optimsimplex: S3 optimsimplex class
In optimsimplex: R Port of the 'Scilab' Optimsimplex Module
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
Description
These functions support the S3 class 'optimsimplex' and are intended to either
create objects of this class or check if an object is of this class.
Usage
1
2
3
4
5
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7
8
9
10
11
12
13
optimsimplex(coords = NULL, fun = NULL, data = NULL, method = NULL,
x0 = NULL, len = NULL, deltausual = NULL, deltazero = NULL,
boundsmax = NULL, boundsmin = NULL, nbve = NULL,
simplex0 = NULL)
optimsimplex.tostring(x)
## S3 method for class 'optimsimplex'
print(x,...)
## S3 method for class 'optimsimplex'
is(x)
Arguments
coords
The matrix of point estimate coordinates in the simplex. The
coords matrix is expected to be a nbve x n matrix, where n is the dimension
of the space and nbve is the number of vertices in the simplex, with nbve>=
n+1. Only used if method is set to NULL.
fun
The function to compute at vertices. The function is expected to
have the following input and output arguments:
myfunction <- function(x, this){
...
return(list(f=f,this=this))
}
where x is a row vector and this a user-defined data, i.e. the data
argument.
data
A user-defined data passed to the function. If data is provided,
it is passed to the callback function both as an input and output argument.
data may be used if the function uses some additionnal parameters. It
is returned as an output parameter because the function may modify the data
while computing the function value. This feature may be used, for example,
to count the number of times that the function has been called.
method
The method used to create the new optimsimplex object, either
'axes', 'pfeffer', 'randbounds', 'spendley' or 'oriented'.
x0
The initial point estimates, as a row vector of length n.
len
The dimension of the simplex. If length is a value, that unique
length is used in all directions. If length is a vector with n values, each
length is used with the corresponding direction. Only used if method
is set to 'axes' or 'spendley'.
deltausual
The absolute delta for non-zero values. Only used if
method is set to 'pfeffer'.
deltazero
The absolute delta for zero values. Only used if
method is set to 'pfeffer'.
boundsmin
A vector of minimum bounds. Only used if method is
set to 'randbounds'.
boundsmax
A vector of maximum bounds. Only used if method is
set to 'randbounds'.
nbve
The total number of vertices in the simplex. Only used if
method is set to 'randbounds'.
simplex0
The initial simplex. Only used if method is set to
'oriented'.
x
An object of class 'optimsimplex'.
...
optional arguments to 'print' or 'plot' methods.
Details
All arguments of optimsimplex are optional. If no input is provided,
the new optimsimplex object is empty.
If method is NULL, the new optimsimplex object is created by
optimsimplex.coords. If coords is NULL, the optimsimplex object
is empty; otherwise, coords is used as the initial vertice coordinates
in the new simplex.
If method is set to 'axes', the initial vertice coordinates are stored
in a nbve x n matrix built as follows:
[,1] | x0[1] .... x0[n] | | len[1]
... 0 |
[,.] | ... ... ... | + | ... ...
... |
[,nbve] | x0[1] ... x0[n] | | 0
... len[n] |
If method is set to 'pfeffer', the new optimsimplex object is created
using the Pfeffer's method, i.e. a relative delta for non-zero values and an
absolute delta for zero values.
If method is set to 'randbounds', the initial vertice coordinates are
stored in a nbve x n matrix consisting of the initial point estimates (on the
first row) and a (nbve-1) x n matrix of randomly sampled numbers between the
specified the bounds. The number of vertices nbve in the optimsimplex
is arbitrary.
If method is set to 'spendley', the new optimsimplex object is created
using the Spendely's method, i.e. a regular simplex made of nbve = n+1
vertices.
If method is set to 'oriented', the new optimsimplex object is created
in sorted order. The new simplex has the same sigma- length of the base
simplex, but is "oriented" depending on the function value. The created
optimsimplex may be used, as Kelley suggests, for a restart of Nelder-Mead
algorithm.
The optimsimplex.tostring function is a utility function, which formats
the content of a optimsimplex object into a single string of characters.
Value
The optimsimplex function returns a list with the following elements:
- newobj
An object of class 'simplex', i.e. a list with the following
elements:
- verbose
The verbose option, controlling the amount of messages.
Set to FALSE.
- x
The coordinates of the vertices, with size nbve x n.
- n
The dimension of the space.
- fv
The values of the function at given vertices. It is a column
matrix of length nbve.
- nbve
The number of vertices.
- data
The updated data input argument.
