CLANTP(3F) CLANTP(3F)
CLANTP - return 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
REAL FUNCTION CLANTP( NORM, UPLO, DIAG, N, AP, WORK )
CHARACTER DIAG, NORM, UPLO
INTEGER N
REAL WORK( * )
COMPLEX AP( * )
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.
CLANTP returns the value
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 matrix norm.
NORM (input) CHARACTER*1
Specifies the value to be returned in CLANTP as described above.
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular. =
'U': Upper triangular
= 'L': Lower triangular
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular. = 'N':
Non-unit triangular
= 'U': Unit triangular
Page 1
CLANTP(3F) CLANTP(3F)
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANTP is set to
zero.
AP (input) 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 (workspace) REAL array, dimension (LWORK),
where LWORK >= N when NORM = 'I'; otherwise, WORK is not
referenced.
CLANTP(3F) CLANTP(3F)
CLANTP - return 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
REAL FUNCTION CLANTP( NORM, UPLO, DIAG, N, AP, WORK )
CHARACTER DIAG, NORM, UPLO
INTEGER N
REAL WORK( * )
COMPLEX AP( * )
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.
CLANTP returns the value
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 matrix norm.
NORM (input) CHARACTER*1
Specifies the value to be returned in CLANTP as described above.
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular. =
'U': Upper triangular
= 'L': Lower triangular
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular. = 'N':
Non-unit triangular
= 'U': Unit triangular
Page 1
CLANTP(3F) CLANTP(3F)
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, CLANTP is set to
zero.
AP (input) 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 (workspace) REAL array, dimension (LWORK),
where LWORK >= N when NORM = 'I'; otherwise, WORK is not
referenced.
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