# lanhe - Man Page

lan{he,sy}: Hermitian/symmetric matrix

## Synopsis

### Functions

real function **clanhe** (norm, uplo, n, a, lda, work)**CLANHE** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.

real function **clansy** (norm, uplo, n, a, lda, work)**CLANSY** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix.

double precision function **dlansy** (norm, uplo, n, a, lda, work)**DLANSY** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.

real function **slansy** (norm, uplo, n, a, lda, work)**SLANSY** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.

double precision function **zlanhe** (norm, uplo, n, a, lda, work)**ZLANHE** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.

double precision function **zlansy** (norm, uplo, n, a, lda, work)**ZLANSY** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix.

## Detailed Description

## Function Documentation

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

**CLANHE** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.

**Purpose:**

CLANHE 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 hermitian matrix A.

**Returns**CLANHE

CLANHE = ( 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 CLANHE as described above.

*UPLO*UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the hermitian matrix A is to be referenced. = 'U': Upper triangular part of A is referenced = 'L': Lower triangular part of A is referenced

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

*A*A is COMPLEX array, dimension (LDA,N) The hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.

*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' or '1' or 'O'; otherwise, WORK is not referenced.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **123** of file **clanhe.f**.

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

**CLANSY** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix.

**Purpose:**

CLANSY 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 symmetric matrix A.

**Returns**CLANSY

CLANSY = ( 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 CLANSY as described above.

*UPLO*UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced. = 'U': Upper triangular part of A is referenced = 'L': Lower triangular part of A is referenced

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

*A*A is COMPLEX array, dimension (LDA,N) The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A 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' or '1' or 'O'; otherwise, WORK is not referenced.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **122** of file **clansy.f**.

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

**DLANSY** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.

**Purpose:**

DLANSY 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 symmetric matrix A.

**Returns**DLANSY

DLANSY = ( 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 DLANSY as described above.

*UPLO*UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced. = 'U': Upper triangular part of A is referenced = 'L': Lower triangular part of A is referenced

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

*A*A is DOUBLE PRECISION array, dimension (LDA,N) The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A 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' or '1' or 'O'; otherwise, WORK is not referenced.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **121** of file **dlansy.f**.

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

**SLANSY** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.

**Purpose:**

SLANSY 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 symmetric matrix A.

**Returns**SLANSY

SLANSY = ( 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 SLANSY as described above.

*UPLO*UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced. = 'U': Upper triangular part of A is referenced = 'L': Lower triangular part of A is referenced

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

*A*A is REAL array, dimension (LDA,N) The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A 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' or '1' or 'O'; otherwise, WORK is not referenced.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **121** of file **slansy.f**.

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

**ZLANHE** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.

**Purpose:**

ZLANHE 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 hermitian matrix A.

**Returns**ZLANHE

ZLANHE = ( 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 ZLANHE as described above.

*UPLO*UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the hermitian matrix A is to be referenced. = 'U': Upper triangular part of A is referenced = 'L': Lower triangular part of A is referenced

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

*A*A is COMPLEX*16 array, dimension (LDA,N) The hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.

*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' or '1' or 'O'; otherwise, WORK is not referenced.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **123** of file **zlanhe.f**.

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

**ZLANSY** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix.

**Purpose:**

ZLANSY 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 symmetric matrix A.

**Returns**ZLANSY

ZLANSY = ( 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 ZLANSY as described above.

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

*A*A is COMPLEX*16 array, dimension (LDA,N) The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A 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' or '1' or 'O'; otherwise, WORK is not referenced.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **122** of file **zlansy.f**.

## Author

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