lanhs(3) Library Functions Manual lanhs(3) NAME lanhs - lanhs: Hessenberg SYNOPSIS Functions real function clanhs (norm, n, a, lda, work) CLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. double precision function dlanhs (norm, n, a, lda, work) DLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. real function slanhs (norm, n, a, lda, work) SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. double precision function zlanhs (norm, n, a, lda, work) ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. Detailed Description Function Documentation real function clanhs (character norm, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work) CLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. Purpose: !> !> CLANHS 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. !> Returns CLANHS !> !> CLANHS = ( 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 CLANHS as described !> above. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. When N = 0, CLANHS is !> set to zero. !> A !> A is COMPLEX 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 !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(N,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. Definition at line 108 of file clanhs.f. double precision function dlanhs (character norm, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work) DLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. Purpose: !> !> DLANHS 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. !> Returns DLANHS !> !> 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. !> Parameters NORM !> NORM is CHARACTER*1 !> Specifies the value to be returned in DLANHS as described !> above. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. When N = 0, DLANHS is !> set to zero. !> A !> A is 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 !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(N,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. Definition at line 107 of file dlanhs.f. real function slanhs (character norm, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work) SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. Purpose: !> !> SLANHS 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. !> Returns SLANHS !> !> SLANHS = ( 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 SLANHS as described !> above. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. When N = 0, SLANHS is !> set to zero. !> A !> A is REAL 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 !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(N,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. Definition at line 107 of file slanhs.f. double precision function zlanhs (character norm, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work) ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. Purpose: !> !> ZLANHS 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. !> Returns ZLANHS !> !> ZLANHS = ( 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 ZLANHS as described !> above. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. When N = 0, ZLANHS is !> set to zero. !> A !> A is COMPLEX*16 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 !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(N,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. Definition at line 108 of file zlanhs.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 lanhs(3)