Man page - lantp(3)

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Manual

lantp

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
real function clantp (character norm, character uplo, character diag,integer n, complex, dimension( * ) ap, real, dimension( * ) work)
double precision function dlantp (character norm, character uplo, characterdiag, integer n, double precision, dimension( * ) ap, double precision,dimension( * ) work)
real function slantp (character norm, character uplo, character diag,integer n, real, dimension( * ) ap, real, dimension( * ) work)
double precision function zlantp (character norm, character uplo, characterdiag, integer n, complex*16, dimension( * ) ap, double precision,dimension( * ) work)
Author

NAME

lantp - lantp: triangular matrix, packed

SYNOPSIS

Functions

real function clantp (norm, uplo, diag, n, ap, work)
CLANTP 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 matrix supplied in packed form.
double precision function dlantp (norm, uplo, diag, n, ap, work)
DLANTP 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 matrix supplied in packed form.
real function slantp (norm, uplo, diag, n, ap, work)
SLANTP 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 matrix supplied in packed form.
double precision function zlantp (norm, uplo, diag, n, ap, work)
ZLANTP 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 matrix supplied in packed form.

Detailed Description

Function Documentation

real function clantp (character norm, character uplo, character diag,integer n, complex, dimension( * ) ap, real, dimension( * ) work)

CLANTP 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 matrix supplied in packed form.

Purpose:

CLANTP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
triangular matrix A, supplied in packed form.

Returns

CLANTP

CLANTP = ( 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 CLANTP 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, CLANTP is
set to zero.

AP

AP is COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = ’U’, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ’L’, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
Note that when DIAG = ’U’, the elements of the array AP
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.

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 dlantp (character norm, character uplo, characterdiag, integer n, double precision, dimension( * ) ap, double precision,dimension( * ) work)

DLANTP 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 matrix supplied in packed form.

Purpose:

DLANTP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
triangular matrix A, supplied in packed form.

Returns

DLANTP

DLANTP = ( 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 DLANTP 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, DLANTP is
set to zero.

AP

AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = ’U’, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ’L’, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
Note that when DIAG = ’U’, the elements of the array AP
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.

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 slantp (character norm, character uplo, character diag,integer n, real, dimension( * ) ap, real, dimension( * ) work)

SLANTP 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 matrix supplied in packed form.

Purpose:

SLANTP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
triangular matrix A, supplied in packed form.

Returns

SLANTP

SLANTP = ( 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 SLANTP 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, SLANTP is
set to zero.

AP

AP is REAL array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = ’U’, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ’L’, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
Note that when DIAG = ’U’, the elements of the array AP
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.

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 zlantp (character norm, character uplo, characterdiag, integer n, complex*16, dimension( * ) ap, double precision,dimension( * ) work)

ZLANTP 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 matrix supplied in packed form.

Purpose:

ZLANTP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
triangular matrix A, supplied in packed form.

Returns

ZLANTP

ZLANTP = ( 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 ZLANTP 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, ZLANTP is
set to zero.

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = ’U’, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ’L’, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
Note that when DIAG = ’U’, the elements of the array AP
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.

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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