CLANTR(3F) CLANTR(3F)
CLANTR - return the value of the one norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a trapezoidal
or triangular matrix A
REAL FUNCTION CLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK )
CHARACTER DIAG, NORM, UPLO
INTEGER LDA, M, N
REAL WORK( * )
COMPLEX A( LDA, * )
CLANTR returns the value of the one norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a
trapezoidal or triangular matrix A.
CLANTR returns the value
CLANTR = ( 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 CLANTR as described above.
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower trapezoidal. =
'U': Upper trapezoidal
= 'L': Lower trapezoidal Note that A is triangular instead of
trapezoidal if M = N.
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A has unit diagonal. = 'N':
Non-unit diagonal
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CLANTR(3F) CLANTR(3F)
= 'U': Unit diagonal
M (input) INTEGER
The number of rows of the matrix A. M >= 0, and if UPLO = 'U', M
<= N. When M = 0, CLANTR is set to zero.
N (input) INTEGER
The number of columns of the matrix A. N >= 0, and if UPLO =
'L', N <= M. When N = 0, CLANTR is set to zero.
A (input) COMPLEX array, dimension (LDA,N)
The trapezoidal matrix A (A is triangular if M = N). If UPLO =
'U', the leading m by n upper trapezoidal part of the array A
contains the upper trapezoidal matrix, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading m by n lower trapezoidal part of the array A contains the
lower trapezoidal matrix, and the strictly upper triangular part
of A is not referenced. Note that when DIAG = 'U', the diagonal
elements of A are not referenced and are assumed to be one.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(M,1).
WORK (workspace) REAL array, dimension (LWORK),
where LWORK >= M when NORM = 'I'; otherwise, WORK is not
referenced.
CLANTR(3F) CLANTR(3F)
CLANTR - return the value of the one norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a trapezoidal
or triangular matrix A
REAL FUNCTION CLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK )
CHARACTER DIAG, NORM, UPLO
INTEGER LDA, M, N
REAL WORK( * )
COMPLEX A( LDA, * )
CLANTR returns the value of the one norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a
trapezoidal or triangular matrix A.
CLANTR returns the value
CLANTR = ( 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 CLANTR as described above.
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower trapezoidal. =
'U': Upper trapezoidal
= 'L': Lower trapezoidal Note that A is triangular instead of
trapezoidal if M = N.
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A has unit diagonal. = 'N':
Non-unit diagonal
Page 1
CLANTR(3F) CLANTR(3F)
= 'U': Unit diagonal
M (input) INTEGER
The number of rows of the matrix A. M >= 0, and if UPLO = 'U', M
<= N. When M = 0, CLANTR is set to zero.
N (input) INTEGER
The number of columns of the matrix A. N >= 0, and if UPLO =
'L', N <= M. When N = 0, CLANTR is set to zero.
A (input) COMPLEX array, dimension (LDA,N)
The trapezoidal matrix A (A is triangular if M = N). If UPLO =
'U', the leading m by n upper trapezoidal part of the array A
contains the upper trapezoidal matrix, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading m by n lower trapezoidal part of the array A contains the
lower trapezoidal matrix, and the strictly upper triangular part
of A is not referenced. Note that when DIAG = 'U', the diagonal
elements of A are not referenced and are assumed to be one.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(M,1).
WORK (workspace) REAL array, dimension (LWORK),
where LWORK >= M when NORM = 'I'; otherwise, WORK is not
referenced.
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