Procedures

Dynamical adjustment of mutation rate:

Allocation of the memory needed by the transformations, forward and backward. 1 FFT distributed on several threads

Allocation of the memory needed by the transformations, forward and backward, for the real case. 1 FFT distributed on several threads

Subroutine to analyse, factorize (symbolic) the matrix of the system

Function that returns an apodized array.

Function that returns $\exp \left(\alpha \sqrt{\left(\frac{x}{\tau_1}\right)^2+ \left(\frac{y}{\tau_2}\right)^2} \right)$

Creates an object OBJ_SURF from an array

Converts a C string to a Fortran string

Subroutine that transforms forward or backward a double complex array. For speed reasons FFTW will always work on the same memory area, until the plans are destroyed of course. 1 FFT distributed on several threads

Subroutine that transforms backward a double real array. For speed reasons FFTW will always work on the same memory area, until the plans are destroyed of course. 1 FFT distributed on several threads

Subroutine that transforms forward a double real array. For speed reasons FFTW will always work on the same memory area, until the plans are destroyed of course. 1 FFT distributed on several threads

Function that returns the theoretical autocorrelation function in an array.
The autocorrelation function is supposed to be obtained from a real surface which must be periodic or nearly periodic (because of the use of FFTs). In addition, the surface is supposed to be 0 mean and normalized ($\sigma = 1$), therefore acf is zero-mean and normalized so that its max value is 1.

Determine the Jacobian matrix of f

Given an order vector, sort a real or integer vector

Check the validity of the inputs to the “ink” routines. Prints warning message if there is an error, and also sets iflag and status_ok.

CHKDER checks the gradients of M functions of N variables.

CHKDER_F is a function/jacobian routine for use with CHKDER_TEST.

CHKDER_TEST tests CHKDER.

Given a positive definite symmetric matrix a(1:n,1:n), with physical dimensions np, this routine constructs its Cholesky decomposition, A=L L^T. On input, only the upper triangle of a need to be given; it is not modified. The Cholesky factor L is returned in the lower triangle of a, except for its diagonal elements which are returned in p(1:n).

Solves the set of linear equations A x = b, where A is a positive- definite symmetric matrix with physical dimensions np. A and P are are input as the output from choldc. Only the lower triangle of A is accessed. B(1:n) is inout as the right-hand side vector. The solution vector is returned in X(1:n). A, n, np, and P are not modified and can be left in place for successive calls with different right-hand sides B. B is not modified unless you identify B and X in the calling sequence, which is allowed.

Subroutine that removes all files with extension .scratch

Subroutine to close the solver

Subroutine to close the SuperLU process, with memory release

Transformation d’une CL de produits de polynômes de Tchebychev en x et y en polynôme classique

Transformation des coefficients de Tchebychev en coefficients de monômes

Transformation du produit $ti(x) \cdot tj(y)$ de Tchebychev en coefficients de monômes $x^i \cdot y^j$

Compressed Column Storage (CCS) is also called the Harwell-Boeing sparse matrix format.

Génération d’une surface polynômiale pour vérification des procédures d’approximation

breeds two parent chromosomes into two offspring chromosomes. breeding occurs through crossover. If the crossover probability test yields true (crossover taking place), either one-point or two-point crossover is used, with equal probabilities.

Determines the parameters of a function that interpolates the one-dimensional gridded data $$[x(i),\mathrm{fcn}(i)] ~\mathrm{for}~ i=1,..,n_x$$ The interpolating function and its derivatives may subsequently be evaluated by the function db1val.

Evaluates the tensor product piecewise polynomial interpolant constructed by the routine db1ink or one of its derivatives at the point xval.

Determines the parameters of a function that interpolates the two-dimensional gridded data $$[x(i),y(j),\mathrm{fcn}(i,j)] ~\mathrm{for}~ i=1,..,n_x ~\mathrm{and}~ j=1,..,n_y$$ The interpolating function and its derivatives may subsequently be evaluated by the function db2val.

Evaluates the tensor product piecewise polynomial interpolant constructed by the routine db2ink or one of its derivatives at the point (xval,yval).

dbintk produces the b-spline coefficients, bcoef, of the b-spline of order k with knots t(i), i=1,…,n+k, which takes on the value y(i) at x(i), i=1,…,n. the spline or any of its derivatives can be evaluated by calls to dbvalu.

dbknot chooses a knot sequence for interpolation of order k at the data points x(i), i=1,..,n. the n+k knots are placed in the array t. k knots are placed at each endpoint and not-a-knot end conditions are used. the remaining knots are placed at data points if n is even and between data points if n is odd. the rightmost knot is shifted slightly to the right to insure proper interpolation at x(n) (see page 350 of the reference).

