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## man page of LAPACK-3

### LAPACK-3: returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute

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LAPACK-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 triangular band matrix A, with ( k + 1 ) diagonals## SYNOPSIS

DOUBLE PRECISION FUNCTION ZLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK ) CHARACTER DIAG, NORM, UPLO INTEGER K, LDAB, N DOUBLE PRECISION WORK( * ) COMPLEX*16 AB( LDAB, * )## PURPOSE

ZLANTB 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.## DESCRIPTION

ZLANTB returns the value ZLANTB = ( 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.## ARGUMENTS

NORM (input) CHARACTER*1 Specifies the value to be returned in ZLANTB 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 N (input) INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANTB 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*16 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) 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)

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