!-*-f90-*-
!
!  Interfaces: Linear Algebra support
!
! LU
!
  function gsl_linalg_lu_decomp (a, p, signum) &
       bind(c, name='gsl_linalg_LU_decomp')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, p
    integer(c_int) :: signum
    integer(c_int) :: gsl_linalg_lu_decomp
  end function gsl_linalg_lu_decomp
  function gsl_linalg_complex_lu_decomp (a, p, signum) &
       bind(c, name='gsl_linalg_complex_LU_decomp')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, p
    integer(c_int) :: signum
    integer(c_int) :: gsl_linalg_complex_lu_decomp
  end function gsl_linalg_complex_lu_decomp
  function gsl_linalg_lu_solve (lu, p, b, x) &
       bind(c, name='gsl_linalg_LU_solve')
    import :: c_ptr, c_int
    type(c_ptr), value :: lu, p, b, x
    integer(c_int) :: gsl_linalg_lu_solve
  end function gsl_linalg_lu_solve
  function gsl_linalg_complex_lu_solve (lu, p, b, x) &
       bind(c, name='gsl_linalg_complex_LU_solve')
    import :: c_ptr, c_int
    type(c_ptr), value :: lu, p, b, x
    integer(c_int) :: gsl_linalg_complex_lu_solve
  end function gsl_linalg_complex_lu_solve
  function gsl_linalg_lu_svx (lu, p, x) &
       bind(c, name='gsl_linalg_LU_svx')
    import :: c_ptr, c_int
    type(c_ptr), value :: lu, p, x
    integer(c_int) :: gsl_linalg_lu_svx
  end function gsl_linalg_lu_svx
  function gsl_linalg_complex_lu_svx (lu, p, x) &
       bind(c, name='gsl_linalg_complex_LU_svx')
    import :: c_ptr, c_int
    type(c_ptr), value :: lu, p, x
    integer(c_int) :: gsl_linalg_complex_lu_svx
  end function gsl_linalg_complex_lu_svx
  function gsl_linalg_lu_refine (a, lu, p, b, x, residual) &
       bind(c, name='gsl_linalg_LU_refine')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, lu, p, b, x, residual
    integer(c_int) :: gsl_linalg_lu_refine
  end function gsl_linalg_lu_refine
  function gsl_linalg_complex_lu_refine (a, lu, p, b, x, residual) &
       bind(c, name='gsl_linalg_complex_LU_refine')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, lu, p, b, x, residual
    integer(c_int) :: gsl_linalg_complex_lu_refine
  end function gsl_linalg_complex_lu_refine
  function gsl_linalg_lu_invert (lu, p, inv) &
       bind(c, name='gsl_linalg_LU_invert')
    import :: c_ptr, c_int
    type(c_ptr), value :: lu, p, inv
    integer(c_int) :: gsl_linalg_lu_invert
  end function gsl_linalg_lu_invert
  function gsl_linalg_complex_lu_invert (lu, p, inv) &
       bind(c, name='gsl_linalg_complex_LU_invert')
    import :: c_ptr, c_int
    type(c_ptr), value :: lu, p, inv
    integer(c_int) :: gsl_linalg_complex_lu_invert
  end function gsl_linalg_complex_lu_invert
  function gsl_linalg_lu_invx (lu, p) &
       bind(c, name='gsl_linalg_LU_invx')
    import :: c_ptr, c_int
    type(c_ptr), value :: lu, p
    integer(c_int) :: gsl_linalg_lu_invx
  end function gsl_linalg_lu_invx
  function gsl_linalg_complex_lu_invx (lu, p) &
       bind(c, name='gsl_linalg_complex_LU_invx')
    import :: c_ptr, c_int
    type(c_ptr), value :: lu, p
    integer(c_int) :: gsl_linalg_complex_lu_invx
  end function gsl_linalg_complex_lu_invx
   function gsl_linalg_lu_det(lu, signum) bind(c, name='gsl_linalg_LU_det')
    import :: c_ptr, c_double, c_int
    type(c_ptr), value :: lu
    integer(c_int), value :: signum
    real(c_double) :: gsl_linalg_lu_det
  end function gsl_linalg_lu_det
  function gsl_linalg_complex_lu_det(lu, signum) &
       bind(c, name='gsl_linalg_complex_LU_det')
    import :: c_ptr, c_int, gsl_complex
    type(c_ptr), value :: lu
    integer(c_int), value :: signum
    type(gsl_complex) :: gsl_linalg_complex_lu_det
  end function gsl_linalg_complex_lu_det
  function gsl_linalg_lu_lndet(lu) bind(c, name='gsl_linalg_LU_lndet')
    import :: c_ptr, c_double
    type(c_ptr), value :: lu
    real(c_double) :: gsl_linalg_lu_lndet
  end function gsl_linalg_lu_lndet
  function gsl_linalg_complex_lu_lndet(lu) &
       bind(c, name='gsl_linalg_complex_LU_lndet')
    import :: c_ptr, c_double
    type(c_ptr), value :: lu
    real(c_double) :: gsl_linalg_complex_lu_lndet
  end function gsl_linalg_complex_lu_lndet
  function gsl_linalg_lu_sgndet(lu, signum) bind(c, name='gsl_linalg_LU_sgndet')
    import :: c_ptr, c_double, c_int
    type(c_ptr), value :: lu
    integer(c_int), value :: signum
    integer(c_int) :: gsl_linalg_lu_sgndet
  end function gsl_linalg_lu_sgndet
  function gsl_linalg_complex_lu_sgndet(lu, signum) &
       bind(c, name='gsl_linalg_complex_LU_sgndet')
    import :: c_ptr, c_int, gsl_complex
    type(c_ptr), value :: lu
    integer(c_int), value :: signum
    type(gsl_complex) :: gsl_linalg_complex_lu_sgndet
  end function gsl_linalg_complex_lu_sgndet
!