Returns in w the LU-factorization (without pivoting) of the banded matrix a of order nrow with (nbandl + 1 + nbandu) bands or diagonals in the work array w .

Companion routine to dbnfac. it returns the solution x of the linear system a*x = b in place of b, given the lu-factorization for a in the work array w from dbnfac.

Calculates the value of all (possibly) nonzero basis functions at x of order max(jhigh,(j+1)*(index-1)), where t(k) <= x <= t(n+1) and j=iwork is set inside the routine on the first call when index=1. ileft is such that t(ileft) <= x < t(ileft+1). a call to dintrv(t,n+1,x,ilo,ileft,mflag) produces the proper ileft. dbspvn calculates using the basic algorithm needed in dbspvd. if only basis functions are desired, setting jhigh=k and index=1 can be faster than calling dbspvd, but extra coding is required for derivatives (index=2) and dbspvd is set up for this purpose.

dbtpcf computes b-spline interpolation coefficients for nf sets of data stored in the columns of the array fcn. the b-spline coefficients are stored in the rows of bcoef however. each interpolation is based on the n abcissa stored in the array x, and the n+k knots stored in the array t. the order of each interpolation is k. the work array must be of length at least 2k(n+1).

Evaluates the b-representation (t,a,n,k) of a b-spline at x for the function value on ideriv=0 or any of its derivatives on ideriv=1,2,…,k-1. right limiting values (right derivatives) are returned except at the right end point x=t(n+1) where left limiting values are computed. the spline is defined on t(k) <= x <= t(n+1). dbvalu returns a fatal error message when x is outside of this interval.

decode genotype into phenotype parameters ph(k) are x,y coordinates [ 0 < x,y < 1 ]

When no more transformation is needed, the memory is released. 1 FFT distributed on several threads

Plans are no more needed as no additional transformation will occur. 1 FFT distributed on several threads

Kind of particular 2D autocorrelation function. Numerical derivatives.

Computes the largest integer ileft in 1 <= ileft <= lxt such that XT(ileft) <= x where XT(*) is a subdivision of the x interval. precisely,

Function that returns the system directory separator

Subroutine that keeps only the directory from a file path

DOGLEG finds the minimizing combination of Gauss-Newton and gradient steps.

Just empties a string

Encode phenotype parameters into integer genotype ph(k) are x,y coordinates [ 0 < x,y < 1 ]

FFTW3 is no more useful from here. 1 FFT distributed on several threads

ENORM computes the Euclidean norm of a vector.

ENORM2 computes the Euclidean norm of a vector.

Function that extends an array for FFT processing.

Kind of particular 2D autocorrelation function

Converts a Fortran string to a C string

Subroutine to factorize the system

Subroutine to factorize the matrix of the system

FDJAC1 estimates an N by N jacobian matrix using forward differences.

FDJAC2 estimates an M by N jacobian matrix using forward differences.

Subroutine that keeps only the file from a path

Subroutine that actually does nothing yet. Maybe, there will be extra memory that could be released here?

Subroutine to free the factors if applicable

Subroutine to transform the elemental entries into assembled CC vectors

Wrapper for the user’s function that is used by the main pikaia routine The x input to this function comes from pikaia, and will be between [0,1].

subroutine generating coefficients for kth-order interpolation

génère une surface

Generates a random number on [-2^63, 2^63-1]-interval

Generates a random number on [0,1]-real-interval

Generates a random number on [0,1)-real-interval

Generates a random number on (0,1)-real-interval

Full generational replacement: accumulate offspring into new population array

GET_UNIT returns a free FORTRAN unit number.

Provide for a free unit, from here John Burkardt website

HYBRD seeks a zero of N nonlinear equations in N variables.

HYBRD1 seeks a zero of N nonlinear equations in N variables.

HYBRD1_F is a function routine for use with HYBRD1_TEST.

HYBRD1_TEST tests HYBRD1.

HYBRJ seeks a zero of N nonlinear equations in N variables.

HYBRJ1 seeks a zero of N equations in N variables by Powell’s method.

HYBRJ1_F is a function/jacobian routine for use with HYBRJ1_TEST.

HYBRJ1_TEST tests HYBRJ1.

Initializes by an array with array-length init_key is the array for initializing keys

Subroutine to initialize the FFTW3 process 1 FFT distributed on several threads. Complex case.

Subroutine to initialize the FFTW3 process 1 FFT distributed on several threads Real case.

