algebra_linear 1.2.0

Pure-Rust BLAS, LAPACK, and sparse LU
Documentation 
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// Reference-LAPACK bindings for the reference-parity harness.
//
// Development only. `build.rs` compiles this file against a locally built LAPACK
// 3.12.1 when the `dev_lapack` feature is on; a normal build never sees it, and
// the crate ships no reference library.
//
// They call the reference's column-major C interface (`LAPACK_*`). Never use
// `LAPACKE_*`: it is the row-major API and would transpose every matrix, making
// the comparison meaningless.
//
// LAPACK is BSD-3-Clause; see LICENSE.

#include "reference.h"

// Only the reference is ever linked here, so the shim's library-selection macros
// collapse to the C-interface names.
#define FN_DGESV LAPACK_dgesv
#define FN_ZGESV LAPACK_zgesv
#define FN_DPOTRF LAPACK_dpotrf
#define FN_ZPOTRF LAPACK_zpotrf
#define FN_DSYEV LAPACK_dsyev
#define FN_DGEEV LAPACK_dgeev
#define FN_ZHEEV LAPACK_zheev
#define FN_DGESVD LAPACK_dgesvd
#define FN_DGETRF LAPACK_dgetrf
#define FN_DGETRI LAPACK_dgetri
#define FN_ZGETRF LAPACK_zgetrf
#define FN_ZGETRI LAPACK_zgetri

// Computes the solution to a system of linear equations
// <https://www.netlib.org/lapack/explore-html/d8/d72/dgesv_8f.html>
void c_dgesv(const int32_t *n,
             const int32_t *nrhs,
             double *a,
             const int32_t *lda,
             int32_t *ipiv,
             double *b,
             const int32_t *ldb,
             int32_t *info) {
    FN_DGESV(n, nrhs, a, lda, ipiv, b, ldb, info);
}

// Computes the solution to a real system of linear equations
// <https://www.netlib.org/lapack/explore-html/d1/ddc/zgesv_8f.html>
void c_zgesv(const int32_t *n,
             const int32_t *nrhs,
             COMPLEX64 *a,
             const int32_t *lda,
             int32_t *ipiv,
             COMPLEX64 *b,
             const int32_t *ldb,
             int32_t *info) {
    FN_ZGESV(n, nrhs, a, lda, ipiv, b, ldb, info);
}

// Computes the Cholesky factorization of a real symmetric positive definite matrix
// <https://www.netlib.org/lapack/explore-html/d0/d8a/dpotrf_8f.html>
void c_dpotrf(C_BOOL upper,
              const int32_t *n,
              double *a,
              const int32_t *lda,
              int32_t *info) {
    const char *uplo = upper == C_TRUE ? "U" : "L";
    FN_DPOTRF(uplo, n, a, lda, info);
}

// Computes the Cholesky factorization of a complex Hermitian positive definite matrix A.
// <https://www.netlib.org/lapack/explore-html/d1/db9/zpotrf_8f.html>
void c_zpotrf(C_BOOL upper,
              const int32_t *n,
              COMPLEX64 *a,
              const int32_t *lda,
              int32_t *info) {
    const char *uplo = upper == C_TRUE ? "U" : "L";
    FN_ZPOTRF(uplo, n, a, lda, info);
}

// Computes the eigenvalues and eigenvectors of a symmetric matrix
// <https://netlib.org/lapack/explore-html/dd/d4c/dsyev_8f.html>
void c_dsyev(C_BOOL calc_v,
             C_BOOL upper,
             const int32_t *n,
             double *a,
             const int32_t *lda,
             double *w,
             double *work,
             const int32_t *lwork,
             int32_t *info) {
    const char *jobz = calc_v == C_TRUE ? "V" : "N";
    const char *uplo = upper == C_TRUE ? "U" : "L";
    FN_DSYEV(jobz, uplo, n, a, lda, w, work, lwork, info);
}

