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-rw-r--r--scilab/modules/interpolation/Makefile.in2
-rw-r--r--scilab/modules/interpolation/help/en_US/bsplin3val.xml30
-rw-r--r--scilab/modules/interpolation/help/en_US/interp.xml151
-rw-r--r--scilab/modules/interpolation/help/en_US/linear_interpn.xml72
-rw-r--r--scilab/modules/interpolation/help/en_US/lsq_splin.xml44
-rw-r--r--scilab/modules/interpolation/help/en_US/splin.xml123
-rw-r--r--scilab/modules/interpolation/help/en_US/splin2d.xml116
-rw-r--r--scilab/modules/interpolation/help/en_US/splin3d.xml79
-rw-r--r--scilab/modules/interpolation/help/ja_JP/bsplin3val.xml32
-rw-r--r--scilab/modules/interpolation/help/ja_JP/interp.xml131
-rw-r--r--scilab/modules/interpolation/help/ja_JP/linear_interpn.xml69
-rw-r--r--scilab/modules/interpolation/help/ja_JP/lsq_splin.xml42
-rw-r--r--scilab/modules/interpolation/help/ja_JP/splin.xml110
-rw-r--r--scilab/modules/interpolation/help/ja_JP/splin2d.xml35
-rw-r--r--scilab/modules/interpolation/help/ja_JP/splin3d.xml84
-rw-r--r--scilab/modules/interpolation/help/mml/bsplin3val_equation1.mml77
-rw-r--r--scilab/modules/interpolation/help/mml/interp_equation1.mml256
-rw-r--r--scilab/modules/interpolation/help/mml/interp_equation2.mml66
-rw-r--r--scilab/modules/interpolation/help/mml/interp_equation3.mml80
-rw-r--r--scilab/modules/interpolation/help/mml/interp_equation4.mml122
-rw-r--r--scilab/modules/interpolation/help/mml/linear_interpn_equation1.mml59
-rw-r--r--scilab/modules/interpolation/help/mml/linear_interpn_equation2.mml116
-rw-r--r--scilab/modules/interpolation/help/mml/linear_interpn_equation3.mml85
-rw-r--r--scilab/modules/interpolation/help/mml/lsq_splin_equation1.mml112
-rw-r--r--scilab/modules/interpolation/help/mml/splin2d_equation_1.mml101
-rw-r--r--scilab/modules/interpolation/help/mml/splin3d_equation1.mml62
-rw-r--r--scilab/modules/interpolation/help/mml/splin_equation1.mml86
-rw-r--r--scilab/modules/interpolation/help/mml/splin_equation2.mml54
-rw-r--r--scilab/modules/interpolation/help/mml/splin_equation3.mml46
-rw-r--r--scilab/modules/interpolation/help/mml/splin_equation4.mml58
-rw-r--r--scilab/modules/interpolation/help/mml/splin_equation5.mml110
-rw-r--r--scilab/modules/interpolation/help/pt_BR/bsplin3val.xml29
-rw-r--r--scilab/modules/interpolation/help/pt_BR/interp.xml166
-rw-r--r--scilab/modules/interpolation/help/pt_BR/linear_interpn.xml60
-rw-r--r--scilab/modules/interpolation/help/pt_BR/lsq_splin.xml52
-rw-r--r--scilab/modules/interpolation/help/pt_BR/splin.xml119
-rw-r--r--scilab/modules/interpolation/help/pt_BR/splin2d.xml41
-rw-r--r--scilab/modules/interpolation/help/pt_BR/splin3d.xml124
38 files changed, 1094 insertions, 2107 deletions
diff --git a/scilab/modules/interpolation/Makefile.in b/scilab/modules/interpolation/Makefile.in
index fe36c6e..9488eaf 100644
--- a/scilab/modules/interpolation/Makefile.in
+++ b/scilab/modules/interpolation/Makefile.in
@@ -474,9 +474,11 @@ NMEDIT = @NMEDIT@
474OBJDUMP = @OBJDUMP@ 474OBJDUMP = @OBJDUMP@
475OBJEXT = @OBJEXT@ 475OBJEXT = @OBJEXT@
476OCAMLC = @OCAMLC@ 476OCAMLC = @OCAMLC@
477OCAMLCFLAGS = @OCAMLCFLAGS@
477OCAMLDEP = @OCAMLDEP@ 478OCAMLDEP = @OCAMLDEP@
478OCAMLLEX = @OCAMLLEX@ 479OCAMLLEX = @OCAMLLEX@
479OCAMLOPT = @OCAMLOPT@ 480OCAMLOPT = @OCAMLOPT@
481OCAMLOPTFLAGS = @OCAMLOPTFLAGS@
480OCAMLYACC = @OCAMLYACC@ 482OCAMLYACC = @OCAMLYACC@
481OPENMPI_CC = @OPENMPI_CC@ 483OPENMPI_CC = @OPENMPI_CC@
482OPENMPI_CFLAGS = @OPENMPI_CFLAGS@ 484OPENMPI_CFLAGS = @OPENMPI_CFLAGS@
diff --git a/scilab/modules/interpolation/help/en_US/bsplin3val.xml b/scilab/modules/interpolation/help/en_US/bsplin3val.xml
index d579ac5..02e62fb 100644
--- a/scilab/modules/interpolation/help/en_US/bsplin3val.xml
+++ b/scilab/modules/interpolation/help/en_US/bsplin3val.xml
@@ -1,5 +1,8 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="bsplin3val" xml:lang="en"> 2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
3 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
4 xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
5 xml:id="bsplin3val" xml:lang="en">
3 <refnamediv> 6 <refnamediv>
4 <refname>bsplin3val</refname> 7 <refname>bsplin3val</refname>
5 <refpurpose>3d spline arbitrary derivative evaluation 8 <refpurpose>3d spline arbitrary derivative evaluation
@@ -8,7 +11,7 @@
8 </refnamediv> 11 </refnamediv>
9 <refsynopsisdiv> 12 <refsynopsisdiv>
10 <title>Syntax</title> 13 <title>Syntax</title>
11 <synopsis>[dfp]=bsplin3val(xp,yp,zp,tl,der)</synopsis> 14 <synopsis>dfp = bsplin3val(xp, yp, zp, tl, der)</synopsis>
12 </refsynopsisdiv> 15 </refsynopsisdiv>
13 <refsection> 16 <refsection>
14 <title>Arguments</title> 17 <title>Arguments</title>
@@ -58,13 +61,13 @@
58 <literal>s</literal>. The derivative to compute is specified by the 61 <literal>s</literal>. The derivative to compute is specified by the
59 argument <literal>der=[ox,oy,oz]</literal> : 62 argument <literal>der=[ox,oy,oz]</literal> :
60 </para> 63 </para>
61 <informalequation> 64 <para>
62 <mediaobject> 65 <latex style="display" fontsize="18"
63 <imageobject> 66 alt="dfp(i)=∂^{oxoyoz}/(∂^ox.∂^oy.∂^oz) s(xp(i),yp(i),zp(i))">
64 <imagedata align="center" fileref="../mml/bsplin3val_equation1.mml"/> 67 dfp(i)=\frac{\partial^{ox\,oy\,oz}}{\partial ^{ox}\,\partial ^{oy}\,\partial ^{oz}}
65 </imageobject> 68 s\left(xp(i),yp(i),zp(i)\right)
66 </mediaobject> 69 </latex>
67 </informalequation> 70 </para>
68 <para> 71 <para>
69 So <literal>der=[0 0 0]</literal> corresponds to 72 So <literal>der=[0 0 0]</literal> corresponds to
70 <emphasis>s</emphasis>, <literal>der=[1 0 0]</literal> to 73 <emphasis>s</emphasis>, <literal>der=[1 0 0]</literal> to
@@ -123,13 +126,4 @@ fxxyz_i = bsplin3val(xp,yp,zp,tl,[2 1 1])
123 </member> 126 </member>
124 </simplelist> 127 </simplelist>
125 </refsection> 128 </refsection>
126 <refsection>
127 <title>History</title>
128 <revhistory>
129 <revision>
130 <revnumber>5.4.0</revnumber>
131 <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
132 </revision>
133 </revhistory>
134 </refsection>
135</refentry> 129</refentry>
diff --git a/scilab/modules/interpolation/help/en_US/interp.xml b/scilab/modules/interpolation/help/en_US/interp.xml
index 49ad16f..dcb89e5 100644
--- a/scilab/modules/interpolation/help/en_US/interp.xml
+++ b/scilab/modules/interpolation/help/en_US/interp.xml
@@ -1,12 +1,18 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="interp" xml:lang="en"> 2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
3 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
4 xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
5 xml:id="interp" xml:lang="en">
3 <refnamediv> 6 <refnamediv>
4 <refname>interp</refname> 7 <refname>interp</refname>
5 <refpurpose>cubic spline evaluation function</refpurpose> 8 <refpurpose>cubic spline evaluation function</refpurpose>
6 </refnamediv> 9 </refnamediv>
7 <refsynopsisdiv> 10 <refsynopsisdiv>
8 <title>Syntax</title> 11 <title>Syntax</title>
9 <synopsis>[ yp [,yp1 [,yp2 [,yp3]]]] = interp(xp, x, y, d [, out_mode])</synopsis> 12 <synopsis>
13 [yp, yp1, yp2, yp3] = interp(xp, x, y, d)
14 [yp, yp1, yp2, yp3] = interp(xp, x, y, d, out_mode)
15 </synopsis>
10 </refsynopsisdiv> 16 </refsynopsisdiv>
11 <refsection> 17 <refsection>
12 <title>Arguments</title> 18 <title>Arguments</title>
@@ -15,14 +21,18 @@
15 <term>x,y</term> 21 <term>x,y</term>
16 <listitem> 22 <listitem>
17 <para> 23 <para>
18 real vectors of same size <literal>n</literal>: Coordinates of data points on which the interpolation and the related cubic spline (called <literal>s(X)</literal> in the following) or sub-spline function is based and built. 24 real vectors of same size <literal>n</literal>: Coordinates of data points on
25 which the interpolation and the related cubic spline (called <literal>s(X)</literal>
26 in the following) or sub-spline function is based and built.
19 </para> 27 </para>
20 </listitem> 28 </listitem>
21 </varlistentry> 29 </varlistentry>
22 <varlistentry> 30 <varlistentry>
23 <term>d</term> 31 <term>d</term>
24 <listitem> 32 <listitem>
25 <para>real vector of size(x): The derivative s'(x). Most often, s'(x) will be priorly estimated through the function splin(x, y,..) 33 <para>
34 real vector of size(x): The derivative s'(x). Most often, s'(x) will be
35 priorly estimated through the function splin(x, y,..)
26 </para> 36 </para>
27 </listitem> 37 </listitem>
28 </varlistentry> 38 </varlistentry>
@@ -30,7 +40,8 @@
30 <term>out_mode</term> 40 <term>out_mode</term>
31 <listitem> 41 <listitem>
32 <para> 42 <para>
33 (optional) string defining <literal>s(X)</literal> for <literal>X</literal> outside <latex>[x_1,\ x_n]</latex>. 43 (optional) string defining <literal>s(X)</literal> for <literal>X</literal>
44 outside [x<subscript>1</subscript>, x<subscript>n</subscript>].
34 Possible values: "by_zero" | "by_nan" | "C0" | "natural" | "linear" | "periodic" 45 Possible values: "by_zero" | "by_nan" | "C0" | "natural" | "linear" | "periodic"
35 </para> 46 </para>
36 </listitem> 47 </listitem>
@@ -39,7 +50,8 @@
39 <term>xp</term> 50 <term>xp</term>
40 <listitem> 51 <listitem>
41 <para> 52 <para>
42 real vector or matrix: abscissae at which <literal>Y</literal> is unknown and must be estimated with <literal>s(xp)</literal> 53 real vector or matrix: abscissae at which <literal>Y</literal> is unknown
54 and must be estimated with <literal>s(xp)</literal>
43 </para> 55 </para>
44 </listitem> 56 </listitem>
45 </varlistentry> 57 </varlistentry>
@@ -47,7 +59,8 @@
47 <term>yp</term> 59 <term>yp</term>
48 <listitem> 60 <listitem>
49 <para> 61 <para>
50 vector or matrix of size(xp): <literal>yp(i) = s(xp(i))</literal> or <literal>yp(i,j) = s(xp(i,j))</literal> 62 vector or matrix of size(xp): <literal>yp(i) = s(xp(i))</literal> or
63 <literal>yp(i,j) = s(xp(i,j))</literal>
51 </para> 64 </para>
52 </listitem> 65 </listitem>
53 </varlistentry> 66 </varlistentry>
@@ -55,7 +68,8 @@
55 <term>yp1, yp2, yp3</term> 68 <term>yp1, yp2, yp3</term>
56 <listitem> 69 <listitem>
57 <para> 70 <para>
58 vectors (or matrices) of size(x): elementwise evaluation of the derivatives <literal>s'(xp)</literal>, <literal>s''(xp)</literal> and <literal>s'''(xp)</literal>. 71 vectors (or matrices) of size(x): elementwise evaluation of the derivatives
72 <literal>s'(xp)</literal>, <literal>s''(xp)</literal> and <literal>s'''(xp)</literal>.
59 </para> 73 </para>
60 </listitem> 74 </listitem>
61 </varlistentry> 75 </varlistentry>
@@ -64,16 +78,61 @@
64 <refsection> 78 <refsection>
65 <title>Description</title> 79 <title>Description</title>
66 <para> 80 <para>
67 The cubic spline function <literal>s(X)</literal> interpolating the <literal>(x,y)</literal> set of given points is a continuous and derivable piece-wise function defined over <latex>[x_1,\ x_n]</latex>. It consists of a set of cubic polynomials, each one <latex>p_k(X)</latex> being defined on <latex>[x_k,\ x_{k+1}]</latex> and connected in values and slopes to both its neighbours. Thus, we can state that for each <latex>X\ \in\ [x_k,\ x_{k+1}],\ s(X) = p_k(X)</latex>, such that 81 The cubic spline function <literal>s(X)</literal> interpolating the <literal>(x,y)</literal>
68 <latex>s(x_i) = y_i,\quad \mbox{and}\quad s'(x_i) = d_i</latex>. Then, interp() evaluates <literal>s(X)</literal> (and <literal>s'(X), s''(X), s'''(X)</literal> if needed) at <literal>xp(i)</literal>, such that 82 set of given points is a continuous and derivable piece-wise function defined over
83 [x<subscript>1</subscript>, x<subscript>n</subscript>]. It consists of a set of cubic polynomials, each one
84 p<subscript>k</subscript>(X) being defined on [x<subscript>k</subscript>, x<subscript>k+1</subscript>]
85 and connected in values and slopes to both its neighbours. Thus, we can state that for each
86 <emphasis>
87 X &#8712; [x<subscript>k</subscript>, x<subscript>k+1</subscript>],
88 s(X) = p<subscript>k</subscript>(X)
89 </emphasis>, such that
90 <emphasis>
91 s(x<subscript>i</subscript>) = y<subscript>i</subscript>,  and  
92 s'(x<subscript>i</subscript>) = d<subscript>i</subscript>
93 </emphasis>.
