* `kron` and `.*.` are extended to boolean arrays.
* `gamma` is extended to incomplete gamma integrals.
* `close` is extended to close the help browser, xcos, or the variables browser or editor GUIs.
+* `polyint` is introduced to compute polynomial antiderivatives.
Help pages:
* [#16613](https://bugzilla.scilab.org/16613): Neither `.*.` nor `kron()` worked with boolean or sparse boolean matrices.
* [#16617](https://bugzilla.scilab.org/16617): `gamma` did not support incomplete gamma integrals.
* [#16618](https://bugzilla.scilab.org/16618): `close` could not close the help browser, xcos, nor the variable editor or browser.
+* [#16620](https://bugzilla.scilab.org/16620): `derivat` had no reciprocal `polyint` polynomial integration function.
* [#16622](https://bugzilla.scilab.org/16622): `inv` could no longer be overloaded for hypermatrices of decimal or complex numbers.
* [#16623](https://bugzilla.scilab.org/16623): `rand(2,2,2)^2` yielded a wrong result instead of trying to call the `%s_p_s` overload for input hypermatrices.
* [#16629](https://bugzilla.scilab.org/16629): `interp1`'s documentation did not tell the spline edges conditions ; extrapolation modes were poorly explained. ; the description of the result's size was completely wrong ; x as an option was not documented. A wrong extrapolation value could silently return a wrong result. There was some dead code like `if varargin(5)==%nan`. A bugged error message yielded its own error. When x is implicit, the argument index in error messages could be wrong. `periodic` and `edgevalue` extrapolation modes were not available. `linear` extrapolation was not available for splines. When `xp` is an hypermatrix with `size(xp,1)==1`, the size of the result was irregular/wrong.
pol2des
pol2str
polfact
+polyint
rowcompr
sylm
systmat
--- /dev/null
+<?xml version="1.0" encoding="UTF-8"?>
+<!--
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2020 - Samuel GOUGEON - Le Mans Université
+ *
+ * This file is hereby licensed under the terms of the GNU GPL v2.0,
+ * pursuant to article 5.3.4 of the CeCILL v.2.1.
+ * This file was originally licensed under the terms of the CeCILL v2.1,
+ * and continues to be available under such terms.
+ * For more information, see the COPYING file which you should have received
+ * along with this program.
+ *
+ -->
+<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
+ xmlns:svg="http://www.w3.org/2000/svg" xmlns:db="http://docbook.org/ns/docbook"
+ xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="polyint">
+ <refnamediv>
+ <refname>polyint</refname>
+ <refpurpose>
+ Polynomial integration
+ </refpurpose>
+ </refnamediv>
+ <refsynopsisdiv>
+ <title>Syntax</title>
+ <synopsis>
+ polyint // example
+ Q = polyint(P)
+ Q = polyint(P, Const)
+ </synopsis>
+ </refsynopsisdiv>
+ <refsection>
+ <title>Arguments</title>
+ <variablelist>
+ <varlistentry>
+ <term>P, Q</term>
+ <listitem>
+ arrays (from scalars to hypermatrices) of polynomials with real or complex
+ coefficients, of same size.
+ <para/>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Const</term>
+ <listitem>
+ Set of real or complex constants of integration.
+ <literal>length(Const)</literal> sets the number of consecutive integrations
+ to perform. By default, 0 is used.
+ <varname>Const</varname> can be one of the following:
+ <itemizedlist>
+ <listitem>
+ a scalar: then only the first antiderivatives are computed, and all use
+ the same <varname>Const</varname> value.
+ </listitem>
+ <listitem>
+ an array of size size(P): then only the first antiderivatives are computed,
+ with the respective <literal>Const(i)</literal> for <literal>Q(i)</literal>.
+ </listitem>
+ <listitem>
+ a list that can mix scalars, arrays of size size(P), or undefined elements.
+ Then <literal>Const(i)</literal> is used for the i<superscript>th</superscript>
+ antiderivatives. Undefined elements are equivalent to 0.
+ </listitem>
+ </itemizedlist>
+ <para/>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ </refsection>
+ <refsection>
+ <title>Description</title>
+ <para>
+ polyint(..) computes the first or any n<superscript>th</superscript> antiderivative
+ of each polynomial of the input array.
