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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>givens</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="givens"> Givens transformation</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>U=givens(xy)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>U=givens(x,y)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[U,c]=givens(xy)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[U,c]=givens(x,y)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>x,y</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: two real or complex numbers</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>xy</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>:  real or complex size 2 column vector</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>U</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: 2x2 unitary matrix</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>c</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>:  real or complex size 2 column vector</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P><VERB>U = givens(x, y)</VERB> or <VERB>U = givens(xy)</VERB> with <VERB>xy = [x;y]</VERB>
    returns a <VERB>2</VERB>x<VERB>2</VERB> unitary matrix <VERB>U</VERB> such that:</P>
    <P><VERB>U*xy=[r;0]=c</VERB>.</P>
    <P>
    Note that <VERB>givens(x,y)</VERB> and <VERB>givens([x;y])</VERB> are equivalent.</P>
  </DESCRIPTION>
  <EXAMPLE>
<![CDATA[
A=[3,4;5,6];
U=givens(A(:,1));
U*A
 ]]>
  </EXAMPLE>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>qr</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
