slangb.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 179 行

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      REAL             FUNCTION <a name="SLANGB.1"></a><a href="slangb.f.html#SLANGB.1">SLANGB</a>( NORM, N, KL, KU, AB, LDAB,
     $                 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            KL, KU, LDAB, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               AB( LDAB, * ), 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="SLANGB.19"></a><a href="slangb.f.html#SLANGB.1">SLANGB</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 an
</span><span class="comment">*</span><span class="comment">  n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
</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="SLANGB.26"></a><a href="slangb.f.html#SLANGB.1">SLANGB</a> returns the value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     <a name="SLANGB.28"></a><a href="slangb.f.html#SLANGB.1">SLANGB</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="SLANGB.45"></a><a href="slangb.f.html#SLANGB.1">SLANGB</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="SLANGB.49"></a><a href="slangb.f.html#SLANGB.1">SLANGB</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">  KL      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of sub-diagonals of the matrix A.  KL &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KU      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of super-diagonals of the matrix A.  KU &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AB      (input) REAL array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment">          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
</span><span class="comment">*</span><span class="comment">          column of A is stored in the j-th column of the array AB as
</span><span class="comment">*</span><span class="comment">          follows:
</span><span class="comment">*</span><span class="comment">          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)&lt;=i&lt;=min(n,j+kl).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDAB    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array AB.  LDAB &gt;= KL+KU+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'; 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">
</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, K, L
      REAL               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.83"></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.86"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.87"></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, 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.96"></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 = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
               VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
   10       CONTINUE
   20    CONTINUE
      ELSE IF( ( <a name="LSAME.106"></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 = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
               SUM = SUM + ABS( AB( I, J ) )
   30       CONTINUE
            VALUE = MAX( VALUE, SUM )
   40    CONTINUE
      ELSE IF( <a name="LSAME.118"></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
            K = KU + 1 - J
            DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
               WORK( I ) = WORK( I ) + ABS( AB( K+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.135"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'F'</span> ) ) .OR. ( <a name="LSAME.135"></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
            L = MAX( 1, J-KU )
            K = KU + 1 - J + L
            CALL <a name="SLASSQ.144"></a><a href="slassq.f.html#SLASSQ.1">SLASSQ</a>( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
   90    CONTINUE
         VALUE = SCALE*SQRT( SUM )
      END IF
<span class="comment">*</span><span class="comment">
</span>      <a name="SLANGB.149"></a><a href="slangb.f.html#SLANGB.1">SLANGB</a> = VALUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SLANGB.152"></a><a href="slangb.f.html#SLANGB.1">SLANGB</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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