Initializes me%mt(nn) with a seed

Initializes me%mt(nn) with a seed

Vector initialization: 1 … n

OBJ_SURF initialization, every unit is m

Subroutine to initialize the matrices of the solver

Interpolate evenly spaced points

Interpolate evenly spaced points, taking into account the borders

Interpolate 2D evenly spaced points, taking into account the borders

Function that returns true if the operating system is linux

Resulting polynomial surface, determined by linear least squares

Subroutine that returns a list of subdirectories

Subroutine that returns a list of files in a directory

LMDER minimizes M functions in N variables by the Levenberg-Marquardt method.

LMDER1 minimizes M functions in N variables by Levenberg-Marquardt method.

LMDER1_2_F is a function/jacobian routine for use with LMDER1_2_TEST.

LMDER1_2_TEST tests LMDER1.

LMDER1_F is a function/jacobian routine for use with LMDER1_TEST.

LMDER1_TEST tests LMDER1.

LMDIF minimizes M functions in N variables by the Levenberg-Marquardt method.

LMDIF1 minimizes M functions in N variables using Levenberg-Marquardt method.

LMDIF1_2_F is a function routine for use with LMDIF1_2_TEST.

LMDIF1_2_TEST tests LMDIF1.

LMDIF1_F is a function routine for use with LMDIF1_TEST.

LMDIF1_TEST tests LMDIF1.

LMPAR computes a parameter for the Levenberg-Marquardt method.

LMSTR minimizes M functions in N variables using Levenberg-Marquardt method.

LMSTR1 minimizes M functions in N variables using Levenberg-Marquardt method.

LMSTR1_2_F is a function/jacobian routine for use with LMSTR1_2_TEST.

LMSTR1_2_TEST tests LMSTR1.

LMSTR1_F is a function/jacobian routine for use with LMSTR1_TEST.

LMSTR1_TEST tests LMSTR1.

Converts uppercase to lowercase, adapted from here

Subroutine that creates the folders of a file path

Creates forward and backward plans. 1 FFT distributed on several threads

Creates forward and backward plans. 1 FFT distributed on several threads

Subroutine that creates a directory

mMltiplication of the system coefficient by a random factor

Function that returns the parameters of a function that approximates a data set. The parameters determination is achieved by non linear least squares approximation.

Function that returns the parameters of a function that approximates a data set. The parameters determination is achieved by linear least squares approximation.

Introduces random mutation in a genotype. Mutations occur at rate pmut at all gene loci.

Replaces old population by new; recomputes fitnesses & ranks

Subroutine that opens a .sur file and transfers it contents into an object OBJ_SURF

Subroutine that creates a vector containing the folders of a file path

PI returns the value of pi.

Optimization (maximization) of user-supplied “fitness” function over n-dimensional parameter space x using a basic genetic algorithm method.

Subroutine to prepare the SULU_ENV components

$[A] \{x\}$, assembled CC format

$[A] \{x\}$, elemental CC format

Print a progress bar on the terminal

QFORM produces the explicit QR factorization of a matrix.

QFORM_TEST tests QFORM.

QRFAC computes a QR factorization using Householder transformations.

QRSOLV solves a rectangular linear system A*x=b in the least squares sense.

R1MPYQ computes A*Q, where Q is the product of Householder transformations.

R1UPDT re-triangularizes a matrix after a rank one update.

R8_UNIFORM_01 returns a unit pseudorandom R8.

R8MAT_PRINT prints an R8MAT.

R8MAT_PRINT_SOME prints some of an R8MAT.

R8VEC_PRINT prints an R8VEC.

Subroutine that opens a surface file .dat

Subroutine that opens a surface file .sur or .dat

Write generation report to standard output

Restrict evenly spaced points

Restrict evenly spaced points, taking into account the borders

Interpolate 2D evenly spaced points, taking into account the borders

Initialize the random number generator with the input seed value.

Ranks initial population. Calls external sort routine to produce key index and rank order of input array arrin (which is not altered).

Return integer array p which indexes array a in increasing order. Array a is not disturbed. The Quicksort algorithm is used.

RUN_GNUPLOT runs GNUPLOT with a given command file.

RWUPDT computes the decomposition of triangular matrix augmented by one row.

Subroutine that saves a surface file .dat

Transform a SCALE_SURF object into a OBJ_SURF object

Selects two parents from the population, using roulette wheel algorithm with the relative fitnesses of the phenotypes as the “hit” probabilities.

Constructor for the pikaia_class. The routine must be called before the solve routine can be used.