94 Then, interp() evaluates <literal>s(X)</literal> (and <literal>s'(X), s''(X), s'''(X)</literal>
95 if needed) at <literal>xp(i)</literal>, such that
96 </para>
97 <para>
98 <table align="center">
99 <tr align="center">
100 <td><emphasis>
101 yp<subscript>i</subscript> = s(xp<subscript>i</subscript>)
102    or   
103 yp<subscript>ij</subscript> = s(xp<subscript>ij</subscript>)
104 </emphasis>
105 </td>
106 </tr>
107 <tr align="center">
108 <td><emphasis>
109 yp1<subscript>i</subscript> = s'(xp<subscript>i</subscript>)
110    or   
111 yp1<subscript>ij</subscript> = s'(xp<subscript>ij</subscript>)
112 </emphasis>
113 </td>
114 </tr>
115 <tr align="center">
116 <td><emphasis>
117 yp2<subscript>i</subscript> = s''(xp<subscript>i</subscript>)
118    or   
119 yp2<subscript>ij</subscript> = s''(xp<subscript>ij</subscript>)
120 </emphasis>
121 </td>
122 </tr>
123 <tr align="center">
124 <td><emphasis>
125 yp3<subscript>i</subscript> = s'''(xp<subscript>i</subscript>)
126    or   
127 yp3<subscript>ij</subscript> = s'''(xp<subscript>ij</subscript>)
128 </emphasis>
129 </td>
130 </tr>
131 </table>
69 </para> 132 </para>
70 <latex style="display" align="center"><![CDATA[ yp_i = s(xp_i) \quad or \quad yp_{i,j} = s(xp_{i,j}) ]]></latex>
71 <latex style="display" align="center"><![CDATA[ yp1_i = s'(xp_i) \quad or \quad yp1_{i,j} = s'(xp_{i,j}) ]]></latex>
72 <latex style="display" align="center"><![CDATA[ yp2_i = s''(xp_i) \quad or \quad yp2_{i,j} = s''(xp_{i,j}) ]]></latex>
73 <latex style="display" align="center"><![CDATA[ yp3_i = s'''(xp_i) \quad or \quad yp3_{i,j} = s'''(xp_{i,j}) ]]></latex>
74 <para> 133 <para>
75 The <literal>out_mode</literal> parameter set the evaluation rule 134 The <literal>out_mode</literal> parameter set the evaluation rule
76 for extrapolation, i.e. for <literal>xp(i)</literal> outside <latex>[x_1,\ x_n]</latex> : 135 for extrapolation, i.e. for <literal>xp(i)</literal> outside [x<subscript>1</subscript>, x<subscript>n</subscript>] :
77 </para> 136 </para>
78 <variablelist> 137 <variablelist>
79 <varlistentry> 138 <varlistentry>
@@ -91,28 +150,55 @@
91 <varlistentry> 150 <varlistentry>
92 <term>"C0"</term> 151 <term>"C0"</term>
93 <listitem> 152 <listitem>
94 <para>the extrapolation is defined as follows :</para> 153 <para>the extrapolation is defined as follows :
95 <latex style="display" align="center"><![CDATA[ xp_i < x_1 \Rightarrow yp_i = y_1 ]]></latex> 154 <table align="center">
96 <latex style="display" align="center"><![CDATA[ xp_i > x_n \Rightarrow yp_i = y_n ]]></latex> 155 <tr align="center"><td><emphasis>
156 xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
157 yp<subscript>i</subscript> = y<subscript>1</subscript>
158 </emphasis></td></tr>
159 <tr align="center"><td><emphasis>
160 xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
161 yp<subscript>i</subscript> = y<subscript>n</subscript>
162 </emphasis></td></tr>
163 </table>
164 </para>
97 </listitem> 165 </listitem>
98 </varlistentry> 166 </varlistentry>
99 <varlistentry> 167 <varlistentry>
100 <term>"natural"</term> 168 <term>"natural"</term>
101 <listitem> 169 <listitem>
102 <para> 170 <para>
103 the extrapolation is defined as follows (<latex>p_i(x)</latex> being the polynomial defining 171 the extrapolation is defined as follows (p<subscript>i</subscript>(x) being the polynomial defining
104 <literal>s(X)</literal> on <latex>[x_i,\ x_{i+1}]</latex>) 172 <literal>s(X)</literal> on [x<subscript>i</subscript>, x<subscript>i+1</subscript>]):
105 </para> 173 </para>
106 <latex style="display" align="center"><![CDATA[ xp_i < x_1 \Rightarrow yp_i = p_1(xp_i) ]]></latex> 174 <table align="center">
107 <latex style="display" align="center"><![CDATA[ xp_i > x_n \Rightarrow yp_i = p_{n-1}(xp_i) ]]></latex> 175 <tr align="center"><td><emphasis>
176 xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
177 yp<subscript>i</subscript> = p<subscript>1</subscript>(xp<subscript>i</subscript>)
178 </emphasis></td></tr>
179 <tr align="center"><td><emphasis>
180 xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
181 yp<subscript>i</subscript> = p<subscript>n-1</subscript>(xp<subscript>i</subscript>)
182 </emphasis></td></tr>
183 </table>
108 </listitem> 184 </listitem>
109 </varlistentry> 185 </varlistentry>
110 <varlistentry> 186 <varlistentry>
111 <term>"linear"</term> 187 <term>"linear"</term>
112 <listitem> 188 <listitem>
113 <para>the extrapolation is defined as follows :</para> 189 <para>the extrapolation is defined as follows :</para>
114 <latex style="display" align="center"><![CDATA[ xp_i < x_1 \Rightarrow yp_i = y_1 + d_1.(xp_i - x_1) ]]></latex> 190 <table align="center">
115 <latex style="display" align="center"><![CDATA[ xp_i > x_n \Rightarrow yp_i = y_n + d_n.(xp_i - x_n) ]]></latex> 191 <tr align="center"><td><emphasis>
192 xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
193 yp<subscript>i</subscript> = y<subscript>1</subscript> +
194 d<subscript>1</subscript>.(xp<subscript>i</subscript> - x<subscript>1</subscript>)
195 </emphasis></td></tr>
196 <tr align="center"><td><emphasis>
197 xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
198 yp<subscript>i</subscript> = y<subscript>n</subscript> +
199 d<subscript>n</subscript>.(xp<subscript>i</subscript> - x<subscript>n</subscript>)
200 </emphasis></td></tr>
201 </table>
116 </listitem> 202 </listitem>
117 </varlistentry> 203 </varlistentry>
118 <varlistentry> 204 <varlistentry>
@@ -121,7 +207,13 @@
121 <para> 207 <para>
122 <literal>s(X)</literal> is extended by periodicity: 208 <literal>s(X)</literal> is extended by periodicity:
123 </para> 209 </para>
124 <latex style="display" align="center"><![CDATA[ yp_i = s( x_1 + ( (xp_i-x_1)\ \mbox{modulo}\ [x_n-x_1] ) ) ]]></latex> 210 <table align="center">
211 <tr><td><emphasis>
212 yp<subscript>i</subscript> = s( x<subscript>1</subscript> +
213 (xp<subscript>i</subscript> - x<subscript>1</subscript>) modulo 
214 (x<subscript>n</subscript>-x<subscript>1</subscript>) )
215 </emphasis></td></tr>
216 </table>
125 </listitem> 217 </listitem>
126 </varlistentry> 218 </varlistentry>
127 </variablelist> 219 </variablelist>
@@ -220,13 +312,4 @@ xtitle(" different way to evaluate a spline outside its domain")
220 </member> 312 </member>
221 </simplelist> 313 </simplelist>
222 </refsection> 314 </refsection>
223 <refsection>
224 <title>History</title>
225 <revhistory>
226 <revision>
227 <revnumber>5.4.0</revnumber>
228 <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
229 </revision>
230 </revhistory>
231 </refsection>
232</refentry> 315</refentry>
diff --git a/scilab/modules/interpolation/help/en_US/linear_interpn.xml b/scilab/modules/interpolation/help/en_US/linear_interpn.xml
index 0668b72..501e1d2 100644
--- a/scilab/modules/interpolation/help/en_US/linear_interpn.xml
+++ b/scilab/modules/interpolation/help/en_US/linear_interpn.xml
@@ -1,12 +1,18 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="linear_interpn" xml:lang="en"> 2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
3 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
4 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
5 xmlns:scilab="http://www.scilab.org" xml:id="linear_interpn" xml:lang="en">
3 <refnamediv> 6 <refnamediv>
4 <refname>linear_interpn</refname> 7 <refname>linear_interpn</refname>
5 <refpurpose>n dimensional linear interpolation</refpurpose> 8 <refpurpose>n dimensional linear interpolation</refpurpose>
6 </refnamediv> 9 </refnamediv>
7 <refsynopsisdiv> 10 <refsynopsisdiv>
8 <title>Syntax</title> 11 <title>Syntax</title>
9 <synopsis>vp = linear_interpn(xp1,xp2,..,xpn, x1, ..., xn, v [,out_mode])</synopsis> 12 <synopsis>
13 vp = linear_interpn(xp1,xp2,..,xpn, x1,...,xn, v)
14 vp = linear_interpn(xp1,xp2,..,xpn, x1,...,xn, v, out_mode)
15 </synopsis>
10 </refsynopsisdiv> 16 </refsynopsisdiv>
11 <refsection> 17 <refsection>
12 <title>Arguments</title> 18 <title>Arguments</title>
@@ -46,8 +52,7 @@
46 <term>vp</term> 52 <term>vp</term>
47 <listitem> 53 <listitem>
48 <para> 54 <para>
49 vector or matrix of same size than <literal>xp1, ..., 55 vector or matrix of same size than <literal>xp1, ..., xpn
50 xpn
51 </literal> 56 </literal>
52 </para> 57 </para>
53 </listitem> 58 </listitem>
@@ -63,38 +68,46 @@
63 and the values <literal>v</literal> of a function (says 68 and the values <literal>v</literal> of a function (says
64 <emphasis>f</emphasis>) at the grid points : 69 <emphasis>f</emphasis>) at the grid points :
65 </para> 70 </para>
66 <informalequation> 71 <para>
67 <mediaobject> 72 <table align="center">
68 <imageobject> 73 <tr><td>
69 <imagedata align="center" fileref="../mml/linear_interpn_equation1.mml"/> 74 v(i<subscript>1</subscript>,
70 </imageobject> 75 i<subscript>2</subscript>,…,
71 </mediaobject> 76 i<subscript>n</subscript>) =
72 </informalequation> 77 <emphasis>f</emphasis>(x1(i<subscript>1</subscript>),
78 x2(i<subscript>2</subscript>),…,
79 xn(i<subscript>n</subscript>))
80 </td>
81 </tr>
82 </table>
83 </para>
73 <para>this function computes the linear interpolant of 84 <para>this function computes the linear interpolant of
74 <emphasis>f</emphasis> from the grid (called <emphasis>s</emphasis> in the 85 <emphasis>f</emphasis> from the grid (called <emphasis>s</emphasis> in the
75 following) at the points which coordinates are defined by the vectors (or 86 following) at the points which coordinates are defined by the vectors (or
76 matrices) <literal>xp1, xp2, ..., xpn</literal>: 87 matrices) <literal>xp1, xp2, ..., xpn</literal>:
77 </para> 88 </para>
78 <informalequation> 89 <para>
79 <mediaobject> 90 <table align="center">
80 <imageobject> 91 <tr align="center">
81 <imagedata align="center" fileref="../mml/linear_interpn_equation2.mml"/> 92 <td>vp(i) = <emphasis>s</emphasis>(xp1(i), xp2(i), …, xpn(i))</td></tr>
82 </imageobject> 93 <tr align="center"><td>or</td></tr>
83 </mediaobject> 94 <tr align="center">
84 </informalequation> 95 <td>vp(i,j) = <emphasis>s</emphasis>(xp1(i,j), xp2(i,j), …, xpn(i,j))</td>
96 </tr>
97 </table>
98 in case the xpk are matrices.
99 </para>
85 <para> 100 <para>
86 The <literal>out_mode</literal> parameter set the evaluation rule 101 The <literal>out_mode</literal> parameter set the evaluation rule
87 for extrapolation: if we note 102 for extrapolation: if we note
88 <emphasis>Pi=(xp1(i),xp2(i),...,xpn(i))</emphasis> then 103 <emphasis>Pi=(xp1(i),xp2(i),...,xpn(i))</emphasis> then
89 <literal>out_mode</literal> defines the evaluation rule when: 104 <literal>out_mode</literal> defines the evaluation rule when:
90 </para> 105 </para>
91 <informalequation> 106 <para>
92 <mediaobject> 107 <table align="center">
93 <imageobject> 108 <tr><td>P(i) ∉ [x1(1), x1($)] × [x2(1), x2($)] × … × [xn(1), xn($)]</td></tr>
94 <imagedata align="center" fileref="../mml/linear_interpn_equation3.mml"/> 109 </table>
95 </imageobject> 110 </para>
96 </mediaobject>
97 </informalequation>
98 <para>The different choices are:</para> 111 <para>The different choices are:</para>
99 <variablelist> 112 <variablelist>
100 <varlistentry> 113 <varlistentry>
@@ -285,13 +298,4 @@ show_window()
285 </member> 298 </member>
286 </simplelist> 299 </simplelist>
287 </refsection> 300 </refsection>
288 <refsection>
289 <title>History</title>
290 <revhistory>
291 <revision>
292 <revnumber>5.4.0</revnumber>
293 <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
294 </revision>
295 </revhistory>
296 </refsection>
297</refentry> 301</refentry>
diff --git a/scilab/modules/interpolation/help/en_US/lsq_splin.xml b/scilab/modules/interpolation/help/en_US/lsq_splin.xml
index 5da6902..40298ca 100644
--- a/scilab/modules/interpolation/help/en_US/lsq_splin.xml
+++ b/scilab/modules/interpolation/help/en_US/lsq_splin.xml
@@ -1,12 +1,31 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="lsq_splin" xml:lang="en"> 2<!--
3 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
4 * Copyright (C) R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
5 * Copyright (C) B. Pincon (interface Scilab)
6 *
7 * This file is hereby licensed under the terms of the GNU GPL v2.0,
8 * pursuant to article 5.3.4 of the CeCILL v.2.1.
9 * This file was originally licensed under the terms of the CeCILL v2.1,
10 * and continues to be available under such terms.
11 * For more information, see the COPYING file which you should have received
12 * along with this program.
13 *
14 -->
15<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
16 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
17 xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
18 xml:id="lsq_splin" xml:lang="en">
3 <refnamediv> 19 <refnamediv>
4 <refname>lsq_splin</refname> 20 <refname>lsq_splin</refname>
5 <refpurpose>weighted least squares cubic spline fitting</refpurpose> 21 <refpurpose>weighted least squares cubic spline fitting</refpurpose>
6 </refnamediv> 22 </refnamediv>
7 <refsynopsisdiv> 23 <refsynopsisdiv>
8 <title>Syntax</title> 24 <title>Syntax</title>
9 <synopsis>[y, d] = lsq_splin(xd, yd [, wd], x)</synopsis> 25 <synopsis>
26 [y, d] = lsq_splin(xd, yd, x)
27 [y, d] = lsq_splin(xd, yd, wd, x)
28 </synopsis>
10 </refsynopsisdiv> 29 </refsynopsisdiv>
11 <refsection> 30 <refsection>
12 <title>Arguments</title> 31 <title>Arguments</title>
@@ -59,15 +78,14 @@
59 breakpoints <emphasis>x1 &lt; x2 &lt; ... &lt; xn</emphasis> then the 78 breakpoints <emphasis>x1 &lt; x2 &lt; ... &lt; xn</emphasis> then the
60 resulting spline <emphasis>s</emphasis> is such that: 79 resulting spline <emphasis>s</emphasis> is such that:
61 </para> 80 </para>
62 <informalequation>
63 <mediaobject>
64 <imageobject>
65 <imagedata align="center" fileref="../mml/lsq_splin_equation1.mml"/>
66 </imageobject>
67 </mediaobject>
68 </informalequation>
69 <para> 81 <para>
70 for all <emphasis>fin S</emphasis>, i.e. realizes the minimum of 82 <latex style="display" fontsize="18" alt="∑_k=1→m wd(k).[s(xd(k))-yd(k)]² ⬅ ∑_k=1→m wd(k).[f(xd(k))-yd(k)]²">
83 \sum_{k=1}^m wd(k)\left(s(xd(k))-yd(k)\right)^2 \,\leftarrow\,
84 \sum_{k=1}^m wd(k)\left(f(xd(k))-yd(k)\right)^2
85 </latex>
86 </para>
87 <para>
88 for all <emphasis>f in S</emphasis>, i.e. realizes the minimum of
71 the sum of the squared errors over all functions of 89 the sum of the squared errors over all functions of
72 <emphasis>S</emphasis>. 90 <emphasis>S</emphasis>.
73 </para> 91 </para>
@@ -161,6 +179,12 @@ show_window()
161 <title>See also</title> 179 <title>See also</title>
162 <simplelist type="inline"> 180 <simplelist type="inline">
163 <member> 181 <member>
182 <link linkend="backslash">backslash</link>
183 </member>
184 <member>
185 <link linkend="datafit">datafit</link>
186 </member>
187 <member>
164 <link linkend="interp">interp</link> 188 <link linkend="interp">interp</link>
165 </member> 189 </member>
166 <member> 190 <member>
diff --git a/scilab/modules/interpolation/help/en_US/splin.xml b/scilab/modules/interpolation/help/en_US/splin.xml
index 050925c..fe2adad 100644
--- a/scilab/modules/interpolation/help/en_US/splin.xml
+++ b/scilab/modules/interpolation/help/en_US/splin.xml
@@ -1,12 +1,32 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin" xml:lang="en"> 2<!--
3 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
4 * Copyright (C) F. N. Fritsch (pchim.f Slatec routine is used for monotonous interpolation)
5 * Copyright (C) B. Pincon (interface Scilab)
6 *
7 * This file is hereby licensed under the terms of the GNU GPL v2.0,
8 * pursuant to article 5.3.4 of the CeCILL v.2.1.
9 * This file was originally licensed under the terms of the CeCILL v2.1,
10 * and continues to be available under such terms.
11 * For more information, see the COPYING file which you should have received
12 * along with this program.
13 *
14 -->
15<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
16 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
17 xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
18 xml:id="splin" xml:lang="en">
3 <refnamediv> 19 <refnamediv>
4 <refname>splin</refname> 20 <refname>splin</refname>
5 <refpurpose>cubic spline interpolation</refpurpose> 21 <refpurpose>cubic spline interpolation</refpurpose>
6 </refnamediv> 22 </refnamediv>
7 <refsynopsisdiv> 23 <refsynopsisdiv>
8 <title>Syntax</title> 24 <title>Syntax</title>
9 <synopsis>d = splin(x, y [,spline_type [, der]])</synopsis> 25 <synopsis>
26 d = splin(x, y)
27 d = splin(x, y, spline_type)
28 d = splin(x, y, spline_type, der)
29 </synopsis>
10 </refsynopsisdiv> 30 </refsynopsisdiv>
11 <refsection> 31 <refsection>
12 <title>Arguments</title> 32 <title>Arguments</title>
@@ -77,13 +97,12 @@
77 using the following conditions (considering n points 97 using the following conditions (considering n points
78 x1,...,xn): 98 x1,...,xn):
79 </para> 99 </para>
80 <informalequation> 100 <para>
81 <mediaobject> 101 <latex fontsize="18" alt="s′′′(x₂⁻)=s′′′(x₂⁺), s′′′(x{n-1}⁻)=s′′′(x{n-1}⁺)">
82 <imageobject> 102 s'''(x_2^-) = s'''(x_2^+) \\
83 <imagedata align="center" fileref="../mml/splin_equation1.mml"/> 103 s'''(x_{n-1}^-) = s'''(x_{n-1}^+)
84 </imageobject> 104 </latex>
85 </mediaobject> 105 </para>
86 </informalequation>
87 </listitem> 106 </listitem>
88 </varlistentry> 107 </varlistentry>
89 <varlistentry> 108 <varlistentry>
@@ -93,26 +112,24 @@
93 points derivatives which must be provided as the last argument 112 points derivatives which must be provided as the last argument
94 <literal>der</literal>: 113 <literal>der</literal>:
95 </para> 114 </para>
96 <informalequation> 115 <para>
97 <mediaobject> 116 <table align="center">
98 <imageobject> 117 <tr align="center"><td><emphasis>s'(x<subscript>1</subscript>) = der(1)</emphasis></td></tr>
99 <imagedata align="center" fileref="../mml/splin_equation2.mml"/> 118 <tr align="center"><td><emphasis>s'(x<subscript>n</subscript>) = der(2)</emphasis></td></tr>
100 </imageobject> 119 </table>
101 </mediaobject> 120 </para>
102 </informalequation>
103 </listitem> 121 </listitem>
104 </varlistentry> 122 </varlistentry>
105 <varlistentry> 123 <varlistentry>
106 <term>"natural"</term> 124 <term>"natural"</term>
107 <listitem> 125 <listitem>
108 <para>the cubic spline is computed by using the conditions:</para> 126 <para>the cubic spline is computed by using the conditions:</para>
109 <informalequation> 127 <para>
110 <mediaobject> 128 <table align="center">
111 <imageobject> 129 <tr align="center"><td><emphasis>s''(x<subscript>1</subscript>) = 0</emphasis></td></tr>
112 <imagedata align="center" fileref="../mml/splin_equation3.mml"/> 130 <tr align="center"><td><emphasis>s''(x<subscript>n</subscript>) = 0</emphasis></td></tr>
113 </imageobject> 131 </table>
114 </mediaobject> 132 </para>
115 </informalequation>
116 </listitem> 133 </listitem>
117 </varlistentry> 134 </varlistentry>
118 <varlistentry> 135 <varlistentry>
@@ -122,13 +139,20 @@
122 a periodic cubic spline is computed (<literal>y</literal> must 139 a periodic cubic spline is computed (<literal>y</literal> must
123 verify <emphasis>y1=yn</emphasis>) by using the conditions: 140 verify <emphasis>y1=yn</emphasis>) by using the conditions:
124 </para> 141 </para>
125 <informalequation> 142 <para>
126 <mediaobject> 143 <table align="center">
127 <imageobject> 144 <tr align="center">
128 <imagedata align="center" fileref="../mml/splin_equation4.mml"/> 145 <td>
129 </imageobject> 146 <emphasis>s'(x<subscript>1</subscript>) = s'(x<subscript>n</subscript>)</emphasis>
130 </mediaobject> 147 </td>
131 </informalequation> 148 </tr>
149 <tr align="center">
150 <td>
151 <emphasis>s''(x<subscript>1</subscript>) = s''(x<subscript>n</subscript>)</emphasis>
152 </td>
153 </tr>
154 </table>
155 </para>
132 </listitem> 156 </listitem>
133 </varlistentry> 157 </varlistentry>
134 <varlistentry> 158 <varlistentry>
@@ -140,13 +164,16 @@
140 the <emphasis>di</emphasis> such that <emphasis>s</emphasis> is 164 the <emphasis>di</emphasis> such that <emphasis>s</emphasis> is
141 monotone on each interval: 165 monotone on each interval:
142 </para> 166 </para>
143 <informalequation> 167 <para>
144 <mediaobject> 168 <itemizedlist>
145 <imageobject> 169 <listitem>
146 <imagedata align="center" fileref="../mml/splin_equation5.mml"/> 170 If y(i) ≤ y(i+1), s is increasing on <literal>[x(i), x(i+1)]</literal>.
147 </imageobject> 171 </listitem>
148 </mediaobject> 172 <listitem>
149 </informalequation> 173 If y(i) ≥ y(i+1), s is increasing on <literal>[x(i), x(i+1)]</literal>.
174 </listitem>
175 </itemizedlist>
176 </para>
150 </listitem> 177 </listitem>
151 </varlistentry> 178 </varlistentry>
152 <varlistentry> 179 <varlistentry>
@@ -176,16 +203,18 @@
176 <refsection> 203 <refsection>
177 <title>Remarks</title> 204 <title>Remarks</title>
178 <para> 205 <para>
179 From an accuracy point of view use essentially the <emphasis role="bold">clamped</emphasis> type if you know the end point derivatives, 206 From an accuracy point of view use essentially the <emphasis role="bold">clamped</emphasis>
180 else use <emphasis role="bold">not_a_knot</emphasis>. But if the 207 type if you know the end point derivatives, else use <emphasis role="bold">not_a_knot</emphasis>.
181 underlying approximated function is periodic use the <emphasis role="bold">periodic</emphasis> type. Under the good assumptions these 208 But if the underlying approximated function is periodic use the
209 <emphasis role="bold">periodic</emphasis> type. Under the good assumptions these
182 kind of splines got an <literal>O(h^4)</literal> asymptotic behavior of 210 kind of splines got an <literal>O(h^4)</literal> asymptotic behavior of
183 the error. Don't use the <emphasis role="bold">natural</emphasis> type 211 the error. Don't use the <emphasis role="bold">natural</emphasis> type
184 unless the underlying function have zero second end points 212 unless the underlying function have zero second end points
185 derivatives. 213 derivatives.