+ </para>
+ </refsection>
+ <refsection>
+ <title>Examples</title>
+ <para>
+ Single integration (first order):
+ </para>
+ <programlisting role="example"><![CDATA[
+s = %s;
+P = [-2, s ; s^2-3, s-2*s^3]
+polyint(P)
+polyint(P, 1)
+polyint(P, [1 2 ; 3 4])
+ ]]></programlisting>
+ <screen><![CDATA[
+--> P = [-2, s ; s^2-3, s-2*s^3]
+ P =
+ -2 s
+ -3 +s² s -2s³
+
+--> polyint(P)
+ ans =
+ -2s 0.5s²
+ -3s +0.3333333s³ 0.5s² -0.5s⁴
+
+--> polyint(P, 1)
+ ans =
+ 1 -2s 1 +0.5s²
+ 1 -3s +0.3333333s³ 1 +0.5s² -0.5s⁴
+
+--> polyint(P, [1 2 ; 3 4])
+ ans =
+ 1 -2s 2 +0.5s²
+ 3 -3s +0.3333333s³ 4 +0.5s² -0.5s⁴
+]]></screen>
+ <para/>
+ <para>
+ Multiple integrations:
+ </para>
+ <programlisting role="example"><![CDATA[
+s = %s;
+polyint(1-3*s, list(-1,1))
+P = [3 ; 1-s ; 6*s^2-2]
+polyint(P, list(2, [-2 1 0]))
+polyint(P, list(, [-2 1 0]))
+
+k = list(); k(5) = 0;
+polyint(1+0*s, k)
+1 / factorial(5)
+ ]]></programlisting>
+ <screen><![CDATA[
+--> polyint(1-3*s, list(-1,1))
+ ans =
+ 1 -s +0.5s² -0.5s³
+
+--> P = [3 ; 1-s ; 6*s^2-2]
+ P =
+ 3
+ 1 -s
+ -2 +6s²
+
+--> polyint(P, list(2, [-2 1 0]))
+ ans =
+ -2 +2s +1.5s²
+ 1 +2s +0.5s² -0.1666667s³
+ 2s -s² +0.5s⁴
+
+--> polyint(P, list(, [-2 1 0]))
+ ans =
+ -2 +1.5s²
+ 1 +0.5s² -0.1666667s³
+ -s² +0.5s⁴
+
+
+--> k = list(); k(5) = 0;
+--> polyint(1+0*s, k)
+ ans =
+ 0.0083333s⁵
+
+--> 1 / factorial(5)
+ ans =
+ 0.0083333
+]]></screen>
+ </refsection>
+ <refsection role="see also">
+ <title>See also</title>
+ <simplelist type="inline">
+ <member>
+ <link linkend="derivat">derivat</link>
+ </member>
+ </simplelist>
+ </refsection>
+ <refsection role="history">
+ <title>History</title>
+ <revhistory>
+ <revision>
+ <revnumber>6.1.1</revnumber>
+ <revdescription>
+ polyint() introduced.
+ </revdescription>
+ </revision>
+ </revhistory>
+ </refsection>
+</refentry>
--- /dev/null
+// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+// Copyright (C) 2020 - Samuel GOUGEON - Le Mans Université
+//
+// This file is hereby licensed under the terms of the GNU GPL v2.0,
+// pursuant to article 5.3.4 of the CeCILL v.2.1.
+// This file was originally licensed under the terms of the CeCILL v2.1,
+// and continues to be available under such terms.
+// For more information, see the COPYING file which you should have received
+// along with this program.
+
+function M = polyint(M, cstes)
+ // M : array (from scalar to hypermatrix) of polynomials with real or
+ // complex coefficients
+ // Cstes: Integration constants (real or complex): scalar, array of size
+ // size(M), or list of mixed scalar or sized(M) arrays or
+ // undefined elements (valued as 0).
