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langt(3) LAPACK langt(3)

NAME

langt - langt: general matrix, tridiagonal

SYNOPSIS

Functions


real function clangt (norm, n, dl, d, du)
CLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. double precision function dlangt (norm, n, dl, d, du)
DLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. real function slangt (norm, n, dl, d, du)
SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. double precision function zlangt (norm, n, dl, d, du)
ZLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

Detailed Description

Function Documentation

real function clangt (character norm, integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du)

CLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

Purpose:



 CLANGT  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 tridiagonal matrix A.

Returns

CLANGT 



    CLANGT = ( 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 CLANGT as described


          above.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.  When N = 0, CLANGT is


          set to zero.

DL



          DL is COMPLEX array, dimension (N-1)


          The (n-1) sub-diagonal elements of A.

D



          D is COMPLEX array, dimension (N)


          The diagonal elements of A.

DU



          DU is COMPLEX array, dimension (N-1)


          The (n-1) super-diagonal elements of A.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

double precision function dlangt (character norm, integer n, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du)

DLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

Purpose:



 DLANGT  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 tridiagonal matrix A.

Returns

DLANGT 



    DLANGT = ( 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 DLANGT as described


          above.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.  When N = 0, DLANGT is


          set to zero.

DL



          DL is DOUBLE PRECISION array, dimension (N-1)


          The (n-1) sub-diagonal elements of A.

D



          D is DOUBLE PRECISION array, dimension (N)


          The diagonal elements of A.

DU



          DU is DOUBLE PRECISION array, dimension (N-1)


          The (n-1) super-diagonal elements of A.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

real function slangt (character norm, integer n, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du)

SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

Purpose:



 SLANGT  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 tridiagonal matrix A.

Returns

SLANGT 



    SLANGT = ( 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 SLANGT as described


          above.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.  When N = 0, SLANGT is


          set to zero.

DL



          DL is REAL array, dimension (N-1)


          The (n-1) sub-diagonal elements of A.

D



          D is REAL array, dimension (N)


          The diagonal elements of A.

DU



          DU is REAL array, dimension (N-1)


          The (n-1) super-diagonal elements of A.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

double precision function zlangt (character norm, integer n, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du)

ZLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

Purpose:



 ZLANGT  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 tridiagonal matrix A.

Returns

ZLANGT 



    ZLANGT = ( 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 ZLANGT as described


          above.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.  When N = 0, ZLANGT is


          set to zero.

DL



          DL is COMPLEX*16 array, dimension (N-1)


          The (n-1) sub-diagonal elements of A.

D



          D is COMPLEX*16 array, dimension (N)


          The diagonal elements of A.

DU



          DU is COMPLEX*16 array, dimension (N-1)


          The (n-1) super-diagonal elements of A.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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