFit_error(bb, ss, ww, nin->axis[0].size, amp, dec); |
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out[0] = amp; |
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out[1] = dec; |
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out[2] = error; |
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vec += vecSize; |
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out += 3; |
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} |
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return 0; |
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} |
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