clantr(3S)

NAME
     CLANTR - return the value of the one norm, or the Frobenius norm, or the
     infinity norm, or the element of largest absolute value of a trapezoidal
     or triangular matrix A

SYNOPSIS
     REAL FUNCTION CLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK )

         CHARACTER DIAG, NORM, UPLO

         INTEGER   LDA, M, 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
     CLANTR returns the value of the one norm, or the Frobenius norm, or the
     infinity norm, or the element of largest absolute value of a trapezoidal
     or triangular matrix A.

DESCRIPTION
     CLANTR returns the value

        CLANTR = ( 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 CLANTR as described above.

     UPLO    (input) CHARACTER*1
             Specifies whether the matrix A is upper or lower trapezoidal.  =
             'U':  Upper trapezoidal
             = 'L':  Lower trapezoidal Note that A is triangular instead of
             trapezoidal if M = N.

     DIAG    (input) CHARACTER*1
             Specifies whether or not the matrix A has unit diagonal.  = 'N':
             Non-unit diagonal
             = 'U':  Unit diagonal

     M       (input) INTEGER
             The number of rows of the matrix A.  M >= 0, and if UPLO = 'U', M
             <= N.  When M = 0, CLANTR is set to zero.

     N       (input) INTEGER
             The number of columns of the matrix A.  N >= 0, and if UPLO =
             'L', N <= M.  When N = 0, CLANTR is set to zero.

     A       (input) COMPLEX array, dimension (LDA,N)
             The trapezoidal matrix A (A is triangular if M = N).  If UPLO =
             'U', the leading m by n upper trapezoidal part of the array A
             contains the upper trapezoidal matrix, and the strictly lower
             triangular part of A is not referenced.  If UPLO = 'L', the
             leading m by n lower trapezoidal part of the array A contains the
             lower trapezoidal matrix, and the strictly upper triangular part
             of A is not referenced.  Note that when DIAG = 'U', the diagonal
             elements of A are not referenced and are assumed to be one.

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

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

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

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