?lantr

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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?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

float LAPACKE_slantr (char * norm, char * uplo, char * diag, lapack_int * m, lapack_int * n, const float * a, lapack_int * lda, float * work);

double LAPACKE_dlantr (char * norm, char * uplo, char * diag, lapack_int * m, lapack_int * n, const double * a, lapack_int * lda, double * work);

float LAPACKE_clantr (char * norm, char * uplo, char * diag, lapack_int * m, lapack_int * n, const lapack_complex_float * a, lapack_int * lda, float * work);

double LAPACKE_zlantr (char * norm, char * uplo, char * diag, lapack_int * m, lapack_int * n, const lapack_complex_double * a, lapack_int * lda, double * work);

Include Files

mkl.h

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

A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.

norm

Specifies the value to be returned by the routine:

= 'M' or 'm': val = max(abs(A_ij)), 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

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

Specifies whether or not the matrix A has unit diagonal.

= 'N': Non-unit diagonal

= 'U': Unit diagonal.

m

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

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

Array, size at least max(1, lda*n) for column major and max(1, lda*m) for row major layout.

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

The leading dimension of the array a.

lda≥ max(m,1)for column major layout and ≥max(1,n) for row major layout.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?lantr