Author(s)
Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)
Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)
References
"A Simplex Method for Function Minimization", Nelder, J. A. and Mead, R. The
Computer Journal, January, 1965, 308-313
"Sequential Application of Simplex Designs in Optimisation and Evolutionary
Operation", W. Spendley, G. R. Hext, F. R. Himsworth, Technometrics, Vol. 4, No.
4 (Nov., 1962), pp. 441-461, Section 3.1
"A New Method of Constrained Optimization and a Comparison With Other Methods",
M. J. Box, The Computer Journal 1965 8(1):42-52, 1965 by British Computer
Society
"Detection and Remediation of Stagnation in the Nelder-Mead Algorithm Using a
Sufficient Decrease Condition", SIAM J. on Optimization, Kelley C.T., 1999
"Multi-Directional Search: A Direct Search Algorithm for Parallel Machines", by
E. Boyd, Kenneth W. Kennedy, Richard A. Tapia, Virginia Joanne Torczon,
Virginia Joanne Torczon, 1989, Phd Thesis, Rice University
"Grid Restrained Nelder-Mead Algorithm", Arpad Burmen, Janez Puhan, Tadej Tuma,
Computational Optimization and Applications, Volume 34 , Issue 3 (July 2006),
Pages: 359 - 375
"A convergent variant of the Nelder-Mead algorithm", C. J. Price, I. D. Coope,
D. Byatt, Journal of Optimization Theory and Applications, Volume 113 , Issue 1
(April 2002), Pages: 5 - 19,
"Global Optimization Of Lennard-Jones Atomic Clusters", Ellen Fan, Thesis,
February 26, 2002, McMaster University
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
myfun <- function(x,this){return(list(f=sum(x^2),this=this))}
mat <- matrix(c(0,1,0,0,0,1),ncol=2)
optimsimplex()
optimsimplex(coords=mat,x0=1:4,fun=myfun)
optimsimplex(method='axes',x0=1:4,fun=myfun)
optimsimplex(method='pfeffer',x0=1:6,fun=myfun)
opt <- optimsimplex(method='randbounds',x0=1:6,boundsmin=rep(0,6),
boundsmax=rep(10,6),fun=myfun)
opt
optimsimplex(method='spendley',x0=1:6,fun=myfun,len=10)
optimsimplex(method='oriented',simplex=opt$newobj,fun=myfun)
Example output
Loading required package: optimbase
Loading required package: Matrix
Simplex:
Dimension: n=0
Number of vertices: nbve=0
Empty simplex (zero dimension)
Data:
NULL
Simplex:
Dimension: n=2
Number of vertices: nbve=3
Vertex #1/3 : fv=0.000000e+00, x=0.000000e+00 0.000000e+00
Vertex #2/3 : fv=1.000000e+00, x=1.000000e+00 0.000000e+00
Vertex #3/3 : fv=1.000000e+00, x=0.000000e+00 1.000000e+00
Data:
NULL
Simplex:
Dimension: n=4
Number of vertices: nbve=5
Vertex #1/5 : fv=3.000000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00
Vertex #2/5 : fv=3.300000e+01, x=2.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00
Vertex #3/5 : fv=3.500000e+01, x=1.000000e+00 3.000000e+00 3.000000e+00 4.000000e+00
Vertex #4/5 : fv=3.700000e+01, x=1.000000e+00 2.000000e+00 4.000000e+00 4.000000e+00
Vertex #5/5 : fv=3.900000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 5.000000e+00
Data:
NULL
Simplex:
Dimension: n=6
Number of vertices: nbve=7
Vertex #1/7 : fv=9.100000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #2/7 : fv=9.110250e+01, x=1.050000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #3/7 : fv=9.141000e+01, x=1.000000e+00 2.100000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #4/7 : fv=9.192250e+01, x=1.000000e+00 2.000000e+00 3.150000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #5/7 : fv=9.264000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.200000e+00 5.000000e+00 6.000000e+00
Vertex #6/7 : fv=9.356250e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.250000e+00 6.000000e+00
Vertex #7/7 : fv=9.469000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.300000e+00
Data:
NULL
Simplex:
Dimension: n=6
Number of vertices: nbve=7
Vertex #1/7 : fv=9.100000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #2/7 : fv=3.956782e+02, x=9.838290e+00 8.584698e+00 4.244985e+00 8.269441e+00 8.755147e+00 7.882450e+00
Vertex #3/7 : fv=2.398924e+02, x=6.529599e+00 1.774449e+00 8.843778e+00 8.855656e+00 6.921412e-01 6.082267e+00
Vertex #4/7 : fv=2.002761e+02, x=1.925050e+00 1.194435e+00 6.728839e+00 9.608816e+00 6.603613e+00 3.732195e+00
Vertex #5/7 : fv=3.879412e+02, x=5.596409e+00 7.508644e+00 9.247877e+00 8.167674e+00 8.869313e+00 8.327233e+00
