clanhe(3S)

NAME
     CLANHE - return the value of the one norm, or the Frobenius norm, or the
     infinity norm, or the element of largest absolute value of a complex
     hermitian matrix A

SYNOPSIS
     REAL FUNCTION CLANHE( NORM, UPLO, N, A, LDA, WORK )

         CHARACTER NORM, UPLO

         INTEGER   LDA, N

         REAL      WORK( * )

         COMPLEX   A( LDA, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CLANHE 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
     hermitian matrix A.

DESCRIPTION
     CLANHE returns the value

        CLANHE = ( 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  matrix norm.
ARGUMENTS
     NORM    (input) CHARACTER*1
             Specifies the value to be returned in CLANHE as described above.

     UPLO    (input) CHARACTER*1
             Specifies whether the upper or lower triangular part of the
             hermitian matrix A is to be referenced.  = 'U':  Upper triangular
             part of A is referenced
             = 'L':  Lower triangular part of A is referenced

     N       (input) INTEGER
             The order of the matrix A.  N >= 0.  When N = 0, CLANHE is set to
             zero.

     A       (input) COMPLEX array, dimension (LDA,N)
             The hermitian matrix A.  If UPLO = 'U', the leading n by n upper
             triangular part of A contains the upper triangular part of the
             matrix A, and the strictly lower triangular part of A is not
             referenced.  If UPLO = 'L', the leading n by n lower triangular
             part of A contains the lower triangular part of the matrix A, and
             the strictly upper triangular part of A is not referenced. Note
             that the imaginary parts of the diagonal elements need not be set
             and are assumed to be zero.

     LDA     (input) INTEGER
             The leading dimension of the array A.  LDA >= max(N,1).

     WORK    (workspace) REAL array, dimension (LWORK),
             where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK
             is not referenced.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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