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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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