Vertex #6/7 : fv=1.376873e+02, x=2.956203e-01 4.055369e+00 2.819156e+00 4.340912e+00 8.013717e+00 5.490275e+00
Vertex #7/7 : fv=3.068899e+02, x=6.232398e-01 6.470984e+00 7.233314e+00 9.785516e+00 4.162846e+00 9.960995e+00
Data:
NULL
Simplex:
Dimension: n=6
Number of vertices: nbve=7
Vertex #1/7 : fv=9.100000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #2/7 : fv=1.015603e+02, x=1.901060e+00 2.193954e+00 3.193954e+00 4.193954e+00 5.193954e+00 6.193954e+00
Vertex #3/7 : fv=1.029745e+02, x=1.193954e+00 2.901060e+00 3.193954e+00 4.193954e+00 5.193954e+00 6.193954e+00
Vertex #4/7 : fv=1.043887e+02, x=1.193954e+00 2.193954e+00 3.901060e+00 4.193954e+00 5.193954e+00 6.193954e+00
Vertex #5/7 : fv=1.058029e+02, x=1.193954e+00 2.193954e+00 3.193954e+00 4.901060e+00 5.193954e+00 6.193954e+00
Vertex #6/7 : fv=1.072171e+02, x=1.193954e+00 2.193954e+00 3.193954e+00 4.193954e+00 5.901060e+00 6.193954e+00
Vertex #7/7 : fv=1.086313e+02, x=1.193954e+00 2.193954e+00 3.193954e+00 4.193954e+00 5.193954e+00 6.901060e+00
Data:
NULL
Simplex:
Dimension: n=6
Number of vertices: nbve=7
Vertex #1/7 : fv=9.100000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #2/7 : fv=9.078311e+01, x=-8.849358e-01 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #3/7 : fv=1.020927e+02, x=1.000000e+00 3.884936e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #4/7 : fv=8.324337e+01, x=1.000000e+00 2.000000e+00 1.115064e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #5/7 : fv=7.947350e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 2.115064e+00 5.000000e+00 6.000000e+00
Vertex #6/7 : fv=1.134023e+02, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 6.884936e+00 6.000000e+00
Vertex #7/7 : fv=7.193375e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 4.115064e+00
Data:
NULL
optimsimplex documentation built on Jan. 29, 2022, 1:09 a.m.
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Description Usage Arguments Details Value Author(s) References Examples
Description
These functions support the S3 class 'optimsimplex' and are intended to either create objects of this class or check if an object is of this class.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 | optimsimplex(coords = NULL, fun = NULL, data = NULL, method = NULL,
x0 = NULL, len = NULL, deltausual = NULL, deltazero = NULL,
boundsmax = NULL, boundsmin = NULL, nbve = NULL,
simplex0 = NULL)
optimsimplex.tostring(x)
## S3 method for class 'optimsimplex'
print(x,...)
## S3 method for class 'optimsimplex'
is(x)
|
Arguments
coords |
The matrix of point estimate coordinates in the simplex. The
coords matrix is expected to be a nbve x n matrix, where n is the dimension
of the space and nbve is the number of vertices in the simplex, with nbve>=
n+1. Only used if | ||||
fun |
The function to compute at vertices. The function is expected to have the following input and output arguments:
where x is a row vector and this a user-defined data, i.e. the | ||||
data |
A user-defined data passed to the function. If data is provided,
it is passed to the callback function both as an input and output argument.
| ||||
method |
The method used to create the new optimsimplex object, either 'axes', 'pfeffer', 'randbounds', 'spendley' or 'oriented'. | ||||
x0 |
The initial point estimates, as a row vector of length n. | ||||
len |
The dimension of the simplex. If length is a value, that unique
length is used in all directions. If length is a vector with n values, each
length is used with the corresponding direction. Only used if | ||||
deltausual |
The absolute delta for non-zero values. Only used if
| ||||
deltazero |
The absolute delta for zero values. Only used if
| ||||
boundsmin |
A vector of minimum bounds. Only used if | ||||
boundsmax |
A vector of maximum bounds. Only used if | ||||
nbve |
The total number of vertices in the simplex. Only used if
| ||||
simplex0 |
The initial simplex. Only used if | ||||
x |
An object of class 'optimsimplex'. | ||||
... |
optional arguments to 'print' or 'plot' methods. |
Details
All arguments of optimsimplex are optional. If no input is provided,
the new optimsimplex object is empty.
