Mercurial > octave
view liboctave/numeric/CollocWt.cc @ 21202:f7121e111991
maint: indent #ifdef blocks in liboctave and src directories.
* Array-C.cc, Array-b.cc, Array-ch.cc, Array-d.cc, Array-f.cc, Array-fC.cc,
Array-i.cc, Array-idx-vec.cc, Array-s.cc, Array-str.cc, Array-util.cc,
Array-voidp.cc, Array.cc, CColVector.cc, CDiagMatrix.cc, CMatrix.cc,
CNDArray.cc, CRowVector.cc, CSparse.cc, CSparse.h, DiagArray2.cc, MArray-C.cc,
MArray-d.cc, MArray-f.cc, MArray-fC.cc, MArray-i.cc, MArray-s.cc, MArray.cc,
MDiagArray2.cc, MSparse-C.cc, MSparse-d.cc, MSparse.h, MatrixType.cc,
PermMatrix.cc, Range.cc, Sparse-C.cc, Sparse-b.cc, Sparse-d.cc, Sparse.cc,
boolMatrix.cc, boolNDArray.cc, boolSparse.cc, chMatrix.cc, chNDArray.cc,
dColVector.cc, dDiagMatrix.cc, dMatrix.cc, dNDArray.cc, dRowVector.cc,
dSparse.cc, dSparse.h, dim-vector.cc, fCColVector.cc, fCDiagMatrix.cc,
fCMatrix.cc, fCNDArray.cc, fCRowVector.cc, fColVector.cc, fDiagMatrix.cc,
fMatrix.cc, fNDArray.cc, fRowVector.cc, idx-vector.cc, int16NDArray.cc,
int32NDArray.cc, int64NDArray.cc, int8NDArray.cc, intNDArray.cc,
uint16NDArray.cc, uint32NDArray.cc, uint64NDArray.cc, uint8NDArray.cc,
blaswrap.c, cquit.c, f77-extern.cc, f77-fcn.c, f77-fcn.h, lo-error.c, quit.cc,
quit.h, CmplxAEPBAL.cc, CmplxCHOL.cc, CmplxGEPBAL.cc, CmplxHESS.cc, CmplxLU.cc,
CmplxQR.cc, CmplxQRP.cc, CmplxSCHUR.cc, CmplxSVD.cc, CollocWt.cc, DASPK.cc,
DASRT.cc, DASSL.cc, EIG.cc, LSODE.cc, ODES.cc, Quad.cc, base-lu.cc, base-qr.cc,
dbleAEPBAL.cc, dbleCHOL.cc, dbleGEPBAL.cc, dbleHESS.cc, dbleLU.cc, dbleQR.cc,
dbleQRP.cc, dbleSCHUR.cc, dbleSVD.cc, eigs-base.cc, fCmplxAEPBAL.cc,
fCmplxCHOL.cc, fCmplxGEPBAL.cc, fCmplxHESS.cc, fCmplxLU.cc, fCmplxQR.cc,
fCmplxQRP.cc, fCmplxSCHUR.cc, fCmplxSVD.cc, fEIG.cc, floatAEPBAL.cc,
floatCHOL.cc, floatGEPBAL.cc, floatHESS.cc, floatLU.cc, floatQR.cc,
floatQRP.cc, floatSCHUR.cc, floatSVD.cc, lo-mappers.cc, lo-specfun.cc,
oct-convn.cc, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-rand.cc,
oct-spparms.cc, randgamma.c, randmtzig.c, randpoisson.c, sparse-chol.cc,
sparse-dmsolve.cc, sparse-lu.cc, sparse-qr.cc, mx-defs.h, dir-ops.cc,
file-ops.cc, file-stat.cc, lo-sysdep.cc, mach-info.cc, oct-env.cc,
oct-group.cc, oct-openmp.h, oct-passwd.cc, oct-syscalls.cc, oct-time.cc,
oct-uname.cc, pathlen.h, sysdir.h, syswait.h, cmd-edit.cc, cmd-hist.cc,
data-conv.cc, f2c-main.c, glob-match.cc, lo-array-errwarn.cc,
lo-array-gripes.cc, lo-cutils.c, lo-cutils.h, lo-ieee.cc, lo-math.h,
lo-regexp.cc, lo-utils.cc, oct-base64.cc, oct-glob.cc, oct-inttypes.cc,
oct-inttypes.h, oct-locbuf.cc, oct-mutex.cc, oct-refcount.h, oct-rl-edit.c,
oct-rl-hist.c, oct-shlib.cc, oct-sort.cc, pathsearch.cc, singleton-cleanup.cc,
sparse-sort.cc, sparse-util.cc, statdefs.h, str-vec.cc, unwind-prot.cc,
url-transfer.cc, display-available.h, main-cli.cc, main-gui.cc, main.in.cc,
mkoctfile.in.cc, octave-config.in.cc, shared-fcns.h:
indent #ifdef blocks in liboctave and src directories.
