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AutoDiff


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 License FreeBSD:

 Copyright (c) 2016  Martin de La Gorce
 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 THE COPYRIGHT OWNER OR 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.
 
 The views and conclusions contained in the software and documentation are those
 of the authors and should not be interpreted as representing official policies,
 either expressed or implied, of the FreeBSD Project.



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 License FreeBSD:



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AutoDiffJacobianAutoDiff


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 AutoDiffJacobianAutoDiff returns the jacobian of function evaluated at x using Automatic
 Differentiation 


  J = AutoDiffJacobianAutoDiff(func,x)
  J = AutoDiffJacobianAutoDiff(func,x,range)

 Inputs:
     func    : handle to the function
     x       : location where the jacobian is evaluated  
     range   : (optional) vector of integer indices in [1,numel(x)]
 Outputs:
     J       : jacobian matrix of function f evaluated at x

 Description:
     returns the jacobian matrix of function f evaluated at x
     if a range is specified , only the columns corresponding to the range
     indices are computed. The computation is donc using Automatic
     Differentiation (Not to be confounded with Finite Differences method)
     This is numerically more precise and, if the Jacobian is large and
     sparse this might be much faster (see examples)
    
 Examples:

 % Simple example

 f=@(x) [sin(x(1)) cos(x(2)) tan(x(1)*x(2))]
 full(AutoDiffJacobianAutoDiff(f,[1,1]))
 AutoDiffJacobianFiniteDiff(f,[1,1])
 
 %Speedup illustration 

 f=@(x) (log(x(1:end-1))-tan(x(2:end)))
 tic; JAD=AutoDiffJacobianAutoDiff(f,0.5*ones(1,5000));timeAD=toc;
 tic; JFD=sparse(AutoDiffJacobianFiniteDiff(f,0.5*ones(1,5000)));timeFD=toc;
 fprintf('speedup AD vs FD = %2.1f\n',timeFD/timeAD)
 fprintf('max abs difference = %e\n',full(max(abs(JAD(:)-JFD(:)))));

 % N-D array support

 f=@(x) sum(x.^2,3)
 
 Documentation created  by Martin de La Gorce




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 AutoDiffJacobianAutoDiff returns the jacobian of function evaluated at x usi...



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GaussianIntegrationRule


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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
 Copyright (C) 2016-2020 William H. Greene



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   This library is free software; you can redistribute it and/or
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ODEImpl


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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
 Copyright (C) 2020-2021 William H. Greene



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PDE1dImpl


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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
 Copyright (C) 2016-2021 William H. Greene



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PDEMeshMapper


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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
   Copyright (C) 2016-2021 William H. Greene



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PDEOptions


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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
   Copyright (C) 2016-2021 William H. Greene



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SysVec


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   This library is free software; you can redistribute it and/or
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   as published by the Free Software Foundation; either version 3
   of the License, or (at your option) any later version.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
 Copyright (C) 2020-2021 William H. Greene



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callVarargFunc


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   This library is free software; you can redistribute it and/or
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   as published by the Free Software Foundation; either version 3
   of the License, or (at your option) any later version.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
   Copyright (C) 2016-2021 William H. Greene



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decicShampine


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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
 Copyright (C) 2016-2021 William H. Greene



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findJacobianGroups


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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
 Copyright (C) 2020 William H. Greene



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multiprod


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MULTIPROD  Multiplying 1-D or 2-D subarrays contained in two N-D arrays.
   C = MULTIPROD(A,B) is equivalent  to C = MULTIPROD(A,B,[1 2],[1 2])
   C = MULTIPROD(A,B,[D1 D2]) is eq. to C = MULTIPROD(A,B,[D1 D2],[D1 D2])
   C = MULTIPROD(A,B,D1) is equival. to C = MULTIPROD(A,B,D1,D1)

   MULTIPROD performs multiple matrix products, with array expansion (AX)
   enabled. Its first two arguments A and B are "block arrays" of any
   size, containing one or more 1-D or 2-D subarrays, called "blocks" (*).
   For instance, a 5×6×3 array may be viewed as an array containing five
   6×3 blocks. In this case, its size is denoted by 5×(6×3). The 1 or 2
   adjacent dimensions along which the blocks are contained are called the
   "internal dimensions" (IDs) of the array (°).

   1) 2-D by 2-D BLOCK(S) (*)
         C = MULTIPROD(A, B, [DA1 DA2], [DB1 DB2]) contains the products
         of the P×Q matrices in A by the R×S matrices in B. [DA1 DA2] are
         the IDs of A; [DB1 DB2] are the IDs of B.

