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 is INTEGER


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


          set to zero.



          DL is COMPLEX array, dimension (N-1)


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



          D is COMPLEX array, dimension (N)


          The diagonal elements of A.



          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.

Definition at line 105 of file clangt.f.

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 is INTEGER


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


          set to zero.



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


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



          D is DOUBLE PRECISION array, dimension (N)


          The diagonal elements of A.



          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.

Definition at line 105 of file dlangt.f.

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 is INTEGER


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


          set to zero.



          DL is REAL array, dimension (N-1)


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



          D is REAL array, dimension (N)


          The diagonal elements of A.



          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.

Definition at line 105 of file slangt.f.

double precision function zlangt (character norm, integer n, complex16, dimension( ) dl, complex16, dimension( ) d, complex16, 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 is INTEGER


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


          set to zero.



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


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



          D is COMPLEX*16 array, dimension (N)


          The diagonal elements of A.



          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.

Definition at line 105 of file zlangt.f.

Author

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