xclange.f

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*** This subroutine includes all of the CLANGE function instead of
*** simply wrapping it in a subroutine to avoid possible differences in
*** the way complex values are returned by various Fortran compilers.
*** For example, if we simply wrap the function and compile this file
*** with gfortran and the library that provides CLANGE is compiled with
*** a compiler that uses the g77 (f2c-compatible) calling convention for
*** complex-valued functions, all hell will break loose.
 
      SUBROUTINE xclange ( NORM, M, N, A, LDA, WORK, VALUE )
 
***   DOUBLE PRECISION FUNCTION CLANGE( NORM, M, N, A, LDA, WORK )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            LDA, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   WORK( * )
      COMPLEX*16         A( LDA, * )
*     ..
*
*  Purpose
*  =======
*
*  CLANGE  returns the value of the one norm,  or the Frobenius norm, or
*  the  infinity norm,  or the  element of  largest absolute value  of a
*  complex matrix A.
*
*  Description
*  ===========
*
*  CLANGE returns the value
*
*     CLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*              (
*              ( norm1(A),         NORM = '1', 'O' or 'o'
*              (
*              ( normI(A),         NORM = 'I' or 'i'
*              (
*              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
*
*  where  norm1  denotes the  one norm of a matrix (maximum column sum),
*  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
*  normF  denotes the  Frobenius norm of a matrix (square root of sum of
*  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
*
*  Arguments
*  =========
*
*  NORM    (input) CHARACTER*1
*          Specifies the value to be returned in CLANGE as described
*          above.
*
*  M       (input) INTEGER
*          The number of rows of the matrix A.  M >= 0.  When M = 0,
*          CLANGE is set to zero.
*
*  N       (input) INTEGER
*          The number of columns of the matrix A.  N >= 0.  When N = 0,
*          CLANGE is set to zero.
*
*  A       (input) COMPLEX*16 array, dimension (LDA,N)
*          The m by n matrix A.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(M,1).
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
*          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
*          referenced.
*
* =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J
      DOUBLE PRECISION   SCALE, SUM, VALUE
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           classq
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max, min, sqrt
*     ..
*     .. Executable Statements ..
*
      IF( min( m, n ).EQ.0 ) THEN
         VALUE = zero
      ELSE IF( lsame( norm, 'M' ) ) THEN
*
*        Find max(abs(A(i,j))).
*
         VALUE = zero
         DO 20 j = 1, n
            DO 10 i = 1, m
               VALUE = max( VALUE, abs( a( i, j ) ) )
   10       CONTINUE
   20    CONTINUE
      ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
*
*        Find norm1(A).
*
         VALUE = zero
         DO 40 j = 1, n
            sum = zero
            DO 30 i = 1, m
               sum = sum + abs( a( i, j ) )
   30       CONTINUE
            VALUE = max( VALUE, sum )
   40    CONTINUE
      ELSE IF( lsame( norm, 'I' ) ) THEN
*
*        Find normI(A).
*
         DO 50 i = 1, m
            work( i ) = zero
   50    CONTINUE
         DO 70 j = 1, n
            DO 60 i = 1, m
               work( i ) = work( i ) + abs( a( i, j ) )
   60       CONTINUE
   70    CONTINUE
         VALUE = zero
         DO 80 i = 1, m
            VALUE = max( VALUE, work( i ) )
   80    CONTINUE
      ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
*
*        Find normF(A).
*
         scale = zero
         sum = one
         DO 90 j = 1, n
            CALL classq( m, a( 1, j ), 1, scale, sum )
   90    CONTINUE
         VALUE = scale*sqrt( sum )
      END IF
*
***   CLANGE = VALUE
      RETURN
*
*     End of CLANGE
*
      END