Man page - lantb(3)

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Manual

lantb

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
real function clantb (character norm, character uplo, character diag,integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab,real, dimension( * ) work)
double precision function dlantb (character norm, character uplo, characterdiag, integer n, integer k, double precision, dimension( ldab, * ) ab,integer ldab, double precision, dimension( * ) work)
real function slantb (character norm, character uplo, character diag,integer n, integer k, real, dimension( ldab, * ) ab, integer ldab,real, dimension( * ) work)
double precision function zlantb (character norm, character uplo, characterdiag, integer n, integer k, complex*16, dimension( ldab, * ) ab,integer ldab, double precision, dimension( * ) work)
Author

NAME

lantb - lantb: triangular matrix, banded

SYNOPSIS

Functions

real function clantb (norm, uplo, diag, n, k, ab, ldab, work)
CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
double precision function dlantb (norm, uplo, diag, n, k, ab, ldab, work)
DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
real function slantb (norm, uplo, diag, n, k, ab, ldab, work)
SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
double precision function zlantb (norm, uplo, diag, n, k, ab, ldab, work)
ZLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

Detailed Description

Function Documentation

real function clantb (character norm, character uplo, character diag,integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab,real, dimension( * ) work)

CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

Purpose:

CLANTB 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 triangular band matrix A, with ( k + 1 ) diagonals.

Returns

CLANTB

CLANTB = ( 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 CLANTB as described
above.

UPLO

UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= ’U’: Upper triangular
= ’L’: Lower triangular

DIAG

DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= ’N’: Non-unit triangular
= ’U’: Unit triangular

N

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

K

K is INTEGER
The number of super-diagonals of the matrix A if UPLO = ’U’,
or the number of sub-diagonals of the matrix A if UPLO = ’L’.
K >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first k+1 rows of AB. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
Note that when DIAG = ’U’, the elements of the array AB
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= K+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 dlantb (character norm, character uplo, characterdiag, integer n, integer k, double precision, dimension( ldab, * ) ab,integer ldab, double precision, dimension( * ) work)

DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

Purpose:

DLANTB 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 triangular band matrix A, with ( k + 1 ) diagonals.

Returns

DLANTB

DLANTB = ( 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 DLANTB as described
above.

UPLO

UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= ’U’: Upper triangular
= ’L’: Lower triangular

DIAG

DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= ’N’: Non-unit triangular
= ’U’: Unit triangular

N

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

K

K is INTEGER
The number of super-diagonals of the matrix A if UPLO = ’U’,
or the number of sub-diagonals of the matrix A if UPLO = ’L’.
K >= 0.

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first k+1 rows of AB. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
Note that when DIAG = ’U’, the elements of the array AB
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= K+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 slantb (character norm, character uplo, character diag,integer n, integer k, real, dimension( ldab, * ) ab, integer ldab,real, dimension( * ) work)

SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

Purpose:

SLANTB 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 triangular band matrix A, with ( k + 1 ) diagonals.

Returns

SLANTB

SLANTB = ( 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 SLANTB as described
above.

UPLO

UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= ’U’: Upper triangular
= ’L’: Lower triangular

DIAG

DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= ’N’: Non-unit triangular
= ’U’: Unit triangular

N

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

K

K is INTEGER
The number of super-diagonals of the matrix A if UPLO = ’U’,
or the number of sub-diagonals of the matrix A if UPLO = ’L’.
K >= 0.

AB

AB is REAL array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first k+1 rows of AB. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
Note that when DIAG = ’U’, the elements of the array AB
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= K+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 zlantb (character norm, character uplo, characterdiag, integer n, integer k, complex*16, dimension( ldab, * ) ab,integer ldab, double precision, dimension( * ) work)

ZLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

Purpose:

ZLANTB 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 triangular band matrix A, with ( k + 1 ) diagonals.

Returns

ZLANTB

ZLANTB = ( 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 ZLANTB as described
above.

UPLO

UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= ’U’: Upper triangular
= ’L’: Lower triangular

DIAG

DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= ’N’: Non-unit triangular
= ’U’: Unit triangular

N

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

K

K is INTEGER
The number of super-diagonals of the matrix A if UPLO = ’U’,
or the number of sub-diagonals of the matrix A if UPLO = ’L’.
K >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first k+1 rows of AB. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
Note that when DIAG = ’U’, the elements of the array AB
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= K+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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