! QR
!
  function gsl_linalg_qr_decomp (a, tau) bind(c, name='gsl_linalg_QR_decomp')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, tau
    integer(c_int) :: gsl_linalg_qr_decomp
  end function gsl_linalg_qr_decomp
  function gsl_linalg_qr_decomp_r (a, t) bind(c, name='gsl_linalg_QR_decomp_r')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, t
    integer(c_int) :: gsl_linalg_qr_decomp_r
  end function gsl_linalg_qr_decomp_r
  function gsl_linalg_qr_solve (qr, tau, b, x) &
       bind(c, name='gsl_linalg_QR_solve')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, tau, b, x
    integer(c_int) :: gsl_linalg_qr_solve
  end function gsl_linalg_qr_solve
  function gsl_linalg_qr_solve_r (qr, t, b, x) &
       bind(c, name='gsl_linalg_QR_solve_r')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, t, b, x
    integer(c_int) :: gsl_linalg_qr_solve_r
  end function gsl_linalg_qr_solve_r
  function gsl_linalg_qr_svx (qr, tau, x) &
       bind(c, name='gsl_linalg_QR_svx')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, tau, x
    integer(c_int) :: gsl_linalg_qr_svx
  end function gsl_linalg_qr_svx
  function gsl_linalg_qr_lssolve (qr, tau, b, x, residual) &
       bind(c, name='gsl_linalg_QR_lssolve')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, tau, b, x, residual
    integer(c_int) :: gsl_linalg_qr_lssolve
  end function gsl_linalg_qr_lssolve
  function gsl_linalg_qr_lssolve_r (qr, t, b, x, work) &
       bind(c, name='gsl_linalg_QR_lssolve_r')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, t, b, x, work
    integer(c_int) :: gsl_linalg_qr_lssolve_r
  end function gsl_linalg_qr_lssolve_r
  function gsl_linalg_qr_qtvec (qr, tau, v) &
       bind(c, name='gsl_linalg_QR_QTvec')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, tau, v
    integer(c_int) :: gsl_linalg_qr_qtvec
  end function gsl_linalg_qr_qtvec
  function gsl_linalg_qr_qtvec_r (qr, t, v, work) &
       bind(c, name='gsl_linalg_QR_QTvec_r')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, t, v,work
    integer(c_int) :: gsl_linalg_qr_qtvec_r
  end function gsl_linalg_qr_qtvec_r
  function gsl_linalg_qr_qvec (qr, tau, v) &
       bind(c, name='gsl_linalg_QR_Qvec')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, tau, v
    integer(c_int) :: gsl_linalg_qr_qvec
  end function gsl_linalg_qr_qvec
  function gsl_linalg_qr_qtmat (qr, tau, a) &
       bind(c, name='gsl_linalg_QR_QTmat')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, tau, a
    integer(c_int) :: gsl_linalg_qr_qtmat
  end function gsl_linalg_qr_qtmat
  function gsl_linalg_qr_qtmat_r (qr, t, a, work) &
       bind(c, name='gsl_linalg_QR_QTmat_r')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, t, a, work
    integer(c_int) :: gsl_linalg_qr_qtmat_r
  end function gsl_linalg_qr_qtmat_r
  function gsl_linalg_qr_rsolve (qr, b, x) &
       bind(c, name='gsl_linalg_QR_Rsolve')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, b, x
    integer(c_int) :: gsl_linalg_qr_rsolve
  end function gsl_linalg_qr_rsolve
  function gsl_linalg_qr_rsvx (qr, x) &
       bind(c, name='gsl_linalg_QR_Rsvx')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, x
    integer(c_int) :: gsl_linalg_qr_rsvx
  end function gsl_linalg_qr_rsvx
  function gsl_linalg_qr_unpack (qr, tau, q, r) &
       bind(c, name='gsl_linalg_QR_unpack')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, tau, q, r
    integer(c_int) :: gsl_linalg_qr_unpack
  end function gsl_linalg_qr_unpack
  function gsl_linalg_qr_unpack_r (qr, t, q, r) &
       bind(c, name='gsl_linalg_QR_unpack_r')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, t, q, r
    integer(c_int) :: gsl_linalg_qr_unpack_r
  end function gsl_linalg_qr_unpack_r
  function gsl_linalg_qr_qrsolve (q, r, b, x) &
       bind(c, name='gsl_linalg_QR_QRsolve')
    import :: c_ptr, c_int
    type(c_ptr), value :: q, r, b, x
    integer(c_int) :: gsl_linalg_qr_qrsolve
