clantb-f(3)

clantb.f –

Synopsis

Functions/Subroutines

REAL function clantb (NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

Function/Subroutine Documentation

REAL function clantb (characterNORM, characterUPLO, characterDIAG, integerN, integerK, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )WORK)

CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

Purpose:

 CLANTB 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.

Returns:

CLANTB

 CLANTB = ( 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.

Parameters:

NORM

 NORM is CHARACTER*1
 Specifies the value to be returned in CLANTB as described
 above.

UPLO

 UPLO is CHARACTER*1
 Specifies whether the matrix A is upper or lower triangular.
 = 'U': Upper triangular
 = 'L': Lower triangular

DIAG

 DIAG is CHARACTER*1
 Specifies whether or not the matrix A is unit triangular.
 = 'N': Non-unit triangular
 = 'U': Unit triangular

 N is INTEGER
 The order of the matrix A. N >= 0. When N = 0, CLANTB is
 set to zero.

 K is 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 is COMPLEX 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

 LDAB is INTEGER
 The leading dimension of the array AB. LDAB >= K+1.

WORK

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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 141 of file clantb.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.