Migrating a Linear Algebra Operation Library (LAPACK)

Replaceability

The external interfaces provided by KML_LAPACK are the same as those provided by MKL_LAPACK in terms of interface parameters and function names, and can be directly replaced.

Table 1 describes the mapping between alternative interfaces and Fortran interfaces of MKL_LAPACK. Only optimized interfaces are provided.

**Table 1** LAPACK replacement mapping
MKL Interface	KML Interface	Data Type	Description
?getrf	?getrf	s, d, c, z	Computes the LU factorization of matrix A.
?geqrf	?geqrf	s, d, c, z	Computes the QR factorization of a matrix.
?gerqf	?gerqf	s, d, c, z	Computes the RQ factorization of a matrix.
?geqlf	?geqlf	s, d, c, z	Computes the QL factorization of a matrix.
?gelqf	?gelqf	s, d, c, z	Computes the LQ factorization of a matrix.
?ppsv	?ppsv	s, d, c, z	Computes the Cholesky factorization of matrix A and solves a system of linear equations based on the factorization result.
?ptsv	?ptsv	s, d, c, z	Solves a system of linear equations, in which the coefficient matrix A is a conjugate symmetric positive definite tridiagonal matrix.
?getri	?getri	s, d, c, z	Computes the inverse matrix based on the LU factorization result obtained using ?getrf.
?syevd	?syevd	s, d	Computes all the eigenvalues and eigenvectors of a symmetric (Hermitian) matrix.
?heevd	?heevd	c, z	Computes all the eigenvalues and eigenvectors of a symmetric (Hermitian) matrix.
?sytrd	?sytrd	s, d	Transforms a symmetric matrix to a symmetric tridiagonal matrix by means of similarity transformation.
?hetrd	?hetrd	c, z	Transforms a Hermitian matrix to a symmetric tridiagonal matrix by means of similarity transformation.
?potrf	?potrf	s, d, c, z	Computes the Cholesky factorization of a symmetric positive definite matrix or Hermitian positive definite matrix.
?pttrf	?pttrf	s, d, c, z	Computes the LDL^* or U^*DU factorization of a real (conjugate) symmetric positive definite tridiagonal matrix A
?potri	?potri	s, d, c, z	Computes the inverse of a symmetric positive definite matrix.
?gesv	?gesv	s, d, c, z	Solves a system of linear equations , where is an matrix. and are matrices.
?orglq	?orglq	s, d	Generates a real or complex matrix Q with orthonormal rows. The matrix is defined as the first M rows of the product of K N-order elementary reflectors.
?unglq	?unglq	c, z	Generates a real or complex matrix Q with orthonormal rows. The matrix is defined as the first M rows of the product of K N-order elementary reflectors.
?ormlq	?ormlq	s, d	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by calling ?gelqf.
?unmlq	?unmlq	c, z	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by calling ?gelqf.
?orgql	?orgql	s, d	Generates a real or complex matrix Q with orthonormal columns. The matrix is defined as the first N columns of the product of K M-order elementary reflectors.
?ungql	?ungql	c, z	Generates a real or complex matrix Q with orthonormal columns. The matrix is defined as the first N columns of the product of K M-order elementary reflectors.
?ormql	?ormql	s, d	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by calling ?geqlf.
?unmql	?unmql	c, z	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by calling ?geqlf.
?orgqr	?orgqr	s, d	Generates a real or complex matrix Q with orthonormal rows. The matrix is defined as the first M rows of the product of K N-order elementary reflectors.
?ungqr	?ungqr	c, z	Generates a real or complex matrix Q with orthonormal rows. The matrix is defined as the first M rows of the product of K N-order elementary reflectors.
?orgrq	?orgrq	s, d	Generates a real or complex matrix Q with orthonormal rows. The matrix is defined as the first M rows of the product of K N-order elementary reflectors.
?ungrq	?ungrq	c, z	Generates a real or complex matrix Q with orthonormal rows. The matrix is defined as the first M rows of the product of K N-order elementary reflectors.
?ormrq	?ormrq	s, d	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by calling ?gerqf.
?unmrq	?unmrq	c, z	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by calling ?gerqf.
?ormqr	?ormqr	s, d	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by calling ?geqrf.
?unmqr	?unmqr	c, z	Computes $\text{[math]}$ or $\text{[math]}$ , where Q is returned by calling ?geqrf.
?syev	?syev	s, d	Computes all the eigenvalues and eigenvectors of a symmetric (Hermitian) matrix.
