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langb(3) LAPACK langb(3)

NAME

langb - langb: general matrix, banded

SYNOPSIS

Functions


real function clangb (norm, n, kl, ku, ab, ldab, work)
CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. double precision function dlangb (norm, n, kl, ku, ab, ldab, work)
DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. real function slangb (norm, n, kl, ku, ab, ldab, work)
SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. double precision function zlangb (norm, n, kl, ku, ab, ldab, work)
ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Detailed Description

Function Documentation

real function clangb (character norm, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:

!>
!> CLANGB  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the element of  largest absolute value  of an
!> n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
!>

Returns

CLANGB 

!>
!>    CLANGB = ( 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 CLANGB as described
!>          above.
!>

N

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

KL

!>          KL is INTEGER
!>          The number of sub-diagonals of the matrix A.  KL >= 0.
!>

KU

!>          KU is INTEGER
!>          The number of super-diagonals of the matrix A.  KU >= 0.
!>

AB

!>          AB is COMPLEX array, dimension (LDAB,N)
!>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
!>          column of A is stored in the j-th column of the array AB as
!>          follows:
!>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
!>

WORK

!>          WORK is REAL array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
!>          referenced.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

double precision function dlangb (character norm, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work)

DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:

!>
!> DLANGB  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the element of  largest absolute value  of an
!> n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
!>

Returns

DLANGB 

!>
!>    DLANGB = ( 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 DLANGB as described
!>          above.
!>

N

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

KL

!>          KL is INTEGER
!>          The number of sub-diagonals of the matrix A.  KL >= 0.
!>

KU

!>          KU is INTEGER
!>          The number of super-diagonals of the matrix A.  KU >= 0.
!>

AB

!>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
!>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
!>          column of A is stored in the j-th column of the array AB as
!>          follows:
!>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
!>

WORK

!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
!>          referenced.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

real function slangb (character norm, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:

!>
!> SLANGB  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the element of  largest absolute value  of an
!> n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
!>

Returns

SLANGB 

!>
!>    SLANGB = ( 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 SLANGB as described
!>          above.
!>

N

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

KL

!>          KL is INTEGER
!>          The number of sub-diagonals of the matrix A.  KL >= 0.
!>

KU

!>          KU is INTEGER
!>          The number of super-diagonals of the matrix A.  KU >= 0.
!>

AB

!>          AB is REAL array, dimension (LDAB,N)
!>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
!>          column of A is stored in the j-th column of the array AB as
!>          follows:
!>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
!>

WORK

!>          WORK is REAL array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
!>          referenced.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

double precision function zlangb (character norm, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work)

ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:

!>
!> ZLANGB  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the element of  largest absolute value  of an
!> n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
!>

Returns

ZLANGB 

!>
!>    ZLANGB = ( 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 ZLANGB as described
!>          above.
!>

N

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

KL

!>          KL is INTEGER
!>          The number of sub-diagonals of the matrix A.  KL >= 0.
!>

KU

!>          KU is INTEGER
!>          The number of super-diagonals of the matrix A.  KU >= 0.
!>

AB

!>          AB is COMPLEX*16 array, dimension (LDAB,N)
!>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
!>          column of A is stored in the j-th column of the array AB as
!>          follows:
!>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
!>

WORK

!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
!>          referenced.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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