DLANHS(1) LAPACK auxiliary routine (version 3.2) DLANHS(1)[top]NAMEDLANHS - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hes‐ senberg matrix ASYNOPSISDOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK ) CHARACTER NORM INTEGER LDA, N DOUBLE PRECISION A( LDA, * ), WORK( * )PURPOSEDLANHS returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A.DESCRIPTIONDLANHS returns the value DLANHS = ( 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 DLANHS as described above. N (input) INTEGER The order of the matrix A. N >= 0. When N = 0, DLANHS is set to zero. A (input) DOUBLE PRECISION array, dimension (LDA,N) The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(N,1). WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐ enced. LAPACK auxiliary routine (versioNovember 2008 DLANHS(1)

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