---
name: "dlantr"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dlantr/3lapack"
---

# dlantr(3lapack)

returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A

## NAME

DLANTR - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A

## SYNOPSIS

- DOUBLE PRECISION

  FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK )

- CHARACTER

  DIAG, NORM, UPLO

- INTEGER

  LDA, M, N

- DOUBLE

  PRECISION A( LDA, \* ), WORK( \* )

## PURPOSE

DLANTR  returns the value of the one norm,  or the Frobenius norm, or the  infinity norm,  or the  element of  largest absolute value  of a trapezoidal or triangular matrix A.

## DESCRIPTION

DLANTR returns the value\
\
    DLANTR = ( 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.

## ARGUMENTS

- NORM (input) CHARACTER\*1

  Specifies the value to be returned in DLANTR as described above.

- UPLO (input) 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 (input) CHARACTER\*1

  Specifies whether or not the matrix A has unit diagonal. = 'N':  Non-unit diagonal\
   \= 'U':  Unit diagonal

- M (input) INTEGER

  The number of rows of the matrix A.  M \>= 0, and if UPLO = 'U', M \<= N.  When M = 0, DLANTR is set to zero.

- N (input) INTEGER

  The number of columns of the matrix A.  N \>= 0, and if UPLO = 'L', N \<= M.  When N = 0, DLANTR is set to zero.

- A (input) DOUBLE PRECISION 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 (input) INTEGER

  The leading dimension of the array A.  LDA \>= max(M,1).

- WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),

  where LWORK \>= M when NORM = 'I'; otherwise, WORK is not referenced.