# lanht - Man Page

lan{ht,st}: Hermitian/symmetric matrix, tridiagonal

## Synopsis

### Functions

real function **clanht** (norm, n, d, e)**CLANHT** 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 tridiagonal matrix.

double precision function **dlanst** (norm, n, d, e)**DLANST** 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 tridiagonal matrix.

real function **slanst** (norm, n, d, e)**SLANST** 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 tridiagonal matrix.

double precision function **zlanht** (norm, n, d, e)**ZLANHT** 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 tridiagonal matrix.

## Detailed Description

## Function Documentation

### real function clanht (character norm, integer n, real, dimension( * ) d, complex, dimension( * ) e)

**CLANHT** 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 tridiagonal matrix.

**Purpose:**

CLANHT 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 tridiagonal matrix A.

**Returns**CLANHT

CLANHT = ( 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 CLANHT as described above.

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

*D*D is REAL array, dimension (N) The diagonal elements of A.

*E*E is COMPLEX array, dimension (N-1) The (n-1) sub-diagonal or super-diagonal elements of A.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **100** of file **clanht.f**.

### double precision function dlanst (character norm, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e)

**DLANST** 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 tridiagonal matrix.

**Purpose:**

DLANST 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 tridiagonal matrix A.

**Returns**DLANST

DLANST = ( 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 DLANST as described above.

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

*D*D is DOUBLE PRECISION array, dimension (N) The diagonal elements of A.

*E*E is DOUBLE PRECISION array, dimension (N-1) The (n-1) sub-diagonal or super-diagonal elements of A.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **99** of file **dlanst.f**.

### real function slanst (character norm, integer n, real, dimension( * ) d, real, dimension( * ) e)

**SLANST** 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 tridiagonal matrix.

**Purpose:**

SLANST 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 tridiagonal matrix A.

**Returns**SLANST

SLANST = ( 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 SLANST as described above.

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

*D*D is REAL array, dimension (N) The diagonal elements of A.

*E*E is REAL array, dimension (N-1) The (n-1) sub-diagonal or super-diagonal elements of A.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **99** of file **slanst.f**.

### double precision function zlanht (character norm, integer n, double precision, dimension( * ) d, complex*16, dimension( * ) e)

**ZLANHT** 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 tridiagonal matrix.

**Purpose:**

ZLANHT 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 tridiagonal matrix A.

**Returns**ZLANHT

ZLANHT = ( 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 ZLANHT as described above.

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

*D*D is DOUBLE PRECISION array, dimension (N) The diagonal elements of A.

*E*E is COMPLEX*16 array, dimension (N-1) The (n-1) sub-diagonal or super-diagonal elements of A.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **100** of file **zlanht.f**.

## Author

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