  end function gsl_linalg_qr_qrsolve
  function gsl_linalg_qr_update (q, r, w, v) &
       bind(c, name='gsl_linalg_QR_update')
    import :: c_ptr, c_int
    type(c_ptr), value :: q, r, w, v
    integer(c_int) :: gsl_linalg_qr_update
  end function gsl_linalg_qr_update
  function gsl_linalg_r_solve (r, b, x) &
       bind(c, name='gsl_linalg_R_solve')
    import :: c_ptr, c_int
    type(c_ptr), value :: r, b, x
    integer(c_int) :: gsl_linalg_r_solve
  end function gsl_linalg_r_solve
  function gsl_linalg_r_svx (r, x) &
       bind(c, name='gsl_linalg_R_svx')
    import :: c_ptr, c_int
    type(c_ptr), value :: r, x
    integer(c_int) :: gsl_linalg_r_svx
  end function gsl_linalg_r_svx
  function gsl_linalg_qrpt_decomp (a, tau, p, signum, norm) &
       bind(c, name='gsl_linalg_QRPT_decomp')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, tau, p, norm
    integer(c_int), intent(out) :: signum
    integer(c_int) :: gsl_linalg_qrpt_decomp
  end function gsl_linalg_qrpt_decomp
  function gsl_linalg_qrpt_decomp2 (a, q, r, tau, p, signum, norm) &
       bind(c, name='gsl_linalg_QRPT_decomp2')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, q, r, tau, p, norm
    integer(c_int), intent(out) :: signum
    integer(c_int) :: gsl_linalg_qrpt_decomp2
  end function gsl_linalg_qrpt_decomp2
  function gsl_linalg_qrpt_solve (qr, tau, p, b, x) &
       bind(c, name='gsl_linalg_QRPT_solve')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, tau, p, b, x
    integer(c_int) :: gsl_linalg_qrpt_solve
  end function gsl_linalg_qrpt_solve
  function gsl_linalg_qrpt_svx (qr, tau, p, x) &
       bind(c, name='gsl_linalg_QRPT_svx')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, tau, p, x
    integer(c_int) :: gsl_linalg_qrpt_svx
  end function gsl_linalg_qrpt_svx
  function gsl_linalg_qrpt_lssolve (qr, tau, p, b, x, r) &
       bind(c, name='gsl_linalg_QRPT_lssolve')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, tau, p, b, x, r
    integer(c_int) :: gsl_linalg_qrpt_lssolve
  end function gsl_linalg_qrpt_lssolve
  function gsl_linalg_qrpt_lssolve2 (qr, tau, p, b, rank, x, r) &
       bind(c, name='gsl_linalg_QRPT_lssolve2')
    import :: c_ptr, c_int, c_size_t
    type(c_ptr), value :: qr, tau, p, b, x, r
    integer(c_size_t), value :: rank
    integer(c_int) :: gsl_linalg_qrpt_lssolve2
  end function gsl_linalg_qrpt_lssolve2
  function gsl_linalg_qrpt_qrsolve (q, r, p, b, x) &
       bind(c, name='gsl_linalg_QRPT_QRsolve')
    import :: c_ptr, c_int
    type(c_ptr), value :: q, r, p, b, x
    integer(c_int) :: gsl_linalg_qrpt_qrsolve
  end function gsl_linalg_qrpt_qrsolve
  function gsl_linalg_qrpt_update (q, r, p, w, v) &
       bind(c, name='gsl_linalg_QRPT_update')
    import :: c_ptr, c_int
    type(c_ptr), value :: q, r, p, w, v
    integer(c_int) :: gsl_linalg_qrpt_update
  end function gsl_linalg_qrpt_update
  function gsl_linalg_qrpt_rsolve (qr, p, b, x) &
       bind(c, name='gsl_linalg_QRPT_Rsolve')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, p, b, x
    integer(c_int) :: gsl_linalg_qrpt_rsolve
  end function gsl_linalg_qrpt_rsolve
  function gsl_linalg_qrpt_rsvx (qr, p, x) &
       bind(c, name='gsl_linalg_QRPT_Rsvx')
    import :: c_ptr, c_int
    type(c_ptr), value :: qr, p, x
    integer(c_int) :: gsl_linalg_qrpt_rsvx
  end function gsl_linalg_qrpt_rsvx
  function gsl_linalg_qrpt_rank (qr, tol) &
       bind(c, name='gsl_linalg_QRPT_rank')
    import :: c_ptr, c_size_t, c_double
    type(c_ptr), value :: qr
    real(c_double), value :: tol
    integer(c_size_t) :: gsl_linalg_qrpt_rank
  end function gsl_linalg_qrpt_rank
  function gsl_linalg_qrpt_rcond (qr, rcond, wk) &
       bind(c, name='gsl_linalg_QRPT_rcond')
    import :: c_ptr, c_int, c_double
    type(c_ptr), value :: qr, wk
    real(c_double) :: rcond
    integer(c_int) :: gsl_linalg_qrpt_rcond
  end function gsl_linalg_qrpt_rcond
!
