slansy.f.html

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      REAL             FUNCTION <a name="SLANSY.1"></a><a href="slansy.f.html#SLANSY.1">SLANSY</a>( NORM, UPLO, 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, UPLO
      INTEGER            LDA, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               A( LDA, * ), WORK( * )
<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="SLANSY.18"></a><a href="slansy.f.html#SLANSY.1">SLANSY</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">  real symmetric 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="SLANSY.25"></a><a href="slansy.f.html#SLANSY.1">SLANSY</a> returns the value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     <a name="SLANSY.27"></a><a href="slansy.f.html#SLANSY.1">SLANSY</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="SLANSY.44"></a><a href="slansy.f.html#SLANSY.1">SLANSY</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">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies whether the upper or lower triangular part of the
</span><span class="comment">*</span><span class="comment">          symmetric matrix A is to be referenced.
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangular part of A is referenced
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangular part of A is referenced
</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="SLANSY.54"></a><a href="slansy.f.html#SLANSY.1">SLANSY</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) REAL array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          The symmetric matrix A.  If UPLO = 'U', the leading n by n
</span><span class="comment">*</span><span class="comment">          upper triangular part of A contains the upper triangular part
</span><span class="comment">*</span><span class="comment">          of the matrix A, and the strictly lower triangular part of A
</span><span class="comment">*</span><span class="comment">          is not referenced.  If UPLO = 'L', the leading n by n lower
</span><span class="comment">*</span><span class="comment">          triangular part of A contains the lower triangular part of
</span><span class="comment">*</span><span class="comment">          the matrix A, and the strictly upper triangular part of A is
</span><span class="comment">*</span><span class="comment">          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) REAL array, dimension (MAX(1,LWORK)),
</span><span class="comment">*</span><span class="comment">          where LWORK &gt;= N when NORM = 'I' or '1' or 'O'; otherwise,
</span><span class="comment">*</span><span class="comment">          WORK is not 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>      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, J
      REAL               ABSA, SCALE, SUM, VALUE
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SLASSQ.84"></a><a href="slassq.f.html#SLASSQ.1">SLASSQ</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.87"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.88"></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">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, MAX, 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.97"></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
         IF( <a name="LSAME.102"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
            DO 20 J = 1, N
               DO 10 I = 1, J
                  VALUE = MAX( VALUE, ABS( A( I, J ) ) )
   10          CONTINUE
   20       CONTINUE
         ELSE
            DO 40 J = 1, N
               DO 30 I = J, N
                  VALUE = MAX( VALUE, ABS( A( I, J ) ) )
   30          CONTINUE
   40       CONTINUE
         END IF
      ELSE IF( ( <a name="LSAME.115"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'I'</span> ) ) .OR. ( <a name="LSAME.115"></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 normI(A) ( = norm1(A), since A is symmetric).
</span><span class="comment">*</span><span class="comment">
</span>         VALUE = ZERO
         IF( <a name="LSAME.121"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
            DO 60 J = 1, N
               SUM = ZERO
               DO 50 I = 1, J - 1
                  ABSA = ABS( A( I, J ) )
                  SUM = SUM + ABSA
                  WORK( I ) = WORK( I ) + ABSA
   50          CONTINUE
               WORK( J ) = SUM + ABS( A( J, J ) )
   60       CONTINUE
            DO 70 I = 1, N
               VALUE = MAX( VALUE, WORK( I ) )
   70       CONTINUE
         ELSE
            DO 80 I = 1, N
               WORK( I ) = ZERO
   80       CONTINUE
            DO 100 J = 1, N
               SUM = WORK( J ) + ABS( A( J, J ) )
               DO 90 I = J + 1, N
                  ABSA = ABS( A( I, J ) )
                  SUM = SUM + ABSA
                  WORK( I ) = WORK( I ) + ABSA
   90          CONTINUE
               VALUE = MAX( VALUE, SUM )
  100       CONTINUE
         END IF
      ELSE IF( ( <a name="LSAME.148"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'F'</span> ) ) .OR. ( <a name="LSAME.148"></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
         IF( <a name="LSAME.154"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
            DO 110 J = 2, N
               CALL <a name="SLASSQ.156"></a><a href="slassq.f.html#SLASSQ.1">SLASSQ</a>( J-1, A( 1, J ), 1, SCALE, SUM )
  110       CONTINUE
         ELSE
            DO 120 J = 1, N - 1
               CALL <a name="SLASSQ.160"></a><a href="slassq.f.html#SLASSQ.1">SLASSQ</a>( N-J, A( J+1, J ), 1, SCALE, SUM )
  120       CONTINUE
         END IF
         SUM = 2*SUM
         CALL <a name="SLASSQ.164"></a><a href="slassq.f.html#SLASSQ.1">SLASSQ</a>( N, A, LDA+1, SCALE, SUM )
         VALUE = SCALE*SQRT( SUM )
      END IF
<span class="comment">*</span><span class="comment">
</span>      <a name="SLANSY.168"></a><a href="slansy.f.html#SLANSY.1">SLANSY</a> = VALUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SLANSY.171"></a><a href="slansy.f.html#SLANSY.1">SLANSY</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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