table of contents
| langb(3) | Library Functions Manual | 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 = ( 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 123 of file clangb.f.
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 = ( 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 122 of file dlangb.f.
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 = ( 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 122 of file slangb.f.
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 = ( 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 123 of file zlangb.f.
Author¶
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