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lanht(3) LAPACK lanht(3)

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, double precision, 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, double precision, 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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