Man page - lanht(3)

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Manual

lanht

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
real function clanht (character norm, integer n, real, dimension( * ) d,complex, dimension( * ) e)
double precision function dlanst (character norm, integer n, doubleprecision, dimension( * ) d, double precision, dimension( * ) e)
real function slanst (character norm, integer n, real, dimension( * ) d,real, dimension( * ) e)
double precision function zlanht (character norm, integer n, doubleprecision, dimension( * ) d, complex*16, dimension( * ) e)
Author

NAME

lanht - lan{ht,st}: Hermitian/symmetric matrix, tridiagonal

SYNOPSIS

Functions

real function clanht (norm, n, d, e)
CLANHT returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix.
double precision function dlanst (norm, n, d, e)
DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.
real function slanst (norm, n, d, e)
SLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.
double precision function zlanht (norm, n, d, e)
ZLANHT returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix.

Detailed Description

Function Documentation

real function clanht (character norm, integer n, real, dimension( * ) d,complex, dimension( * ) e)

CLANHT returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix.

Purpose:

CLANHT returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
complex Hermitian tridiagonal matrix A.

Returns

CLANHT

CLANHT = ( 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 CLANHT as described
above.

N

N is INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANHT is
set to zero.

D

D is REAL array, dimension (N)
The diagonal elements of A.

E

E is COMPLEX array, dimension (N-1)
The (n-1) sub-diagonal or super-diagonal elements of A.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

double precision function dlanst (character norm, integer n, doubleprecision, dimension( * ) d, double precision, dimension( * ) e)

DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.

Purpose:

DLANST returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real symmetric tridiagonal matrix A.

Returns

DLANST

DLANST = ( 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 DLANST as described
above.

N

N is INTEGER
The order of the matrix A. N >= 0. When N = 0, DLANST is
set to zero.

D

D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of A.

E

E is DOUBLE PRECISION array, dimension (N-1)
The (n-1) sub-diagonal or super-diagonal elements of A.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

real function slanst (character norm, integer n, real, dimension( * ) d,real, dimension( * ) e)

SLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.

Purpose:

SLANST returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real symmetric tridiagonal matrix A.

Returns

SLANST

SLANST = ( 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 SLANST as described
above.

N

N is INTEGER
The order of the matrix A. N >= 0. When N = 0, SLANST is
set to zero.

D

D is REAL array, dimension (N)
The diagonal elements of A.

E

E is REAL array, dimension (N-1)
The (n-1) sub-diagonal or super-diagonal elements of A.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

double precision function zlanht (character norm, integer n, doubleprecision, dimension( * ) d, complex*16, dimension( * ) e)

ZLANHT returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix.

Purpose:

ZLANHT returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
complex Hermitian tridiagonal matrix A.

Returns

ZLANHT

ZLANHT = ( 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 ZLANHT as described
above.

N

N is INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANHT is
set to zero.

D

D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of A.

E

E is COMPLEX*16 array, dimension (N-1)
The (n-1) sub-diagonal or super-diagonal elements of A.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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