table of contents
| lantp(3) | LAPACK | lantp(3) |
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 = ( 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function dlantp (character norm, character uplo, character diag, 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 = ( 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 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 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 = ( 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function zlantp (character norm, character uplo, character diag, 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 = ( 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |