Provided by: liblapack-doc_3.12.1-4_all 
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.
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.
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.
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.
Author
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Version 3.12.0 Sun Jul 20 2025 01:40:05 lanhs(3)