186 </para> 214 </para>
187 <para> 215 <para>
188 The <emphasis role="bold">monotone</emphasis>, <emphasis role="bold">fast</emphasis> (or <emphasis role="bold">fast_periodic</emphasis>) type may be useful in some cases, 216 The <emphasis role="bold">monotone</emphasis>, <emphasis role="bold">fast</emphasis>
217 (or <emphasis role="bold">fast_periodic</emphasis>) type may be useful in some cases,
189 for instance to limit oscillations (these kind of sub-splines have an 218 for instance to limit oscillations (these kind of sub-splines have an
190 <literal>O(h^3)</literal> asymptotic behavior of the error). 219 <literal>O(h^3)</literal> asymptotic behavior of the error).
191 </para> 220 </para>
@@ -193,7 +222,8 @@
193 If <emphasis>n=2</emphasis> (and <literal>spline_type</literal> is 222 If <emphasis>n=2</emphasis> (and <literal>spline_type</literal> is
194 not <emphasis role="bold">clamped</emphasis>) linear interpolation is 223 not <emphasis role="bold">clamped</emphasis>) linear interpolation is
195 used. If <emphasis>n=3</emphasis> and <literal>spline_type</literal> is 224 used. If <emphasis>n=3</emphasis> and <literal>spline_type</literal> is
196 <emphasis role="bold">not_a_knot</emphasis>, then a <emphasis role="bold">fast</emphasis> sub-spline type is in fact computed. 225 <emphasis role="bold">not_a_knot</emphasis>, then a <emphasis role="bold">fast</emphasis>
226 sub-spline type is in fact computed.
197 </para> 227 </para>
198 </refsection> 228 </refsection>
199 <refsection> 229 <refsection>
@@ -274,13 +304,4 @@ show_window()
274 </member> 304 </member>
275 </simplelist> 305 </simplelist>
276 </refsection> 306 </refsection>
277 <refsection>
278 <title>History</title>
279 <revhistory>
280 <revision>
281 <revnumber>5.4.0</revnumber>
282 <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
283 </revision>
284 </revhistory>
285 </refsection>
286</refentry> 307</refentry>
diff --git a/scilab/modules/interpolation/help/en_US/splin2d.xml b/scilab/modules/interpolation/help/en_US/splin2d.xml
index 91f8c18..8c88f38 100644
--- a/scilab/modules/interpolation/help/en_US/splin2d.xml
+++ b/scilab/modules/interpolation/help/en_US/splin2d.xml
@@ -1,50 +1,52 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin2d" xml:lang="en"> 2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
3 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
4 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
5 xmlns:scilab="http://www.scilab.org" xml:id="splin2d" xml:lang="en">
3 <refnamediv> 6 <refnamediv>
4 <refname>splin2d</refname> 7 <refname>splin2d</refname>
5 <refpurpose>bicubic spline gridded 2d interpolation</refpurpose> 8 <refpurpose>bicubic spline gridded 2d interpolation</refpurpose>
6 </refnamediv> 9 </refnamediv>
7 <refsynopsisdiv> 10 <refsynopsisdiv>
8 <title>Syntax</title> 11 <title>Syntax</title>
9 <synopsis>C = splin2d(x, y, z, [,spline_type])</synopsis> 12 <synopsis>
13 C = splin2d(x, y, z)
14 C = splin2d(x, y, z, spline_type)
15 </synopsis>
10 </refsynopsisdiv> 16 </refsynopsisdiv>
11 <refsection> 17 <refsection>
12 <title>Arguments</title> 18 <title>Arguments</title>
13 <variablelist> 19 <variablelist>
14 <varlistentry> 20 <varlistentry>
15 <term>x</term> 21 <term>x, y</term>
16 <listitem> 22 <listitem>
17 <para> a 1-by-nx matrix of doubles, the x coordinate of the interpolation points. We must have x(i)&lt;x(i+1), for i=1,2,...,nx-1. 23 <para>
18 </para> 24 rows of nx and ny real numbers, in strictly increasing order: the
19 </listitem> 25 <varname>x</varname> and <varname>y</varname> coordinates building
20 </varlistentry> 26 the grid of the interpolation points (nodes).
21 <varlistentry>
22 <term>y</term>
23 <listitem>
24 <para>a 1-by-ny matrix of doubles, the y coordinate of the interpolation points.
25 We must have y(i)&lt;y(i+1), for i=1,2,...,ny-1.
26 </para> 27 </para>
27 </listitem> 28 </listitem>
28 </varlistentry> 29 </varlistentry>
29 <varlistentry> 30 <varlistentry>
30 <term>z</term> 31 <term>z</term>
31 <listitem> 32 <listitem>
32 <para>a nx-by-ny matrix of doubles, the function values. 33 <para>a nx-by-ny matrix of real numbers: the function values.
33 </para> 34 </para>
34 </listitem> 35 </listitem>
35 </varlistentry> 36 </varlistentry>
36 <varlistentry> 37 <varlistentry>
37 <term>spline_type</term> 38 <term>spline_type</term>
38 <listitem> 39 <listitem>
39 <para>a 1-by-1 matrix of strings, the typof of spline to compute. 40 <para>"not_a_knot" or "periodic" string: the type of spline to compute.
40 Available values are spline_type="not_a_knot" and spline_type="periodic".
41 </para> 41 </para>
42 </listitem> 42 </listitem>
43 </varlistentry> 43 </varlistentry>
44 <varlistentry> 44 <varlistentry>
45 <term>C</term> 45 <term>C</term>
46 <listitem> 46 <listitem>
47 <para>the coefficients of the bicubic patches. This output argument of splin2d is the input argument of the interp2d function. 47 <para>
48 the coefficients of the bicubic patches. This output argument of splin2d
49 is the input argument of the interp2d function.
48 </para> 50 </para>
49 </listitem> 51 </listitem>
50 </varlistentry> 52 </varlistentry>
@@ -54,37 +56,38 @@
54 <title>Description</title> 56 <title>Description</title>
55 <para>This function computes a bicubic spline or sub-spline 57 <para>This function computes a bicubic spline or sub-spline
56 <emphasis>s</emphasis> which interpolates the 58 <emphasis>s</emphasis> which interpolates the
57 <emphasis>(xi,yj,zij)</emphasis> points, ie, we have 59 <emphasis>(x<subscript>i </subscript>,y<subscript>j </subscript>,z<subscript>ij </subscript>)</emphasis>
58 <emphasis>s(xi,yj)=zij</emphasis> for all <emphasis>i=1,..,nx</emphasis> 60 points, ie, we have
61 <emphasis>s(x<subscript>i </subscript>,y<subscript>j </subscript>)=z<subscript>ij </subscript></emphasis>
62 for all <emphasis>i=1,..,nx</emphasis>
59 and <emphasis>j=1,..,ny</emphasis>. The resulting spline 63 and <emphasis>j=1,..,ny</emphasis>. The resulting spline
60 <emphasis>s</emphasis> is defined by the triplet 64 <emphasis>s</emphasis> is defined by the triplet
61 <literal>(x,y,C)</literal> where <literal>C</literal> is the vector (of 65 <literal>(x,y,C)</literal> where <varname>C</varname> is the vector (of
62 length 16(nx-1)(ny-1)) with the coefficients of each of the (nx-1)(ny-1) 66 length 16(nx-1)(ny-1)) with the coefficients of each of the (nx-1)(ny-1)
63 bicubic patches : on <emphasis>[x(i) x(i+1)]x[y(j) y(j+1)]</emphasis>, 67 bicubic patches : on <emphasis>[x(i),x(i+1)] × [y(j),y(j+1)]</emphasis>,
64 <emphasis>s</emphasis> is defined by : 68 <emphasis>s</emphasis> is defined by
65 </para> 69 </para>
66 <informalequation> 70 <latex style="display" fontsize="18"
67 <mediaobject> 71 alt="s(x,y) = ∑_m=1→4 ∑_n=1→4 c_ij(m,n).(x-x_i)^{m-1}.(y-y_j)^{n-1}">
68 <imageobject> 72 s(x,y)=\sum_{k=1}^4\sum_{l=1}^4 c_{ij}(k,l)\cdot(x-x_i)^{k-1}\cdot(y-y_j)^{l-1}
69 <imagedata align="center" fileref="../mml/splin2d_equation_1.mml"/> 73 </latex>
70 </imageobject>
71 </mediaobject>
72 </informalequation>
73 <para> 74 <para>
74 The evaluation of <emphasis>s</emphasis> at some points must be done 75 The evaluation of <emphasis>s</emphasis> at some points must be done by the
75 by the <link linkend="interp2d">interp2d</link> function. Several kind of 76 <link linkend="interp2d">interp2d</link> function. Several kind of splines may be
76 splines may be computed by selecting the appropriate 77 computed by selecting the appropriate <varname>spline_type</varname> parameter.
77 <literal>spline_type</literal> parameter. The method used to compute the 78 The method used to compute the bicubic spline (or sub-spline) is the old fashioned
78 bicubic spline (or sub-spline) is the old fashioned one 's, i.e. to 79 one's, i.e. to compute on each grid point
79 compute on each grid point <emphasis>(xi,yj)</emphasis> an approximation 80 <emphasis>(x<subscript>i </subscript>,y<subscript>j </subscript>)</emphasis>
80 of the first derivatives <emphasis>ds/dx(xi,yj)</emphasis> and 81 an approximation of the first derivatives
81 <emphasis>ds/dy(xi,yj)</emphasis> and of the cross derivative 82 <emphasis>ds/dx(x<subscript>i </subscript>,y<subscript>j </subscript>)</emphasis> and
82 <emphasis>d2s/dxdy(xi,yj)</emphasis>. Those derivatives are computed by 83 <emphasis>ds/dy(x<subscript>i </subscript>,y<subscript>j </subscript>)</emphasis> and
83 the mean of 1d spline schemes leading to a C2 function 84 of the cross derivative
84 (<emphasis>s</emphasis> is twice continuously differentiable) or by the 85 <emphasis>d2s/dxdy(x<subscript>i </subscript>,y<subscript>j </subscript>)</emphasis>.
85 mean of a local approximation scheme leading to a C1 function only. This 86 Those derivatives are computed by the mean of 1d spline schemes leading to a C2 function
86 scheme is selected with the <literal>spline_type</literal> parameter (see 87 (<emphasis>s</emphasis> is twice continuously differentiable) or by the mean of a local
87 <link linkend="splin">splin</link> for details) : 88 approximation scheme leading to a C1 function only. This scheme is selected with the
89 <varname>spline_type</varname> parameter (see <link linkend="splin">splin</link> for
90 details) :
88 </para> 91 </para>
89 <variablelist> 92 <variablelist>
90 <varlistentry> 93 <varlistentry>
@@ -110,21 +113,24 @@
110 <refsection> 113 <refsection>
111 <title>Remarks</title> 114 <title>Remarks</title>
112 <para> 115 <para>
113 From an accuracy point of view use essentially the <emphasis role="bold">not_a_knot</emphasis> type or <emphasis role="bold">periodic</emphasis> type if the underlying interpolated 116 From an accuracy point of view use essentially the
114 function is periodic. 117 <emphasis role="bold">not_a_knot</emphasis> type or
118 <emphasis role="bold">periodic</emphasis> type if the underlying interpolated function
119 is periodic.
115 </para> 120 </para>
116 <para> 121 <para>
117 The <emphasis role="bold">natural</emphasis>, <emphasis role="bold">monotone</emphasis>, <emphasis role="bold">fast</emphasis> (or 122 The <emphasis role="bold">natural</emphasis>, <emphasis role="bold">monotone</emphasis>,
118 <emphasis role="bold">fast_periodic</emphasis>) type may be useful in some 123 <emphasis role="bold">fast</emphasis> (or <emphasis role="bold">fast_periodic</emphasis>)
119 cases, for instance to limit oscillations (<emphasis role="bold">monotone</emphasis> being the most powerful for that). 124 type may be useful in some cases, for instance to limit oscillations
125 (<emphasis role="bold">monotone</emphasis> being the most powerful for that).
120 </para> 126 </para>
121 <para>To get the coefficients of the bi-cubic patches in a more friendly 127 <para>To get the coefficients of the bi-cubic patches in a more friendly
122 way you can use <literal>c = matrix(C, [4,4,nx-1,ny-1])</literal> then 128 way you can use <literal>c = matrix(C, [4,4,nx-1,ny-1])</literal> then
123 the coefficient <emphasis>(k,l)</emphasis> of the patch 129 the coefficient <emphasis>(k,l)</emphasis> of the patch
124 <emphasis>(i,j)</emphasis> (see equation here before) is stored at 130 <emphasis>(i,j)</emphasis> (see equation here before) is stored at
125 <literal>c(k,l,i,j)</literal>. Nevertheless the <link linkend="interp2d">interp2d</link> function wait for the big vector 131 <literal>c(k,l,i,j)</literal>. Nevertheless the <link linkend="interp2d">interp2d</link>
126 <literal>C</literal> and not for the hypermatrix <literal>c</literal> 132 function wait for the big vector <varname>C</varname> and not for the hypermatrix
127 (note that one can easily retrieve <literal>C</literal> from 133 <literal>c</literal> (note that one can easily retrieve <varname>C</varname> from
128 <literal>c</literal> with <literal>C=c(:)</literal>). 134 <literal>c</literal> with <literal>C=c(:)</literal>).
129 </para> 135 </para>
130 </refsection> 136 </refsection>
@@ -194,7 +200,6 @@ xtitle("natural")
194subplot(2,2,4) 200subplot(2,2,4)
195plot3d1(xp, yp, ZP4, flag=[2 2 4]) 201plot3d1(xp, yp, ZP4, flag=[2 2 4])
196xtitle("monotone") 202xtitle("monotone")
197show_window()
198 ]]></programlisting> 203 ]]></programlisting>
199 <scilab:image> 204 <scilab:image>
200 // example 2 : different interpolation functions on random data 205 // example 2 : different interpolation functions on random data
@@ -265,13 +270,4 @@ xtitle("subspline (monotone)")
265 </member> 270 </member>
266 </simplelist> 271 </simplelist>
267 </refsection> 272 </refsection>
268 <refsection>
269 <title>History</title>
270 <revhistory>
271 <revision>
272 <revnumber>5.4.0</revnumber>
273 <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
274 </revision>
275 </revhistory>
276 </refsection>
277</refentry> 273</refentry>
diff --git a/scilab/modules/interpolation/help/en_US/splin3d.xml b/scilab/modules/interpolation/help/en_US/splin3d.xml
index 7538ff9..0265541 100644
--- a/scilab/modules/interpolation/help/en_US/splin3d.xml
+++ b/scilab/modules/interpolation/help/en_US/splin3d.xml
@@ -1,12 +1,31 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin3d" xml:lang="en"> 2<!--
3 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
4 * Copyright (C) R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
5 * Copyright (C) B. Pincon (interface Scilab)
6 *
7 * This file is hereby licensed under the terms of the GNU GPL v2.0,
8 * pursuant to article 5.3.4 of the CeCILL v.2.1.
9 * This file was originally licensed under the terms of the CeCILL v2.1,
10 * and continues to be available under such terms.
11 * For more information, see the COPYING file which you should have received
12 * along with this program.
13 *
14 -->
15<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
16 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
17 xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
18 xml:id="splin3d" xml:lang="en">
3 <refnamediv> 19 <refnamediv>
4 <refname>splin3d</refname> 20 <refname>splin3d</refname>
5 <refpurpose>spline gridded 3d interpolation</refpurpose> 21 <refpurpose>spline gridded 3d interpolation</refpurpose>
6 </refnamediv> 22 </refnamediv>
7 <refsynopsisdiv> 23 <refsynopsisdiv>
8 <title>Syntax</title> 24 <title>Syntax</title>
9 <synopsis>tl = splin3d(x, y, z, v, [order])</synopsis> 25 <synopsis>
26 tl = splin3d(x, y, z, v)
27 tl = splin3d(x, y, z, v, order)
28 </synopsis>
10 </refsynopsisdiv> 29 </refsynopsisdiv>
11 <refsection> 30 <refsection>
12 <title>Arguments</title> 31 <title>Arguments</title>
@@ -57,23 +76,22 @@
57 in a B-spline-tensor representation of <emphasis>s</emphasis>. The 76 in a B-spline-tensor representation of <emphasis>s</emphasis>. The
58 evaluation of <emphasis>s</emphasis> at some points must be done by the 77 evaluation of <emphasis>s</emphasis> at some points must be done by the
59 <link linkend="interp3d">interp3d</link> function (to compute 78 <link linkend="interp3d">interp3d</link> function (to compute
60 <emphasis>s</emphasis> and its first derivatives) or by the <link linkend="bsplin3val">bsplin3val</link> function (to compute an arbitrary 79 <emphasis>s</emphasis> and its first derivatives) or by the
80 <link linkend="bsplin3val">bsplin3val</link> function (to compute an arbitrary
61 derivative of <emphasis>s</emphasis>) . Several kind of splines may be 81 derivative of <emphasis>s</emphasis>) . Several kind of splines may be
62 computed by selecting the order of the spline in each direction 82 computed by selecting the order of the spline in each direction
63 <literal>order=[kx,ky,kz]</literal>. 83 <literal>order=[kx,ky,kz]</literal>.
