ZLANGB(3F) ZLANGB(3F)
ZLANGB - 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 band
matrix A, with kl sub-diagonals and ku super-diagonals
DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB, WORK )
CHARACTER NORM
INTEGER KL, KU, LDAB, N
DOUBLE PRECISION WORK( * )
COMPLEX*16 AB( LDAB, * )
ZLANGB 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.
ZLANGB returns the value
ZLANGB = ( 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 ZLANGB as described above.
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANGB is set to
zero.
KL (input) INTEGER
The number of sub-diagonals of the matrix A. KL >= 0.
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ZLANGB(3F) ZLANGB(3F)
KU (input) INTEGER
The number of super-diagonals of the matrix A. KU >= 0.
AB (input) COMPLEX*16 array, dimension (LDAB,N)
The band matrix A, stored in rows 1 to KL+KU+1. The j-th column
of A is stored in the j-th column of the array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= N when NORM = 'I'; otherwise, WORK is not
referenced.
ZLANGB(3F) ZLANGB(3F)
ZLANGB - 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 band
matrix A, with kl sub-diagonals and ku super-diagonals
DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB, WORK )
CHARACTER NORM
INTEGER KL, KU, LDAB, N
DOUBLE PRECISION WORK( * )
COMPLEX*16 AB( LDAB, * )
ZLANGB 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.
ZLANGB returns the value
ZLANGB = ( 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 ZLANGB as described above.
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANGB is set to
zero.
KL (input) INTEGER
The number of sub-diagonals of the matrix A. KL >= 0.
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ZLANGB(3F) ZLANGB(3F)
KU (input) INTEGER
The number of super-diagonals of the matrix A. KU >= 0.
AB (input) COMPLEX*16 array, dimension (LDAB,N)
The band matrix A, stored in rows 1 to KL+KU+1. The j-th column
of A is stored in the j-th column of the array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= N when NORM = 'I'; otherwise, WORK is not
referenced.
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