! LQ decomposition
!
  integer(c_int) function gsl_linalg_lq_decomp(a, tau) &
       bind(c, name='gsl_linalg_LQ_decomp')
    import :: c_int, c_ptr
    type(c_ptr), value :: a, tau
  end function gsl_linalg_lq_decomp
  integer(c_int) function gsl_linalg_lq_lssolve(lq, tau, b, x, residual) &
       bind(c, name='gsl_linalg_LQ_lssolve')
    import :: c_int, c_ptr
    type(c_ptr), value :: lq, tau, b, x, residual
  end function gsl_linalg_lq_lssolve
  integer(c_int) function gsl_linalg_lq_unpack(lq, tau, q, l) &
       bind(c, name='gsl_linalg_LQ_unpack')
    import :: c_int, c_ptr
    type(c_ptr), value :: lq, tau, q, l
  end function gsl_linalg_lq_unpack
  integer(c_int) function gsl_linalg_lq_qtvec(lq, tau, v) &
       bind(c, name='gsl_linalg_LQ_QTvec')
    import :: c_int, c_ptr
    type(c_ptr), value :: lq, tau, v
  end function gsl_linalg_lq_qtvec
!  
! Complete orthogonal decomposition (COD)
!
  function gsl_linalg_cod_decomp (a, tau_q, tau_z, p, rank, work) &
       bind(c, name='gsl_linalg_COD_decomp')
    import :: c_ptr, c_int, c_size_t
    type(c_ptr), value :: a, tau_q, tau_z, p, work
    integer(c_size_t) :: rank
    integer(c_int) :: gsl_linalg_cod_decomp
  end function gsl_linalg_cod_decomp
  function gsl_linalg_cod_decomp_e (a, tau_q, tau_z, p, tol, rank, work) &
       bind(c, name='gsl_linalg_COD_decomp_e')
    import :: c_ptr, c_int, c_size_t, c_double
    type(c_ptr), value :: a, tau_q, tau_z, p, work
    real(c_double), value :: tol
    integer(c_size_t) :: rank
    integer(c_int) :: gsl_linalg_cod_decomp_e
  end function gsl_linalg_cod_decomp_e
  function gsl_linalg_cod_lssolve (qrzt, tau_q, tau_z, p, rank, b, x, residual) &
       bind(c, name='gsl_linalg_COD_lssolve')
    import :: c_ptr, c_int, c_size_t
    type(c_ptr), value :: qrzt, tau_q, tau_z, p, b, x, residual
    integer(c_size_t), value :: rank
    integer(c_int) :: gsl_linalg_cod_lssolve
  end function gsl_linalg_cod_lssolve
  function gsl_linalg_cod_lssolve2 (lambda, qrzt, tau_q, tau_z, p, rank, b, &
       x, residual, s, work) bind(c, name='gsl_linalg_COD_lssolve2')
    import :: c_ptr, c_int, c_size_t, c_double
    real(c_double), value :: lambda
    type(c_ptr), value :: qrzt, tau_q, tau_z, p, b, x, residual, s, work
    integer(c_size_t), value :: rank
    integer(c_int) :: gsl_linalg_cod_lssolve2
  end function gsl_linalg_cod_lssolve2
  function gsl_linalg_cod_unpack (qrzt, tau_q, tau_z, p, rank, q, r, z) &
       bind(c, name='gsl_linalg_COD_unpack')
    import :: c_ptr, c_int, c_size_t
    type(c_ptr), value :: qrzt, tau_q, tau_z, p, q, r, z
    integer(c_size_t), value :: rank
    integer(c_int) :: gsl_linalg_cod_unpack
  end function gsl_linalg_cod_unpack
  function gsl_linalg_cod_matz (qrzt, tau_z, rank, a, work) &
       bind(c, name='gsl_linalg_COD_matZ')
    import :: c_ptr, c_int, c_size_t
    type(c_ptr), value :: qrzt, tau_z, a, work
    integer(c_size_t), value :: rank
    integer(c_int) :: gsl_linalg_cod_matz
  end function gsl_linalg_cod_matz
!
! SVD
!
  function gsl_linalg_sv_decomp (a, v, s, work) &
       bind(c, name='gsl_linalg_SV_decomp')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, v, s, work
    integer(c_int) :: signum
    integer(c_int) :: gsl_linalg_sv_decomp
  end function gsl_linalg_sv_decomp
  function gsl_linalg_sv_decomp_mod (a, x, v, s, work) &
       bind(c, name='gsl_linalg_SV_decomp_mod')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, x, v, s, work
    integer(c_int) :: signum
    integer(c_int) :: gsl_linalg_sv_decomp_mod
  end function gsl_linalg_sv_decomp_mod
  function gsl_linalg_sv_decomp_jacobi (a, v, s) &
       bind(c, name='gsl_linalg_SV_decomp_jacobi')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, v, s
    integer(c_int) :: signum
    integer(c_int) :: gsl_linalg_sv_decomp_jacobi
  end function gsl_linalg_sv_decomp_jacobi
  function gsl_linalg_sv_solve (u, v, s, b, x) &
       bind(c, name='gsl_linalg_SV_solve')
    import :: c_ptr, c_int
    type(c_ptr), value :: u, v, s, b, x
    integer(c_int) :: signum
    integer(c_int) :: gsl_linalg_sv_solve
  end function gsl_linalg_sv_solve
  function gsl_linalg_sv_leverage(u, h) &
       bind(c, name='gsl_linalg_SV_leverage')
    import :: c_ptr, c_int
    type(c_ptr), value :: u, h
    integer(c_int) :: gsl_linalg_sv_leverage
  end function gsl_linalg_sv_leverage
!