author | Rik <rik@octave.org> |
---|---|
date | Sat, 06 Feb 2016 06:40:13 -0800 |
parents | d48fdf3a8c0c |
children | 40de9f8f23a6 |
line wrap: on
line source
/* Copyright (C) 1993-2015 John W. Eaton This file is part of Octave. Octave 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 3 of the License, or (at your option) any later version. Octave 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 Octave; see the file COPYING. If not, see <http://www.gnu.org/licenses/>. */ #ifdef HAVE_CONFIG_H # include <config.h> #endif #include <iostream> #include <cfloat> #include "CollocWt.h" #include "f77-fcn.h" #include "lo-error.h" // The following routines jcobi, dif, and dfopr are based on the code // found in Villadsen, J. and M. L. Michelsen, Solution of Differential // Equation Models by Polynomial Approximation, Prentice-Hall (1978) // pages 418-420. // // Translated to C++ by jwe. // Compute the first three derivatives of the node polynomial. // // n0 (alpha,beta) n1 // p (x) = (x) * p (x) * (1 - x) // nt n // // at the interpolation points. Each of the parameters n0 and n1 // may be given the value 0 or 1. The total number of points // nt = n + n0 + n1 // // The values of root must be known before a call to dif is possible. // They may be computed using jcobi. static void dif (octave_idx_type nt, double *root, double *dif1, double *dif2, double *dif3) { // Evaluate derivatives of node polynomial using recursion formulas. for (octave_idx_type i = 0; i < nt; i++) { double x = root[i]; dif1[i] = 1.0; dif2[i] = 0.0; dif3[i] = 0.0; for (octave_idx_type j = 0; j < nt; j++) { if (j != i) { double y = x - root[j]; dif3[i] = y * dif3[i] + 3.0 * dif2[i]; dif2[i] = y * dif2[i] + 2.0 * dif1[i]; dif1[i] = y * dif1[i]; } } } } // Compute the zeros of the Jacobi polynomial. // // (alpha,beta) // p (x) // n // // Use dif to compute the derivatives of the node // polynomial // // n0 (alpha,beta) n1 // p (x) = (x) * p (x) * (1 - x) // nt n // // at the interpolation points. // // See Villadsen and Michelsen, pages 131-132 and 418. // // Input parameters: // // nd : the dimension of the vectors dif1, dif2, dif3, and root // // n : the degree of the jacobi polynomial, (i.e. the number // of interior interpolation points) // // n0 : determines whether x = 0 is included as an // interpolation point // // n0 = 0 ==> x = 0 is not included // n0 = 1 ==> x = 0 is included // // n1 : determines whether x = 1 is included as an // interpolation point // // n1 = 0 ==> x = 1 is not included // n1 = 1 ==> x = 1 is included // // alpha : the value of alpha in the description of the jacobi // polynomial // // beta : the value of beta in the description of the jacobi // polynomial // // For a more complete explanation of alpha an beta, see Villadsen // and Michelsen, pages 57 to 59. // // Output parameters: // // root : one dimensional vector containing on exit the // n + n0 + n1 zeros of the node polynomial used in the // interpolation routine // // dif1 : one dimensional vector containing the first derivative // of the node polynomial at the zeros // // dif2 : one dimensional vector containing the second derivative // of the node polynomial at the zeros // // dif3 : one dimensional vector containing the third derivative // of the node polynomial at the zeros static bool jcobi (octave_idx_type n, octave_idx_type n0, octave_idx_type n1, double alpha, double beta, double *dif1, double *dif2, double *dif3, double *root) { assert (n0 == 0 || n0 == 1); assert (n1 == 0 || n1 == 1); octave_idx_type nt = n + n0 + n1; assert (nt > 1); // -- first evaluation of coefficients in recursion formulas. // -- recursion coefficients are stored in dif1 and dif2. double ab = alpha + beta; double ad = beta - alpha; double ap = beta * alpha; dif1[0] = (ad / (ab + 2.0) + 1.0) / 2.0; dif2[0] = 0.0; if (n >= 2) { for (octave_idx_type i = 1; i < n; i++) { double z1 = i; double z = ab + 2 * z1; dif1[i] = (ab * ad / z / (z + 2.0) + 1.0) / 2.0; if (i == 1) dif2[i] = (ab + ap + z1) / z / z / (z + 1.0); else { z *= z; double y = z1 * (ab + z1); y *= (ap + y); dif2[i] = y / z / (z - 1.0); } } } // Root determination by Newton method with suppression of previously // determined roots. double x = 0.0; for (octave_idx_type i = 0; i < n; i++) { bool done = false; int k = 0; while (! done) { double xd = 0.0; double xn = 1.0; double xd1 = 0.0; double xn1 = 0.0; for (octave_idx_type j = 0; j < n; j++) { double xp = (dif1[j] - x) * xn - dif2[j] * xd; double xp1 = (dif1[j] - x) * xn1 - dif2[j] * xd1 - xn; xd = xn; xd1 = xn1; xn = xp; xn1 = xp1; } double zc = 1.0; double z = xn / xn1; if (i != 0) { for (octave_idx_type j = 1; j <= i; j++) zc -= z / (x - root[j-1]); } z /= zc; x -= z; // Famous last words: 100 iterations should be more than // enough in all cases. if (++k > 100 || xisnan (z)) return false; if (std::abs (z) <= 100 * std::numeric_limits<double>::epsilon ()) done = true; } root[i] = x; x += sqrt (std::numeric_limits<double>::epsilon ()); } // Add interpolation points at x = 0 and/or x = 1. if (n0 != 0) { for (octave_idx_type i = n; i > 0; i--) root[i] = root[i-1]; root[0] = 0.0; } if (n1 != 0) root[nt-1] = 1.0; dif (nt, root, dif1, dif2, dif3); return true; } // Compute derivative weights for orthogonal collocation. // // See Villadsen and Michelsen, pages 133-134, 419. // // Input parameters: // // nd : the dimension of the vectors dif1, dif2, dif3, and root // // n : the degree of the jacobi polynomial, (i.e. the number // of interior interpolation points) // // n0 : determines whether x = 0 is included as an // interpolation point // // n0 = 0 ==> x = 0 is not included // n0 = 1 ==> x = 0 is included // // n1 : determines whether x = 1 is included as an // interpolation point // // n1 = 0 ==> x = 1 is not included // n1 = 1 ==> x = 1 is included // // i : the index of the node for which the weights are to be // calculated // // id : indicator // // id = 1 ==> first derivative weights are computed // id = 2 ==> second derivative weights are computed // id = 3 ==> gaussian weights are computed (in this // case, the value of i is irrelevant) // // Output parameters: // // dif1 : one dimensional vector containing the first derivative // of the node polynomial at the zeros // // dif2 : one dimensional vector containing the second derivative // of the node polynomial at the zeros // // dif3 : one dimensional vector containing the third derivative // of the node polynomial at the zeros // // vect : one dimensional vector of computed weights static void dfopr (octave_idx_type n, octave_idx_type n0, octave_idx_type n1, octave_idx_type i, octave_idx_type id, double *dif1, double *dif2, double *dif3, double *root, double *vect) { assert (n0 == 0 || n0 == 1); assert (n1 == 0 || n1 == 1); octave_idx_type nt = n + n0 + n1; assert (nt > 1); assert (id == 1 || id == 2 || id == 3); if (id != 3) assert (i >= 0 && i < nt); // Evaluate discretization matrices and Gaussian quadrature weights. // Quadrature weights are normalized to sum to one. if (id != 3) { for (octave_idx_type j = 0; j < nt; j++) { if (j == i) { if (id == 1) vect[i] = dif2[i] / dif1[i] / 2.0; else vect[i] = dif3[i] / dif1[i] / 3.0; } else { double y = root[i] - root[j]; vect[j] = dif1[i] / dif1[j] / y; if (id == 2) vect[j] = vect[j] * (dif2[i] / dif1[i] - 2.0 / y); } } } else { double y = 0.0; for (octave_idx_type j = 0; j < nt; j++) { double x = root[j]; double ax = x * (1.0 - x); if (n0 == 0) ax = ax / x / x; if (n1 == 0) ax = ax / (1.0 - x) / (1.0 - x); vect[j] = ax / (dif1[j] * dif1[j]); y += vect[j]; } for (octave_idx_type j = 0; j < nt; j++) vect[j] = vect[j] / y; } } // Error handling. void CollocWt::error (const char* msg) { (*current_liboctave_error_handler) ("CollocWt: fatal error '%s'", msg); } CollocWt& CollocWt::set_left (double val) { if (val >= rb) error ("CollocWt: left bound greater than right bound"); lb = val; initialized = 0; return *this; } CollocWt& CollocWt::set_right (double val) { if (val <= lb) error ("CollocWt: right bound less than left bound"); rb = val; initialized = 0; return *this; } void CollocWt::init (void) { // Check for possible errors. double wid = rb - lb; if (wid <= 0.0) { error ("CollocWt: width less than or equal to zero"); return; } octave_idx_type nt = n + inc_left + inc_right; if (nt < 0) error ("CollocWt: total number of collocation points less than zero"); else if (nt == 0) return; Array<double> dif1 (dim_vector (nt, 1)); double *pdif1 = dif1.fortran_vec (); Array<double> dif2 (dim_vector (nt, 1)); double *pdif2 = dif2.fortran_vec (); Array<double> dif3 (dim_vector (nt, 1)); double *pdif3 = dif3.fortran_vec (); Array<double> vect (dim_vector (nt, 1)); double *pvect = vect.fortran_vec (); r.resize (nt, 1); q.resize (nt, 1); A.resize (nt, nt); B.resize (nt, nt); double *pr = r.fortran_vec (); // Compute roots. if (! jcobi (n, inc_left, inc_right, Alpha, Beta, pdif1, pdif2, pdif3, pr)) error ("jcobi: newton iteration failed"); octave_idx_type id; // First derivative weights. id = 1; for (octave_idx_type i = 0; i < nt; i++) { dfopr (n, inc_left, inc_right, i, id, pdif1, pdif2, pdif3, pr, pvect); for (octave_idx_type j = 0; j < nt; j++) A(i,j) = vect(j); } // Second derivative weights. id = 2; for (octave_idx_type i = 0; i < nt; i++) { dfopr (n, inc_left, inc_right, i, id, pdif1, pdif2, pdif3, pr, pvect); for (octave_idx_type j = 0; j < nt; j++) B(i,j) = vect(j); } // Gaussian quadrature weights. id = 3; double *pq = q.fortran_vec (); dfopr (n, inc_left, inc_right, id, id, pdif1, pdif2, pdif3, pr, pq); initialized = 1; } std::ostream& operator << (std::ostream& os, const CollocWt& a) { if (a.left_included ()) os << "left boundary is included\n"; else os << "left boundary is not included\n"; if (a.right_included ()) os << "right boundary is included\n"; else os << "right boundary is not included\n"; os << "\n"; os << a.Alpha << " " << a.Beta << "\n\n" << a.r << "\n\n" << a.q << "\n\n" << a.A << "\n" << a.B << "\n"; return os; }