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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