slansb (l) - Linux Manuals
slansb: 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 symmetric band matrix A, with k super-diagonals
Command to display slansb
manual in Linux: $ man l slansb
NAME
SLANSB - 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 symmetric band matrix A, with k super-diagonals
SYNOPSIS
- REAL FUNCTION
-
SLANSB( NORM, UPLO, N, K, AB, LDAB,
WORK )
-
CHARACTER
NORM, UPLO
-
INTEGER
K, LDAB, N
-
REAL
AB( LDAB, * ), WORK( * )
PURPOSE
SLANSB 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 symmetric band matrix A, with k super-diagonals.
DESCRIPTION
SLANSB returns the value
SLANSB
= ( max(abs(A(i,j))), NORM = aqMaq or aqmaq
(
( norm1(A), NORM = aq1aq, aqOaq or aqoaq
(
( normI(A), NORM = aqIaq or aqiaq
(
( normF(A), NORM = aqFaq, aqfaq, aqEaq or aqeaq
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 SLANSB as described
above.
- UPLO (input) CHARACTER*1
-
Specifies whether the upper or lower triangular part of the
band matrix A is supplied.
= aqUaq: Upper triangular part is supplied
= aqLaq: Lower triangular part is supplied
- N (input) INTEGER
-
The order of the matrix A. N >= 0. When N = 0, SLANSB is
set to zero.
- K (input) INTEGER
-
The number of super-diagonals or sub-diagonals of the
band matrix A. K >= 0.
- AB (input) REAL array, dimension (LDAB,N)
-
The upper or lower triangle of the symmetric 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 = aqUaq, AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
if UPLO = aqLaq, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
- LDAB (input) INTEGER
-
The leading dimension of the array AB. LDAB >= K+1.
- WORK (workspace) REAL array, dimension (MAX(1,LWORK)),
-
where LWORK >= N when NORM = aqIaq or aq1aq or aqOaq; otherwise,
WORK is not referenced.
Pages related to slansb
- slansb (3)
- slansf (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A in RFP format
- slansp (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
- slanst (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
- slansy (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A
- slaneg (l) - computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T - sigma I = L D L^T
- slangb (l) - 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 band matrix A, with kl sub-diagonals and ku super-diagonals
- slange (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
- slangt (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
- slanhs (l) - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A