?heev	?heev	c, z	Computes all the eigenvalues and eigenvectors of a symmetric (Hermitian) matrix.
?pttrs	?pttrs	s, d, c, z	Solves the tridiagonal equation AX = B, where the coefficient matrix A is the ?pttrf factorization result.
?ptts2	?ptts2	s, d, c, z	Solves the tridiagonal equation AX = B, where the coefficient matrix A is the ?pttrf factorization result.
?lasr	?lasr	s, d, c, z	Performs a plane rotation operation on matrix A.
?gtsv	?gtsv	s, d, c, z	Solves the system of linear equations A X = B*, where A is a general tridiagonal coefficient matrix.
?gttrf	?gttrf	s, d, c, z	Computes the LU factorization of general tridiagonal matrix A.
?gttrs	?gttrs	s, d, c, z	Solves the tridiagonal equation A X = B, A^T X = B, or A^H * X = B, where coefficient matrix A is the ?gttrf factorization result.
?sytrd_2stage	?sytrd_2stage	s, d, c, z	Transforms a symmetric or Hermitian matrix A to a symmetric or Hermitian tridiagonal matrix T.
?trtrs	?trtrs	s, d, c, z	Solves the trigonometric equation A X = B* or A^T * X = B.
?laset	?laset	s, d, c, z	Initializes an m n* matrix and sets the diagonal elements to beta and the non-diagonal elements to alpha.
?sptrf	?sptrf	s, d, c, z	Computes the LDL^* or U*DU factorization of a packed symmetric matrix.
?hptrf	?hptrf	s, d, c, z	Computes the LDL^* or U*DU factorization of a packed Hermitian matrix.
?pptrf	?pptrf	s, d, c, z	Computes the LLT or UTU factorization of a symmetric positive definite matrix in packed format.
?pptrs	?pptrs	s, d, c, z	Solves the tridiagonal equation A X = B, A^T X = B, or A^H * X = B. The coefficient matrix A is obtained by calling ?gttrf.
?pptri	?pptri	s, d, c, z	Computes the inverse matrix of a symmetric positive definite matrix stored in packed format.
?getrs	?getrs	s, d, c, z	Solves the general linear equation A X = B, A^T X = B, or A^H * X = B. The coefficient matrix A is obtained by calling ?getrf.
?posv	?posv	s, d, c, z	Solves the system of linear equations , where A is an positive definite matrix of real symmetry or conjugate symmetry, and X and B are matrices.
?trtri	?trtri	s, d, c, z	Computes the inverse matrix of an upper/lower triangular matrix.
?laswp	?laswp	s, d, c, z	Performs a series of row exchange operations on a matrix.
?lascl	?lascl	s, d, c, z	Performs scalar operations on a matrix.
?lange	?lange	s, d, c, z	Computes the norms of a matrix, including 1-norm, F-norm, and infinite norm.
?sgesv	?gesv	ds, zc	Solves a system of linear equations , where is an matrix. and are matrices.
?gels	?gels	s, d, c, z	Uses QR or LQ factorization to solve an overdetermined or underdetermined linear system with full rank matrix.
?gelsd	?gelsd	s, d, c, z	Computes the minimum-norm solution to a linear least squares problem using a divide and conquer method.
?gelss	?gelss	s, d, c, z	Computes the minimum-norm solution to a linear least squares problem using SVD.
?steqr	?steqr	s, d, c, z	Computes the eigenvalues and eigenvectors of a symmetric tridiagonal matrix through QL or QR factorization.
?gtts2	?gtts2	s, d, c, z	Solves the tridiagonal equation A X = B, A^T X = B, or A^H * X = B, where coefficient matrix A is the ?gttrf factorization result.
?ormbr	?ormbr	s, d	Computes C = Q * C, Q^T * C, C * Q, C * Q^T, C = P * C, P^T * C, C * P, or C * P^T.
?unmbr	?unmbr	c, z	Computes C = Q * C, Q^T * C, C * Q, C * Q^T, C = P * C, P^T * C, C * P, or C * P^T.
?orgtr	?orgtr	s, d	Generates an orthogonal matrix Q through reflector factors computed by a call to SYTRD.
?ungtr	?ungtr	c, z	Generates an orthogonal matrix Q through reflector factors computed by a call to SYTRD.
?lacpy	?lacpy	s, d, c, z	Copies all or some elements of matrix A to matrix B.
?stedc	?stedc	s, d, c, z	Computes the eigenvalues of a symmetric tridiagonal matrix using the Divide-and-Conquer algorithm.
?gesvd	?gesvd	s, d, c, z	Performs singular value decomposition (SVD) on a general matrix.
?gebrd	?gebrd	s, d, c, z	Transforms a general matrix to a bidiagonal matrix.
?bdsdc	?bdsdc	s, d	Computes SVD of an N*N upper/lower bidiagonal matrix B using a divide and conquer algorithm.
?gesdd	?gesdd	s, d, c, z	Computes SVD of a rectangular matrix using a divide and conquer algorithm to compute left and right singular vectors.
?bdsqr	?bdsqr	s, d, c, z	Solves singular values or left and right singular vectors using SVD of the QR algorithm for a bidiagonal matrix.