! Cholesky
!
  function gsl_linalg_cholesky_decomp1 (a) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a
    integer(c_int) :: gsl_linalg_cholesky_decomp1
  end function gsl_linalg_cholesky_decomp1
  function gsl_linalg_cholesky_decomp (a) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a
    integer(c_int) :: gsl_linalg_cholesky_decomp
  end function gsl_linalg_cholesky_decomp
  function gsl_linalg_complex_cholesky_decomp (a) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a
    integer(c_int) :: gsl_linalg_complex_cholesky_decomp
  end function gsl_linalg_complex_cholesky_decomp
  function gsl_linalg_cholesky_solve (chol, b, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: chol, b, x
    integer(c_int) :: gsl_linalg_cholesky_solve
  end function gsl_linalg_cholesky_solve
  function gsl_linalg_complex_cholesky_solve (chol, b, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: chol, b, x
    integer(c_int) :: gsl_linalg_complex_cholesky_solve
  end function gsl_linalg_complex_cholesky_solve
  function gsl_linalg_cholesky_svx (chol, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: chol, x
    integer(c_int) :: gsl_linalg_cholesky_svx
  end function gsl_linalg_cholesky_svx
  function gsl_linalg_complex_cholesky_svx (chol, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: chol, x
    integer(c_int) :: gsl_linalg_complex_cholesky_svx
  end function gsl_linalg_complex_cholesky_svx
  function gsl_linalg_cholesky_invert (chol) bind(c)
    import :: c_ptr, c_int
    integer(c_int) :: gsl_linalg_cholesky_invert
    type(c_ptr), value :: chol
  end function gsl_linalg_cholesky_invert
  function gsl_linalg_complex_cholesky_invert (chol) bind(c)
    import :: c_ptr, c_int
    integer(c_int) :: gsl_linalg_complex_cholesky_invert
    type(c_ptr), value :: chol
  end function gsl_linalg_complex_cholesky_invert
  function gsl_linalg_cholesky_decomp2 (a,s) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a,s
    integer(c_int) :: gsl_linalg_cholesky_decomp2
  end function gsl_linalg_cholesky_decomp2
  function gsl_linalg_cholesky_solve2 (chol, s, b, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: chol, s, b, x
    integer(c_int) :: gsl_linalg_cholesky_solve2
  end function gsl_linalg_cholesky_solve2
  function gsl_linalg_cholesky_svx2 (chol, s, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: chol, s, x
    integer(c_int) :: gsl_linalg_cholesky_svx2
  end function gsl_linalg_cholesky_svx2
  function gsl_linalg_cholesky_scale (a,s) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a,s
    integer(c_int) :: gsl_linalg_cholesky_scale
  end function gsl_linalg_cholesky_scale
  function gsl_linalg_cholesky_scale_apply (a,s) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a,s
    integer(c_int) :: gsl_linalg_cholesky_scale_apply
  end function gsl_linalg_cholesky_scale_apply
  function gsl_linalg_cholesky_rcond (chol, rcond, work) &
       bind(c)
    import :: c_ptr, c_int, c_double
    type(c_ptr), value :: chol, work
    real(c_double), intent(inout) :: rcond
    integer(c_int) :: gsl_linalg_cholesky_rcond
  end function gsl_linalg_cholesky_rcond
!
! pivoted Cholesky
!
  function gsl_linalg_pcholesky_decomp (a, p) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, p
    integer(c_int) :: gsl_linalg_pcholesky_decomp
  end function gsl_linalg_pcholesky_decomp
  function gsl_linalg_pcholesky_solve (ldlt, p, b, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: ldlt, p, b, x
    integer(c_int) :: gsl_linalg_pcholesky_solve
  end function gsl_linalg_pcholesky_solve
  function gsl_linalg_pcholesky_svx (ldlt, p, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: ldlt, p, x
    integer(c_int) :: gsl_linalg_pcholesky_svx
  end function gsl_linalg_pcholesky_svx
  function gsl_linalg_pcholesky_invert (ldlt, p, ainv) bind(c)
    import :: c_ptr, c_int
    integer(c_int) :: gsl_linalg_pcholesky_invert
    type(c_ptr), value :: ldlt, p, ainv
  end function gsl_linalg_pcholesky_invert
  function gsl_linalg_pcholesky_decomp2 (a, p,s) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, p,s
    integer(c_int) :: gsl_linalg_pcholesky_decomp2
  end function gsl_linalg_pcholesky_decomp2
  function gsl_linalg_pcholesky_solve2 (ldlt, p, s, b, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: ldlt, p, s, b, x
    integer(c_int) :: gsl_linalg_pcholesky_solve2
  end function gsl_linalg_pcholesky_solve2
  function gsl_linalg_pcholesky_svx2 (ldlt, p, s, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: ldlt, p, s, x
    integer(c_int) :: gsl_linalg_pcholesky_svx2
  end function gsl_linalg_pcholesky_svx2
  function gsl_linalg_pcholesky_rcond (ldlt, p, rcond, work) &
       bind(c)
    import :: c_ptr, c_int, c_double
    type(c_ptr), value :: ldlt, p, work
    real(c_double), intent(inout) :: rcond
    integer(c_int) :: gsl_linalg_pcholesky_rcond
  end function gsl_linalg_pcholesky_rcond
!
