# ?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 )

## 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

norm

  CHARACTER*1. Specifies the vaule 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

  COMPLEX*16 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.

Parent topic: Auxiliary Routines