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lange(3) Library Functions Manual 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 

!>
!>    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 

!>          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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 114 of file clange.f.

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 

!>
!>    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 

!>          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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 113 of file dlange.f.

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 

!>
!>    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 

!>          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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 113 of file slange.f.

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 

!>
!>    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 

!>          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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 114 of file zlange.f.

Author

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