CLANSB(3F) CLANSB(3F)
CLANSB - return 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
REAL FUNCTION CLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )
CHARACTER NORM, UPLO
INTEGER K, LDAB, N
REAL WORK( * )
COMPLEX AB( LDAB, * )
CLANSB 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.
CLANSB returns the value
CLANSB = ( 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.
NORM (input) CHARACTER*1
Specifies the value to be returned in CLANSB as described above.
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the band
matrix A is supplied. = 'U': Upper triangular part is supplied
= 'L': Lower triangular part is supplied
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANSB is set to
zero.
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CLANSB(3F) CLANSB(3F)
K (input) INTEGER
The number of super-diagonals or sub-diagonals of the band matrix
A. K >= 0.
AB (input) COMPLEX 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 =
'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).
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' or '1' or 'O'; otherwise, WORK
is not referenced.
CLANSB(3F) CLANSB(3F)
CLANSB - return 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
REAL FUNCTION CLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )
CHARACTER NORM, UPLO
INTEGER K, LDAB, N
REAL WORK( * )
COMPLEX AB( LDAB, * )
CLANSB 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.
CLANSB returns the value
CLANSB = ( 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.
NORM (input) CHARACTER*1
Specifies the value to be returned in CLANSB as described above.
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the band
matrix A is supplied. = 'U': Upper triangular part is supplied
= 'L': Lower triangular part is supplied
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANSB is set to
zero.
Page 1
CLANSB(3F) CLANSB(3F)
K (input) INTEGER
The number of super-diagonals or sub-diagonals of the band matrix
A. K >= 0.
AB (input) COMPLEX 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 =
'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).
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' or '1' or 'O'; otherwise, WORK
is not referenced.
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