table of contents
| lantr(3) | LAPACK | lantr(3) |
NAME¶
lantr - lantr: triangular matrix
SYNOPSIS¶
Functions¶
real function clantr (norm, uplo, diag, m, n, a, lda, work)
CLANTR returns the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a trapezoidal or
triangular matrix. double precision function dlantr (norm, uplo,
diag, m, n, a, lda, work)
DLANTR returns the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a trapezoidal or
triangular matrix. real function slantr (norm, uplo, diag, m, n, a,
lda, work)
SLANTR returns the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a trapezoidal or
triangular matrix. double precision function zlantr (norm, uplo,
diag, m, n, a, lda, work)
ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a trapezoidal or
triangular matrix.
Detailed Description¶
Function Documentation¶
real function clantr (character norm, character uplo, character diag, integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work)¶
CLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
Purpose:
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.
Returns
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 consistent matrix norm.
Parameters
NORM is CHARACTER*1
Specifies the value to be returned in CLANTR as described
above.
UPLO
UPLO is 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
DIAG is CHARACTER*1
Specifies whether or not the matrix A has unit diagonal.
= 'N': Non-unit diagonal
= 'U': Unit diagonal
M
M is 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
N is 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
A is 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(M,1).
WORK
WORK is REAL array, dimension (MAX(1,LWORK)),
where LWORK >= M when NORM = 'I'; otherwise, WORK is not
referenced.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function dlantr (character norm, character uplo, character diag, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)¶
DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
Purpose:
DLANTR 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.
Returns
DLANTR = ( 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 DLANTR as described
above.
UPLO
UPLO is 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
DIAG is CHARACTER*1
Specifies whether or not the matrix A has unit diagonal.
= 'N': Non-unit diagonal
= 'U': Unit diagonal
M
M is INTEGER
The number of rows of the matrix A. M >= 0, and if
UPLO = 'U', M <= N. When M = 0, DLANTR is set to zero.
N
N is INTEGER
The number of columns of the matrix A. N >= 0, and if
UPLO = 'L', N <= M. When N = 0, DLANTR is set to zero.
A
A is DOUBLE PRECISION 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(M,1).
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= M when NORM = 'I'; otherwise, WORK is not
referenced.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
real function slantr (character norm, character uplo, character diag, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work)¶
SLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
Purpose:
SLANTR 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.
Returns
SLANTR = ( 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 SLANTR as described
above.
UPLO
UPLO is 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
DIAG is CHARACTER*1
Specifies whether or not the matrix A has unit diagonal.
= 'N': Non-unit diagonal
= 'U': Unit diagonal
M
M is INTEGER
The number of rows of the matrix A. M >= 0, and if
UPLO = 'U', M <= N. When M = 0, SLANTR is set to zero.
N
N is INTEGER
The number of columns of the matrix A. N >= 0, and if
UPLO = 'L', N <= M. When N = 0, SLANTR is set to zero.
A
A is REAL 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(M,1).
WORK
WORK is REAL array, dimension (MAX(1,LWORK)),
where LWORK >= M when NORM = 'I'; otherwise, WORK is not
referenced.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function zlantr (character norm, character uplo, character diag, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)¶
ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
Purpose:
ZLANTR 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.
Returns
ZLANTR = ( 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 ZLANTR as described
above.
UPLO
UPLO is 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
DIAG is CHARACTER*1
Specifies whether or not the matrix A has unit diagonal.
= 'N': Non-unit diagonal
= 'U': Unit diagonal
M
M is INTEGER
The number of rows of the matrix A. M >= 0, and if
UPLO = 'U', M <= N. When M = 0, ZLANTR is set to zero.
N
N is INTEGER
The number of columns of the matrix A. N >= 0, and if
UPLO = 'L', N <= M. When N = 0, ZLANTR is set to zero.
A
A is COMPLEX*16 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(M,1).
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= M when NORM = 'I'; otherwise, WORK is not
referenced.
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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