# lange - Man Page

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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