p_A1B1_Ed: Internal C++ functions

Description

These are internal C++ functions called from corresponding R functions when use_cpp = TRUE. Direct access by the user is not assumed. All parameters are assumed to be appropriately structured.

Usage

p_A1B1_Ed(
  quantile,
  A,
  B,
  mu,
  m,
  stop_on_error,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
p_A1B1_El(
  quantile,
  A,
  B,
  mu,
  m,
  stop_on_error,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
p_A1B1_Ec(
  quantile,
  A,
  B,
  mu,
  m,
  stop_on_error,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
d_A1I1_Ed(quantile, LA, m, thr_margin = 100)
p_imhof_Ed(
  quantile,
  A,
  B,
  mu,
  autoscale_args,
  stop_on_error,
  tol_zero,
  epsabs,
  epsrel,
  limit
)
d_broda_Ed(
  quantile,
  A,
  B,
  mu,
  autoscale_args,
  stop_on_error,
  tol_zero,
  epsabs,
  epsrel,
  limit
)
d_butler_Ed(
  quantile,
  A,
  B,
  mu,
  order_spa,
  stop_on_error,
  tol_zero,
  epsabs,
  epsrel,
  maxiter
)
p_butler_Ed(
  quantile,
  A,
  B,
  mu,
  order_spa,
  stop_on_error,
  tol_zero,
  epsabs,
  epsrel,
  maxiter
)
Ap_int_E(A, mu, p_ = 1, thr_margin = 100, tol_zero = 2.2e-14)
ABpq_int_E(A, LB, mu, p_ = 1, q_ = 1, thr_margin = 100, tol_zero = 2.2e-14)
ABDpqr_int_E(
  A,
  LB,
  D,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  thr_margin = 100,
  tol_zero = 2.2e-14
)
ApIq_int_cE(A, p_ = 1, q_ = 1, thr_margin = 100)
ApIq_int_nE(A, mu, p_ = 1, q_ = 1, thr_margin = 100)
ApIq_npi_cE(
  LA,
  bA,
  p_ = 1,
  q_ = 1,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100
)
ApIq_npi_nEd(
  LA,
  bA,
  mu,
  p_ = 1,
  q_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 1L
)
ApBq_int_E(
  A,
  LB,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100,
  tol_zero = 2.2e-14
)
ApBq_npi_Ed(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBIqr_int_cEd(
  A,
  LB,
  bB,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100,
  tol_zero = 2.2e-14
)
ApBIqr_int_nEd(
  A,
  LB,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBIqr_npi_Ed(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
IpBDqr_gen_Ed(
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBDqr_int_Ed(
  A,
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBDqr_npi_Ed(
  A,
  LB,
  D,
  bA,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApIq_npi_nEc(
  LA,
  bA,
  mu,
  p_ = 1,
  q_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 1L
)
ApBq_npi_Ec(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBIqr_int_nEc(
  A,
  LB,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBIqr_npi_Ec(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
IpBDqr_gen_Ec(
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBDqr_int_Ec(
  A,
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBDqr_npi_Ec(
  A,
  LB,
  D,
  bA,
  bB,
  bD,
  mu,
  p_ = 1,
  q_ = 1,
  r_ = 1,
  m = 100L,
  thr_margin = 100,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApIq_npi_nEl(
  LA,
  bA,
  mu,
  p_ = 1L,
  q_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 1L
)
ApBq_npi_El(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1L,
  q_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBIqr_int_nEl(
  A,
  LB,
  bB,
  mu,
  p_ = 1L,
  q_ = 1L,
  r_ = 1L,
  m = 100L,
  error_bound = TRUE,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBIqr_npi_El(
  A,
  LB,
  bA,
  bB,
  mu,
  p_ = 1L,
  q_ = 1L,
  r_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
IpBDqr_gen_El(
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1L,
  q_ = 1L,
  r_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBDqr_int_El(
  A,
  LB,
  D,
  bB,
  bD,
  mu,
  p_ = 1L,
  q_ = 1L,
  r_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
ApBDqr_npi_El(
  A,
  LB,
  D,
  bA,
  bB,
  bD,
  mu,
  p_ = 1L,
  q_ = 1L,
  r_ = 1L,
  m = 100L,
  thr_margin = 100L,
  nthreads = 0L,
  tol_zero = 2.2e-14
)
rqfpE(nit, A, B, D, p_, q_, r_, mu, Sigma)

Value

All return a list via Rcpp::List of the following (as appropriate):

$ans: Exact moment, from double or long double
$ansseq: Series for the moment, from Eigen::Array
$errseq: Series of errors, from Eigen::Array
$twosided: Logical, from bool
$dimnished: Logical, from bool