   2) 2-D by 1-D BLOCK(S) (*)
         C = MULTIPROD(A, B, [DA1 DA2], DB1) contains the products of the
         P×Q matrices in A by the R-element vectors in B. The latter are
         considered to be R×1 matrices. [DA1 DA2] are the IDs of A; DB1 is
         the ID of B.

   3) 1-D by 2-D BLOCK(S) (*)
         C = MULTIPROD(A, B, DA1, [DB1 DB2]) contains the products of the 
         Q-element vectors in A by the R×S matrices in B. The vectors in A
         are considered to be 1×Q matrices. DA1 is the ID of A; [DB1 DB2]
         are the IDs of B.

   4) 1-D BY 1-D BLOCK(S) (*)
      (a) If either SIZE(A, DA1) == 1 or SIZE(B, DB1) == 1, or both,
             C = MULTIPROD(A, B, DA1, DB1) returns products of scalars by 
             vectors, or vectors by scalars or scalars by scalars.
      (b) If SIZE(A, DA1) == SIZE(B, DB1), 
             C = MULTIPROD(A, B, [0 DA1], [DB1 0]) or 
             C = MULTIPROD(A, B, DA1, DB1) virtually turns the vectors
             contained in A and B into 1×P and P×1 matrices, respectively,
             then returns their products, similar to scalar products.
             Namely, C = DOT2(A, B, DA1, DB1) is equivalent to 
             C = MULTIPROD(CONJ(A), B, [0 DA1], [DB1 0]).
      (c) Without limitations on the length of the vectors in A and B,
             C = MULTIPROD(A, B, [DA1 0], [0 DB1]) turns the vectors
             contained in A and B into P×1 and 1×Q matrices, respectively,
             then returns their products, similar to outer products.
             Namely, C = OUTER(A, B, DA1, DB1) is equivalent to
             C = MULTIPROD(CONJ(A), B, [DA1 0], [0 DB1]).

   Common constraints for all syntaxes:
      The external dimensions of A and B must either be identical or 
      compatible with AX rules. The internal dimensions of each block
      array must be adjacent (DA2 == DA1 + 1 and DB2 == DB1 + 1 are
      required). DA1 and DB1 are allowed to be larger than NDIMS(A) and
      NDIMS(B). In syntaxes 1, 2, and 3, Q == R is required, unless the
      blocks in A or B are scalars. 

   Array expansion (AX):
      AX is a powerful generalization to N-D of the concept of scalar
      expansion. Indeed, A and B may be scalars, vectors, matrices or
      multi-dimensional arrays. Scalar expansion is the virtual
      replication or annihilation of a scalar which allows you to combine
      it, element by element, with an array X of any size (e.g. X+10,
      X*10, or []-10). Similarly, in MULTIPROD, the purpose of AX is to
      automatically match the size of the external dimensions (EDs) of A
      and B, so that block-by-block products can be performed. ED matching
      is achieved by means of a dimension shift followed by a singleton
      expansion:
      1) Dimension shift (see SHIFTDIM).
            Whenever DA1 ~= DB1, a shift is applied to impose DA1 == DB1.
            If DA1 > DB1, B is shifted to the right by DA1 - DB1 steps.
            If DB1 > DA1, A is shifted to the right by DB1 - DA1 steps.
      2) Singleton expansion (SX).
            Whenever an ED of either A or B is singleton and the
            corresponding ED of the other array is not, the mismatch is
            fixed by virtually replicating the array (or diminishing it to
            length 0) along that dimension.
 
   MULTIPROD is a generalization for N-D arrays of the matrix
   multiplication function MTIMES, with AX enabled. Vector inner, outer,
   and cross products generalized for N-D arrays and with AX enabled are
   performed by DOT2, OUTER, and CROSS2 (MATLAB Central, file #8782).
   Elementwise multiplications (see TIMES) and other elementwise binary
   operations with AX enabled are performed by BAXFUN (MATLAB Central,
   file #23084). Together, these functions make up the ARRAYLAB toolbox.