64 </para> 84 </para>
65 </refsection> 85 <para>
66 <refsection> 86 Remark : This function works under the conditions
67 <title>Remark</title> 87 <table align="center" style="float:center">
68 <para>This function works under the conditions:</para> 88 <tr><td>nx, ny, nz ≥ 3</td></tr>
69 <informalequation> 89 <tr><td>2 ≤ kx &lt; nx</td></tr>
70 <mediaobject> 90 <tr><td>2 ≤ ky &lt; ny</td></tr>
71 <imageobject> 91 <tr><td>2 ≤ kz &lt; nz</td></tr>
72 <imagedata align="center" fileref="../mml/splin3d_equation1.mml"/> 92 </table>
73 </imageobject> 93 </para>
74 </mediaobject> 94 <para>An error is yielded when they are not respected.</para>
75 </informalequation>
76 <para>an error being issued when they are not respected.</para>
77 </refsection> 95 </refsection>
78 <refsection> 96 <refsection>
79 <title>Examples</title> 97 <title>Examples</title>
@@ -95,15 +113,14 @@ vp_exact = f(xp,yp,zp);
95vp_interp = interp3d(xp,yp,zp, tl); 113vp_interp = interp3d(xp,yp,zp, tl);
96er = max(abs(vp_exact - vp_interp)) 114er = max(abs(vp_exact - vp_interp))
97// now retry with n=20 and see the error 115// now retry with n=20 and see the error
98 ]]></programlisting> 116 ]]></programlisting>
99 117 <para/>
100 <programlisting role="example"><![CDATA[ 118 <programlisting role="example"><![CDATA[
101
102// example 2 (see linear_interpn help page which have the 119// example 2 (see linear_interpn help page which have the
103// same example with trilinear interpolation) 120// same example with trilinear interpolation)
104// ============================================================================= 121// =============================================================================
105 122
106exec("SCI/modules/interpolation/demos/interp_demo.sci") 123exec("SCI/modules/interpolation/demos/interp_demo.sci", -1);
107func = "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2"; 124func = "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
108deff("v=f(x,y,z)",func); 125deff("v=f(x,y,z)",func);
109n = 5; 126n = 5;
@@ -116,7 +133,7 @@ m = 41;
116direction = ["z=" "z=" "z=" "x=" "y="]; 133direction = ["z=" "z=" "z=" "x=" "y="];
117val = [ 0.1 0.5 0.9 0.5 0.5]; 134val = [ 0.1 0.5 0.9 0.5 0.5];
118ebox = [0 1 0 1 0 1]; 135ebox = [0 1 0 1 0 1];
119XF=[]; YF=[]; ZF=[]; VF=[]; 136[XF, YF, ZF, VF] = ([], [], [], []);
120for i = 1:length(val) 137for i = 1:length(val)
121 [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(direction(i), val(i), ebox, m, m, m); 138 [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(direction(i), val(i), ebox, m, m, m);
122 Vm = interp3d(Xm,Ym,Zm, tl); 139 Vm = interp3d(Xm,Ym,Zm, tl);
@@ -126,19 +143,18 @@ for i = 1:length(val)
126 [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1); 143 [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1);
127 XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf]; 144 XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
128end 145end
129nb_col = 128; 146
130vmin = min(VF); vmax = max(VF); 147clf
148[nb_col, vmin, vmax] = (128, min(VF), max(VF));
131color_example = dsearch(VF,linspace(vmin,vmax,nb_col+1)); 149color_example = dsearch(VF,linspace(vmin,vmax,nb_col+1));
132gcf().color_map = jetcolormap(nb_col); 150gcf().color_map = jetcolormap(nb_col);
133clf();
134gca().hiddencolor = gca().background; 151gca().hiddencolor = gca().background;
135colorbar(vmin,vmax) 152colorbar(vmin,vmax)
136plot3d(XF, YF, list(ZF,color_example), flag=[-1 6 4]) 153plot3d(XF, YF, list(ZF,color_example), flag=[-1 6 4])
137xtitle("3d spline interpolation of "+func) 154title("3d spline interpolation of "+func, "fontsize",3)
138show_window() 155 ]]></programlisting>
139 ]]></programlisting>
140 <scilab:image localized="true"> 156 <scilab:image localized="true">
141 exec("SCI/modules/interpolation/demos/interp_demo.sci") 157 exec("SCI/modules/interpolation/demos/interp_demo.sci", -1);
142 func = "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2"; 158 func = "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
143 deff("v=f(x,y,z)",func); 159 deff("v=f(x,y,z)",func);
144 n = 5; 160 n = 5;
@@ -185,13 +201,4 @@ show_window()
185 </member> 201 </member>
186 </simplelist> 202 </simplelist>
187 </refsection> 203 </refsection>
188 <refsection>
189 <title>History</title>
190 <revhistory>
191 <revision>
192 <revnumber>5.4.0</revnumber>
193 <revremark>previously, imaginary part of input arguments were implicitly ignored.</revremark>
194 </revision>
195 </revhistory>
196 </refsection>
197</refentry> 204</refentry>
diff --git a/scilab/modules/interpolation/help/ja_JP/bsplin3val.xml b/scilab/modules/interpolation/help/ja_JP/bsplin3val.xml
index 1bdbf7f..555d738 100644
--- a/scilab/modules/interpolation/help/ja_JP/bsplin3val.xml
+++ b/scilab/modules/interpolation/help/ja_JP/bsplin3val.xml
@@ -1,12 +1,15 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="bsplin3val" xml:lang="ja"> 2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
3 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
4 xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
5 xml:id="bsplin3val" xml:lang="ja">
3 <refnamediv> 6 <refnamediv>
4 <refname>bsplin3val</refname> 7 <refname>bsplin3val</refname>
5 <refpurpose>3次元スプラインの任意微分評価関数</refpurpose> 8 <refpurpose>3次元スプラインの任意微分評価関数</refpurpose>
6 </refnamediv> 9 </refnamediv>
7 <refsynopsisdiv> 10 <refsynopsisdiv>
8 <title>呼び出し手順</title> 11 <title>呼び出し手順</title>
9 <synopsis>[dfp]=bsplin3val(xp,yp,zp,tl,der)</synopsis> 12 <synopsis>dfp = bsplin3val(xp, yp, zp, tl, der)</synopsis>
10 </refsynopsisdiv> 13 </refsynopsisdiv>
11 <refsection> 14 <refsection>
12 <title>引数</title> 15 <title>引数</title>
@@ -57,13 +60,13 @@
57 計算する微分値は引数<literal>der=[ox,oy,oz]</literal>で 60 計算する微分値は引数<literal>der=[ox,oy,oz]</literal>で
58 指定されます : 61 指定されます :
59 </para> 62 </para>
60 <informalequation> 63 <para>
61 <mediaobject> 64 <latex style="display" fontsize="18"
62 <imageobject> 65 alt="dfp(i)=∂^{oxoyoz}/(∂^ox.∂^oy.∂^oz) s(xp(i),yp(i),zp(i))">
63 <imagedata align="center" fileref="../mml/bsplin3val_equation1.mml"/> 66 dfp(i)=\frac{\partial^{ox\,oy\,oz}}{\partial ^{ox}\,\partial ^{oy}\,\partial ^{oz}}
64 </imageobject> 67 s\left(xp(i),yp(i),zp(i)\right)
65 </mediaobject> 68 </latex>
66 </informalequation> 69 </para>
67 <para> 70 <para>
68 この場合,<literal>der=[0 0 0]</literal> は 71 この場合,<literal>der=[0 0 0]</literal> は
69 <emphasis>s</emphasis>, <literal>der=[1 0 0]</literal>は 72 <emphasis>s</emphasis>, <literal>der=[1 0 0]</literal>は
@@ -115,15 +118,4 @@ fxxyz_i = bsplin3val(xp,yp,zp,tl,[2 1 1])
115 </member> 118 </member>
116 </simplelist> 119 </simplelist>
117 </refsection> 120 </refsection>
118 <refsection>
119 <title>履歴</title>
120 <revhistory>
121 <revision>
122 <revnumber>5.4.0</revnumber>
123 <revremark>
124 以前は,入力引数の虚部は暗黙的に無視されていました.
125 </revremark>
126 </revision>
127 </revhistory>
128 </refsection>
129</refentry> 121</refentry>
diff --git a/scilab/modules/interpolation/help/ja_JP/interp.xml b/scilab/modules/interpolation/help/ja_JP/interp.xml
index e0b9a11..dce04d5 100644
--- a/scilab/modules/interpolation/help/ja_JP/interp.xml
+++ b/scilab/modules/interpolation/help/ja_JP/interp.xml
@@ -1,12 +1,18 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="interp" xml:lang="ja"> 2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
3 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
4 xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
5 xml:id="interp" xml:lang="ja">
3 <refnamediv> 6 <refnamediv>
4 <refname>interp</refname> 7 <refname>interp</refname>
5 <refpurpose>3次スプライン評価関数</refpurpose> 8 <refpurpose>3次スプライン評価関数</refpurpose>
6 </refnamediv> 9 </refnamediv>
7 <refsynopsisdiv> 10 <refsynopsisdiv>
8 <title>呼び出し手順</title> 11 <title>呼び出し手順</title>
9 <synopsis>[yp [,yp1 [,yp2 [,yp3]]]]=interp(xp, x, y, d [, out_mode])</synopsis> 12 <synopsis>
13 [yp, yp1, yp2, yp3] = interp(xp, x, y, d)
14 [yp, yp1, yp2, yp3] = interp(xp, x, y, d, out_mode)
15 </synopsis>
10 </refsynopsisdiv> 16 </refsynopsisdiv>
11 <refsection> 17 <refsection>
12 <title>引数</title> 18 <title>引数</title>
@@ -35,7 +41,7 @@
35 <term>out_mode</term> 41 <term>out_mode</term>
36 <listitem> 42 <listitem>
37 <para> 43 <para>
38 (オプション)<latex>[x_1,\ x_n]</latex>の外側で. 44 (オプション)[x<subscript>1</subscript>, x<subscript>n</subscript>]の外側で.
39 <literal>X</literal> に対する<literal>s(X)</literal>を定義します. 45 <literal>X</literal> に対する<literal>s(X)</literal>を定義します.
40 利用可能な値: "by_zero" | "by_nan" | "C0" | "natural" | "linear" | "periodic" 46 利用可能な値: "by_zero" | "by_nan" | "C0" | "natural" | "linear" | "periodic"
41 </para> 47 </para>
@@ -77,20 +83,59 @@
77 <title>説明</title> 83 <title>説明</title>
78 <para> 84 <para>
79 指定した点の<literal>(x,y)</literal> 集合を補間する3次スプライン関数 <literal>s(X)</literal> 85 指定した点の<literal>(x,y)</literal> 集合を補間する3次スプライン関数 <literal>s(X)</literal>
80 は,<latex>[x_1,\ x_n]</latex>の範囲で定義された,連続で微分可能な関数です. 86 は,[x<subscript>1</subscript>, x<subscript>n</subscript>]の範囲で定義された,連続で微分可能な関数です.
81 これは,3次元多項式の集合からなり,その各々は<latex>p_k(X)</latex>が 87 これは,3次元多項式の集合からなり,その各々はp<subscript>k</subscript>(X)が
82 <latex>[x_k,\ x_{k+1}]</latex>で定義され, 88 [x<subscript>k</subscript>, x<subscript>k+1</subscript>]で定義され,
83 隣接する多項式と値と傾きで接続されています. 89 隣接する多項式と値と傾きで接続されています. つまり,
84 つまり, <latex>X\ \in\ [x_k,\ x_{k+1}],\ s(X) = p_k(X)</latex>の各々について, 90 <emphasis>
85 <latex>s(x_i) = y_i,\quad \mbox{and}\quad s'(x_i) = d_i</latex>を記述できます. 91 X &#8712; [x<subscript>k</subscript>, x<subscript>k+1</subscript>],
92 s(X) = p<subscript>k</subscript>(X)
93 </emphasis> の各々について,
94 <emphasis>
95 s(x<subscript>i</subscript>) = y<subscript>i</subscript>,  and  
96 s'(x<subscript>i</subscript>) = d<subscript>i</subscript>
97 </emphasis>
98 を記述できます.
99 </para>
100 <para>
101 <table align="center">
102 <tr align="center">
103 <td><emphasis>
104 yp<subscript>i</subscript> = s(xp<subscript>i</subscript>)
105    or   
106 yp<subscript>ij</subscript> = s(xp<subscript>ij</subscript>)
107 </emphasis>
108 </td>
109 </tr>
110 <tr align="center">
111 <td><emphasis>
112 yp1<subscript>i</subscript> = s'(xp<subscript>i</subscript>)
113    or   
114 yp1<subscript>ij</subscript> = s'(xp<subscript>ij</subscript>)
115 </emphasis>
116 </td>
117 </tr>
118 <tr align="center">
119 <td><emphasis>
120 yp2<subscript>i</subscript> = s''(xp<subscript>i</subscript>)
121    or   
122 yp2<subscript>ij</subscript> = s''(xp<subscript>ij</subscript>)
123 </emphasis>
124 </td>
125 </tr>
126 <tr align="center">
127 <td><emphasis>
128 yp3<subscript>i</subscript> = s'''(xp<subscript>i</subscript>)
129    or   
130 yp3<subscript>ij</subscript> = s'''(xp<subscript>ij</subscript>)
131 </emphasis>
132 </td>
133 </tr>
134 </table>
86 </para> 135 </para>
87 <latex style="display" align="center"><![CDATA[ yp_i = s(xp_i) \quad or \quad yp_{i,j} = s(xp_{i,j}) ]]></latex>
88 <latex style="display" align="center"><![CDATA[ yp1_i = s'(xp_i) \quad or \quad yp1_{i,j} = s'(xp_{i,j}) ]]></latex>
89 <latex style="display" align="center"><![CDATA[ yp2_i = s''(xp_i) \quad or \quad yp2_{i,j} = s''(xp_{i,j}) ]]></latex>
90 <latex style="display" align="center"><![CDATA[ yp3_i = s'''(xp_i) \quad or \quad yp3_{i,j} = s'''(xp_{i,j}) ]]></latex>
91 <para> 136 <para>
92 <literal>out_mode</literal>パラメータは 137 <literal>out_mode</literal>パラメータは
93 補外,すなわち,<literal>xp(i)</literal>が<latex>[x_1,\ x_n]</latex> の範囲にない場合 138 補外,すなわち,<literal>xp(i)</literal>が[x<subscript>1</subscript>, x<subscript>n</subscript>] の範囲にない場合
94 の評価規則を設定します : 139 の評価規則を設定します :
95 </para> 140 </para>
96 <variablelist> 141 <variablelist>
@@ -109,28 +154,55 @@
109 <varlistentry> 154 <varlistentry>
110 <term>"C0"</term> 155 <term>"C0"</term>
111 <listitem> 156 <listitem>
112 <para>以下のように定義される補外 :</para> 157 <para>以下のように定義される補外 :
113 <latex style="display" align="center"><![CDATA[ xp_i < x_1 \Rightarrow yp_i = y_1 ]]></latex> 158 <table align="center">
114 <latex style="display" align="center"><![CDATA[ xp_i > x_n \Rightarrow yp_i = y_n ]]></latex> 159 <tr align="center"><td><emphasis>
160 xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
161 yp<subscript>i</subscript> = y<subscript>1</subscript>
162 </emphasis></td></tr>
163 <tr align="center"><td><emphasis>
164 xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
165 yp<subscript>i</subscript> = y<subscript>n</subscript>
166 </emphasis></td></tr>
167 </table>
168 </para>
115 </listitem> 169 </listitem>
116 </varlistentry> 170 </varlistentry>
117 <varlistentry> 171 <varlistentry>
118 <term>"natural"</term> 172 <term>"natural"</term>
119 <listitem> 173 <listitem>
120 <para>以下のように定義される補外 174 <para>以下のように定義される補外
121 (<latex>p_i(x)</latex> は,<latex>[x_i,\ x_{i+1}]</latex> 175 (p<subscript>i</subscript>(x) は,[x<subscript>i</subscript>, x<subscript>i+1</subscript>]
122 において<literal>s(X)</literal>を定義する多項式です) 176 において<literal>s(X)</literal>を定義する多項式です)
123 </para> 177 </para>
124 <latex style="display" align="center"><![CDATA[ xp_i < x_1 \Rightarrow yp_i = p_1(xp_i) ]]></latex> 178 <table align="center">
125 <latex style="display" align="center"><![CDATA[ xp_i > x_n \Rightarrow yp_i = p_{n-1}(xp_i) ]]></latex> 179 <tr align="center"><td><emphasis>
180 xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
181 yp<subscript>i</subscript> = p<subscript>1</subscript>(xp<subscript>i</subscript>)
182 </emphasis></td></tr>
183 <tr align="center"><td><emphasis>
184 xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
185 yp<subscript>i</subscript> = p<subscript>n-1</subscript>(xp<subscript>i</subscript>)
186 </emphasis></td></tr>
187 </table>
126 </listitem> 188 </listitem>
127 </varlistentry> 189 </varlistentry>
128 <varlistentry> 190 <varlistentry>
129 <term>"linear"</term> 191 <term>"linear"</term>
130 <listitem> 192 <listitem>
131 <para>補外は以下のように定義されます :</para> 193 <para>補外は以下のように定義されます :</para>
132 <latex style="display" align="center"><![CDATA[ xp_i < x_1 \Rightarrow yp_i = y_1 + d_1.(xp_i - x_1) ]]></latex> 194 <table align="center">
133 <latex style="display" align="center"><![CDATA[ xp_i > x_n \Rightarrow yp_i = y_n + d_n.(xp_i - x_n) ]]></latex> 195 <tr align="center"><td><emphasis>
196 xp<subscript>i</subscript> &lt; x<subscript>1</subscript>  ⇒ 
197 yp<subscript>i</subscript> = y<subscript>1</subscript> +
198 d<subscript>1</subscript>.(xp<subscript>i</subscript> - x<subscript>1</subscript>)
199 </emphasis></td></tr>
200 <tr align="center"><td><emphasis>
201 xp<subscript>i</subscript> > x<subscript>n</subscript>  ⇒ 
202 yp<subscript>i</subscript> = y<subscript>n</subscript> +
203 d<subscript>n</subscript>.(xp<subscript>i</subscript> - x<subscript>n</subscript>)
204 </emphasis></td></tr>
205 </table>
134 </listitem> 206 </listitem>
135 </varlistentry> 207 </varlistentry>
136 <varlistentry> 208 <varlistentry>
@@ -139,7 +211,11 @@
139 <para> 211 <para>
140 <literal>s</literal> は周期性により拡張されます. 212 <literal>s</literal> は周期性により拡張されます.
141 </para> 213 </para>
142 <latex style="display" align="center"><![CDATA[ yp_i = s( x_1 + ( (xp_i-x_1)\ \mbox{modulo}\ [x_n-x_1] ) ) ]]></latex> 214 <table align="center">
215 <tr><td><emphasis>
216 yp<subscript>i</subscript> = s( x<subscript>1</subscript> + (xp<subscript>i</subscript> - x<subscript>1</subscript>) modulo (x<subscript>n</subscript>-x<subscript>1</subscript>) )
217 </emphasis></td></tr>
218 </table>
143 </listitem> 219 </listitem>
144 </varlistentry> 220 </varlistentry>
145 </variablelist> 221 </variablelist>
@@ -237,13 +313,4 @@ xtitle(" different way to evaluate a spline outside its domain")
237 </member> 313 </member>
238 </simplelist> 314 </simplelist>
239 </refsection> 315 </refsection>
240 <refsection>
241 <title>履歴</title>
242 <revhistory>
243 <revision>
244 <revnumber>5.4.0</revnumber>
245 <revremark>以前では, 入力引数の虚部は暗黙のうちに無視されていました.</revremark>
246 </revision>
247 </revhistory>
248 </refsection>
249</refentry> 316</refentry>
diff --git a/scilab/modules/interpolation/help/ja_JP/linear_interpn.xml b/scilab/modules/interpolation/help/ja_JP/linear_interpn.xml
index 752ae52..db6acbb 100644
--- a/scilab/modules/interpolation/help/ja_JP/linear_interpn.xml
+++ b/scilab/modules/interpolation/help/ja_JP/linear_interpn.xml
@@ -1,12 +1,18 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="linear_interpn" xml:lang="ja"> 2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
3 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
4 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
5 xmlns:scilab="http://www.scilab.org" xml:id="linear_interpn" xml:lang="ja">
3 <refnamediv> 6 <refnamediv>
4 <refname>linear_interpn</refname> 7 <refname>linear_interpn</refname>
5 <refpurpose>n 次元線形補間</refpurpose> 8 <refpurpose>n 次元線形補間</refpurpose>
6 </refnamediv> 9 </refnamediv>
7 <refsynopsisdiv> 10 <refsynopsisdiv>
8 <title>呼び出し手順</title> 11 <title>呼び出し手順</title>
9 <synopsis>vp = linear_interpn(xp1,xp2,..,xpn, x1, ..., xn, v [,out_mode])</synopsis> 12 <synopsis>
13 vp = linear_interpn(xp1,xp2,..,xpn, x1,...,xn, v)
14 vp = linear_interpn(xp1,xp2,..,xpn, x1,...,xn, v, out_mode)
15 </synopsis>
10 </refsynopsisdiv> 16 </refsynopsisdiv>
11 <refsection> 17 <refsection>
12 <title>引数</title> 18 <title>引数</title>
@@ -62,37 +68,45 @@
62 n個のベクトル<literal>x1 ,x2,..., xn</literal>で定義された n次元グリッド 68 n個のベクトル<literal>x1 ,x2,..., xn</literal>で定義された n次元グリッド
63 とそのグリッドにおける関数(例えば <emphasis>f</emphasis>)の値を次のように指定すると: 69 とそのグリッドにおける関数(例えば <emphasis>f</emphasis>)の値を次のように指定すると:
64 </para> 70 </para>
65 <informalequation> 71 <para>
66 <mediaobject> 72 <table align="center">
67 <imageobject> 73 <tr><td>
68 <imagedata align="center" fileref="../mml/linear_interpn_equation1.mml"/> 74 v(i<subscript>1</subscript>,
69 </imageobject> 75 i<subscript>2</subscript>,…,
70 </mediaobject> 76 i<subscript>n</subscript>) =
71 </informalequation> 77 <emphasis>f</emphasis>(x1(i<subscript>1</subscript>),
78 x2(i<subscript>2</subscript>),…,
79 xn(i<subscript>n</subscript>))
80 </td>
81 </tr>
82 </table>
83 </para>
72 <para> 84 <para>
73 この関数は, ベクトル<literal>xp1, xp2, ..., xpn</literal>(または行列)により定義された座標にある 85 この関数は, ベクトル<literal>xp1, xp2, ..., xpn</literal>(または行列)により定義された座標にある
74 (以下 <emphasis>s</emphasis> と呼ぶ)グリッドから次のように 86 (以下 <emphasis>s</emphasis> と呼ぶ)グリッドから次のように
75 <emphasis>f</emphasis>の線形補間を計算します: 87 <emphasis>f</emphasis>の線形補間を計算します:
76 </para> 88 </para>
77 <informalequation> 89 <para>
78 <mediaobject> 90 <table align="center">
79 <imageobject> 91 <tr align="center">
80 <imagedata align="center" fileref="../mml/linear_interpn_equation2.mml"/> 92 <td>vp(i) = <emphasis>s</emphasis>(xp1(i), xp2(i), …, xpn(i))</td></tr>
81 </imageobject> 93 <tr align="center"><td>or</td></tr>
82 </mediaobject> 94 <tr align="center">
83 </informalequation> 95 <td>vp(i,j) = <emphasis>s</emphasis>(xp1(i,j), xp2(i,j), …, xpn(i,j))</td>
96 </tr>
97 </table>
98 in case the xpk are matrices.
