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.TH "mdfl2d" 2 "March 12, 1998" "Fractales Group" "Scilab Function"
.so ../sci.an
.SH NAME
mdfl2d - Discrete Legendre spectrum estimation on 2d measure
.sp
Author: Christophe Canus
.sp
This routine estimates the discrete Legendre spectrum on a
pre-multifractal 2d measure.
.sp
.sp
.SH Usage
\f(CR[\fPalpha,fl_alpha\f(CR]\fP=mdfl2d(mu_n,N,n)
.SH Input parameters
.RS
.TP
o
\fBmu_n\fP : strictly positive real matrix
\f(CR[\fPnux_n,nuy_n\f(CR]\fP
Contains the pre-multifractal measure.
.TP
o
\fBN\fP : strictly positive real (integer) scalar
Contains the number of Hoelder exponents.
.TP
o
\fBn\fP : strictly positive real (integer) scalar
Contains the final resolution.
.RE
.SH Output parameters
.RS
.TP
o
\fBalpha\fP : real vector \f(CR[\fP1,N\f(CR]\fP
Contains the Hoelder exponents.
.TP
o
\fBfl_alpha\fP : real vector \f(CR[\fP1,N\f(CR]\fP
Contains the dimensions.
.RE
.SH Description
.SH Parameters
The discrete Legendre spectrum \fIfl_alpha\fP is estimated on the
finite finer resolution of the 2d measure \fImu_n\fP. The three steps
of the estimation are:
.RS
.TP
o
estimation of the discrete partition function;
.TP
o
estimation of the Reyni exponents;
.TP
o
estimation of the Legendre transform.
.RE
.SH Algorithm details
The discrete partition function is estimated by coarse-graining masses
mu_n into non-overlapping boxes of increasing diameter (box
method). If \fInux_n\fP and \fInuy_n\fP are power of 2, 2\(ha\fIn\fP
corresponds to the coarser scale.
The Reyni exponents are estimated by least square linear regression.
The Legendre transform of the mass exponent function is estimated with
the linear-time Legendre transform.
.SH See also
\fBmdznq1d,mdznq2d,reynitq,linearlt,mdfl1d\fP.
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