zlanhs.f.html

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      DOUBLE PRECISION FUNCTION <a name="ZLANHS.1"></a><a href="zlanhs.f.html#ZLANHS.1">ZLANHS</a>( NORM, N, A, LDA, WORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          NORM
      INTEGER            LDA, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   WORK( * )
      COMPLEX*16         A( LDA, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="ZLANHS.19"></a><a href="zlanhs.f.html#ZLANHS.1">ZLANHS</a>  returns the value of the one norm,  or the Frobenius norm, or
</span><span class="comment">*</span><span class="comment">  the  infinity norm,  or the  element of  largest absolute value  of a
</span><span class="comment">*</span><span class="comment">  Hessenberg matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Description
</span><span class="comment">*</span><span class="comment">  ===========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="ZLANHS.26"></a><a href="zlanhs.f.html#ZLANHS.1">ZLANHS</a> returns the value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     <a name="ZLANHS.28"></a><a href="zlanhs.f.html#ZLANHS.1">ZLANHS</a> = ( max(abs(A(i,j))), NORM = 'M' or 'm'
</span><span class="comment">*</span><span class="comment">              (
</span><span class="comment">*</span><span class="comment">              ( norm1(A),         NORM = '1', 'O' or 'o'
</span><span class="comment">*</span><span class="comment">              (
</span><span class="comment">*</span><span class="comment">              ( normI(A),         NORM = 'I' or 'i'
</span><span class="comment">*</span><span class="comment">              (
</span><span class="comment">*</span><span class="comment">              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where  norm1  denotes the  one norm of a matrix (maximum column sum),
</span><span class="comment">*</span><span class="comment">  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
</span><span class="comment">*</span><span class="comment">  normF  denotes the  Frobenius norm of a matrix (square root of sum of
</span><span class="comment">*</span><span class="comment">  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NORM    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies the value to be returned in <a name="ZLANHS.45"></a><a href="zlanhs.f.html#ZLANHS.1">ZLANHS</a> as described
</span><span class="comment">*</span><span class="comment">          above.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.  When N = 0, <a name="ZLANHS.49"></a><a href="zlanhs.f.html#ZLANHS.1">ZLANHS</a> is
</span><span class="comment">*</span><span class="comment">          set to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input) COMPLEX*16 array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          The n by n upper Hessenberg matrix A; the part of A below the
</span><span class="comment">*</span><span class="comment">          first sub-diagonal is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(N,1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
</span><span class="comment">*</span><span class="comment">          where LWORK &gt;= N when NORM = 'I'; otherwise, WORK is not
</span><span class="comment">*</span><span class="comment">          referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, J
      DOUBLE PRECISION   SCALE, SUM, VALUE
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.74"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.75"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="ZLASSQ.78"></a><a href="zlassq.f.html#ZLASSQ.1">ZLASSQ</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, MAX, MIN, SQRT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 ) THEN
         VALUE = ZERO
      ELSE IF( <a name="LSAME.87"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'M'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Find max(abs(A(i,j))).
</span><span class="comment">*</span><span class="comment">
</span>         VALUE = ZERO
         DO 20 J = 1, N
            DO 10 I = 1, MIN( N, J+1 )
               VALUE = MAX( VALUE, ABS( A( I, J ) ) )
   10       CONTINUE
   20    CONTINUE
      ELSE IF( ( <a name="LSAME.97"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'O'</span> ) ) .OR. ( NORM.EQ.<span class="string">'1'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Find norm1(A).
</span><span class="comment">*</span><span class="comment">
</span>         VALUE = ZERO
         DO 40 J = 1, N
            SUM = ZERO
            DO 30 I = 1, MIN( N, J+1 )
               SUM = SUM + ABS( A( I, J ) )
   30       CONTINUE
            VALUE = MAX( VALUE, SUM )
   40    CONTINUE
      ELSE IF( <a name="LSAME.109"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'I'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Find normI(A).
</span><span class="comment">*</span><span class="comment">
</span>         DO 50 I = 1, N
            WORK( I ) = ZERO
   50    CONTINUE
         DO 70 J = 1, N
            DO 60 I = 1, MIN( N, J+1 )
               WORK( I ) = WORK( I ) + ABS( A( I, J ) )
   60       CONTINUE
   70    CONTINUE
         VALUE = ZERO
         DO 80 I = 1, N
            VALUE = MAX( VALUE, WORK( I ) )
   80    CONTINUE
      ELSE IF( ( <a name="LSAME.125"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'F'</span> ) ) .OR. ( <a name="LSAME.125"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'E'</span> ) ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Find normF(A).
</span><span class="comment">*</span><span class="comment">
</span>         SCALE = ZERO
         SUM = ONE
         DO 90 J = 1, N
            CALL <a name="ZLASSQ.132"></a><a href="zlassq.f.html#ZLASSQ.1">ZLASSQ</a>( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
   90    CONTINUE
         VALUE = SCALE*SQRT( SUM )
      END IF
<span class="comment">*</span><span class="comment">
</span>      <a name="ZLANHS.137"></a><a href="zlanhs.f.html#ZLANHS.1">ZLANHS</a> = VALUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="ZLANHS.140"></a><a href="zlanhs.f.html#ZLANHS.1">ZLANHS</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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