// Computes the eigenvalues and eigenvectors of a general matrix
// <https://www.netlib.org/lapack/explore-html/d9/d28/dgeev_8f.html>
void c_dgeev(C_BOOL calc_vl,
             C_BOOL calc_vr,
             const int32_t *n,
             double *a,
             const int32_t *lda,
             double *wr,
             double *wi,
             double *vl,
             const int32_t *ldvl,
             double *vr,
             const int32_t *ldvr,
             double *work,
             const int32_t *lwork,
             int32_t *info) {
    const char *jobvl = calc_vl == C_TRUE ? "V" : "N";
    const char *jobvr = calc_vr == C_TRUE ? "V" : "N";
    FN_DGEEV(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info);
}

// Computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
// <https://www.netlib.org/lapack/explore-html/d6/dee/zheev_8f.html>
void c_zheev(
    C_BOOL calc_v,
    C_BOOL upper,
    int32_t const *n,
    COMPLEX64 *a,
    int32_t const *lda,
    double *w,
    COMPLEX64 *work,
    int32_t const *lwork,
    double *rwork,
    int32_t *info) {
    const char *jobz = calc_v == C_TRUE ? "V" : "N";
    const char *uplo = upper == C_TRUE ? "U" : "L";
    FN_ZHEEV(jobz, uplo, n, a, lda, w, work, lwork, rwork, info);
}

// Computes the singular value decomposition (SVD)
// <https://www.netlib.org/lapack/explore-html/d8/d2d/dgesvd_8f.html>
void c_dgesvd(int32_t jobu_code,
              int32_t jobvt_code,
              const int32_t *m,
              const int32_t *n,
              double *a,
              const int32_t *lda,
              double *s,
              double *u,
              const int32_t *ldu,
              double *vt,
              const int32_t *ldvt,
              double *work,
              const int32_t *lwork,
              int32_t *info) {
    const char *jobu = jobu_code == SVD_CODE_A   ? "A"
                       : jobu_code == SVD_CODE_S ? "S"
                       : jobu_code == SVD_CODE_O ? "O"
                                                 : "N";
    const char *jobvt = jobvt_code == SVD_CODE_A   ? "A"
                        : jobvt_code == SVD_CODE_S ? "S"
                        : jobvt_code == SVD_CODE_O ? "O"
                                                   : "N";
    FN_DGESVD(jobu, jobvt, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, info);
}

// Computes the LU factorization of a general (m,n) matrix
// <https://www.netlib.org/lapack/explore-html/d3/d6a/dgetrf_8f.html>
void c_dgetrf(const int32_t *m,
              const int32_t *n,
              double *a,
              const int32_t *lda,
              int32_t *ipiv,
              int32_t *info) {
    FN_DGETRF(m, n, a, lda, ipiv, info);
}

// Computes the inverse of a matrix using the LU factorization computed by dgetrf
// <https://www.netlib.org/lapack/explore-html/df/da4/dgetri_8f.html>
void c_dgetri(const int32_t *n,
              double *a,
              const int32_t *lda,
              const int32_t *ipiv,
              double *work,
              const int32_t *lwork,
              int32_t *info) {
    FN_DGETRI(n, a, lda, ipiv, work, lwork, info);
}

// Computes the LU factorization of a general (m,n) matrix
// <https://www.netlib.org/lapack/explore-html/dd/dd1/zgetrf_8f.html>
void c_zgetrf(const int32_t *m,
              const int32_t *n,
              COMPLEX64 *a,
              const int32_t *lda,
              int32_t *ipiv,
              int32_t *info) {
    FN_ZGETRF(m, n, a, lda, ipiv, info);
}

// Computes the inverse of a matrix using the LU factorization computed by zgetrf
// <https://www.netlib.org/lapack/explore-html/d0/db3/zgetri_8f.html>
void c_zgetri(const int32_t *n,
              COMPLEX64 *a,
              const int32_t *lda,
              const int32_t *ipiv,
              COMPLEX64 *work,
              const int32_t *lwork,
              int32_t *info) {
    FN_ZGETRI(n, a, lda, ipiv, work, lwork, info);
}