table of contents
| lanhp(3) | LAPACK | lanhp(3) |
NAME¶
lanhp - lan{hp,sp}: Hermitian/symmetric matrix, packed
SYNOPSIS¶
Functions¶
real function clanhp (norm, uplo, n, ap, work)
CLANHP returns the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a complex
Hermitian matrix supplied in packed form. real function clansp (norm,
uplo, n, ap, work)
CLANSP returns the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a symmetric
matrix supplied in packed form. double precision function dlansp
(norm, uplo, n, ap, work)
DLANSP returns the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a symmetric
matrix supplied in packed form. real function slansp (norm, uplo, n,
ap, work)
SLANSP returns the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a symmetric
matrix supplied in packed form. double precision function zlanhp
(norm, uplo, n, ap, work)
ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a complex
Hermitian matrix supplied in packed form. double precision function
zlansp (norm, uplo, n, ap, work)
ZLANSP returns the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a symmetric
matrix supplied in packed form.
Detailed Description¶
Function Documentation¶
real function clanhp (character norm, character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) work)¶
CLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.
Purpose:
CLANHP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
complex hermitian matrix A, supplied in packed form.
Returns
CLANHP = ( 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 CLANHP as described
above.
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
hermitian matrix A is supplied.
= 'U': Upper triangular part of A is supplied
= 'L': Lower triangular part of A is supplied
N
N is INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANHP is
set to zero.
AP
AP is COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.
WORK
WORK is REAL array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
real function clansp (character norm, character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) work)¶
CLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
Purpose:
CLANSP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
complex symmetric matrix A, supplied in packed form.
Returns
CLANSP = ( 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 CLANSP as described
above.
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is supplied.
= 'U': Upper triangular part of A is supplied
= 'L': Lower triangular part of A is supplied
N
N is INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANSP is
set to zero.
AP
AP is COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric 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.
WORK
WORK is REAL array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function dlansp (character norm, character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) work)¶
DLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
Purpose:
DLANSP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real symmetric matrix A, supplied in packed form.
Returns
DLANSP = ( 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 DLANSP as described
above.
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is supplied.
= 'U': Upper triangular part of A is supplied
= 'L': Lower triangular part of A is supplied
N
N is INTEGER
The order of the matrix A. N >= 0. When N = 0, DLANSP is
set to zero.
AP
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric 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.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
real function slansp (character norm, character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) work)¶
SLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
Purpose:
SLANSP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real symmetric matrix A, supplied in packed form.
Returns
SLANSP = ( 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 SLANSP as described
above.
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is supplied.
= 'U': Upper triangular part of A is supplied
= 'L': Lower triangular part of A is supplied
N
N is INTEGER
The order of the matrix A. N >= 0. When N = 0, SLANSP is
set to zero.
AP
AP is REAL array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric 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.
WORK
WORK is REAL array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function zlanhp (character norm, character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) work)¶
ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.
Purpose:
ZLANHP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
complex hermitian matrix A, supplied in packed form.
Returns
ZLANHP = ( 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 ZLANHP as described
above.
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
hermitian matrix A is supplied.
= 'U': Upper triangular part of A is supplied
= 'L': Lower triangular part of A is supplied
N
N is INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANHP is
set to zero.
AP
AP is COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function zlansp (character norm, character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) work)¶
ZLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
Purpose:
ZLANSP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
complex symmetric matrix A, supplied in packed form.
Returns
ZLANSP = ( 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 ZLANSP as described
above.
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is supplied.
= 'U': Upper triangular part of A is supplied
= 'L': Lower triangular part of A is supplied
N
N is INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANSP is
set to zero.
AP
AP is COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric 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.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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