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slantb (3)
  • >> slantb (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         slantb - return the value of the one norm, or the  Frobenius
         norm,  or the infinity norm, or the element of largest abso-
         lute value of an n by n triangular band matrix A, with ( k +
         1 ) diagonals
    
    SYNOPSIS
         REAL FUNCTION SLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK
                   )
    
         CHARACTER DIAG, NORM, UPLO
    
         INTEGER K, LDAB, N
    
         REAL AB( LDAB, * ), WORK( * )
    
    
    
         #include <sunperf.h>
    
         double slantb(char norm, char uplo, char diag, int n, int k,
                   float *sab, int ldab) ;
    
    PURPOSE
         SLANTB  returns the value of the one norm,  or the Frobenius
         norm,  or  the   infinity  norm,  or the element of  largest
         absolute value  of an n by n triangular band matrix A,  with
         ( k + 1 ) diagonals.
    
    
    DESCRIPTION
         SLANTB returns the value
    
            SLANTB = ( 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  SLANTB  as
                   described above.
    
         UPLO      (input) CHARACTER*1
                   Specifies whether the matrix A is upper  or  lower
                   triangular.  = 'U':  Upper triangular
                   = 'L':  Lower triangular
    
         DIAG      (input) CHARACTER*1
                   Specifies whether or not the matrix A is unit tri-
                   angular.  = 'N':  Non-unit triangular
                   = 'U':  Unit triangular
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.  When N  =  0,
                   SLANTB is set to zero.
    
         K         (input) INTEGER
                   The number of super-diagonals of the matrix  A  if
                   UPLO  = 'U', or the number of sub-diagonals of the
                   matrix A if UPLO = 'L'.  K >= 0.
    
         AB        (input) REAL array, dimension (LDAB,N)
                   The upper  or  lower  triangular  band  matrix  A,
                   stored  in  the  first  k+1  rows of AB.  The j-th
                   column of A is stored in the j-th  column  of  the
                   array AB as follows:  if UPLO = 'U', AB(k+1+i-j,j)
                   = A(i,j) for  max(1,j-k)<=i<=j;  if  UPLO  =  'L',
                   AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).  Note
                   that when DIAG = 'U', the elements of the array AB
                   corresponding  to  the  diagonal  elements  of the
                   matrix A are not referenced, but are assumed to be
                   one.
    
         LDAB      (input) INTEGER
                   The leading dimension of the array  AB.   LDAB  >=
                   K+1.
    
         WORK      (workspace) REAL array, dimension (LWORK),
                   where LWORK >= N when NORM = 'I'; otherwise,  WORK
                   is not referenced.
    
    
    
    


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