lanht(3)

Library Functions Manual

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

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

          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.

Definition at line 100 of file clanht.f.

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

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

          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.

Definition at line 99 of file dlanst.f.

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

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

          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.

Definition at line 99 of file slanst.f.

double precision function zlanht (character norm, integer n, double precision, dimension( * ) d, complex16, 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 is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, ZLANHT is
          set to zero.

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

          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.

Definition at line 100 of file zlanht.f.

Author

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