   Input and output format:
      The size of the EDs of C is determined by AX. Block size is
      determined as follows, for each of the above-listed syntaxes:
      1) C contains P×S matrices along IDs MAX([DA1 DA2], [DB1 DB2]).
      2) Array     Block size     ID(s)
         ----------------------------------------------------
         A         P×Q  (2-D)     [DA1 DA2]
         B         R    (1-D)     DB1
         C (a)     P    (1-D)     MAX(DA1, DB1)
         C (b)     P×Q  (2-D)     MAX([DA1 DA2], [DB1 DB1+1])
         ----------------------------------------------------
         (a) The 1-D blocks in B are not scalars (R > 1).
         (b) The 1-D blocks in B are scalars (R = 1).
      3) Array     Block size     ID(s)
         ----------------------------------------------------
         A           Q  (1-D)     DA1
         B         R×S  (2-D)     [DB1 DB2]
         C (a)       S  (1-D)     MAX(DA1, DB1)
         C (b)     R×S  (2-D)     MAX([DA1 DA1+1], [DB1 DB2])
         ----------------------------------------------------
         (a) The 1-D blocks in A are not scalars (Q > 1).
         (b) The 1-D blocks in A are scalars (Q = 1).
      4)     Array     Block size         ID(s)
         --------------------------------------------------------------
         (a) A         P        (1-D)     DA1
             B         Q        (1-D)     DB1
             C         MAX(P,Q) (1-D)     MAX(DA1, DB1)
         --------------------------------------------------------------
         (b) A         P        (1-D)     DA1
             B         P        (1-D)     DB1
             C         1        (1-D)     MAX(DA1, DB1)
         --------------------------------------------------------------
         (c) A         P        (1-D)     DA1
             B         Q        (1-D)     DB1
             C         P×Q      (2-D)     MAX([DA1 DA1+1], [DB1 DB1+1])
         --------------------------------------------------------------

   Terminological notes:
   (*) 1-D and 2-D blocks are generically referred to as "vectors" and 
       "matrices", respectively. However, both may be also called
       scalars if they have a single element. Moreover, matrices with a
       single row or column (e.g. 1×3 or 3×1) may be also called row
       vectors or column vectors.
   (°) Not to be confused with the "inner dimensions" of the two matrices
       involved in a product X * Y, defined as the 2nd dimension of X and
       the 1st of Y (DA2 and DB1 in syntaxes 1, 2, 3).

   Examples:
    1) If  A is .................... a 5×(6×3)×2 array,
       and B is .................... a 5×(3×4)×2 array,
       C = MULTIPROD(A, B, [2 3]) is a 5×(6×4)×2 array.

       A single matrix A pre-multiplies each matrix in B
       If  A is ........................... a (1×3)    single matrix,
       and B is ........................... a 10×(3×4) 3-D array,
       C = MULTIPROD(A, B, [1 2], [3 4]) is a 10×(1×4) 3-D array.

       Each matrix in A pre-multiplies each matrix in B (all possible
       combinations)
       If  A is .................... a (6×3)×5   array,
       and B is .................... a (3×4)×1×2 array,
       C = MULTIPROD(A, B, [1 2]) is a (6×4)×5×2 array.

   2a) If  A is ........................... a 5×(6×3)×2 4-D array,
       and B is ........................... a 5×(3)×2   3-D array,
       C = MULTIPROD(A, B, [2 3], [2]) is   a 5×(6)×2   3-D array.

   2b) If  A is ........................... a 5×(6×3)×2 4-D array,
       and B is ........................... a 5×(1)×2   3-D array,
       C = MULTIPROD(A, B, [2 3], [2]) is   a 5×(6×3)×2 4-D array.

   4a) If both A and B are .................. 5×(6)×2   3-D arrays,
       C = MULTIPROD(A, B, 2) is .......... a 5×(1)×2   3-D array, while
   4b) C = MULTIPROD(A, B, [2 0], [0 2]) is a 5×(6×6)×2 4-D array

   See also DOT2, OUTER, CROSS2, BAXFUN, MULTITRANSP.



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MULTIPROD  Multiplying 1-D or 2-D subarrays contained in two N-D arrays.



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numericalJacobian


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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
 Copyright (C) 2020 William H. Greene



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   This library is free software; you can redistribute it and/or
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pde1dm


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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
 Copyright (C) 2016-2021 William H. Greene



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   This library is free software; you can redistribute it and/or
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pdeRefineMesh


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   This library is free software; you can redistribute it and/or
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   as published by the Free Software Foundation; either version 3
   of the License, or (at your option) any later version.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
 Copyright (C) 2016-2021 William H. Greene



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   This library is free software; you can redistribute it and/or
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pdepe


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 provide replacement for pdepe function in octave



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 provide replacement for pdepe function in octave




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post_install


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disp('$$$ post_install called');
instDir=[desc.dir '/inst']
mkdir(instDir);



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disp('$$$ post_install called');
instDir=[desc.dir '/inst']
mkdir(instDir);




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prtMat


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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
   Copyright (C) 2016-2021 William H. Greene



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   This library is free software; you can redistribute it and/or
   modify...



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prtShortVec


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# type: sq_string
# elements: 1
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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
   Copyright (C) 2016-2021 William H. Greene



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# length: 80
  
   This library is free software; you can redistribute it and/or
   modify...



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zerosLike


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   This library 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.
  
   This library 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 library; if not, visit
   http://www.gnu.org/licenses/gpl.html or write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
 
   Copyright (C) 2016-2020 William H. Greene



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# type: sq_string
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   This library is free software; you can redistribute it and/or
   modify...