Arguments

quantile: Scalar of quantile $q$, passed as double
A, B, D: Argument matrices passed as Eigen::Matrix. Symmetry is assumed.
mu: Mean vector $\bm{\mu}$ for $\mathbf{x}$ passed as Eigen::Array. For d_broda_Ed(), assumed to be rotated by the eigenvectors of $\mathbf{A} - q \mathbf{B}$
m: Integer to specify the order of polynomials at which the series expression is truncated. Passed as Eigen::Index (aka std::ptrdiff_t or long long int)
stop_on_error: bool to specify whether execution is stopped upon error in numerical integration or root finding
thr_margin: Optional argument to adjust the threshold for scaling. See “Scaling” in d1_i.
nthreads: int to specify the number of threads in OpenMP-enabled functions. See “Multithreading” in qfrm.
tol_zero: Tolerance against which numerical zero is determined
LA, LB: Eigenvalues of the argument matrices passed as Eigen::Array
autoscale_args: Factor to which the largest absolute eigenvalue of $\mathbf{A} - q \mathbf{B}$ is scaled, passed as double
epsrel, epsabs, limit, maxiter: Optional arguments passed to gsl_integration_qagi() or gsl_root_test_delta()
order_spa: int to specify order of saddlepoint approximation
p_, q_, r_: Exponents for $\mathbf{A}$, $\mathbf{B}$, and $\mathbf{D}$. Passed as double or long double.
bA, bB, bD: Scaling coefficients for $\mathbf{A}$, $\mathbf{B}$, and $\mathbf{D}$. Passed as double or long double.
error_bound: bool to specify whether the error bound is returned
nit: int to specify the number of iteration or sample size
Sigma: Covariance matrix $\mathbf{\Sigma}$ for $\mathbf{x}$. Passed as Eigen::Matrix.

Functions

p_A1B1_Ed(): pqfm_A1B1(), double
p_A1B1_El(): pqfm_A1B1(), long double
p_A1B1_Ec(): pqfm_A1B1(), coefficient-wise scaling
d_A1I1_Ed(): dqfm_A1I1()
p_imhof_Ed(): pqfm_imhof()
d_broda_Ed(): dqfm_broda()
d_butler_Ed(): dqfm_butler()
p_butler_Ed(): pqfm_butler()
Ap_int_E(): qfm_Ap_int()
ABpq_int_E(): qfpm_ABpq_int()
ABDpqr_int_E(): qfpm_ABDpqr_int()
ApIq_int_cE(): qfrm_ApIq_int(), central
ApIq_int_nE(): qfrm_ApIq_int(), noncentral
ApIq_npi_cE(): qfrm_ApIq_npi(), central
ApIq_npi_nEd(): qfrm_ApIq_npi(), noncentral, double
ApBq_int_E(): qfrm_ApBq_int()
ApBq_npi_Ed(): qfrm_ApBq_npi(), double
ApBIqr_int_cEd(): qfmrm_ApBIqr_int(), central
ApBIqr_int_nEd(): qfmrm_ApBIqr_int(), noncentral, double
ApBIqr_npi_Ed(): qfmrm_ApBIqr_npi(), double
IpBDqr_gen_Ed(): qfmrm_IpBDqr_gen(), double
ApBDqr_int_Ed(): qfmrm_ApBDqr_int(), double
ApBDqr_npi_Ed(): qfmrm_ApBDqr_npi(), double
ApIq_npi_nEc(): qfrm_ApIq_npi(), noncentral, coefficient-wise scaling
ApBq_npi_Ec(): qfrm_ApBq_npi(), coefficient-wise scaling
ApBIqr_int_nEc(): qfmrm_ApBIqr_int(), noncentral, coefficient-wise scaling
ApBIqr_npi_Ec(): qfmrm_ApBIqr_npi(), coefficient-wise scaling
IpBDqr_gen_Ec(): qfmrm_IpBDqr_gen(), double
ApBDqr_int_Ec(): qfmrm_ApBDqr_int(), coefficient-wise scaling
ApBDqr_npi_Ec(): qfmrm_ApBDqr_npi(), coefficient-wise scaling
ApIq_npi_nEl(): qfrm_ApIq_npi(), noncentral, long double
ApBq_npi_El(): qfrm_ApBq_npi(), long double
ApBIqr_int_nEl(): qfmrm_ApBIqr_int(), noncentral, long double
ApBIqr_npi_El(): qfmrm_ApBIqr_npi(), long double
IpBDqr_gen_El(): qfmrm_IpBDqr_gen(), long double
ApBDqr_int_El(): qfmrm_ApBDqr_int(), long double
ApBDqr_npi_El(): qfmrm_ApBDqr_npi(), long double
rqfpE(): rqfp()

Details

ApIq_int_nmE() calls the C function gsl_sf_hyperg_1F1() from GSL via RcppGSL.