99 </para>
84 <para> 100 <para>
85 <literal>out_mode</literal> パラメータは捕外の評価規則を設定します: 101 <literal>out_mode</literal> パラメータは捕外の評価規則を設定します:
86 <emphasis>Pi=(xp1(i),xp2(i),...,xpn(i))</emphasis> とすると, 102 <emphasis>Pi=(xp1(i),xp2(i),...,xpn(i))</emphasis> とすると,
87 <literal>out_mode</literal> は次の場合に評価規則を定義します: 103 <literal>out_mode</literal> は次の場合に評価規則を定義します:
88 </para> 104 </para>
89 <informalequation> 105 <para>
90 <mediaobject> 106 <table align="center">
91 <imageobject> 107 <tr><td>P(i) ∉ [x1(1), x1($)] × [x2(1), x2($)] × … × [xn(1), xn($)]</td></tr>
92 <imagedata align="center" fileref="../mml/linear_interpn_equation3.mml"/> 108 </table>
93 </imageobject> 109 </para>
94 </mediaobject>
95 </informalequation>
96 <para>その他の選択肢は以下があります:</para> 110 <para>その他の選択肢は以下があります:</para>
97 <variablelist> 111 <variablelist>
98 <varlistentry> 112 <varlistentry>
@@ -280,13 +294,4 @@ show_window()
280 </member> 294 </member>
281 </simplelist> 295 </simplelist>
282 </refsection> 296 </refsection>
283 <refsection>
284 <title>履歴</title>
285 <revhistory>
286 <revision>
287 <revnumber>5.4.0</revnumber>
288 <revremark>以前では, 入力引数の虚部は暗黙のうちに無視されていました.</revremark>
289 </revision>
290 </revhistory>
291 </refsection>
292</refentry> 297</refentry>
diff --git a/scilab/modules/interpolation/help/ja_JP/lsq_splin.xml b/scilab/modules/interpolation/help/ja_JP/lsq_splin.xml
index d0b2df4..549a9fc 100644
--- a/scilab/modules/interpolation/help/ja_JP/lsq_splin.xml
+++ b/scilab/modules/interpolation/help/ja_JP/lsq_splin.xml
@@ -1,12 +1,31 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="lsq_splin" xml:lang="ja"> 2<!--
3 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
4 * Copyright (C) R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
5 * Copyright (C) B. Pincon (interface Scilab)
6 *
7 * This file is hereby licensed under the terms of the GNU GPL v2.0,
8 * pursuant to article 5.3.4 of the CeCILL v.2.1.
9 * This file was originally licensed under the terms of the CeCILL v2.1,
10 * and continues to be available under such terms.
11 * For more information, see the COPYING file which you should have received
12 * along with this program.
13 *
14 -->
15<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
16 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
17 xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
18 xml:id="lsq_splin" xml:lang="ja">
3 <refnamediv> 19 <refnamediv>
4 <refname>lsq_splin</refname> 20 <refname>lsq_splin</refname>
5 <refpurpose>重み付き最小二乗三次スプラインフィッティング</refpurpose> 21 <refpurpose>重み付き最小二乗三次スプラインフィッティング</refpurpose>
6 </refnamediv> 22 </refnamediv>
7 <refsynopsisdiv> 23 <refsynopsisdiv>
8 <title>呼び出し手順</title> 24 <title>呼び出し手順</title>
9 <synopsis>[y, d] = lsq_splin(xd, yd [, wd], x)</synopsis> 25 <synopsis>
26 [y, d] = lsq_splin(xd, yd, x)
27 [y, d] = lsq_splin(xd, yd, wd, x)
28 </synopsis>
10 </refsynopsisdiv> 29 </refsynopsisdiv>
11 <refsection> 30 <refsection>
12 <title>パラメータ</title> 31 <title>パラメータ</title>
@@ -65,13 +84,12 @@
65 あらゆる3次スプライン関数の空間とする場合, 84 あらゆる3次スプライン関数の空間とする場合,
66 得られるスプライン <emphasis>s</emphasis>は次のようになります: 85 得られるスプライン <emphasis>s</emphasis>は次のようになります:
67 </para> 86 </para>
68 <informalequation> 87 <para>
69 <mediaobject> 88 <latex style="display" fontsize="18" alt="∑_k=1→m wd(k).[s(xd(k))-yd(k)]² ⬅ ∑_k=1→m wd(k).[f(xd(k))-yd(k)]²">
70 <imageobject> 89 \sum_{k=1}^m wd(k)\left(s(xd(k))-yd(k)\right)^2 \,\leftarrow\,
71 <imagedata align="center" fileref="../mml/lsq_splin_equation1.mml"/> 90 \sum_{k=1}^m wd(k)\left(f(xd(k))-yd(k)\right)^2
72 </imageobject> 91 </latex>
73 </mediaobject> 92 </para>
74 </informalequation>
75 <para> 93 <para>
76 ただし,<emphasis>fはSの中の任意の値</emphasis>. 94 ただし,<emphasis>fはSの中の任意の値</emphasis>.
77 すなわち,<emphasis>S</emphasis>の任意の関数について, 95 すなわち,<emphasis>S</emphasis>の任意の関数について,
@@ -148,6 +166,12 @@ show_window()
148 <title>参照</title> 166 <title>参照</title>
149 <simplelist type="inline"> 167 <simplelist type="inline">
150 <member> 168 <member>
169 <link linkend="backslash">backslash</link>
170 </member>
171 <member>
172 <link linkend="datafit">datafit</link>
173 </member>
174 <member>
151 <link linkend="interp">interp</link> 175 <link linkend="interp">interp</link>
152 </member> 176 </member>
153 <member> 177 <member>
diff --git a/scilab/modules/interpolation/help/ja_JP/splin.xml b/scilab/modules/interpolation/help/ja_JP/splin.xml
index 27e3cfd..b5458b0 100644
--- a/scilab/modules/interpolation/help/ja_JP/splin.xml
+++ b/scilab/modules/interpolation/help/ja_JP/splin.xml
@@ -1,12 +1,32 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin" xml:lang="ja"> 2<!--
3 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
4 * Copyright (C) F. N. Fritsch (pchim.f Slatec routine is used for monotonous interpolation)
5 * Copyright (C) B. Pincon (interface Scilab)
6 *
7 * This file is hereby licensed under the terms of the GNU GPL v2.0,
8 * pursuant to article 5.3.4 of the CeCILL v.2.1.
9 * This file was originally licensed under the terms of the CeCILL v2.1,
10 * and continues to be available under such terms.
11 * For more information, see the COPYING file which you should have received
12 * along with this program.
13 *
14 -->
15<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
16 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
17 xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
18 xml:id="splin" xml:lang="ja">
3 <refnamediv> 19 <refnamediv>
4 <refname>splin</refname> 20 <refname>splin</refname>
5 <refpurpose>3次スプライン補間</refpurpose> 21 <refpurpose>3次スプライン補間</refpurpose>
6 </refnamediv> 22 </refnamediv>
7 <refsynopsisdiv> 23 <refsynopsisdiv>
8 <title>呼び出し手順</title> 24 <title>呼び出し手順</title>
9 <synopsis>d = splin(x, y [,spline_type [, der]])</synopsis> 25 <synopsis>
26 d = splin(x, y)
27 d = splin(x, y, spline_type)
28 d = splin(x, y, spline_type, der)
29 </synopsis>
10 </refsynopsisdiv> 30 </refsynopsisdiv>
11 <refsection> 31 <refsection>
12 <title>引数</title> 32 <title>引数</title>
@@ -79,13 +99,12 @@
79 <para>これはデフォルトで, 99 <para>これはデフォルトで,
80 3次スプラインが以下の条件 (n個の点 x1,...,xnを考慮)により計算されます: 100 3次スプラインが以下の条件 (n個の点 x1,...,xnを考慮)により計算されます:
81 </para> 101 </para>
82 <informalequation> 102 <para>
83 <mediaobject> 103 <latex fontsize="18" alt="s′′′(x₂⁻)=s′′′(x₂⁺), s′′′(x{n-1}⁻)=s′′′(x{n-1}⁺)">
84 <imageobject> 104 s'''(x_2^-) = s'''(x_2^+) \\
85 <imagedata align="center" fileref="../mml/splin_equation1.mml"/> 105 s'''(x_{n-1}^-) = s'''(x_{n-1}^+)
86 </imageobject> 106 </latex>
87 </mediaobject> 107 </para>
88 </informalequation>
89 </listitem> 108 </listitem>
90 </varlistentry> 109 </varlistentry>
91 <varlistentry> 110 <varlistentry>
@@ -95,26 +114,24 @@
95 を用いて計算されます.この微係数は最後の引数<literal>der</literal> 114 を用いて計算されます.この微係数は最後の引数<literal>der</literal>
96 で指定されます: 115 で指定されます:
97 </para> 116 </para>
98 <informalequation> 117 <para>
99 <mediaobject> 118 <table align="center">
100 <imageobject> 119 <tr align="center"><td><emphasis>s'(x<subscript>1</subscript>) = der(1)</emphasis></td></tr>
101 <imagedata align="center" fileref="../mml/splin_equation2.mml"/> 120 <tr align="center"><td><emphasis>s'(x<subscript>n</subscript>) = der(2)</emphasis></td></tr>
102 </imageobject> 121 </table>
103 </mediaobject> 122 </para>
104 </informalequation>
105 </listitem> 123 </listitem>
106 </varlistentry> 124 </varlistentry>
107 <varlistentry> 125 <varlistentry>
108 <term>"natural"</term> 126 <term>"natural"</term>
109 <listitem> 127 <listitem>
110 <para>3次スプラインは次の条件により計算されます:</para> 128 <para>3次スプラインは次の条件により計算されます:</para>
111 <informalequation> 129 <para>
112 <mediaobject> 130 <table align="center">
113 <imageobject> 131 <tr align="center"><td><emphasis>s''(x<subscript>1</subscript>) = 0</emphasis></td></tr>
114 <imagedata align="center" fileref="../mml/splin_equation3.mml"/> 132 <tr align="center"><td><emphasis>s''(x<subscript>n</subscript>) = 0</emphasis></td></tr>
115 </imageobject> 133 </table>
116 </mediaobject> 134 </para>
117 </informalequation>
118 </listitem> 135 </listitem>
119 </varlistentry> 136 </varlistentry>
120 <varlistentry> 137 <varlistentry>
@@ -123,13 +140,20 @@
123 <para>周期的3次スプラインは次の条件により計算されます 140 <para>周期的3次スプラインは次の条件により計算されます
124 (<literal>y</literal>は<emphasis>y1=yn</emphasis>を確認する必要があります): 141 (<literal>y</literal>は<emphasis>y1=yn</emphasis>を確認する必要があります):
125 </para> 142 </para>
126 <informalequation> 143 <para>
127 <mediaobject> 144 <table align="center">
128 <imageobject> 145 <tr align="center">
129 <imagedata align="center" fileref="../mml/splin_equation4.mml"/> 146 <td>
130 </imageobject> 147 <emphasis>s'(x<subscript>1</subscript>) = s'(x<subscript>n</subscript>)</emphasis>
131 </mediaobject> 148 </td>
132 </informalequation> 149 </tr>
150 <tr align="center">
151 <td>
152 <emphasis>s''(x<subscript>1</subscript>) = s''(x<subscript>n</subscript>)</emphasis>
153 </td>
154 </tr>
155 </table>
156 </para>
133 </listitem> 157 </listitem>
134 </varlistentry> 158 </varlistentry>
135 <varlistentry> 159 <varlistentry>
@@ -141,13 +165,16 @@
141 各区間で単調となるような<emphasis>di</emphasis> 165 各区間で単調となるような<emphasis>di</emphasis>
142 に関するローカルなスキームにより計算されます: 166 に関するローカルなスキームにより計算されます:
143 </para> 167 </para>
144 <informalequation> 168 <para>
145 <mediaobject> 169 <itemizedlist>
146 <imageobject> 170 <listitem>
147 <imagedata align="center" fileref="../mml/splin_equation5.mml"/> 171 If y(i) ≤ y(i+1), s is increasing on <literal>[x(i), x(i+1)]</literal>.
148 </imageobject> 172 </listitem>
149 </mediaobject> 173 <listitem>
150 </informalequation> 174 If y(i) ≥ y(i+1), s is increasing on <literal>[x(i), x(i+1)]</literal>.
175 </listitem>
176 </itemizedlist>
177 </para>
151 </listitem> 178 </listitem>
152 </varlistentry> 179 </varlistentry>
153 <varlistentry> 180 <varlistentry>
@@ -281,13 +308,4 @@ show_window()
281 </member> 308 </member>
282 </simplelist> 309 </simplelist>
283 </refsection> 310 </refsection>
284 <refsection>
285 <title>履歴</title>
286 <revhistory>
287 <revision>
288 <revnumber>5.4.0</revnumber>
289 <revremark>以前では, 入力引数の虚部は暗黙のうちに無視されていました.</revremark>
290 </revision>
291 </revhistory>
292 </refsection>
293</refentry> 311</refentry>
diff --git a/scilab/modules/interpolation/help/ja_JP/splin2d.xml b/scilab/modules/interpolation/help/ja_JP/splin2d.xml
index effe141..f5ebc84 100644
--- a/scilab/modules/interpolation/help/ja_JP/splin2d.xml
+++ b/scilab/modules/interpolation/help/ja_JP/splin2d.xml
@@ -1,12 +1,18 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin2d" xml:lang="ja"> 2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
3 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
4 xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
5 xml:id="splin2d" xml:lang="ja">
3 <refnamediv> 6 <refnamediv>
4 <refname>splin2d</refname> 7 <refname>splin2d</refname>
5 <refpurpose>双3次スプラインのグリッド2次元補間</refpurpose> 8 <refpurpose>双3次スプラインのグリッド2次元補間</refpurpose>
6 </refnamediv> 9 </refnamediv>
7 <refsynopsisdiv> 10 <refsynopsisdiv>
8 <title>呼び出し手順</title> 11 <title>呼び出し手順</title>
9 <synopsis>C = splin2d(x, y, z, [,spline_type])</synopsis> 12 <synopsis>
13 C = splin2d(x, y, z)
14 C = splin2d(x, y, z, spline_type)
15 </synopsis>
10 </refsynopsisdiv> 16 </refsynopsisdiv>
11 <refsection> 17 <refsection>
12 <title>引数</title> 18 <title>引数</title>
@@ -71,13 +77,11 @@
71 (長さ16(nx-1)(ny-1)の)ベクトルです, 77 (長さ16(nx-1)(ny-1)の)ベクトルです,
72 <emphasis>s</emphasis>は次のように定義されます : 78 <emphasis>s</emphasis>は次のように定義されます :
73 </para> 79 </para>
74 <informalequation> 80 <para>
75 <mediaobject> 81 <latex style="display" fontsize="18" alt="s(x,y) = ∑_m=1→4 ∑_n=1→4 c_ij(m,n).(x-x_i)^{m-1}.(y-y_j)^{n-1}">
76 <imageobject> 82 s(x,y)=\sum_{k=1}^4\sum_{l=1}^4 c_{ij}(k,l)\cdot(x-x_i)^{k-1}\cdot(y-y_j)^{l-1}
77 <imagedata align="center" fileref="../mml/splin2d_equation_1.mml"/> 83 </latex>
78 </imageobject> 84 </para>
79 </mediaobject>
80 </informalequation>
81 <para> 85 <para>
82 いくつかの点で<link linkend="interp2d">interp2d</link>関数により 86 いくつかの点で<link linkend="interp2d">interp2d</link>関数により
83 <emphasis>s</emphasis>の評価を行う必要があります. 87 <emphasis>s</emphasis>の評価を行う必要があります.
@@ -125,7 +129,8 @@
125 基本となる補間関数に周期性がある場合には<emphasis role="bold">periodic</emphasis>型を使用してください. 129 基本となる補間関数に周期性がある場合には<emphasis role="bold">periodic</emphasis>型を使用してください.
126 </para> 130 </para>
127 <para> 131 <para>
128 <emphasis role="bold">natural</emphasis>, <emphasis role="bold">monotone</emphasis>, <emphasis role="bold">fast</emphasis> (または 132 <emphasis role="bold">natural</emphasis>, <emphasis role="bold">monotone</emphasis>,
133 <emphasis role="bold">fast</emphasis> (または
129 <emphasis role="bold">fast_periodic</emphasis>) 型は, 134 <emphasis role="bold">fast_periodic</emphasis>) 型は,
130 例えば発振を防止したい場合(<emphasis role="bold">monotone</emphasis> 135 例えば発振を防止したい場合(<emphasis role="bold">monotone</emphasis>
131 がこの用途には最も強力です)に有用です. 136 がこの用途には最も強力です)に有用です.
@@ -207,7 +212,6 @@ xtitle("natural")
207subplot(2,2,4) 212subplot(2,2,4)
208plot3d1(xp, yp, ZP4, flag=[2 2 4]) 213plot3d1(xp, yp, ZP4, flag=[2 2 4])
209xtitle("monotone") 214xtitle("monotone")
210show_window()
211 ]]></programlisting> 215 ]]></programlisting>
212 <scilab:image> 216 <scilab:image>
213 // example 2 : different interpolation functions on random data 217 // example 2 : different interpolation functions on random data
@@ -277,13 +281,4 @@ xtitle("subspline (monotone)")
277 </member> 281 </member>
278 </simplelist> 282 </simplelist>
279 </refsection> 283 </refsection>
280 <refsection>
281 <title>履歴</title>
282 <revhistory>
283 <revision>
284 <revnumber>5.4.0</revnumber>
285 <revremark>以前では, 入力引数の虚部は暗黙のうちに無視されていました.</revremark>
286 </revision>
287 </revhistory>
288 </refsection>
289</refentry> 284</refentry>
diff --git a/scilab/modules/interpolation/help/ja_JP/splin3d.xml b/scilab/modules/interpolation/help/ja_JP/splin3d.xml
index 9874aa6..6b0581c 100644
--- a/scilab/modules/interpolation/help/ja_JP/splin3d.xml
+++ b/scilab/modules/interpolation/help/ja_JP/splin3d.xml
@@ -1,12 +1,31 @@
1<?xml version="1.0" encoding="UTF-8"?> 1<?xml version="1.0" encoding="UTF-8"?>
2<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:id="splin3d" xml:lang="ja"> 2<!--
3 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
4 * Copyright (C) R.F. Boisvert, C. De Boor (código da biblioteca FORTRAN CMLIB)
5 * Copyright (C) B. Pincon (interface Scilab)
6 *
7 * This file is hereby licensed under the terms of the GNU GPL v2.0,
8 * pursuant to article 5.3.4 of the CeCILL v.2.1.
9 * This file was originally licensed under the terms of the CeCILL v2.1,
10 * and continues to be available under such terms.
11 * For more information, see the COPYING file which you should have received
12 * along with this program.