If method is NULL, the new optimsimplex object is created by
optimsimplex.coords. If coords is NULL, the optimsimplex object
is empty; otherwise, coords is used as the initial vertice coordinates
in the new simplex.
If method is set to 'axes', the initial vertice coordinates are stored
in a nbve x n matrix built as follows:
| [,1] | | | x0[1] | .... | x0[n] | | | | | len[1] | ... | 0 | | | |
| [,.] | | | ... | ... | ... | | | + | | | ... | ... | ... | | |
| [,nbve] | | | x0[1] | ... | x0[n] | | | | | 0 | ... | len[n] | | | |
If method is set to 'pfeffer', the new optimsimplex object is created
using the Pfeffer's method, i.e. a relative delta for non-zero values and an
absolute delta for zero values.
If method is set to 'randbounds', the initial vertice coordinates are
stored in a nbve x n matrix consisting of the initial point estimates (on the
first row) and a (nbve-1) x n matrix of randomly sampled numbers between the
specified the bounds. The number of vertices nbve in the optimsimplex
is arbitrary.
If method is set to 'spendley', the new optimsimplex object is created
using the Spendely's method, i.e. a regular simplex made of nbve = n+1
vertices.
If method is set to 'oriented', the new optimsimplex object is created
in sorted order. The new simplex has the same sigma- length of the base
simplex, but is "oriented" depending on the function value. The created
optimsimplex may be used, as Kelley suggests, for a restart of Nelder-Mead
algorithm.
The optimsimplex.tostring function is a utility function, which formats
the content of a optimsimplex object into a single string of characters.
Value
The optimsimplex function returns a list with the following elements:
- newobj
An object of class 'simplex', i.e. a list with the following elements:
- verbose
The verbose option, controlling the amount of messages. Set to FALSE.
- x
The coordinates of the vertices, with size nbve x n.
- n
The dimension of the space.
- fv
The values of the function at given vertices. It is a column matrix of length nbve.
- nbve
The number of vertices.
- data
The updated
datainput argument.
Author(s)
Author of Scilab optimsimplex module: Michael Baudin (INRIA - Digiteo)
Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)
References
"A Simplex Method for Function Minimization", Nelder, J. A. and Mead, R. The Computer Journal, January, 1965, 308-313
"Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation", W. Spendley, G. R. Hext, F. R. Himsworth, Technometrics, Vol. 4, No. 4 (Nov., 1962), pp. 441-461, Section 3.1
"A New Method of Constrained Optimization and a Comparison With Other Methods", M. J. Box, The Computer Journal 1965 8(1):42-52, 1965 by British Computer Society
"Detection and Remediation of Stagnation in the Nelder-Mead Algorithm Using a Sufficient Decrease Condition", SIAM J. on Optimization, Kelley C.T., 1999
"Multi-Directional Search: A Direct Search Algorithm for Parallel Machines", by E. Boyd, Kenneth W. Kennedy, Richard A. Tapia, Virginia Joanne Torczon, Virginia Joanne Torczon, 1989, Phd Thesis, Rice University
"Grid Restrained Nelder-Mead Algorithm", Arpad Burmen, Janez Puhan, Tadej Tuma, Computational Optimization and Applications, Volume 34 , Issue 3 (July 2006), Pages: 359 - 375
"A convergent variant of the Nelder-Mead algorithm", C. J. Price, I. D. Coope, D. Byatt, Journal of Optimization Theory and Applications, Volume 113 , Issue 1 (April 2002), Pages: 5 - 19,
"Global Optimization Of Lennard-Jones Atomic Clusters", Ellen Fan, Thesis, February 26, 2002, McMaster University
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 | myfun <- function(x,this){return(list(f=sum(x^2),this=this))}
mat <- matrix(c(0,1,0,0,0,1),ncol=2)
optimsimplex()
optimsimplex(coords=mat,x0=1:4,fun=myfun)
optimsimplex(method='axes',x0=1:4,fun=myfun)
optimsimplex(method='pfeffer',x0=1:6,fun=myfun)
opt <- optimsimplex(method='randbounds',x0=1:6,boundsmin=rep(0,6),
boundsmax=rep(10,6),fun=myfun)
opt
optimsimplex(method='spendley',x0=1:6,fun=myfun,len=10)
optimsimplex(method='oriented',simplex=opt$newobj,fun=myfun)
|
