fix #968 zp2tf function

CHANGELOG.md

@@ -15,6 +15,7 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
   - [#967](http://github.com/Nelson-numerical-software/nelson/issues/967) control system module template.
   - `abcdchk` Verifies the dimensional compatibility of matrices A, B, C, and D.
   - [#944](http://github.com/Nelson-numerical-software/nelson/issues/944) `mag2db`, `db2mag`, `pow2db`, `db2pow` functions.
+  - [#968](http://github.com/Nelson-numerical-software/nelson/issues/968) `zp2tf`: Zero-pole to transfer function conversion.
 
 ### Changed
 

modules/signal_processing/functions/zp2tf.m

@@ -0,0 +1,63 @@
+%=============================================================================
+% Copyright (c) 2016-present Allan CORNET (Nelson)
+%=============================================================================
+% This file is part of the Nelson.
+%=============================================================================
+% LICENCE_BLOCK_BEGIN
+% SPDX-License-Identifier: LGPL-3.0-or-later
+% LICENCE_BLOCK_END
+%=============================================================================
+function varargout = zp2tf(varargin)
+  narginchk(3, 3);
+  nargoutchk(0, 2);
+  z = varargin{1};
+  p = varargin{2};
+  k = varargin{3};
+
+  den = computesDenominator(p);
+  varargout{1} = computesNumerator(z, k, den);
+
+  if nargout > 1
+    varargout{2} = den;
+  end
+end
+%=============================================================================
+function den = computesDenominator(p)
+  den = real(poly(p(:)));
+end
+%=============================================================================
+function num = computesNumerator(z, k, den)
+  num = [];
+  denc = size(den, 2);
+  k = k(:);
+  kr = size(k, 1);
+  if isempty(z)
+    if (denc - 1 > 0)
+      num = [zeros(kr, denc - 1), k];
+    else
+      num = k;
+    end
+  else
+    zc = size(z, 2);
+    if kr ~= zc
+      if ((size(z, 1) - 1) ~= 0)
+        error('Input argument #1 and #3 should have the same column size.');
+      else
+        error('First argument must be a column vector.');
+      end
+    else
+      num = [];
+      for nidx = 1:zc
+        zidx = z(:, nidx);
+        pidx = real(poly(zidx) * k(nidx));
+        zr = zeros(1, denc - length(pidx));
+        if isempty(num)
+          num = [zr, pidx];
+        else
+          num(nidx, :) = [zr, pidx];
+        end
+      end
+    end
+  end
+end
+%=============================================================================

modules/signal_processing/help/en_US/xml/zp2tf.xml

@@ -0,0 +1,79 @@
+<?xml version="1.0" encoding="UTF-8" ?>
+<xmldoc>
+  <copyright>SAME AS NELSON SOFTWARE</copyright>
+
+  <language>en_US</language>
+  <keyword>zp2tf</keyword>
+  <short_description
+  >Zero-pole to transfer function conversion.</short_description>
+
+  <syntax>
+    <syntax_item>[NUM, DEN] = zp2tf(Z, P, K)</syntax_item>
+  </syntax>
+
+  <param_input>
+    <param_input_item>
+      <param_name>Z</param_name>
+      <param_description
+      >Locations of zeros, organized in columns for each system output.</param_description>
+    </param_input_item>
+    <param_input_item>
+      <param_name>P</param_name>
+      <param_description
+      >Locations of poles, recorded as a column vector.</param_description>
+    </param_input_item>
+    <param_input_item>
+      <param_name>K</param_name>
+      <param_description>Gains.</param_description>
+    </param_input_item>
+
+  </param_input>
+
+  <param_output>
+    <param_output_item>
+      <param_name>NUM</param_name>
+      <param_description
+      >Coefficients in the numerator, organized by rows corresponding to each system output.</param_description>
+    </param_output_item>
+    <param_output_item>
+      <param_name>DEN</param_name>
+      <param_description
+      >Coefficients in the denominator, arranged as a row vector.</param_description>
+    </param_output_item>
+  </param_output>
+
+  <description>
+    <p><b
+      >[NUM, DEN] = zp2tf(Z, P, K)</b> returns polynomial transfer function representation from zeros and poles.</p>
+  </description>
+
+<examples>
+  <example_item>
+    <example_item_type>nelson</example_item_type>
+    <example_item_description />
+    <example_item_data
+      ><![CDATA[p = [0.5;0.45+0.5i;0.45-0.5i];
+z = [-1;i;-i];       
+k = 1;
+[n, d] = zp2tf(z, p, k)]]>
+    </example_item_data>
+  </example_item>
+</examples>
+
+  <see_also>
+    <see_also_item>
+      <link linkend="${signal_processing}tf2zpk">tf2zpk</link>
+    </see_also_item>
+  </see_also>
+
+  <history>
+    <history_item>
+      <history_version>1.0.0</history_version>
+      <history_description>initial version</history_description>
+    </history_item>
+  </history>
+
+  <authors>
+    <author_item>Allan CORNET</author_item>
+  </authors>
+</xmldoc>

modules/signal_processing/tests/test_zp2tf.m

@@ -0,0 +1,35 @@
+%=============================================================================
+% Copyright (c) 2016-present Allan CORNET (Nelson)
+%=============================================================================
+% This file is part of the Nelson.
+%=============================================================================
+% LICENCE_BLOCK_BEGIN
+% SPDX-License-Identifier: LGPL-3.0-or-later
+% LICENCE_BLOCK_END
+%=============================================================================
+assert_isequal(nargin('zp2tf'), -1);
+assert_isequal(nargout('zp2tf'), -1);
+%=============================================================================
+assert_checkerror('zp2tf([-100 -2.01], [-5 -.9 -20.1], 1)', _('First argument must be a column vector.'))
+%=============================================================================
+[N, D] = zp2tf([-1; -2.01], [-5 -9.9 -20.1], 1);
+N_REF = [0    1.0000    3.0100    2.0100];
+D_REF = [1.0000   35.0000  348.9900  994.9500];
+assert_isapprox(N, N_REF, 1e-3);
+assert_isapprox(D, D_REF, 1e-3);
+%=============================================================================
+[N, D] = zp2tf([], [], 1);
+N_REF = 1;
+D_REF = 1;
+assert_isequal(N, N_REF);
+assert_isequal(D, D_REF);
+%=============================================================================
+z = [49.498, 0; -49.498, 16.362];
+p = [0; -57.753; 53.851; 2.0831];
+k = [18.182; 45.455];
+[N, D] = zp2tf(z, p, k);
+N_REF = 1.0e+04 * [0, 0, 0.0018, 0, -4.4547; 0, 0, 0.0045, -0.0744, 0];
+D_REF = 1.0e+03 * [0.0010, 0.0018, -3.1182, 6.4786, 0];
+assert_isapprox(N, N_REF, 1e-3);
+assert_isapprox(D, D_REF, 1e-3);
+%=============================================================================