13 *
14 -->
15<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
16 xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml"
17 xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
18 xml:id="splin3d" xml:lang="ja">
3 <refnamediv> 19 <refnamediv>
4 <refname>splin3d</refname> 20 <refname>splin3d</refname>
5 <refpurpose>3次元補間グリッドのスプライン</refpurpose> 21 <refpurpose>3次元補間グリッドのスプライン</refpurpose>
6 </refnamediv> 22 </refnamediv>
7 <refsynopsisdiv> 23 <refsynopsisdiv>
8 <title>呼び出し手順</title> 24 <title>呼び出し手順</title>
9 <synopsis>tl = splin3d(x, y, z, v, [order])</synopsis> 25 <synopsis>
26 tl = splin3d(x, y, z, v)
27 tl = splin3d(x, y, z, v, order)
28 </synopsis>
10 </refsynopsisdiv> 29 </refsynopsisdiv>
11 <refsection> 30 <refsection>
12 <title>引数</title> 31 <title>引数</title>
@@ -66,17 +85,15 @@
66 <literal>order=[kx,ky,kz]</literal>を選択することにより 85 <literal>order=[kx,ky,kz]</literal>を選択することにより
67 計算することができます. 86 計算することができます.
68 </para> 87 </para>
69 </refsection> 88 <para>
70 <refsection> 89 注意 : この関数は以下の条件で動作します
71 <title>注意</title> 90 <table align="center" style="float:center">
72 <para>この関数は以下の条件で動作します:</para> 91 <tr><td>nx, ny, nz ≥ 3</td></tr>
73 <informalequation> 92 <tr><td>2 ≤ kx &lt; nx</td></tr>
74 <mediaobject> 93 <tr><td>2 ≤ ky &lt; ny</td></tr>
75 <imageobject> 94 <tr><td>2 ≤ kz &lt; nz</td></tr>
76 <imagedata align="center" fileref="../mml/splin3d_equation1.mml"/> 95 </table>
77 </imageobject> 96 </para>
78 </mediaobject>
79 </informalequation>
80 <para>これらの条件が考慮されない場合にエラーが発生します.</para> 97 <para>これらの条件が考慮されない場合にエラーが発生します.</para>
81 </refsection> 98 </refsection>
82 <refsection> 99 <refsection>
@@ -98,12 +115,13 @@ vp_exact = f(xp,yp,zp);
98vp_interp = interp3d(xp,yp,zp, tl); 115vp_interp = interp3d(xp,yp,zp, tl);
99er = max(abs(vp_exact - vp_interp)) 116er = max(abs(vp_exact - vp_interp))
100// n=20で再試行し,誤差を見る 117// n=20で再試行し,誤差を見る
101 ]]></programlisting> 118 ]]></programlisting>
119 <para/>
102 <programlisting role="example"><![CDATA[ 120 <programlisting role="example"><![CDATA[
103// 例 2 (linear_interpn のヘルプを参照ください, 121// 例 2 (linear_interpn のヘルプを参照ください,
104// trilinear補間に関する同じ例があります) 122// trilinear補間に関する同じ例があります)
105// ============================================================================= 123// =============================================================================
106exec("SCI/modules/interpolation/demos/interp_demo.sci") 124exec("SCI/modules/interpolation/demos/interp_demo.sci", -1);
107func = "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2"; 125func = "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
108deff("v=f(x,y,z)",func); 126deff("v=f(x,y,z)",func);
109n = 5; 127n = 5;
@@ -116,29 +134,28 @@ m = 41;
116dir = ["z=" "z=" "z=" "x=" "y="]; 134dir = ["z=" "z=" "z=" "x=" "y="];
117val = [ 0.1 0.5 0.9 0.5 0.5]; 135val = [ 0.1 0.5 0.9 0.5 0.5];
118ebox = [0 1 0 1 0 1]; 136ebox = [0 1 0 1 0 1];
119XF=[]; YF=[]; ZF=[]; VF=[]; 137[XF, YF, ZF, VF] = ([], [], [], []);
120for i = 1:length(val) 138for i = 1:length(val)
121 [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(dir(i), val(i), ebox, m, m, m); 139 [Xm,Xp,Ym,Yp,Zm,Zp] = slice_parallelepiped(dir(i), val(i), ebox, m, m, m);
122 Vm = interp3d(Xm,Ym,Zm, tl); 140 Vm = interp3d(Xm,Ym,Zm, tl);
123 [xf,yf,zf,vf] = nf3dq(Xm,Ym,Zm,Vm,1); 141 [xf,yf,zf,vf] = nf3dq(Xm,Ym,Zm,Vm,1);
124 XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf]; 142 XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
125 Vp = interp3d(Xp,Yp,Zp, tl); 143 Vp = interp3d(Xp,Yp,Zp, tl);
126 [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1); 144 [xf,yf,zf,vf] = nf3dq(Xp,Yp,Zp,Vp,1);
127 XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf]; 145 XF = [XF xf]; YF = [YF yf]; ZF = [ZF zf]; VF = [VF vf];
128end 146end
129nb_col = 128; 147
130vmin = min(VF); vmax = max(VF); 148clf
149[nb_col, vmin, vmax] = (128, min(VF), max(VF));
131color = dsearch(VF,linspace(vmin,vmax,nb_col+1)); 150color = dsearch(VF,linspace(vmin,vmax,nb_col+1));
132gcf().color_map = jetcolormap(nb_col); 151gcf().color_map = jetcolormap(nb_col);
133clf();
134gca().hiddencolor = gca().background; 152gca().hiddencolor = gca().background;
135colorbar(vmin,vmax) 153colorbar(vmin,vmax)
136plot3d(XF, YF, list(ZF,color), flag=[-1 6 4]) 154plot3d(XF, YF, list(ZF,color), flag=[-1 6 4])
137xtitle("3d spline interpolation of "+func) 155title("3d spline interpolation of "+func, "fontsize",3)
138show_window()
139 ]]></programlisting> 156 ]]></programlisting>
140 <scilab:image localized="true"> 157 <scilab:image localized="true">
141 exec("SCI/modules/interpolation/demos/interp_demo.sci") 158 exec("SCI/modules/interpolation/demos/interp_demo.sci", -1);
142 func = "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2"; 159 func = "v=(x-0.5).^2 + (y-0.5).^3 + (z-0.5).^2";
143 deff("v=f(x,y,z)",func); 160 deff("v=f(x,y,z)",func);
144 n = 5; 161 n = 5;
@@ -185,13 +202,4 @@ show_window()
185 </member> 202 </member>
186 </simplelist> 203 </simplelist>
187 </refsection> 204 </refsection>
188 <refsection>
189 <title>履歴</title>
190 <revhistory>
191 <revision>
192 <revnumber>5.4.0</revnumber>
193 <revremark>以前では, 入力引数の虚部は暗黙のうちに無視されていました.</revremark>
194 </revision>
195 </revhistory>
196 </refsection>
197</refentry> 205</refentry>
diff --git a/scilab/modules/interpolation/help/mml/bsplin3val_equation1.mml b/scilab/modules/interpolation/help/mml/bsplin3val_equation1.mml
deleted file mode 100644
index ee2292b..0000000
--- a/scilab/modules/interpolation/help/mml/bsplin3val_equation1.mml
+++ /dev/null
@@ -1,77 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mi math:fontstyle="italic">dfp</math:mi>
7 <math:mrow>
8 <math:mrow>
9 <math:mo math:stretchy="false">(</math:mo>
10 <math:mi>i</math:mi>
11 <math:mo math:stretchy="false">)</math:mo>
12 </math:mrow>
13 <math:mo math:stretchy="false">=</math:mo>
14 <math:mfrac>
15 <math:msup>
16 <math:mo math:stretchy="false">∂</math:mo>
17 <math:mrow>
18 <math:mrow>
19 <math:mi math:fontstyle="italic">ox</math:mi>
20 <math:mo math:stretchy="false">×</math:mo>
21 <math:mi math:fontstyle="italic">ox</math:mi>
22 </math:mrow>
23 <math:mo math:stretchy="false">×</math:mo>
24 <math:mi math:fontstyle="italic">oz</math:mi>
25 </math:mrow>
26 </math:msup>
27 <math:mrow>
28 <math:mrow>
29 <math:msup>
30 <math:mo math:stretchy="false">∂</math:mo>
31 <math:mi math:fontstyle="italic">ox</math:mi>
32 </math:msup>
33 <math:mo math:stretchy="false">×</math:mo>
34 <math:msup>
35 <math:mo math:stretchy="false">∂</math:mo>
36 <math:mi math:fontstyle="italic">oy</math:mi>
37 </math:msup>
38 </math:mrow>
39 <math:mo math:stretchy="false">×</math:mo>
40 <math:msup>
41 <math:mo math:stretchy="false">∂</math:mo>
42 <math:mi math:fontstyle="italic">oz</math:mi>
43 </math:msup>
44 </math:mrow>
45 </math:mfrac>
46 </math:mrow>
47 <math:mi>s</math:mi>
48 <math:mrow>
49 <math:mo math:stretchy="false">(</math:mo>
50 <math:mrow>
51 <math:mi math:fontstyle="italic">xp</math:mi>
52 <math:mrow>
53 <math:mo math:stretchy="false">(</math:mo>
54 <math:mi>i</math:mi>
55 <math:mo math:stretchy="false">)</math:mo>
56 </math:mrow>
57 <math:mi>,</math:mi>
58 <math:mi math:fontstyle="italic">yp</math:mi>
59 <math:mrow>
60 <math:mo math:stretchy="false">(</math:mo>
61 <math:mi>i</math:mi>
62 <math:mo math:stretchy="false">)</math:mo>
63 </math:mrow>
64 <math:mi>,</math:mi>
65 <math:mi math:fontstyle="italic">zp</math:mi>
66 <math:mrow>
67 <math:mo math:stretchy="false">(</math:mo>
68 <math:mi>i</math:mi>
69 <math:mo math:stretchy="false">)</math:mo>
70 </math:mrow>
71 </math:mrow>
72 <math:mo math:stretchy="false">)</math:mo>
73 </math:mrow>
74 </math:mrow>
75 <math:annotation math:encoding="StarMath 5.0">dfp(i) = {{partial^{ox times ox times oz} } over {partial^{ox} times partial ^{oy} times partial^{oz}}} s(xp(i),yp(i),zp(i))</math:annotation>
76 </math:semantics>
77</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/interp_equation1.mml b/scilab/modules/interpolation/help/mml/interp_equation1.mml
deleted file mode 100644
index aed72bf..0000000
--- a/scilab/modules/interpolation/help/mml/interp_equation1.mml
+++ /dev/null
@@ -1,256 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
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5 <math:mrow>
6 <math:mtable>
7 <math:mtr>
8 <math:mrow>
9 <math:mi math:fontstyle="italic">yp</math:mi>
10 <math:mrow>
11 <math:mrow>
12 <math:mo math:stretchy="false">(</math:mo>
13 <math:mi>i</math:mi>
14 <math:mo math:stretchy="false">)</math:mo>
15 </math:mrow>
16 <math:mo math:stretchy="false">=</math:mo>
17 <math:mi>s</math:mi>
18 </math:mrow>
19 <math:mrow>
20 <math:mo math:stretchy="false">(</math:mo>
21 <math:mrow>
22 <math:mi math:fontstyle="italic">xp</math:mi>
23 <math:mrow>
24 <math:mo math:stretchy="false">(</math:mo>
25 <math:mi>i</math:mi>
26 <math:mo math:stretchy="false">)</math:mo>
27 </math:mrow>
28 </math:mrow>
29 <math:mo math:stretchy="false">)</math:mo>
30 </math:mrow>
31 <math:mtext> or </math:mtext>
32 <math:mi math:fontstyle="italic">yp</math:mi>
33 <math:mrow>
34 <math:mrow>
35 <math:mo math:stretchy="false">(</math:mo>
36 <math:mrow>
37 <math:mi>i</math:mi>
38 <math:mi>,</math:mi>
39 <math:mi>j</math:mi>
40 </math:mrow>
41 <math:mo math:stretchy="false">)</math:mo>
42 </math:mrow>
43 <math:mo math:stretchy="false">=</math:mo>
44 <math:mi>s</math:mi>
45 </math:mrow>
46 <math:mrow>
47 <math:mo math:stretchy="false">(</math:mo>
48 <math:mrow>
49 <math:mi math:fontstyle="italic">xp</math:mi>
50 <math:mrow>
51 <math:mo math:stretchy="false">(</math:mo>
52 <math:mrow>
53 <math:mi>i</math:mi>
54 <math:mi>,</math:mi>
55 <math:mi>j</math:mi>
56 </math:mrow>
57 <math:mo math:stretchy="false">)</math:mo>
58 </math:mrow>
59 </math:mrow>
60 <math:mo math:stretchy="false">)</math:mo>
61 </math:mrow>
62 </math:mrow>
63 </math:mtr>
64 <math:mtr>
65 <math:mrow>
66 <math:mi math:fontstyle="italic">yp1</math:mi>
67 <math:mrow>
68 <math:mrow>
69 <math:mo math:stretchy="false">(</math:mo>
70 <math:mi>i</math:mi>
71 <math:mo math:stretchy="false">)</math:mo>
72 </math:mrow>
73 <math:mo math:stretchy="false">=</math:mo>
74 <math:mi>s</math:mi>
75 </math:mrow>
76 <math:mi>&apos;</math:mi>
77 <math:mrow>
78 <math:mo math:stretchy="false">(</math:mo>
79 <math:mrow>
80 <math:mi math:fontstyle="italic">xp</math:mi>
81 <math:mrow>
82 <math:mo math:stretchy="false">(</math:mo>
83 <math:mi>i</math:mi>
84 <math:mo math:stretchy="false">)</math:mo>
85 </math:mrow>
86 </math:mrow>
87 <math:mo math:stretchy="false">)</math:mo>
88 </math:mrow>
89 <math:mtext> or </math:mtext>
90 <math:mi math:fontstyle="italic">yp1</math:mi>
91 <math:mrow>
92 <math:mrow>
93 <math:mo math:stretchy="false">(</math:mo>
94 <math:mrow>
95 <math:mi>i</math:mi>
96 <math:mi>,</math:mi>
97 <math:mi>j</math:mi>
98 </math:mrow>
99 <math:mo math:stretchy="false">)</math:mo>
100 </math:mrow>
101 <math:mo math:stretchy="false">=</math:mo>
102 <math:mi>s</math:mi>
103 </math:mrow>
104 <math:mi>&apos;</math:mi>
105 <math:mrow>
106 <math:mo math:stretchy="false">(</math:mo>
107 <math:mrow>
108 <math:mi math:fontstyle="italic">xp</math:mi>
109 <math:mrow>
110 <math:mo math:stretchy="false">(</math:mo>
111 <math:mrow>
112 <math:mi>i</math:mi>
113 <math:mi>,</math:mi>
114 <math:mi>j</math:mi>
115 </math:mrow>
116 <math:mo math:stretchy="false">)</math:mo>
117 </math:mrow>
118 </math:mrow>
119 <math:mo math:stretchy="false">)</math:mo>
120 </math:mrow>
121 </math:mrow>
122 </math:mtr>
123 <math:mtr>
124 <math:mrow>
125 <math:mi math:fontstyle="italic">yp2</math:mi>
126 <math:mrow>
127 <math:mrow>
128 <math:mo math:stretchy="false">(</math:mo>
129 <math:mi>i</math:mi>
130 <math:mo math:stretchy="false">)</math:mo>
131 </math:mrow>
132 <math:mo math:stretchy="false">=</math:mo>
133 <math:mi>s</math:mi>
134 </math:mrow>
135 <math:mi>&apos;</math:mi>
136 <math:mi>&apos;</math:mi>
137 <math:mrow>
138 <math:mo math:stretchy="false">(</math:mo>
139 <math:mrow>
140 <math:mi math:fontstyle="italic">xp</math:mi>
141 <math:mrow>
142 <math:mo math:stretchy="false">(</math:mo>
143 <math:mi>i</math:mi>
144 <math:mo math:stretchy="false">)</math:mo>
145 </math:mrow>
146 </math:mrow>
147 <math:mo math:stretchy="false">)</math:mo>
148 </math:mrow>
149 <math:mtext> or </math:mtext>
150 <math:mi math:fontstyle="italic">yp2</math:mi>
151 <math:mrow>
152 <math:mrow>
153 <math:mo math:stretchy="false">(</math:mo>
154 <math:mrow>
155 <math:mi>i</math:mi>
156 <math:mi>,</math:mi>
157 <math:mi>j</math:mi>
158 </math:mrow>
159 <math:mo math:stretchy="false">)</math:mo>
160 </math:mrow>
161 <math:mo math:stretchy="false">=</math:mo>
162 <math:mi>s</math:mi>
163 </math:mrow>
164 <math:mi>&apos;</math:mi>
165 <math:mi>&apos;</math:mi>
166 <math:mrow>
167 <math:mo math:stretchy="false">(</math:mo>
168 <math:mrow>
169 <math:mi math:fontstyle="italic">xp</math:mi>
170 <math:mrow>
171 <math:mo math:stretchy="false">(</math:mo>
172 <math:mrow>
173 <math:mi>i</math:mi>
174 <math:mi>,</math:mi>
175 <math:mi>j</math:mi>
176 </math:mrow>
177 <math:mo math:stretchy="false">)</math:mo>
178 </math:mrow>
179 </math:mrow>
180 <math:mo math:stretchy="false">)</math:mo>
181 </math:mrow>
182 </math:mrow>
183 </math:mtr>
184 <math:mtr>
185 <math:mrow>
186 <math:mi math:fontstyle="italic">yp3</math:mi>
187 <math:mrow>
188 <math:mrow>
189 <math:mo math:stretchy="false">(</math:mo>
190 <math:mi>i</math:mi>
191 <math:mo math:stretchy="false">)</math:mo>
192 </math:mrow>
193 <math:mo math:stretchy="false">=</math:mo>
194 <math:mi>s</math:mi>
195 </math:mrow>
196 <math:mi>&apos;</math:mi>
197 <math:mi>&apos;</math:mi>
198 <math:mi>&apos;</math:mi>
199 <math:mrow>
200 <math:mo math:stretchy="false">(</math:mo>
201 <math:mrow>
202 <math:mi math:fontstyle="italic">xp</math:mi>
203 <math:mrow>
204 <math:mo math:stretchy="false">(</math:mo>
205 <math:mi>i</math:mi>
206 <math:mo math:stretchy="false">)</math:mo>
207 </math:mrow>
208 </math:mrow>
209 <math:mo math:stretchy="false">)</math:mo>
210 </math:mrow>
211 <math:mtext> or </math:mtext>
212 <math:mi math:fontstyle="italic">yp3</math:mi>
213 <math:mrow>
214 <math:mrow>
215 <math:mo math:stretchy="false">(</math:mo>
216 <math:mrow>
217 <math:mi>i</math:mi>
218 <math:mi>,</math:mi>
219 <math:mi>j</math:mi>
220 </math:mrow>
221 <math:mo math:stretchy="false">)</math:mo>
222 </math:mrow>
223 <math:mo math:stretchy="false">=</math:mo>
224 <math:mi>s</math:mi>
225 </math:mrow>
226 <math:mi>&apos;</math:mi>
227 <math:mi>&apos;</math:mi>
228 <math:mi>&apos;</math:mi>
229 <math:mrow>
230 <math:mo math:stretchy="false">(</math:mo>
231 <math:mrow>
232 <math:mi math:fontstyle="italic">xp</math:mi>
233 <math:mrow>
234 <math:mo math:stretchy="false">(</math:mo>
235 <math:mrow>
236 <math:mi>i</math:mi>
237 <math:mi>,</math:mi>
238 <math:mi>j</math:mi>
239 </math:mrow>
240 <math:mo math:stretchy="false">)</math:mo>
241 </math:mrow>
242 </math:mrow>
243 <math:mo math:stretchy="false">)</math:mo>
244 </math:mrow>
245 </math:mrow>
246 </math:mtr>
247 </math:mtable>
248 </math:mrow>
249 <math:annotation math:encoding="StarMath 5.0">alignl stack {