Example output
Loading required package: optimbase
Loading required package: Matrix
Simplex:
Dimension: n=0
Number of vertices: nbve=0
Empty simplex (zero dimension)
Data:
NULL
Simplex:
Dimension: n=2
Number of vertices: nbve=3
Vertex #1/3 : fv=0.000000e+00, x=0.000000e+00 0.000000e+00
Vertex #2/3 : fv=1.000000e+00, x=1.000000e+00 0.000000e+00
Vertex #3/3 : fv=1.000000e+00, x=0.000000e+00 1.000000e+00
Data:
NULL
Simplex:
Dimension: n=4
Number of vertices: nbve=5
Vertex #1/5 : fv=3.000000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00
Vertex #2/5 : fv=3.300000e+01, x=2.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00
Vertex #3/5 : fv=3.500000e+01, x=1.000000e+00 3.000000e+00 3.000000e+00 4.000000e+00
Vertex #4/5 : fv=3.700000e+01, x=1.000000e+00 2.000000e+00 4.000000e+00 4.000000e+00
Vertex #5/5 : fv=3.900000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 5.000000e+00
Data:
NULL
Simplex:
Dimension: n=6
Number of vertices: nbve=7
Vertex #1/7 : fv=9.100000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #2/7 : fv=9.110250e+01, x=1.050000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #3/7 : fv=9.141000e+01, x=1.000000e+00 2.100000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #4/7 : fv=9.192250e+01, x=1.000000e+00 2.000000e+00 3.150000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #5/7 : fv=9.264000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.200000e+00 5.000000e+00 6.000000e+00
Vertex #6/7 : fv=9.356250e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.250000e+00 6.000000e+00
Vertex #7/7 : fv=9.469000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.300000e+00
Data:
NULL
Simplex:
Dimension: n=6
Number of vertices: nbve=7
Vertex #1/7 : fv=9.100000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #2/7 : fv=3.956782e+02, x=9.838290e+00 8.584698e+00 4.244985e+00 8.269441e+00 8.755147e+00 7.882450e+00
Vertex #3/7 : fv=2.398924e+02, x=6.529599e+00 1.774449e+00 8.843778e+00 8.855656e+00 6.921412e-01 6.082267e+00
Vertex #4/7 : fv=2.002761e+02, x=1.925050e+00 1.194435e+00 6.728839e+00 9.608816e+00 6.603613e+00 3.732195e+00
Vertex #5/7 : fv=3.879412e+02, x=5.596409e+00 7.508644e+00 9.247877e+00 8.167674e+00 8.869313e+00 8.327233e+00
Vertex #6/7 : fv=1.376873e+02, x=2.956203e-01 4.055369e+00 2.819156e+00 4.340912e+00 8.013717e+00 5.490275e+00
Vertex #7/7 : fv=3.068899e+02, x=6.232398e-01 6.470984e+00 7.233314e+00 9.785516e+00 4.162846e+00 9.960995e+00
Data:
NULL
Simplex:
Dimension: n=6
Number of vertices: nbve=7
Vertex #1/7 : fv=9.100000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #2/7 : fv=1.015603e+02, x=1.901060e+00 2.193954e+00 3.193954e+00 4.193954e+00 5.193954e+00 6.193954e+00
Vertex #3/7 : fv=1.029745e+02, x=1.193954e+00 2.901060e+00 3.193954e+00 4.193954e+00 5.193954e+00 6.193954e+00
Vertex #4/7 : fv=1.043887e+02, x=1.193954e+00 2.193954e+00 3.901060e+00 4.193954e+00 5.193954e+00 6.193954e+00
Vertex #5/7 : fv=1.058029e+02, x=1.193954e+00 2.193954e+00 3.193954e+00 4.901060e+00 5.193954e+00 6.193954e+00
Vertex #6/7 : fv=1.072171e+02, x=1.193954e+00 2.193954e+00 3.193954e+00 4.193954e+00 5.901060e+00 6.193954e+00
Vertex #7/7 : fv=1.086313e+02, x=1.193954e+00 2.193954e+00 3.193954e+00 4.193954e+00 5.193954e+00 6.901060e+00
Data:
NULL
Simplex:
Dimension: n=6
Number of vertices: nbve=7
Vertex #1/7 : fv=9.100000e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #2/7 : fv=9.078311e+01, x=-8.849358e-01 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #3/7 : fv=1.020927e+02, x=1.000000e+00 3.884936e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #4/7 : fv=8.324337e+01, x=1.000000e+00 2.000000e+00 1.115064e+00 4.000000e+00 5.000000e+00 6.000000e+00
Vertex #5/7 : fv=7.947350e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 2.115064e+00 5.000000e+00 6.000000e+00
Vertex #6/7 : fv=1.134023e+02, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 6.884936e+00 6.000000e+00
Vertex #7/7 : fv=7.193375e+01, x=1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 4.115064e+00
Data:
NULL
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