CLANTB(3F) CLANTB(3F)
CLANTB - 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
triangular band matrix A, with ( k + 1 ) diagonals
REAL FUNCTION CLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK )
CHARACTER DIAG, NORM, UPLO
INTEGER K, LDAB, N
REAL WORK( * )
COMPLEX AB( LDAB, * )
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.
CLANTB returns the value
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 matrix norm.
NORM (input) CHARACTER*1
Specifies the value to be returned in CLANTB 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 triangular. = 'N':
Non-unit triangular
= 'U': Unit triangular
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CLANTB(3F) CLANTB(3F)
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANTB 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) 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 (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.
CLANTB(3F) CLANTB(3F)
CLANTB - 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
triangular band matrix A, with ( k + 1 ) diagonals
REAL FUNCTION CLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK )
CHARACTER DIAG, NORM, UPLO
INTEGER K, LDAB, N
REAL WORK( * )
COMPLEX AB( LDAB, * )
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.
CLANTB returns the value
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 matrix norm.
NORM (input) CHARACTER*1
Specifies the value to be returned in CLANTB 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 triangular. = 'N':
Non-unit triangular
= 'U': Unit triangular
Page 1
CLANTB(3F) CLANTB(3F)
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANTB 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) 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 (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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