Subroutine to solve the system $[A]\{x\} = \{b\}$ (sparse A)

Subroutine to solve the system

General hat subroutine that handles the resolution steps:

Main pikaia wrapper used by the class.

Sort 1D arrays, real or integer, according the first one

Sort a vector of integers

Sort a vector of integers and store the order

Sort a vector of reals

Sort a vector of reals and store the order

Steady-state reproduction: insert offspring pair into population only if they are fit enough (replace-random if irep=2 or replace-worst if irep=3).

Function that removes the characters of a string from another string

Function that replaces a string with another string

Transform a OBJ_SURF object into a SCALE_SURF object

Allocation of the memory needed by the transformations, forward and backward. several FFT on single thread each

Allocation of the memory needed by the transformations, forward and backward, for the real case. several FFT on single thread each

Subroutine that transforms forward or bacward a double complex array. For speed reasons FFTW will always work on the same memory area, until the plans are destroyed of course. several FFT on single thread each

Subroutine that transforms backward a real array. For speed reasons FFTW will always work on the same memory area, until the plans are destroyed of course. several FFT on single thread each

Subroutine that transforms forward a real array. For speed reasons FFTW will always work on the same memory area, until the plans are destroyed of course. several FFT on single thread each

When no more transformation is needed, the memory is released. several FFT on single thread each

Plans are no more needed as no additional transformation will occur. several FFT on single thread each

FFTW3 is no more useful from here. several FFT on single thread each

FFTW3 is no more useful from here. several FFT on single thread each

Subroutine to initialize the FFTW3 process several FFT on single thread each Complex case.

Subroutine to initialize the FFTW3 process several FFT on single thread each Real case.

Tableau des dérivées par rapport aux coefficients de tab_tche

Creates forward and backward plans. several FFT on single thread each

Creates forward and backward plans. several FFT on single thread each

Surface définie par un produit de polynômes de Tchebychev en x et y

Valeurs tabulées de polynômes de Tchebychev

Valeur en x du polynôme de Tchebichev de degré n

TEST01 demonstrates the plotting of Y(X) data.

TEST02 demonstrates the plotting of a table of data.

TEST03 plots parameter (X,Y,Z) data.

TEST04 plots vector data.

TEST05 plots Z(X,Y) grid data as a surface.

TEST06 plots Z(X,Y) grid data as contours.

Test interpolation/weighting function for a particular order

TIMESTAMP prints the current YMDHMS date as a time stamp.

TIMESTAMP prints the current YMDHMS date as a time stamp.

Generic subroutine for real or complex arrays that shift the center to the corners

Subroutine to transform an array of complexes so that the center is in the corners

Subroutine to transform an array of reals so that the center is in the corners

Generic subroutine for real or complex arrays that shift the corners to the center

Function to transform an acf complex array so that the acf maximum is in the center

Function to transform an acf real array so that the acf maximum is in the center

Write the heights of an OBJ_SURF object into a 2D array

Writes an OBJ_SURF object in a text file

Convert a C type unit string into value (m)

Convert a unit string into value (m)

Return the next pseudo-random deviate from a sequence which is uniformly distributed in the interval [0,1]

Subroutine that creates a path from vector of folders

The product $\{y\}$ of the system matrix $[A]$ by the solution $\{x\}$, is calculated, and compared to the right hand side $\{b\}$. The calculated error is the absolute error in %.

Writes a height array into a surface file .sur or .dat

Write an object OBJ_SURF in a file

WRITE_VECTOR_DATA writes vector data to a file, for plotting by GNUPLOT.

WRITE_VECTOR_PLOT writes GNUPLOT commands to plot vectors.

WRITE_XY_DATA writes X(1:N), Y(1:N) data to a file.

WRITE_XY_PLOT writes GNUPLOT commands to plot X(1:N), Y(1:N) data.

WRITE_XYY_DATA writes a table of data to a file, for plotting by GNUPLOT.

WRITE_XYY_PLOTS writes GNUPLOT commands to make multiple (X,Y) plots.

WRITE_XYZ_DATA writes X(1:N), Y(1:N), Z(1:N) data to a file.

WRITE_XYZ_PLOT writes commands to plot parametric (X,Y,Z) data.

WRITE_XYZGRID_CONTOUR writes commands to plot contours of Z(X,Y).

WRITE_XYZGRID_DATA writes a file of XYZ grid data.

WRITE_XYZGRID_SURFACE writes a file of GNUPLOT commands to plot a 3D surface.

WRITE_Y_PLOT writes GNUPLOT commands to plot Y(1:N) data.