! modified Cholesky
!
  function gsl_linalg_mcholesky_decomp (a, p, e) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, p, e
    integer(c_int) :: gsl_linalg_mcholesky_decomp
  end function gsl_linalg_mcholesky_decomp
  function gsl_linalg_mcholesky_solve (ldlt, p, b, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: ldlt, p, b, x
    integer(c_int) :: gsl_linalg_mcholesky_solve
  end function gsl_linalg_mcholesky_solve
  function gsl_linalg_mcholesky_svx (ldlt, p, x) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: ldlt, p, x
    integer(c_int) :: gsl_linalg_mcholesky_svx
  end function gsl_linalg_mcholesky_svx
  function gsl_linalg_mcholesky_invert (ldlt, p, ainv) bind(c)
    import :: c_ptr, c_int
    integer(c_int) :: gsl_linalg_mcholesky_invert
    type(c_ptr), value :: ldlt, p, ainv
  end function gsl_linalg_mcholesky_invert
  function gsl_linalg_mcholesky_rcond (ldlt, p, rcond, work) &
       bind(c)
    import :: c_ptr, c_int, c_double
    type(c_ptr), value :: ldlt, p, work
    real(c_double), intent(inout) :: rcond
    integer(c_int) :: gsl_linalg_mcholesky_rcond
  end function gsl_linalg_mcholesky_rcond
  !
  ! LDLT
  !
  function gsl_linalg_ldlt_decomp (a) bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a
    integer(c_int) :: gsl_linalg_ldlt_decomp
  end function gsl_linalg_ldlt_decomp
  integer(c_int) function gsl_linalg_ldlt_solve(ldlt, b, x) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: ldlt, b, x
  end function gsl_linalg_ldlt_solve
  integer(c_int) function gsl_linalg_ldlt_svx(ldlt, x) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: ldlt, x
  end function gsl_linalg_ldlt_svx
  integer(c_int) function gsl_linalg_ldlt_invert(ldlt, ainv) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: ldlt, ainv
  end function gsl_linalg_ldlt_invert
  integer(c_int) function gsl_linalg_ldlt_rcond(ldlt, rcond, w) bind(c)
    import :: c_int, c_ptr, c_double
    type(c_ptr), value :: ldlt, w
    real(c_double) :: rcond
  end function gsl_linalg_ldlt_rcond

!
! Tridiagonal Decomposition of Real Symmetric Matrices
!
  function gsl_linalg_symmtd_decomp (a, tau) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, tau
    integer(c_int) :: gsl_linalg_symmtd_decomp
  end function gsl_linalg_symmtd_decomp
  function gsl_linalg_symmtd_unpack (a, tau, q, diag, subdiag) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, tau, q, diag, subdiag
    integer(c_int) :: gsl_linalg_symmtd_unpack
  end function gsl_linalg_symmtd_unpack
  function gsl_linalg_symmtd_unpack_t (a, diag, subdiag) &
       bind(c, name='gsl_linalg_symmtd_unpack_T')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, diag, subdiag
    integer(c_int) :: gsl_linalg_symmtd_unpack_t
  end function gsl_linalg_symmtd_unpack_t
 
  
  !
  ! Tridiagonal Decomposition of Hermitian Matrices
  !
  function gsl_linalg_hermtd_decomp (a, tau) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, tau
    integer(c_int) :: gsl_linalg_hermtd_decomp
  end function gsl_linalg_hermtd_decomp
  function gsl_linalg_hermtd_unpack (a, tau, q, diag, subdiag) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, tau, q, diag, subdiag
    integer(c_int) :: gsl_linalg_hermtd_unpack
  end function gsl_linalg_hermtd_unpack
  function gsl_linalg_hermtd_unpack_t (a, diag, subdiag) &
       bind(c, name='gsl_linalg_hermtd_unpack_T')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, diag, subdiag
    integer(c_int) :: gsl_linalg_hermtd_unpack_t
  end function gsl_linalg_hermtd_unpack_t
!
! Hessenberg
!
  function gsl_linalg_hessenberg_decomp (a, tau) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, tau
    integer(c_int) :: gsl_linalg_hessenberg_decomp
  end function gsl_linalg_hessenberg_decomp
  function gsl_linalg_hessenberg_unpack (h, tau, u) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: h, tau, u
    integer(c_int) :: gsl_linalg_hessenberg_unpack
  end function gsl_linalg_hessenberg_unpack
  function gsl_linalg_hessenberg_unpack_accum (h, tau, v) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: h, tau, v
    integer(c_int) :: gsl_linalg_hessenberg_unpack_accum
  end function gsl_linalg_hessenberg_unpack_accum
  function gsl_linalg_hessenberg_set_zero (h) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: h
    integer(c_int) :: gsl_linalg_hessenberg_set_zero
  end function gsl_linalg_hessenberg_set_zero
  function gsl_linalg_hesstri_decomp (a, b, u, v, work) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, b, u, v, work
    integer(c_int) :: gsl_linalg_hesstri_decomp
  end function gsl_linalg_hesstri_decomp
!
