cdef extern from "gsl/gsl_linalg.h":
cdef enum gsl_linalg_matrix_mod_t:
GSL_LINALG_MOD_NONE = 0
GSL_LINALG_MOD_TRANSPOSE = 1
GSL_LINALG_MOD_CONJUGATE = 2
int gsl_linalg_matmult ( gsl_matrix * A, gsl_matrix * B, gsl_matrix * C)
int gsl_linalg_matmult_mod ( gsl_matrix * A, gsl_linalg_matrix_mod_t modA, gsl_matrix * B, gsl_linalg_matrix_mod_t modB, gsl_matrix * C)
int gsl_linalg_exponential_ss(gsl_matrix * A, gsl_matrix * eA, gsl_mode_t mode)
# Householder Transformations
double gsl_linalg_householder_transform (gsl_vector * v)
gsl_complex gsl_linalg_complex_householder_transform (gsl_vector_complex * v)
int gsl_linalg_householder_hm (double tau, gsl_vector * v, gsl_matrix * A)
int gsl_linalg_householder_mh (double tau, gsl_vector * v, gsl_matrix * A)
int gsl_linalg_householder_hv (double tau, gsl_vector * v, gsl_vector * w)
int gsl_linalg_householder_hm1 (double tau, gsl_matrix * A)
int gsl_linalg_complex_householder_hm (gsl_complex tau, gsl_vector_complex * v, gsl_matrix_complex * A)
int gsl_linalg_complex_householder_hv (gsl_complex tau, gsl_vector_complex * v, gsl_vector_complex * w)
# Singular Value Decomposition
int gsl_linalg_SV_decomp(gsl_matrix * A, gsl_matrix * V, gsl_vector * S, gsl_vector * work)
int gsl_linalg_SV_decomp_mod(gsl_matrix * A, gsl_matrix * X, gsl_matrix * V, gsl_vector * S, gsl_vector * work)
int gsl_linalg_SV_decomp_jacobi(gsl_matrix * A, gsl_matrix * V, gsl_vector * S)
int gsl_linalg_SV_solve(gsl_matrix * U, gsl_matrix * V, gsl_vector * S, gsl_vector * b, gsl_vector * x)
# LU Decomposition, Gaussian elimination with partial pivoting
int gsl_linalg_LU_decomp(gsl_matrix * A, gsl_permutation * p, int *signum)
int gsl_linalg_LU_solve(gsl_matrix * LU, gsl_permutation * p, gsl_vector * b, gsl_vector * x)
int gsl_linalg_LU_svx(gsl_matrix * LU, gsl_permutation * p, gsl_vector * x)
int gsl_linalg_LU_refine(gsl_matrix * A, gsl_matrix * LU, gsl_permutation * p, gsl_vector * b, gsl_vector * x, gsl_vector * residual)
int gsl_linalg_LU_invert(gsl_matrix * LU, gsl_permutation * p, gsl_matrix * inverse)
double gsl_linalg_LU_det(gsl_matrix * LU, int signum)
double gsl_linalg_LU_lndet(gsl_matrix * LU)
int gsl_linalg_LU_sgndet(gsl_matrix * LU, int signum)
# Complex LU Decomposition
int gsl_linalg_complex_LU_decomp(gsl_matrix_complex * A, gsl_permutation * p, int *signum)
int gsl_linalg_complex_LU_solve(gsl_matrix_complex * LU, gsl_permutation * p, gsl_vector_complex * b, gsl_vector_complex * x)
int gsl_linalg_complex_LU_svx(gsl_matrix_complex * LU, gsl_permutation * p, gsl_vector_complex * x)
int gsl_linalg_complex_LU_refine(gsl_matrix_complex * A, gsl_matrix_complex * LU, gsl_permutation * p, gsl_vector_complex * b, gsl_vector_complex * x, gsl_vector_complex * residual)
# int gsl_complex_linalg_LU_invert(gsl_matrix_complex * LU, gsl_permutation * p, gsl_matrix_complex * inverse)
int gsl_linalg_complex_LU_invert(gsl_matrix_complex * LU, gsl_permutation * p, gsl_matrix_complex * inverse)
gsl_complex gsl_linalg_complex_LU_det(gsl_matrix_complex * LU, int signum)
double gsl_linalg_complex_LU_lndet(gsl_matrix_complex * LU)
gsl_complex gsl_linalg_complex_LU_sgndet(gsl_matrix_complex * LU, int signum)
# QR decomposition
int gsl_linalg_QR_decomp(gsl_matrix * A, gsl_vector * tau)
int gsl_linalg_QR_solve(gsl_matrix * QR, gsl_vector * tau, gsl_vector * b, gsl_vector * x)
int gsl_linalg_QR_svx(gsl_matrix * QR, gsl_vector * tau, gsl_vector * x)
int gsl_linalg_QR_lssolve(gsl_matrix * QR, gsl_vector * tau, gsl_vector * b, gsl_vector * x, gsl_vector * residual)
int gsl_linalg_QR_QRsolve(gsl_matrix * Q, gsl_matrix * R, gsl_vector * b, gsl_vector * x)
int gsl_linalg_QR_Rsolve(gsl_matrix * QR, gsl_vector * b, gsl_vector * x)
