# lanhs - Man Page

lanhs: Hessenberg

## Synopsis

### Functions

real function **clanhs** (norm, n, a, lda, work)**CLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

double precision function **dlanhs** (norm, n, a, lda, work)**DLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

real function **slanhs** (norm, n, a, lda, work)**SLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

double precision function **zlanhs** (norm, n, a, lda, work)**ZLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

## Detailed Description

## Function Documentation

### real function clanhs (character norm, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work)

**CLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

**Purpose:**

CLANHS returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A.

**Returns**CLANHS

CLANHS = ( 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 CLANHS as described above.

*N*N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANHS is set to zero.

*A*A is COMPLEX array, dimension (LDA,N) The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).

*WORK*WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N 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 **108** of file **clanhs.f**.

### double precision function dlanhs (character norm, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)

**DLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

**Purpose:**

DLANHS returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A.

**Returns**DLANHS

DLANHS = ( 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 DLANHS as described above.

*N*N is INTEGER The order of the matrix A. N >= 0. When N = 0, DLANHS is set to zero.

*A*A is DOUBLE PRECISION array, dimension (LDA,N) The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).

*WORK*WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N 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 **107** of file **dlanhs.f**.

### real function slanhs (character norm, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work)

**SLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

**Purpose:**

SLANHS returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A.

**Returns**SLANHS

SLANHS = ( 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 SLANHS as described above.

*N*N is INTEGER The order of the matrix A. N >= 0. When N = 0, SLANHS is set to zero.

*A*A is REAL array, dimension (LDA,N) The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).

*WORK*WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N 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 **107** of file **slanhs.f**.

### double precision function zlanhs (character norm, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)

**ZLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

**Purpose:**

ZLANHS returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A.

**Returns**ZLANHS

ZLANHS = ( 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 ZLANHS as described above.

*N*N is INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANHS is set to zero.

*A*A is COMPLEX*16 array, dimension (LDA,N) The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).

*WORK*WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N 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 **108** of file **zlanhs.f**.

## Author

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