250yp(i) = s(xp(i)) &quot; or &quot; yp(i,j) = s(xp(i,j)) #
251yp1(i) = s&apos;(xp(i)) &quot; or &quot; yp1(i,j) = s&apos;(xp(i,j)) #
252yp2(i) = s&apos;&apos;(xp(i)) &quot; or &quot; yp2(i,j) = s&apos;&apos;(xp(i,j)) #
253yp3(i) = s&apos;&apos;&apos;(xp(i)) &quot; or &quot; yp3(i,j) = s&apos;&apos;&apos;(xp(i,j))
254}</math:annotation>
255 </math:semantics>
256</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/interp_equation2.mml b/scilab/modules/interpolation/help/mml/interp_equation2.mml
deleted file mode 100644
index 955f8e6..0000000
--- a/scilab/modules/interpolation/help/mml/interp_equation2.mml
+++ /dev/null
@@ -1,66 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mtable>
7 <math:mtr>
8 <math:mrow>
9 <math:mi>s</math:mi>
10 <math:mrow>
11 <math:mrow>
12 <math:mo math:stretchy="false">(</math:mo>
13 <math:mi>x</math:mi>
14 <math:mo math:stretchy="false">)</math:mo>
15 </math:mrow>
16 <math:mo math:stretchy="false">=</math:mo>
17 <math:msub>
18 <math:mi>y</math:mi>
19 <math:mn>1</math:mn>
20 </math:msub>
21 </math:mrow>
22 <math:mtext> for </math:mtext>
23 <math:mrow>
24 <math:mi>x</math:mi>
25 <math:mo math:stretchy="false">&lt;</math:mo>
26 <math:msub>
27 <math:mi>x</math:mi>
28 <math:mn>1</math:mn>
29 </math:msub>
30 </math:mrow>
31 </math:mrow>
32 </math:mtr>
33 <math:mtr>
34 <math:mrow>
35 <math:mi>s</math:mi>
36 <math:mrow>
37 <math:mrow>
38 <math:mo math:stretchy="false">(</math:mo>
39 <math:mi>x</math:mi>
40 <math:mo math:stretchy="false">)</math:mo>
41 </math:mrow>
42 <math:mo math:stretchy="false">=</math:mo>
43 <math:msub>
44 <math:mi>y</math:mi>
45 <math:mi>n</math:mi>
46 </math:msub>
47 </math:mrow>
48 <math:mtext> for </math:mtext>
49 <math:mrow>
50 <math:mi>x</math:mi>
51 <math:mo math:stretchy="false">&gt;</math:mo>
52 <math:msub>
53 <math:mi>x</math:mi>
54 <math:mi>n</math:mi>
55 </math:msub>
56 </math:mrow>
57 </math:mrow>
58 </math:mtr>
59 </math:mtable>
60 </math:mrow>
61 <math:annotation math:encoding="StarMath 5.0">alignl stack {
62s(x) = y_1 &quot; for &quot; x &lt; x_1 #
63s(x) = y_n &quot; for &quot; x &gt; x_n
64}</math:annotation>
65 </math:semantics>
66</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/interp_equation3.mml b/scilab/modules/interpolation/help/mml/interp_equation3.mml
deleted file mode 100644
index 978121e..0000000
--- a/scilab/modules/interpolation/help/mml/interp_equation3.mml
+++ /dev/null
@@ -1,80 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mtable>
7 <math:mtr>
8 <math:mrow>
9 <math:mi>s</math:mi>
10 <math:mrow>
11 <math:mrow>
12 <math:mo math:stretchy="false">(</math:mo>
13 <math:mi>x</math:mi>
14 <math:mo math:stretchy="false">)</math:mo>
15 </math:mrow>
16 <math:mo math:stretchy="false">=</math:mo>
17 <math:msub>
18 <math:mi>p</math:mi>
19 <math:mn>1</math:mn>
20 </math:msub>
21 </math:mrow>
22 <math:mrow>
23 <math:mo math:stretchy="false">(</math:mo>
24 <math:mi>x</math:mi>
25 <math:mo math:stretchy="false">)</math:mo>
26 </math:mrow>
27 <math:mtext> for </math:mtext>
28 <math:mrow>
29 <math:mi>x</math:mi>
30 <math:mo math:stretchy="false">&lt;</math:mo>
31 <math:msub>
32 <math:mi>x</math:mi>
33 <math:mn>1</math:mn>
34 </math:msub>
35 </math:mrow>
36 </math:mrow>
37 </math:mtr>
38 <math:mtr>
39 <math:mrow>
40 <math:mi>s</math:mi>
41 <math:mrow>
42 <math:mrow>
43 <math:mo math:stretchy="false">(</math:mo>
44 <math:mi>x</math:mi>
45 <math:mo math:stretchy="false">)</math:mo>
46 </math:mrow>
47 <math:mo math:stretchy="false">=</math:mo>
48 <math:msub>
49 <math:mi>p</math:mi>
50 <math:mrow>
51 <math:mi>n</math:mi>
52 <math:mo math:stretchy="false">−</math:mo>
53 <math:mn>1</math:mn>
54 </math:mrow>
55 </math:msub>
56 </math:mrow>
57 <math:mrow>
58 <math:mo math:stretchy="false">(</math:mo>
59 <math:mi>x</math:mi>
60 <math:mo math:stretchy="false">)</math:mo>
61 </math:mrow>
62 <math:mtext> for </math:mtext>
63 <math:mrow>
64 <math:mi>x</math:mi>
65 <math:mo math:stretchy="false">&gt;</math:mo>
66 <math:msub>
67 <math:mi>x</math:mi>
68 <math:mi>n</math:mi>
69 </math:msub>
70 </math:mrow>
71 </math:mrow>
72 </math:mtr>
73 </math:mtable>
74 </math:mrow>
75 <math:annotation math:encoding="StarMath 5.0">alignl stack {
76s(x) = p_1(x) &quot; for &quot; x &lt; x_1 #
77s(x) = p_{n-1}(x) &quot; for &quot; x &gt; x_n
78}</math:annotation>
79 </math:semantics>
80</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/interp_equation4.mml b/scilab/modules/interpolation/help/mml/interp_equation4.mml
deleted file mode 100644
index 039d20c..0000000
--- a/scilab/modules/interpolation/help/mml/interp_equation4.mml
+++ /dev/null
@@ -1,122 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mtable>
7 <math:mtr>
8 <math:mrow>
9 <math:mi>s</math:mi>
10 <math:mrow>
11 <math:mrow>
12 <math:mo math:stretchy="false">(</math:mo>
13 <math:mi>x</math:mi>
14 <math:mo math:stretchy="false">)</math:mo>
15 </math:mrow>
16 <math:mo math:stretchy="false">=</math:mo>
17 <math:mrow>
18 <math:msub>
19 <math:mi>y</math:mi>
20 <math:mn>1</math:mn>
21 </math:msub>
22 <math:mo math:stretchy="false">+</math:mo>
23 <math:mi>s</math:mi>
24 </math:mrow>
25 </math:mrow>
26 <math:mi>&apos;</math:mi>
27 <math:mrow>
28 <math:mrow>
29 <math:mo math:stretchy="false">(</math:mo>
30 <math:msub>
31 <math:mi>x</math:mi>
32 <math:mn>1</math:mn>
33 </math:msub>
34 <math:mo math:stretchy="false">)</math:mo>
35 </math:mrow>
36 <math:mo math:stretchy="false">⋅</math:mo>
37 <math:mrow>
38 <math:mo math:stretchy="false">(</math:mo>
39 <math:mrow>
40 <math:mi>x</math:mi>
41 <math:mo math:stretchy="false">−</math:mo>
42 <math:msub>
43 <math:mi>x</math:mi>
44 <math:mn>1</math:mn>
45 </math:msub>
46 </math:mrow>
47 <math:mo math:stretchy="false">)</math:mo>
48 </math:mrow>
49 </math:mrow>
50 <math:mtext> for </math:mtext>
51 <math:mrow>
52 <math:mi>x</math:mi>
53 <math:mo math:stretchy="false">&lt;</math:mo>
54 <math:msub>
55 <math:mi>x</math:mi>
56 <math:mn>1</math:mn>
57 </math:msub>
58 </math:mrow>
59 </math:mrow>
60 </math:mtr>
61 <math:mtr>
62 <math:mrow>
63 <math:mi>s</math:mi>
64 <math:mrow>
65 <math:mrow>
66 <math:mo math:stretchy="false">(</math:mo>
67 <math:mi>x</math:mi>
68 <math:mo math:stretchy="false">)</math:mo>
69 </math:mrow>
70 <math:mo math:stretchy="false">=</math:mo>
71 <math:mrow>
72 <math:msub>
73 <math:mi>y</math:mi>
74 <math:mi>n</math:mi>
75 </math:msub>
76 <math:mo math:stretchy="false">+</math:mo>
77 <math:mi>s</math:mi>
78 </math:mrow>
79 </math:mrow>
80 <math:mi>&apos;</math:mi>
81 <math:mrow>
82 <math:mrow>
83 <math:mo math:stretchy="false">(</math:mo>
84 <math:msub>
85 <math:mi>x</math:mi>
86 <math:mi>n</math:mi>
87 </math:msub>
88 <math:mo math:stretchy="false">)</math:mo>
89 </math:mrow>
90 <math:mo math:stretchy="false">⋅</math:mo>
91 <math:mrow>
92 <math:mo math:stretchy="false">(</math:mo>
93 <math:mrow>
94 <math:mi>x</math:mi>
95 <math:mo math:stretchy="false">−</math:mo>
96 <math:msub>
97 <math:mi>x</math:mi>
98 <math:mi>n</math:mi>
99 </math:msub>
100 </math:mrow>
101 <math:mo math:stretchy="false">)</math:mo>
102 </math:mrow>
103 </math:mrow>
104 <math:mtext> for </math:mtext>
105 <math:mrow>
106 <math:mi>x</math:mi>
107 <math:mo math:stretchy="false">&gt;</math:mo>
108 <math:msub>
109 <math:mi>x</math:mi>
110 <math:mi>n</math:mi>
111 </math:msub>
112 </math:mrow>
113 </math:mrow>
114 </math:mtr>
115 </math:mtable>
116 </math:mrow>
117 <math:annotation math:encoding="StarMath 5.0">alignl stack {
118s(x) = y_1 + s&apos;(x_1) cdot (x - x_1) &quot; for &quot; x &lt; x_1 #
119s(x) = y_n + s&apos;(x_n) cdot (x - x_n) &quot; for &quot; x &gt; x_n
120}</math:annotation>
121 </math:semantics>
122</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/linear_interpn_equation1.mml b/scilab/modules/interpolation/help/mml/linear_interpn_equation1.mml
deleted file mode 100644
index 0be654a..0000000
--- a/scilab/modules/interpolation/help/mml/linear_interpn_equation1.mml
+++ /dev/null
@@ -1,59 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mi>v</math:mi>
7 <math:mrow>
8 <math:mrow>
9 <math:mo math:stretchy="false">(</math:mo>
10 <math:mrow>
11 <math:mi math:fontstyle="italic">i1</math:mi>
12 <math:mi>,</math:mi>
13 <math:mi math:fontstyle="italic">i2</math:mi>
14 <math:mi>,</math:mi>
15 <math:mo math:stretchy="false">⋯</math:mo>
16 <math:mi>,</math:mi>
17 <math:mi>i</math:mi>
18 <math:mi>n</math:mi>
19 </math:mrow>
20 <math:mo math:stretchy="false">)</math:mo>
21 </math:mrow>
22 <math:mo math:stretchy="false">=</math:mo>
23 <math:mi>f</math:mi>
24 </math:mrow>
25 <math:mrow>
26 <math:mo math:stretchy="false">(</math:mo>
27 <math:mrow>
28 <math:mi math:fontstyle="italic">x1</math:mi>
29 <math:mrow>
30 <math:mo math:stretchy="false">(</math:mo>
31 <math:mi math:fontstyle="italic">i1</math:mi>
32 <math:mo math:stretchy="false">)</math:mo>
33 </math:mrow>
34 <math:mi>,</math:mi>
35 <math:mi math:fontstyle="italic">x2</math:mi>
36 <math:mrow>
37 <math:mo math:stretchy="false">(</math:mo>
38 <math:mi math:fontstyle="italic">i2</math:mi>
39 <math:mo math:stretchy="false">)</math:mo>
40 </math:mrow>
41 <math:mi>,</math:mi>
42 <math:mo math:stretchy="false">⋯</math:mo>
43 <math:mi>,</math:mi>
44 <math:mi math:fontstyle="italic">xn</math:mi>
45 <math:mrow>
46 <math:mo math:stretchy="false">(</math:mo>
47 <math:mrow>
48 <math:mi>i</math:mi>
49 <math:mi>n</math:mi>
50 </math:mrow>
51 <math:mo math:stretchy="false">)</math:mo>
52 </math:mrow>
53 </math:mrow>
54 <math:mo math:stretchy="false">)</math:mo>
55 </math:mrow>
56 </math:mrow>
57 <math:annotation math:encoding="StarMath 5.0">v(i1,i2, dotsaxis,i{n}) = f(x1(i1),x2(i2),dotsaxis,xn(i{n}))</math:annotation>
58 </math:semantics>
59</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/linear_interpn_equation2.mml b/scilab/modules/interpolation/help/mml/linear_interpn_equation2.mml
deleted file mode 100644
index 4af9596..0000000
--- a/scilab/modules/interpolation/help/mml/linear_interpn_equation2.mml
+++ /dev/null
@@ -1,116 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mtable>
7 <math:mtr>
8 <math:mrow>
9 <math:mi math:fontstyle="italic">vp</math:mi>
10 <math:mrow>
11 <math:mrow>
12 <math:mo math:stretchy="false">(</math:mo>
13 <math:mi>i</math:mi>
14 <math:mo math:stretchy="false">)</math:mo>
15 </math:mrow>
16 <math:mo math:stretchy="false">=</math:mo>
17 <math:mi>s</math:mi>
18 </math:mrow>
19 <math:mrow>
20 <math:mo math:stretchy="false">(</math:mo>
21 <math:mrow>
22 <math:mi math:fontstyle="italic">xp1</math:mi>
23 <math:mrow>
24 <math:mo math:stretchy="false">(</math:mo>
25 <math:mi>i</math:mi>
26 <math:mo math:stretchy="false">)</math:mo>
27 </math:mrow>
28 <math:mi>,</math:mi>
29 <math:mi math:fontstyle="italic">xp2</math:mi>
30 <math:mrow>
31 <math:mo math:stretchy="false">(</math:mo>
32 <math:mi>i</math:mi>
33 <math:mo math:stretchy="false">)</math:mo>
34 </math:mrow>
35 <math:mi>,</math:mi>
36 <math:mo math:stretchy="false">⋯</math:mo>
37 <math:mi>,</math:mi>
38 <math:mi math:fontstyle="italic">xpn</math:mi>
39 <math:mrow>
40 <math:mo math:stretchy="false">(</math:mo>
41 <math:mi>i</math:mi>
42 <math:mo math:stretchy="false">)</math:mo>
43 </math:mrow>
44 </math:mrow>
45 <math:mo math:stretchy="false">)</math:mo>
46 </math:mrow>
47 </math:mrow>
48 </math:mtr>
49 <math:mtr>
50 <math:mrow>
51 <math:mtext>or </math:mtext>
52 <math:mi math:fontstyle="italic">vp</math:mi>
53 <math:mrow>
54 <math:mrow>
55 <math:mo math:stretchy="false">(</math:mo>
56 <math:mrow>
57 <math:mi>i</math:mi>
58 <math:mi>,</math:mi>
59 <math:mi>j</math:mi>
60 </math:mrow>
61 <math:mo math:stretchy="false">)</math:mo>
62 </math:mrow>
63 <math:mo math:stretchy="false">=</math:mo>
64 <math:mi>s</math:mi>
65 </math:mrow>
66 <math:mrow>
67 <math:mo math:stretchy="false">(</math:mo>
68 <math:mrow>
69 <math:mi math:fontstyle="italic">xp1</math:mi>
70 <math:mrow>
71 <math:mo math:stretchy="false">(</math:mo>
72 <math:mrow>
73 <math:mi>i</math:mi>
74 <math:mi>,</math:mi>
75 <math:mi>j</math:mi>
76 </math:mrow>
77 <math:mo math:stretchy="false">)</math:mo>
78 </math:mrow>
79 <math:mi>,</math:mi>
80 <math:mi math:fontstyle="italic">xp2</math:mi>
81 <math:mrow>
82 <math:mo math:stretchy="false">(</math:mo>
83 <math:mrow>
84 <math:mi>i</math:mi>
85 <math:mi>,</math:mi>
86 <math:mi>j</math:mi>
87 </math:mrow>
88 <math:mo math:stretchy="false">)</math:mo>
89 </math:mrow>
90 <math:mi>,</math:mi>
91 <math:mo math:stretchy="false">⋯</math:mo>
92 <math:mi>,</math:mi>
93 <math:mi math:fontstyle="italic">xpn</math:mi>
94 <math:mrow>
95 <math:mo math:stretchy="false">(</math:mo>
96 <math:mrow>
97 <math:mi>i</math:mi>
98 <math:mi>,</math:mi>
99 <math:mi>j</math:mi>
100 </math:mrow>
101 <math:mo math:stretchy="false">)</math:mo>
102 </math:mrow>
103 </math:mrow>
104 <math:mo math:stretchy="false">)</math:mo>
105 </math:mrow>
106 <math:mtext> in case the xpk are matrices</math:mtext>
107 </math:mrow>
108 </math:mtr>
109 </math:mtable>
110 </math:mrow>
111 <math:annotation math:encoding="StarMath 5.0">alignl stack {
112vp(i) = s(xp1(i),xp2(i),dotsaxis,xpn(i)) #
113&quot;or &quot; vp(i,j) = s(xp1(i,j),xp2(i,j),dotsaxis,xpn(i,j)) &quot; in case the xpk are matrices&quot;
114}</math:annotation>
115 </math:semantics>
116</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/linear_interpn_equation3.mml b/scilab/modules/interpolation/help/mml/linear_interpn_equation3.mml
deleted file mode 100644
index 04f3d31..0000000
--- a/scilab/modules/interpolation/help/mml/linear_interpn_equation3.mml
+++ /dev/null
@@ -1,85 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mi>P</math:mi>
7 <math:mrow>
8 <math:mrow>
9 <math:mo math:stretchy="false">(</math:mo>
10 <math:mi>i</math:mi>
11 <math:mo math:stretchy="false">)</math:mo>
12 </math:mrow>
13 <math:mo math:stretchy="false">∉</math:mo>
14 <math:mrow>
15 <math:mrow>
16 <math:mrow>
17 <math:mrow>
18 <math:mo math:stretchy="false">[</math:mo>
19 <math:mrow>
20 <math:mi math:fontstyle="italic">x1</math:mi>
21 <math:mrow>
22 <math:mo math:stretchy="false">(</math:mo>
23 <math:mn>1</math:mn>
24 <math:mo math:stretchy="false">)</math:mo>
25 </math:mrow>
26 <math:mi>,</math:mi>
27 <math:mi math:fontstyle="italic">x1</math:mi>
28 <math:mrow>
29 <math:mo math:stretchy="false">(</math:mo>
30 <math:mi>$</math:mi>
31 <math:mo math:stretchy="false">)</math:mo>
32 </math:mrow>
33 </math:mrow>
34 <math:mo math:stretchy="false">]</math:mo>
35 </math:mrow>
36 <math:mo math:stretchy="false">×</math:mo>
37 <math:mrow>
38 <math:mo math:stretchy="false">[</math:mo>
39 <math:mrow>
40 <math:mi math:fontstyle="italic">x2</math:mi>
41 <math:mrow>
42 <math:mo math:stretchy="false">(</math:mo>
43 <math:mn>1</math:mn>
44 <math:mo math:stretchy="false">)</math:mo>
45 </math:mrow>
46 <math:mi>,</math:mi>
47 <math:mi math:fontstyle="italic">x2</math:mi>
48 <math:mrow>
49 <math:mo math:stretchy="false">(</math:mo>
50 <math:mi>$</math:mi>
51 <math:mo math:stretchy="false">)</math:mo>
52 </math:mrow>
53 </math:mrow>
54 <math:mo math:stretchy="false">]</math:mo>
55 </math:mrow>
56 </math:mrow>
57 <math:mo math:stretchy="false">×</math:mo>
58 <math:mo math:stretchy="false">⋯</math:mo>