! Bidiag
!
  function gsl_linalg_bidiag_decomp (a, tau_u, tau_v) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, tau_u, tau_v
    integer(c_int) :: gsl_linalg_bidiag_decomp
  end function gsl_linalg_bidiag_decomp
  function gsl_linalg_bidiag_unpack (a, tau_u, u, tau_v, v, diag, &
       superdiag) bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, tau_u, tau_v, u, v, diag, superdiag
    integer(c_int) :: gsl_linalg_bidiag_unpack
  end function gsl_linalg_bidiag_unpack
  function gsl_linalg_bidiag_unpack2 (a, tau_u, tau_v, v) &
       bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, tau_u, tau_v, v
    integer(c_int) :: gsl_linalg_bidiag_unpack2
  end function gsl_linalg_bidiag_unpack2
  function gsl_linalg_bidiag_unpack_b (a, diag, superdiag) &
       bind(c, name='gsl_linalg_bidiag_unpack_B')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, diag, superdiag
    integer(c_int) :: gsl_linalg_bidiag_unpack_b
  end function gsl_linalg_bidiag_unpack_b
!
! Householder
!
  function gsl_linalg_householder_transform (v) bind(c)
    import :: c_ptr, c_double
    type(c_ptr), value :: v
    real(c_double) :: gsl_linalg_householder_transform
  end function gsl_linalg_householder_transform
  function gsl_linalg_complex_householder_transform (v) bind(c)
    import :: c_ptr, gsl_complex
    type(c_ptr), value :: v
    type(gsl_complex) :: gsl_linalg_complex_householder_transform
  end function gsl_linalg_complex_householder_transform
  function gsl_linalg_householder_hm (tau, v, a) bind(c)
    import :: c_ptr, c_double, c_int
    real(c_double), value :: tau
    type(c_ptr), value :: v, a
    integer(c_int) :: gsl_linalg_householder_hm
  end function gsl_linalg_householder_hm
  function gsl_linalg_complex_householder_hm (tau, v, a) bind(c)
    import :: c_ptr, c_int, gsl_complex
    type(gsl_complex), value :: tau
    type(c_ptr), value :: v, a
    integer(c_int) :: gsl_linalg_complex_householder_hm
  end function gsl_linalg_complex_householder_hm
  function gsl_linalg_householder_mh (tau, v, a) bind(c)
    import :: c_ptr, c_double, c_int
    real(c_double), value :: tau
    type(c_ptr), value :: v, a
    integer(c_int) :: gsl_linalg_householder_mh
  end function gsl_linalg_householder_mh
  function gsl_linalg_complex_householder_mh (tau, v, a) bind(c)
    import :: c_ptr, c_int, gsl_complex
    type(gsl_complex), value :: tau
    type(c_ptr), value :: v, a
    integer(c_int) :: gsl_linalg_complex_householder_mh
  end function gsl_linalg_complex_householder_mh
  function gsl_linalg_householder_hv (tau, v, w) bind(c)
    import :: c_ptr, c_double, c_int
    real(c_double), value :: tau
    type(c_ptr), value :: v, w
    integer(c_int) :: gsl_linalg_householder_hv
  end function gsl_linalg_householder_hv
  function gsl_linalg_complex_householder_hv (tau, v, w) bind(c)
    import :: c_ptr, c_int, gsl_complex
    type(gsl_complex), value :: tau
    type(c_ptr), value :: v, w
    integer(c_int) :: gsl_linalg_complex_householder_hv
  end function gsl_linalg_complex_householder_hv
  function gsl_linalg_hh_solve (a, b, x) &
       bind(c, name='gsl_linalg_HH_solve')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, b, x
    integer(c_int) :: gsl_linalg_hh_solve
  end function gsl_linalg_hh_solve
  function gsl_linalg_hh_svx (a, x) &
       bind(c, name='gsl_linalg_HH_svx')
    import :: c_ptr, c_int
    type(c_ptr), value :: a, x
    integer(c_int) :: gsl_linalg_hh_svx
  end function gsl_linalg_hh_svx
!
! Tridiagonal
!
  function gsl_linalg_solve_tridiag(diag, e, f, b, x) bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: diag, e, f, b, x
    integer(c_int) :: gsl_linalg_solve_tridiag
  end function gsl_linalg_solve_tridiag
  function gsl_linalg_solve_symm_tridiag(diag, e, b, x) bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: diag, e, b, x
    integer(c_int) :: gsl_linalg_solve_symm_tridiag
  end function gsl_linalg_solve_symm_tridiag
  function gsl_linalg_solve_cyc_tridiag(diag, e, f, b, x) bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: diag, e, f, b, x
    integer(c_int) :: gsl_linalg_solve_cyc_tridiag
  end function gsl_linalg_solve_cyc_tridiag
  function gsl_linalg_solve_symm_cyc_tridiag(diag, e, b, x) bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: diag, e, b, x
    integer(c_int) :: gsl_linalg_solve_symm_cyc_tridiag
  end function gsl_linalg_solve_symm_cyc_tridiag
  function gsl_linalg_qr_matq(QR, tau, A) &
    bind(c, name='gsl_linalg_QR_matQ')
    import :: c_ptr, c_int
    type(c_ptr), value :: QR, tau, A
    integer(c_int) :: gsl_linalg_qr_matq
  end function gsl_linalg_qr_matq
  subroutine gsl_linalg_givens(a, b, c, s) bind(c)
    import :: c_double
    real(c_double), value :: a, b
    real(c_double):: c, s
  end subroutine gsl_linalg_givens
  subroutine gsl_linalg_givens_gv(v, i, j, c, s) bind(c)
    import :: c_ptr, c_size_t, c_double
    type(c_ptr), value :: v
    integer(c_size_t), value :: i, j
    real(c_double), value :: c, s
  end subroutine gsl_linalg_givens_gv
!