The preceding interfaces are Fortran interfaces. When using them in the C language, add an underscore (_) to the end of the interface name, and ensure that the parameter type is pointer. For details, see "Kunpeng Math Library Developer Guide" > "Applied Math Libraries" > "KML_LAPACK Library Functions" > "Function Syntax" in Kunpeng HPCKit 26.1.RC1 Developer Guide.

To use the LAPACKE interfaces (standard C interfaces in MKL), you need to add the compilation of the LAPACKE encapsulation library when compiling the open-source Netlib LAPACK. For details, see Migrating the C-based Library.

Migrating the C-based Library

MKL_LAPACK provides Fortran and LAPACK (encapsulated in the C language) interfaces. The Fortran interfaces provided by KML_LAPACK are the same as those provided by MKL. When the C language is used, replace the header file #include "mkl.h" with #include "klapack.h".

Example:

Use the Fortran interface before the migration:

/* Declare the dgetrf interface */
void dgetrf_(int *m, int *n, double *a, int *lda, int *ipiv, int *info);
......
    int m = 4;
    int n = 4;
    int lda = 4;
    int ipiv[4];
    int info = 0;
    double a[] = {1.80,  5.25,  1.58, -1.11,
                    2.88, -2.95, -2.69, -0.66,
                    2.05, -0.95, -2.90, -0.59,
                    -0.89, -3.80, -1.04,  0.80};
    dgetrf_(&m, &n, a, &lda, ipiv, &info);

Use the LAPACKE interface before the migration:

#include "mkl.h"
......
    int m = 4;
    int n = 4;
    int lda = 4;
    int ipiv[4];
    double a[] = {1.80,  5.25,  1.58, -1.11,
                    2.88, -2.95, -2.69, -0.66,
                    2.05, -0.95, -2.90, -0.59,
                    -0.89, -3.80, -1.04,  0.80};
    int info = LAPACKE_dgetrf(LAPACK_COL_MAJOR, m, n, a, lda, ipiv);

Use the Fortran interface of KML_LAPACK after the migration:

#include "klapack.h"
......
    int m = 4;
    int n = 4;
    int lda = 4;
    int ipiv[4];
    int info = 0;
    double a[] = {1.80,  5.25,  1.58, -1.11,
                    2.88, -2.95, -2.69, -0.66,
                    2.05, -0.95, -2.90, -0.59,
                    -0.89, -3.80, -1.04,  0.80};
    dgetrf_(&m, &n, a, &lda, ipiv, &info);

Similar to the Fortran interface of MKL, the C function declaration of the Fortran interface can be obtained by including klapack.h.

Migrating the Fortran-based Library

The Fortran interfaces are the same as those of MKL. The code does not need to be modified.