# zlangb(3) [centos man page]

zlangb.f(3) LAPACK zlangb.f(3)NAME

zlangb.f-SYNOPSIS

Functions/Subroutines DOUBLE PRECISION function zlangb (NORM, N, KL, KU, AB, LDAB, WORK) ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.Function/Subroutine Documentation DOUBLE PRECISION function zlangb (characterNORM, integerN, integerKL, integerKU, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )WORK) ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. Purpose: 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. Returns: ZLANGB 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 consistent matrix norm. Parameters: NORM NORM is CHARACTER*1 Specifies the value to be returned in ZLANGB as described above. N N is INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANGB is set to zero. KL KL is INTEGER The number of sub-diagonals of the matrix A. KL >= 0. KU KU is INTEGER The number of super-diagonals of the matrix A. KU >= 0. AB AB is 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. WORK WORK is DOUBLE PRECISION 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 125 of file zlangb.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 zlangb.f(3)

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slangb.f(3) LAPACK slangb.f(3)NAME

slangb.f-SYNOPSIS

Functions/Subroutines REAL function slangb (NORM, N, KL, KU, AB, LDAB, WORK) SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.Function/Subroutine Documentation REAL function slangb (characterNORM, integerN, integerKL, integerKU, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )WORK) SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. Purpose: SLANGB 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. Returns: SLANGB SLANGB = ( 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 SLANGB as described above. N N is INTEGER The order of the matrix A. N >= 0. When N = 0, SLANGB is set to zero. KL KL is INTEGER The number of sub-diagonals of the matrix A. KL >= 0. KU KU is INTEGER The number of super-diagonals of the matrix A. KU >= 0. AB AB is REAL 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+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 124 of file slangb.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 slangb.f(3)