lange(3) LAPACK lange(3)

lange - lange: general matrix


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.

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.

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.

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.

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.

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