! Triangular matrices 
! 
  integer(c_int) function gsl_linalg_tri_invert(uplo, diag, t) bind(c)
    import :: c_int, c_ptr
    integer(c_int), value :: uplo, diag
    type(c_ptr), value :: t
  end function gsl_linalg_tri_invert
  integer(c_int) function gsl_linalg_complex_tri_invert(uplo, diag, t) bind(c)
    import :: c_int, c_ptr
    integer(c_int), value :: uplo, diag
    type(c_ptr), value :: t
  end function gsl_linalg_complex_tri_invert
  integer(c_int) function gsl_linalg_tri_ltl(l) bind(c, name='gsl_linalg_tri_LTL')
    import :: c_int, c_ptr
    type(c_ptr), value :: l
  end function gsl_linalg_tri_ltl
  integer(c_int) function gsl_linalg_complex_tri_lhl(l) bind(c, name='gsl_linalg_complex_tri_LHL')
    import :: c_int, c_ptr
    type(c_ptr), value :: l
  end function gsl_linalg_complex_tri_lhl
  integer(c_int) function gsl_linalg_tri_ul(lu) bind(c, name='gsl_linalg_tri_UL')
    import :: c_int, c_ptr
    type(c_ptr), value :: lu
  end function gsl_linalg_tri_ul
  integer(c_int) function gsl_linalg_complex_tri_ul(lu) bind(c, name='gsl_linalg_complex_tri_UL')
    import :: c_int, c_ptr
    type(c_ptr), value :: lu
  end function gsl_linalg_complex_tri_ul
  integer(c_int) function gsl_linalg_tri_rcond(uplo, a, rcond, work) bind(c)
    import :: c_int, c_ptr, c_double
    integer(c_int), value :: uplo
    real(c_double), intent(inout) :: rcond
    type(c_ptr), value :: a, work
  end function gsl_linalg_tri_rcond
!
! Triangular matrices (legacy)
! 
  integer(c_int) function gsl_linalg_tri_upper_invert(t) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: t
  end function
  integer(c_int) function gsl_linalg_tri_lower_invert(t) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: t
  end function
  integer(c_int) function gsl_linalg_tri_upper_unit_invert(t) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: t
  end function
  integer(c_int) function gsl_linalg_tri_lower_unit_invert(t) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: t
  end function
  integer(c_int) function gsl_linalg_tri_upper_rcond(t, rcond, work) bind(c)
    import :: c_int, c_double, c_ptr
    type(c_ptr), value :: t, work
    real(c_double) :: rcond
  end function
  integer(c_int) function gsl_linalg_tri_lower_rcond(t, rcond, work) bind(c)
    import :: c_int, c_double, c_ptr
    type(c_ptr), value :: t, work
    real(c_double) :: rcond
  end function
  !
  ! Banded systems
  !
  integer(c_int) function gsl_linalg_cholesky_band_decomp(a) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: a
  end function gsl_linalg_cholesky_band_decomp
  integer(c_int) function gsl_linalg_cholesky_band_solve(llt, b, x) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: llt, b, x
  end function gsl_linalg_cholesky_band_solve
  integer(c_int) function gsl_linalg_cholesky_band_svx(llt, x) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: llt, x
  end function gsl_linalg_cholesky_band_svx
  integer(c_int) function gsl_linalg_cholesky_band_invert(llt, ainv) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: llt, ainv
  end function gsl_linalg_cholesky_band_invert
  integer(c_int) function gsl_linalg_cholesky_band_unpack(llt, l) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: llt, l
  end function gsl_linalg_cholesky_band_unpack
  integer(c_int) function gsl_linalg_cholesky_band_rcond(llt, rcond, w) bind(c)
    import :: c_int, c_ptr, c_double
    type(c_ptr), value :: llt, w
    real(c_double) :: rcond
  end function gsl_linalg_cholesky_band_rcond
  integer(c_int) function gsl_linalg_ldlt_band_decomp(a) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: a
  end function gsl_linalg_ldlt_band_decomp
  integer(c_int) function gsl_linalg_ldlt_band_solve(ldlt, b, x) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: ldlt, b, x
  end function gsl_linalg_ldlt_band_solve
  integer(c_int) function gsl_linalg_ldlt_band_svx(ldlt, x) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: ldlt, x
  end function gsl_linalg_ldlt_band_svx
  integer(c_int) function gsl_linalg_ldlt_band_invert(ldlt, ainv) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: ldlt, ainv
  end function gsl_linalg_ldlt_band_invert
  integer(c_int) function gsl_linalg_ldlt_band_unpack(ldlt, l, d) bind(c)
    import :: c_int, c_ptr
    type(c_ptr), value :: ldlt, l, d
  end function gsl_linalg_ldlt_band_unpack
  integer(c_int) function gsl_linalg_ldlt_band_rcond(ldlt, rcond, w) bind(c)
    import :: c_int, c_ptr, c_double
    type(c_ptr), value :: ldlt, w
    real(c_double) :: rcond
  end function gsl_linalg_ldlt_band_rcond
  !
  ! Balancing
  !
  function gsl_linalg_balance_matrix (a, d) bind(c)
    import :: c_ptr, c_int
    type(c_ptr), value :: a, d
    integer(c_int) :: gsl_linalg_balance_matrix
  end function gsl_linalg_balance_matrix