p_A1B1_Ed {qfratio}

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)

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.

Details

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

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

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()