?potrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 11/07/2023

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?potrf

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix.

Syntax

lapack_int LAPACKE_spotrf (int matrix_layout , char uplo , lapack_int n , float * a , lapack_int lda );

lapack_int LAPACKE_dpotrf (int matrix_layout , char uplo , lapack_int n , double * a , lapack_int lda );

lapack_int LAPACKE_cpotrf (int matrix_layout , char uplo , lapack_int n , lapack_complex_float * a , lapack_int lda );

lapack_int LAPACKE_zpotrf (int matrix_layout , char uplo , lapack_int n , lapack_complex_double * a , lapack_int lda );

Include Files

mkl.h

Description

The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix A:

`A = U^T* U` for real data, `A = U^H* U` for complex data	if `uplo='U'`
`A = LL^T` for real data, `A = LL^H` for complex data	if `uplo='L'`

where L is a lower triangular matrix and U is upper triangular.

NOTE:

This routine supports the Progress Routine feature. See Progress Function for details.

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

uplo

Must be 'U' or 'L'.

Indicates whether the upper or lower triangular part of A is stored and how A is factored:

If uplo = 'U', the array a stores the upper triangular part of the matrix A, and the strictly lower triangular part of the matrix is not referenced.

If uplo = 'L', the array a stores the lower triangular part of the matrix A, and the strictly upper triangular part of the matrix is not referenced.

n

Specifies the order of the matrix A. The value of n must be at least zero.

a

Array, size max(1, lda*n. The array a contains either the upper or the lower triangular part of the matrix A (see uplo).

lda

The leading dimension of a. Must be at least max(1, n).

Output Parameters

a: The upper or lower triangular part of a is overwritten by the Cholesky factor U or L, as specified by uplo.

Return Values

This function returns a value info.

If info=0, the execution is successful.

If info = -i, parameter i had an illegal value.

If info = i, the leading minor of order i (and therefore the matrix A itself) is not positive-definite, and the factorization could not be completed. This may indicate an error in forming the matrix A.

Application Notes

If uplo = 'U', the computed factor U is the exact factor of a perturbed matrix A + E, where

c(n) is a modest linear function of n, and ε is the machine precision.

A similar estimate holds for uplo = 'L'.

The total number of floating-point operations is approximately (1/3)n³ for real flavors or (4/3)n³ for complex flavors.

After calling this routine, you can call the following routines:

?potrs	to solve `A*X = B`
?pocon	to estimate the condition number of `A`
?potri	to compute the inverse of `A`.

Parent topic: Matrix Factorization: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?potrf

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

Application Notes

See Also