int gsl_linalg_QR_Rsvx(gsl_matrix * QR, gsl_vector * x)
int gsl_linalg_QR_update(gsl_matrix * Q, gsl_matrix * R, gsl_vector * w, gsl_vector * v)
int gsl_linalg_QR_QTvec(gsl_matrix * QR, gsl_vector * tau, gsl_vector * v)
int gsl_linalg_QR_Qvec(gsl_matrix * QR, gsl_vector * tau, gsl_vector * v)
int gsl_linalg_QR_unpack(gsl_matrix * QR, gsl_vector * tau, gsl_matrix * Q, gsl_matrix * R)
int gsl_linalg_R_solve(gsl_matrix * R, gsl_vector * b, gsl_vector * x)
int gsl_linalg_R_svx(gsl_matrix * R, gsl_vector * x)
# Q R P^T decomposition
int gsl_linalg_QRPT_decomp(gsl_matrix * A, gsl_vector * tau, gsl_permutation * p, int *signum, gsl_vector * norm)
int gsl_linalg_QRPT_decomp2(gsl_matrix * A, gsl_matrix * q, gsl_matrix * r, gsl_vector * tau, gsl_permutation * p, int *signum, gsl_vector * norm)
int gsl_linalg_QRPT_solve(gsl_matrix * QR, gsl_vector * tau, gsl_permutation * p, gsl_vector * b, gsl_vector * x)
int gsl_linalg_QRPT_svx(gsl_matrix * QR, gsl_vector * tau, gsl_permutation * p, gsl_vector * x)
int gsl_linalg_QRPT_QRsolve(gsl_matrix * Q, gsl_matrix * R, gsl_permutation * p, gsl_vector * b, gsl_vector * x)
int gsl_linalg_QRPT_Rsolve(gsl_matrix * QR, gsl_permutation * p, gsl_vector * b, gsl_vector * x)
int gsl_linalg_QRPT_Rsvx(gsl_matrix * QR, gsl_permutation * p, gsl_vector * x)
int gsl_linalg_QRPT_update(gsl_matrix * Q, gsl_matrix * R, gsl_permutation * p, gsl_vector * u, gsl_vector * v)
# Cholesky Decomposition
int gsl_linalg_cholesky_decomp(gsl_matrix * A)
int gsl_linalg_cholesky_solve(gsl_matrix * cholesky, gsl_vector * b, gsl_vector * x)
int gsl_linalg_cholesky_svx(gsl_matrix * cholesky, gsl_vector * x)
# Symmetric to symmetric tridiagonal decomposition
int gsl_linalg_symmtd_decomp(gsl_matrix * A, gsl_vector * tau)
int gsl_linalg_symmtd_unpack(gsl_matrix * A, gsl_vector * tau, gsl_matrix * Q, gsl_vector * diag, gsl_vector * subdiag)
int gsl_linalg_symmtd_unpack_T(gsl_matrix * A, gsl_vector * diag, gsl_vector * subdiag)
# Hermitian to symmetric tridiagonal decomposition
int gsl_linalg_hermtd_decomp(gsl_matrix_complex * A, gsl_vector_complex * tau)
int gsl_linalg_hermtd_unpack(gsl_matrix_complex * A, gsl_vector_complex * tau, gsl_matrix_complex * Q, gsl_vector * diag, gsl_vector * subdiag)
int gsl_linalg_hermtd_unpack_T(gsl_matrix_complex * A, gsl_vector * diag, gsl_vector * subdiag)
# Linear Solve Using Householder Transformations
int gsl_linalg_HH_solve(gsl_matrix * A, gsl_vector * b, gsl_vector * x)
int gsl_linalg_HH_svx(gsl_matrix * A, gsl_vector * x)
# Linear solve for a symmetric tridiagonal system
int gsl_linalg_solve_symm_tridiag(gsl_vector * diag, gsl_vector * e, gsl_vector * b, gsl_vector * x)
# Linear solve for a nonsymmetric tridiagonal system
int gsl_linalg_solve_tridiag ( gsl_vector * diag, gsl_vector * abovediag, gsl_vector * belowdiag, gsl_vector * b, gsl_vector * x)
# Linear solve for a symmetric cyclic tridiagonal system
int gsl_linalg_solve_symm_cyc_tridiag(gsl_vector * diag, gsl_vector * e, gsl_vector * b, gsl_vector * x)
# Linear solve for a nonsymmetric cyclic tridiagonal system
int gsl_linalg_solve_cyc_tridiag ( gsl_vector * diag, gsl_vector * abovediag, gsl_vector * belowdiag, gsl_vector * b, gsl_vector * x)
# Bidiagonal decomposition
int gsl_linalg_bidiag_decomp(gsl_matrix * A, gsl_vector * tau_U, gsl_vector * tau_V)
int gsl_linalg_bidiag_unpack(gsl_matrix * A, gsl_vector * tau_U, gsl_matrix * U, gsl_vector * tau_V, gsl_matrix * V, gsl_vector * diag, gsl_vector * superdiag)
int gsl_linalg_bidiag_unpack2(gsl_matrix * A, gsl_vector * tau_U, gsl_vector * tau_V, gsl_matrix * V)
int gsl_linalg_bidiag_unpack_B(gsl_matrix * A, gsl_vector * diag, gsl_vector * superdiag)
# Balancing
int gsl_linalg_balance_columns (gsl_matrix * A, gsl_vector * D)