59 </math:mrow>
60 <math:mo math:stretchy="false">×</math:mo>
61 <math:mrow>
62 <math:mo math:stretchy="false">[</math:mo>
63 <math:mrow>
64 <math:mi math:fontstyle="italic">xn</math:mi>
65 <math:mrow>
66 <math:mo math:stretchy="false">(</math:mo>
67 <math:mn>1</math:mn>
68 <math:mo math:stretchy="false">)</math:mo>
69 </math:mrow>
70 <math:mi>,</math:mi>
71 <math:mi math:fontstyle="italic">xn</math:mi>
72 <math:mrow>
73 <math:mo math:stretchy="false">(</math:mo>
74 <math:mi>$</math:mi>
75 <math:mo math:stretchy="false">)</math:mo>
76 </math:mrow>
77 </math:mrow>
78 <math:mo math:stretchy="false">]</math:mo>
79 </math:mrow>
80 </math:mrow>
81 </math:mrow>
82 </math:mrow>
83 <math:annotation math:encoding="StarMath 5.0">P(i) notin [x1(1), x1($)] times [x2(1), x2($)] times dotsaxis times [xn(1), xn($)] </math:annotation>
84 </math:semantics>
85</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/lsq_splin_equation1.mml b/scilab/modules/interpolation/help/mml/lsq_splin_equation1.mml
deleted file mode 100644
index eb50442..0000000
--- a/scilab/modules/interpolation/help/mml/lsq_splin_equation1.mml
+++ /dev/null
@@ -1,112 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mrow>
7 <math:munderover>
8 <math:mo math:stretchy="false">∑</math:mo>
9 <math:mrow>
10 <math:mi>k</math:mi>
11 <math:mo math:stretchy="false">=</math:mo>
12 <math:mn>1</math:mn>
13 </math:mrow>
14 <math:mi>m</math:mi>
15 </math:munderover>
16 <math:mi math:fontstyle="italic">wd</math:mi>
17 </math:mrow>
18 <math:mrow>
19 <math:mo math:stretchy="false">(</math:mo>
20 <math:mi>k</math:mi>
21 <math:mo math:stretchy="false">)</math:mo>
22 </math:mrow>
23 <math:mover math:accent="true">
24 <math:msup>
25 <math:mrow>
26 <math:mo math:stretchy="false">(</math:mo>
27 <math:mrow>
28 <math:mi>s</math:mi>
29 <math:mrow>
30 <math:mrow>
31 <math:mo math:stretchy="false">(</math:mo>
32 <math:mrow>
33 <math:mi math:fontstyle="italic">xd</math:mi>
34 <math:mrow>
35 <math:mo math:stretchy="false">(</math:mo>
36 <math:mi>k</math:mi>
37 <math:mo math:stretchy="false">)</math:mo>
38 </math:mrow>
39 </math:mrow>
40 <math:mo math:stretchy="false">)</math:mo>
41 </math:mrow>
42 <math:mo math:stretchy="false">−</math:mo>
43 <math:mi math:fontstyle="italic">yd</math:mi>
44 </math:mrow>
45 <math:mrow>
46 <math:mo math:stretchy="false">(</math:mo>
47 <math:mi>k</math:mi>
48 <math:mo math:stretchy="false">)</math:mo>
49 </math:mrow>
50 </math:mrow>
51 <math:mo math:stretchy="false">)</math:mo>
52 </math:mrow>
53 <math:mn>2</math:mn>
54 </math:msup>
55 <math:mo math:stretchy="false">˙</math:mo>
56 </math:mover>
57 <math:mo math:stretchy="false">←</math:mo>
58 <math:mrow>
59 <math:munderover>
60 <math:mo math:stretchy="false">∑</math:mo>
61 <math:mrow>
62 <math:mi>k</math:mi>
63 <math:mo math:stretchy="false">=</math:mo>
64 <math:mn>1</math:mn>
65 </math:mrow>
66 <math:mi>m</math:mi>
67 </math:munderover>
68 <math:mi math:fontstyle="italic">wd</math:mi>
69 </math:mrow>
70 <math:mrow>
71 <math:mo math:stretchy="false">(</math:mo>
72 <math:mi>k</math:mi>
73 <math:mo math:stretchy="false">)</math:mo>
74 </math:mrow>
75 <math:mover math:accent="true">
76 <math:msup>
77 <math:mrow>
78 <math:mo math:stretchy="false">(</math:mo>
79 <math:mrow>
80 <math:mi>f</math:mi>
81 <math:mrow>
82 <math:mrow>
83 <math:mo math:stretchy="false">(</math:mo>
84 <math:mrow>
85 <math:mi math:fontstyle="italic">xd</math:mi>
86 <math:mrow>
87 <math:mo math:stretchy="false">(</math:mo>
88 <math:mi>k</math:mi>
89 <math:mo math:stretchy="false">)</math:mo>
90 </math:mrow>
91 </math:mrow>
92 <math:mo math:stretchy="false">)</math:mo>
93 </math:mrow>
94 <math:mo math:stretchy="false">−</math:mo>
95 <math:mi math:fontstyle="italic">yd</math:mi>
96 </math:mrow>
97 <math:mrow>
98 <math:mo math:stretchy="false">(</math:mo>
99 <math:mi>k</math:mi>
100 <math:mo math:stretchy="false">)</math:mo>
101 </math:mrow>
102 </math:mrow>
103 <math:mo math:stretchy="false">)</math:mo>
104 </math:mrow>
105 <math:mn>2</math:mn>
106 </math:msup>
107 <math:mo math:stretchy="false">˙</math:mo>
108 </math:mover>
109 </math:mrow>
110 <math:annotation math:encoding="StarMath 5.0">sum from {k=1} to m wd(k) dot (s(xd(k)) - yd(k))^2 leftarrow sum from {k=1} to m wd(k) dot (f(xd(k)) - yd(k))^2</math:annotation>
111 </math:semantics>
112</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin2d_equation_1.mml b/scilab/modules/interpolation/help/mml/splin2d_equation_1.mml
deleted file mode 100644
index b77bd7d..0000000
--- a/scilab/modules/interpolation/help/mml/splin2d_equation_1.mml
+++ /dev/null
@@ -1,101 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mi>s</math:mi>
7 <math:mrow>
8 <math:mrow>
9 <math:mo math:stretchy="false">(</math:mo>
10 <math:mrow>
11 <math:mi>x</math:mi>
12 <math:mi>,</math:mi>
13 <math:mi>y</math:mi>
14 </math:mrow>
15 <math:mo math:stretchy="false">)</math:mo>
16 </math:mrow>
17 <math:mo math:stretchy="false">=</math:mo>
18 <math:mrow>
19 <math:munderover>
20 <math:mo math:stretchy="false">∑</math:mo>
21 <math:mrow>
22 <math:mi>k</math:mi>
23 <math:mo math:stretchy="false">=</math:mo>
24 <math:mn>1</math:mn>
25 </math:mrow>
26 <math:mn>4</math:mn>
27 </math:munderover>
28 <math:mrow>
29 <math:munderover>
30 <math:mo math:stretchy="false">∑</math:mo>
31 <math:mrow>
32 <math:mi>l</math:mi>
33 <math:mo math:stretchy="false">=</math:mo>
34 <math:mn>1</math:mn>
35 </math:mrow>
36 <math:mn>4</math:mn>
37 </math:munderover>
38 <math:msub>
39 <math:mi>c</math:mi>
40 <math:mi math:fontstyle="italic">ij</math:mi>
41 </math:msub>
42 </math:mrow>
43 </math:mrow>
44 </math:mrow>
45 <math:mrow>
46 <math:mrow>
47 <math:mrow>
48 <math:mo math:stretchy="false">(</math:mo>
49 <math:mrow>
50 <math:mi>k</math:mi>
51 <math:mi>,</math:mi>
52 <math:mi>l</math:mi>
53 </math:mrow>
54 <math:mo math:stretchy="false">)</math:mo>
55 </math:mrow>
56 <math:mo math:stretchy="false">⋅</math:mo>
57 <math:msup>
58 <math:mrow>
59 <math:mo math:stretchy="false">(</math:mo>
60 <math:mrow>
61 <math:mi>x</math:mi>
62 <math:mo math:stretchy="false">−</math:mo>
63 <math:msub>
64 <math:mi>x</math:mi>
65 <math:mi>i</math:mi>
66 </math:msub>
67 </math:mrow>
68 <math:mo math:stretchy="false">)</math:mo>
69 </math:mrow>
70 <math:mrow>
71 <math:mi>k</math:mi>
72 <math:mo math:stretchy="false">−</math:mo>
73 <math:mn>1</math:mn>
74 </math:mrow>
75 </math:msup>
76 </math:mrow>
77 <math:mo math:stretchy="false">⋅</math:mo>
78 <math:msup>
79 <math:mrow>
80 <math:mo math:stretchy="false">(</math:mo>
81 <math:mrow>
82 <math:mi>y</math:mi>
83 <math:mo math:stretchy="false">−</math:mo>
84 <math:msub>
85 <math:mi>y</math:mi>
86 <math:mi>i</math:mi>
87 </math:msub>
88 </math:mrow>
89 <math:mo math:stretchy="false">)</math:mo>
90 </math:mrow>
91 <math:mrow>
92 <math:mi>l</math:mi>
93 <math:mo math:stretchy="false">−</math:mo>
94 <math:mn>1</math:mn>
95 </math:mrow>
96 </math:msup>
97 </math:mrow>
98 </math:mrow>
99 <math:annotation math:encoding="StarMath 5.0">s(x,y) = sum from {k=1} to 4 sum from {l=1} to 4 c_{ij}(k,l) cdot (x - x_i)^{k-1} cdot (y - y_i)^{l-1}</math:annotation>
100 </math:semantics>
101</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin3d_equation1.mml b/scilab/modules/interpolation/help/mml/splin3d_equation1.mml
deleted file mode 100644
index 5d449e5..0000000
--- a/scilab/modules/interpolation/help/mml/splin3d_equation1.mml
+++ /dev/null
@@ -1,62 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mtable>
7 <math:mtr>
8 <math:mrow>
9 <math:mi math:fontstyle="italic">nx</math:mi>
10 <math:mi>,</math:mi>
11 <math:mi math:fontstyle="italic">ny</math:mi>
12 <math:mi>,</math:mi>
13 <math:mrow>
14 <math:mi math:fontstyle="italic">nz</math:mi>
15 <math:mo math:stretchy="false">≥</math:mo>
16 <math:mn>3</math:mn>
17 </math:mrow>
18 </math:mrow>
19 </math:mtr>
20 <math:mtr>
21 <math:mrow>
22 <math:mrow>
23 <math:mn>2</math:mn>
24 <math:mo math:stretchy="false">≤</math:mo>
25 <math:mi math:fontstyle="italic">kx</math:mi>
26 </math:mrow>
27 <math:mo math:stretchy="false">&lt;</math:mo>
28 <math:mi math:fontstyle="italic">nx</math:mi>
29 </math:mrow>
30 </math:mtr>
31 <math:mtr>
32 <math:mrow>
33 <math:mrow>
34 <math:mn>2</math:mn>
35 <math:mo math:stretchy="false">≤</math:mo>
36 <math:mi math:fontstyle="italic">ky</math:mi>
37 </math:mrow>
38 <math:mo math:stretchy="false">&lt;</math:mo>
39 <math:mi math:fontstyle="italic">ny</math:mi>
40 </math:mrow>
41 </math:mtr>
42 <math:mtr>
43 <math:mrow>
44 <math:mrow>
45 <math:mn>2</math:mn>
46 <math:mo math:stretchy="false">≤</math:mo>
47 <math:mi math:fontstyle="italic">kz</math:mi>
48 </math:mrow>
49 <math:mo math:stretchy="false">&lt;</math:mo>
50 <math:mi math:fontstyle="italic">nz</math:mi>
51 </math:mrow>
52 </math:mtr>
53 </math:mtable>
54 </math:mrow>
55 <math:annotation math:encoding="StarMath 5.0">alignl stack {
56nx,ny,nz &gt;= 3 #
572 &lt;= kx &lt; nx #
582 &lt;= ky &lt; ny #
592 &lt;= kz &lt; nz
60}</math:annotation>
61 </math:semantics>
62</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin_equation1.mml b/scilab/modules/interpolation/help/mml/splin_equation1.mml
deleted file mode 100644
index 059e9da..0000000
--- a/scilab/modules/interpolation/help/mml/splin_equation1.mml
+++ /dev/null
@@ -1,86 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mtable>
7 <math:mtr>
8 <math:mrow>
9 <math:mi>s</math:mi>
10 <math:mi>&apos;</math:mi>
11 <math:mi>&apos;</math:mi>
12 <math:mi>&apos;</math:mi>
13 <math:mrow>
14 <math:mrow>
15 <math:mo math:stretchy="false">(</math:mo>
16 <math:msup>
17 <math:mi math:fontstyle="italic">x2</math:mi>
18 <math:mtext>-</math:mtext>
19 </math:msup>
20 <math:mo math:stretchy="false">)</math:mo>
21 </math:mrow>
22 <math:mo math:stretchy="false">=</math:mo>
23 <math:mi>s</math:mi>
24 </math:mrow>
25 <math:mi>&apos;</math:mi>
26 <math:mi>&apos;</math:mi>
27 <math:mi>&apos;</math:mi>
28 <math:mrow>
29 <math:mo math:stretchy="false">(</math:mo>
30 <math:msup>
31 <math:mi math:fontstyle="italic">x2</math:mi>
32 <math:mtext>+</math:mtext>
33 </math:msup>
34 <math:mo math:stretchy="false">)</math:mo>
35 </math:mrow>
36 </math:mrow>
37 </math:mtr>
38 <math:mtr>
39 <math:mrow>
40 <math:mi>s</math:mi>
41 <math:mi>&apos;</math:mi>
42 <math:mi>&apos;</math:mi>
43 <math:mi>&apos;</math:mi>
44 <math:mrow>
45 <math:mrow>
46 <math:mo math:stretchy="false">(</math:mo>
47 <math:msubsup>
48 <math:mi>x</math:mi>
49 <math:mrow>
50 <math:mi>n</math:mi>
51 <math:mo math:stretchy="false">−</math:mo>
52 <math:mn>1</math:mn>
53 </math:mrow>
54 <math:mtext>-</math:mtext>
55 </math:msubsup>
56 <math:mo math:stretchy="false">)</math:mo>
57 </math:mrow>
58 <math:mo math:stretchy="false">=</math:mo>
59 <math:mi>s</math:mi>
60 </math:mrow>
61 <math:mi>&apos;</math:mi>
62 <math:mi>&apos;</math:mi>
63 <math:mi>&apos;</math:mi>
64 <math:mrow>
65 <math:mo math:stretchy="false">(</math:mo>
66 <math:msubsup>
67 <math:mi>x</math:mi>
68 <math:mrow>
69 <math:mi>n</math:mi>
70 <math:mo math:stretchy="false">−</math:mo>
71 <math:mn>1</math:mn>
72 </math:mrow>
73 <math:mtext>+</math:mtext>
74 </math:msubsup>
75 <math:mo math:stretchy="false">)</math:mo>
76 </math:mrow>
77 </math:mrow>
78 </math:mtr>
79 </math:mtable>
80 </math:mrow>
81 <math:annotation math:encoding="StarMath 5.0">alignl stack {
82s&apos;&apos;&apos;(x2^&quot;-&quot;) = s&apos;&apos;&apos;(x2^&quot;+&quot;) #
83s&apos;&apos;&apos;(x_{n-1}^&quot;-&quot;) = s&apos;&apos;&apos;(x_{n-1}^&quot;+&quot;)
84}</math:annotation>
85 </math:semantics>
86</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin_equation2.mml b/scilab/modules/interpolation/help/mml/splin_equation2.mml
deleted file mode 100644
index f01e392..0000000
--- a/scilab/modules/interpolation/help/mml/splin_equation2.mml
+++ /dev/null
@@ -1,54 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mtable>
7 <math:mtr>
8 <math:mrow>
9 <math:mi>s</math:mi>
10 <math:mi>&apos;</math:mi>
11 <math:mrow>
12 <math:mrow>
13 <math:mo math:stretchy="false">(</math:mo>
14 <math:mi math:fontstyle="italic">x1</math:mi>
15 <math:mo math:stretchy="false">)</math:mo>
16 </math:mrow>
17 <math:mo math:stretchy="false">=</math:mo>
18 <math:mi math:fontstyle="italic">der</math:mi>
19 </math:mrow>
20 <math:mrow>
21 <math:mo math:stretchy="false">(</math:mo>
22 <math:mn>1</math:mn>
23 <math:mo math:stretchy="false">)</math:mo>
24 </math:mrow>
25 </math:mrow>
26 </math:mtr>
27 <math:mtr>
28 <math:mrow>
29 <math:mi>s</math:mi>
30 <math:mi>&apos;</math:mi>
31 <math:mrow>
32 <math:mrow>
33 <math:mo math:stretchy="false">(</math:mo>
34 <math:mi math:fontstyle="italic">xn</math:mi>
35 <math:mo math:stretchy="false">)</math:mo>
36 </math:mrow>
37 <math:mo math:stretchy="false">=</math:mo>
38 <math:mi math:fontstyle="italic">der</math:mi>
39 </math:mrow>
40 <math:mrow>
41 <math:mo math:stretchy="false">(</math:mo>
42 <math:mn>2</math:mn>
43 <math:mo math:stretchy="false">)</math:mo>
44 </math:mrow>
45 </math:mrow>
46 </math:mtr>
47 </math:mtable>
48 </math:mrow>
49 <math:annotation math:encoding="StarMath 5.0">alignl stack {
50s&apos;(x1) = der(1) #
51s&apos;(xn) = der(2)
52}</math:annotation>
53 </math:semantics>
54</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin_equation3.mml b/scilab/modules/interpolation/help/mml/splin_equation3.mml
deleted file mode 100644
index 83989d2..0000000
--- a/scilab/modules/interpolation/help/mml/splin_equation3.mml
+++ /dev/null
@@ -1,46 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mtable>
7 <math:mtr>
8 <math:mrow>
9 <math:mi>s</math:mi>
10 <math:mi>&apos;</math:mi>
11 <math:mi>&apos;</math:mi>
12 <math:mrow>
13 <math:mrow>
14 <math:mo math:stretchy="false">(</math:mo>
15 <math:mi math:fontstyle="italic">x1</math:mi>
16 <math:mo math:stretchy="false">)</math:mo>
17 </math:mrow>
18 <math:mo math:stretchy="false">=</math:mo>
19 <math:mn>0</math:mn>
20 </math:mrow>
21 </math:mrow>
22 </math:mtr>
23 <math:mtr>
24 <math:mrow>
25 <math:mi>s</math:mi>
26 <math:mi>&apos;</math:mi>
27 <math:mi>&apos;</math:mi>
28 <math:mrow>
29 <math:mrow>
30 <math:mo math:stretchy="false">(</math:mo>
31 <math:mi math:fontstyle="italic">xn</math:mi>
32 <math:mo math:stretchy="false">)</math:mo>
33 </math:mrow>
34 <math:mo math:stretchy="false">=</math:mo>
35 <math:mn>0</math:mn>
36 </math:mrow>
37 </math:mrow>
38 </math:mtr>
39 </math:mtable>
40 </math:mrow>
41 <math:annotation math:encoding="StarMath 5.0">alignl stack {
42s&apos;&apos;(x1) = 0 #
43s&apos;&apos;(xn) = 0
44}</math:annotation>
45 </math:semantics>
46</math:math> \ No newline at end of file
diff --git a/scilab/modules/interpolation/help/mml/splin_equation4.mml b/scilab/modules/interpolation/help/mml/splin_equation4.mml
deleted file mode 100644
index 2f1984c..0000000
--- a/scilab/modules/interpolation/help/mml/splin_equation4.mml
+++ /dev/null
@@ -1,58 +0,0 @@
1<?xml version="1.0" encoding="UTF-8"?>
2<!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd">
3<math:math xmlns:math="http://www.w3.org/1998/Math/MathML">
4 <math:semantics>
5 <math:mrow>
6 <math:mtable>
7 <math:mtr>
8 <math:mrow>
9 <math:mi>s</math:mi>
10 <math:mi>&apos;</math:mi>