# ?lantr

Returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.

## Syntax

val = slantr( norm, uplo, diag, m, n, a, lda, work )

val = dlantr( norm, uplo, diag, m, n, a, lda, work )

val = clantr( norm, uplo, diag, m, n, a, lda, work )

val = zlantr( norm, uplo, diag, m, n, a, lda, work )

• mkl.fi

## Description

The function ?lantr returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A.

## Input Parameters

The data types are given for the Fortran interface.

norm

CHARACTER*1. Specifies the value to be returned by the routine:

= 'M' or 'm': `val = max(abs(Aij))`, largest absolute value of the matrix A.

= '1' or 'O' or 'o': `val = norm1(A)`, 1-norm of the matrix A (maximum column sum),

= 'I' or 'i': `val = normI(A)`, infinity norm of the matrix A (maximum row sum),

= 'F', 'f', 'E' or 'e': `val = normF(A)`, Frobenius norm of the matrix A (square root of sum of squares).

uplo

CHARACTER*1.

Specifies whether the matrix A is upper or lower trapezoidal.

= 'U': Upper trapezoidal

= 'L': Lower trapezoidal.

Note that A is triangular instead of trapezoidal if `m = n`.

diag

CHARACTER*1.

Specifies whether or not the matrix A has unit diagonal.

= 'N': Non-unit diagonal

= 'U': Unit diagonal.

m

INTEGER. The number of rows of the matrix A. `m ≥ 0`, and if `uplo = 'U'`, `m ≤ n`.

When `m = 0`, ?lantr is set to zero.

n

INTEGER. The number of columns of the matrix A. `n ≥ 0`, and if `uplo = 'L'`, `n ≤ m`.

When `n = 0`, ?lantr is set to zero.

a

REAL for slantr

DOUBLE PRECISION for dlantr

COMPLEX for clantr

DOUBLE COMPLEX for zlantr

Array, DIMENSION (lda,n).

The trapezoidal matrix A (A is triangular if `m = n)`.

If `uplo = 'U'`, the leading m-by-n upper trapezoidal part of the array a contains the upper trapezoidal matrix, and the strictly lower triangular part of A is not referenced.

If `uplo = 'L'`, the leading m-by-n lower trapezoidal part of the array a contains the lower trapezoidal matrix, and the strictly upper triangular part of A is not referenced. Note that when `diag = 'U'`, the diagonal elements of A are not referenced and are assumed to be one.

lda

INTEGER. The leading dimension of the array a.

`lda ≥ max(m,1)`.

work

REAL for slantr/clantrp.

DOUBLE PRECISION for dlantr/zlantr.

Workspace array, DIMENSION `(max(1,lwork))`, where

`lwork ≥ m` when `norm = 'I'` ; otherwise, work is not referenced.

## Output Parameters

val

REAL for slantr/clantrp.

DOUBLE PRECISION for dlantr/zlantr.

Value returned by the function.

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