table of contents
| lange(3) | LAPACK | lange(3) |
NAME¶
lange - lange: general matrix
SYNOPSIS¶
Functions¶
real function clange (norm, m, n, a, lda, work)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element of a general rectangular
matrix. double precision function dlange (norm, m, n, a, lda, work)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element of a general rectangular
matrix. real function slange (norm, m, n, a, lda, work)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element of a general rectangular
matrix. double precision function zlange (norm, m, n, a, lda, work)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element of a general rectangular
matrix.
Detailed Description¶
Function Documentation¶
real function clange (character norm, integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work)¶
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.
Purpose:
CLANGE 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 matrix A.
Returns
CLANGE = ( 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 CLANGE as described
above.
M
M is INTEGER
The number of rows of the matrix A. M >= 0. When M = 0,
CLANGE is set to zero.
N
N is INTEGER
The number of columns of the matrix A. N >= 0. When N = 0,
CLANGE is set to zero.
A
A is COMPLEX array, dimension (LDA,N)
The m by n matrix A.
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 dlange (character norm, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)¶
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.
Purpose:
DLANGE 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 matrix A.
Returns
DLANGE = ( 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 DLANGE as described
above.
M
M is INTEGER
The number of rows of the matrix A. M >= 0. When M = 0,
DLANGE is set to zero.
N
N is INTEGER
The number of columns of the matrix A. N >= 0. When N = 0,
DLANGE is set to zero.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
The m by n matrix A.
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 slange (character norm, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work)¶
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.
Purpose:
SLANGE 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 matrix A.
Returns
SLANGE = ( 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 SLANGE as described
above.
M
M is INTEGER
The number of rows of the matrix A. M >= 0. When M = 0,
SLANGE is set to zero.
N
N is INTEGER
The number of columns of the matrix A. N >= 0. When N = 0,
SLANGE is set to zero.
A
A is REAL array, dimension (LDA,N)
The m by n matrix A.
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 zlange (character norm, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)¶
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.
Purpose:
ZLANGE 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 matrix A.
Returns
ZLANGE = ( 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 ZLANGE as described
above.
M
M is INTEGER
The number of rows of the matrix A. M >= 0. When M = 0,
ZLANGE is set to zero.
N
N is INTEGER
The number of columns of the matrix A. N >= 0. When N = 0,
ZLANGE is set to zero.
A
A is COMPLEX*16 array, dimension (LDA,N)
The m by n matrix A.
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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