NAMELAPACK-3 - 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
SYNOPSISDOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB, WORK ) CHARACTER NORM INTEGER KL, KU, LDAB, N DOUBLE PRECISION WORK( * ) COMPLEX*16 AB( LDAB, * )
PURPOSEZLANGB 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.
DESCRIPTIONZLANGB 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 consistent matrix norm.
ARGUMENTSNORM (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. 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 (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. LAPACK auxiliary routine (versionMarch 2011 LAPACK-3(3)