+
+ // EXAMPLE
+ // =======
+ if argn(2)==0 then
+ m = mode(); mode(6)
+ M = [ -1+%z, 1+2*%z+%z^2 ; 2-%z^3, 6]
+ mprintf("\n%s", "polyint(M)")
+ I = polyint(M)
+ mprintf("\n%s", "polyint(M, 1)")
+ I = polyint(M, 1)
+ mprintf("\n%s", "polyint(M, [1 2 ; 3 4])")
+ I = polyint(M, [1 2 ; 3 4])
+ mode(m)
+ M = I
+ return
+ end
+
+ s = size(M)
+ n = length(M)
+
+ // CHECKING ARGUMENTS
+ // ==================
+ rhs = argn(2)
+ if type(M)<>2 then
+ msg = _("%s: Argument #%d: Polynomial expected.\n")
+ error(msprintf(msg, "polyint",1))
+ end
+ if ~isdef("cstes","l")
+ cstes = 0
+ end
+ if and(type(cstes)<>[1 15])
+ msg = _("%s: Argument #%d: numbers or list of numbers expected.\n")
+ error(msprintf(msg, "polyint",2))
+ end
+ if type(cstes) <> 15 then
+ cstes = list(cstes)
+ end
+ for i = 1:length(cstes)
+ k = cstes(i)
+ if isdef("k","l")
+ if type(k) <> 1
+ msg = _("%s: Argument #%d(%d): Decimal or complex number expected.\n")
+ error(msprintf(msg, "polyint",2,i))
+ end
+ if length(k)<>1 & or(size(k)<>s)
+ msg = _("%s: Argument #%d(%d): Array of size [%s] expected.\n")
+ ts = strcat(msprintf("%d\n",s(:))," ")
+ error(msprintf(msg, "polyint", 2, i, ts))
+ end
+ end
+ end
+
+ // PROCESSING
+ // ==========
+ vn = poly(0, varn(M))
+ M = matrix(M, -1, 1)
+ for i = cstes
+ if ~isdef("i","l")
+ i = zeros(n,1)
+ elseif length(i)==1
+ i = i * ones(n,1)
+ else
+ i = matrix(i,-1,1)
+ end
+ M = M * vn
+ d = max(max(degree(M),0))
+ p = (0:d) .*. ones(M)
+ c = coeff(M)
+ k = find(p > 0)
+ c(k) = c(k) ./ p(k)
+ c(:,1) = c(:,1) + i
+ M = inv_coeff(c, d, varn(M))
+ end
+
+ M = matrix(M, s)
+endfunction
--- /dev/null
+// =============================================================================
+// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+// Copyright (C) 2020 - Samuel GOUGEON - Le Mans Université
+//
+// This file is distributed under the same license as the Scilab package.
+// =============================================================================
+//
+// <-- CLI SHELL MODE -->
+// <-- NO CHECK REF -->
+
+s = %s;
+P = s^[0 1 ; 2 3];
+
+// SINGLE INTEGRATION
+// ==================
+assert_checkequal(polyint(s), s^2/2);
+Ref0 = s^[1 2 ; 3 4] ./ [1 2 ; 3 4];
+assert_checkequal(polyint(P), Ref0);
+Ref = [0, -s+0.5*s^2 ; -s+s^3/3,-s+0.25*s^4];
+assert_checkequal(polyint(P-1), Ref);
+
+// With consts
+// -----------
+assert_checkequal(polyint(P, 1), Ref0+1);
+assert_checkequal(polyint(P, [1 2 ; 3 4]), Ref0+[1 2 ; 3 4]);
+assert_checkequal(polyint(P, list([1 2 ; 3 4])), Ref0+[1 2 ; 3 4]);
+
+
+// MULTIPLE INTEGRATIONS
+// =====================
+assert_checkequal(polyint(s,list(-1,1)), 1-s+s^3/6);
+
+o = list(); o(5) = 0; // undefined elements #1-4
+assert_checkequal(polyint(1+0*s, o), s^5/factorial(5));
+
+Ref = [-2+2*s+1.5*s^2 ; 1+2*s+0.5*s^2-s^3/6 ; 2*s-s^2+s^4/12];
+assert_checkequal(polyint([3 ; 1-s ; s^2-2], list(2,[-2 1 0]')), Ref);
+Ref = [-2 + 1.5*s^2 ; 1 + 0.5*s^2 - s^3/6 ; -s^2 + s^4/12];
+assert_checkequal(polyint([3 ; 1-s ; s^2-2], list(,[-2 1 0]')), Ref);
+
+
+// ERROR MESSAGES
+// ==============
+assert_checkerror("polyint(1,2,3)", _("Wrong number of input arguments."));
+msg = msprintf(_("%s: Argument #%d: Polynomial expected.\n"), "polyint",1);
+assert_checkerror("polyint(3)", msg);
+msg = _("%s: Argument #%d: numbers or list of numbers expected.\n");
+assert_checkerror("polyint(%s, %f)", msprintf(msg, "polyint",2));
+msg = _("%s: Argument #%d(%d): Decimal or complex number expected.\n");
+assert_checkerror("polyint(%s, list(3,%f))", msprintf(msg, "polyint",2,2));
+msg = _("%s: Argument #%d(%d): Array of size [%s] expected.\n");
+assert_checkerror("polyint(%s, [1 2])", msprintf(msg, "polyint",2,1,"1 1"));
+assert_checkerror("polyint(%s, list([1 2]))", msprintf(msg, "polyint",2,1,"1 1"));
+assert_checkerror("polyint(%s, list([1 2],4))", msprintf(msg, "polyint",2,1,"1 1"));
+assert_checkerror("polyint(%s, list(4,,[1 2]))", msprintf(msg, "polyint",2,3,"1 1"));
projects / scilab.git / commitdiff