mkl_?potrf_compact

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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mkl_?potrf_compact

Computes the Cholesky factorization of a set of symmetric (Hermitian), positive-definite matrices, stored in Compact format (see Compact Format for details).

Syntax

void mkl_spotrf_compact (MKL_LAYOUT layout, MKL_UPLO uplo, MKL_INT n, float * ap, MKL_INT ldap, MKL_INT * info, MKL_COMPACT_PACK format, MKL_INT nm);

void mkl_cpotrf_compact (MKL_LAYOUT layout, MKL_UPLO uplo, MKL_INT n, float * ap, MKL_INT ldap, MKL_INT * info, MKL_COMPACT_PACK format, MKL_INT nm);

void mkl_dpotrf_compact (MKL_LAYOUT layout, MKL_UPLO uplo, MKL_INT n, double * ap, MKL_INT ldap, MKL_INT * info, MKL_COMPACT_PACK format, MKL_INT nm);

void mkl_zpotrf_compact (MKL_LAYOUT layout, MKL_UPLO uplo, MKL_INT n, double * ap, MKL_INT ldap, MKL_INT * info, MKL_COMPACT_PACK format, MKL_INT nm);

Description

The routine forms the Cholesky factorization of a set of symmetric, positive definite (or, for complex data, Hermitian, positive-definite), n x n matrices A_c, stored in Compact format, as:

A_c = U_c^T*U_c (for real data), A_c = U_c^H*U_c (for complex data), if uplo = MKL_UPPER
A_c = L_c*L_c^T (for real data), A_c = L_c*L_c^H (for complex data), if uplo = MKL_LOWER

where L_c is a lower triangular matrix, and U_c is upper triangular. The factorization (output) data will also be stored in Compact format.

Before calling this routine, call mkl_?gepack_compact to store the matrices in the Compact format.

NOTE:

Compact routines have some limitations; see Numerical Limitations.

Input Parameters

layout

Specifies whether two-dimensional array storage is row-major (MKL_ROW_MAJOR) or column-major (MKL_COL_MAJOR).

uplo

Must be MKL_UPPER or MKL_LOWER

Indicates whether the upper or lower triangular part of A_c has been stored and will be factored.

If uplo = MKL_UPPER, the upper triangular part of A_c is stored, and the strictly lower triangular part of A_c is not referenced.

If uplo = MKL_LOWER, the lower triangular part of A_c is stored, and the strictly upper triangular part of A_c is not referenced.

n

The order of A_c; n >= 0.

ldap

Column stride (column-major layout) or row stride (row-major layout) of A_c.

ap

Points to the beginning of the nm A_c matrices. On entry, ap contains either the upper or the lower triangular part of A_c (see uplo).

format

Specifies the format of the compact matrices. See Compact Format or mkl_get_format_compact for details.

nm

Total number of matrices stored in Compact format; nm >= 0.

Application Notes:

Before calling this routine,mkl_?gepack_compact must be called. After calling this routine, mkl_?geunpack_compact should be called, unless another compact routine will be called for the Compact format matrices.

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

Output Parameters

ap: The upper or lower triangular part of A_c, stored in Compact format in ap, is overwritten by its Cholesky factor U_c or L_c (as specified by uplo). ap now points to the beginning of this set of factors, stored in Compact format.
info: The parameter is not currently used in this routine. It is reserved for the future use.

Parent topic: Compact BLAS and LAPACK Functions

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Developer Reference for Intel® oneAPI Math Kernel Library for C

mkl_?potrf_compact