Chapter Contents
NAG Toolbox

# Advice on Replacement Calls for Withdrawn/Superseded Routines

## C05 – Roots of One or More Transcendental Equations

Scheduled for withdrawal at Mark 25.
Replaced by nag_roots_contfn_brent (c05ay).
```Old: function [f] = c05ad_f(xx)
...
end
...
New: function [f, user] = c05ay_f(xx, user)
...
end
...
[x, user, ifail] = c05ay(a, b, eps, eta, 'c05ay_f')```

### c05ag

Scheduled for withdrawal at Mark 25.
Replaced by nag_roots_contfn_brent_interval (c05au).
```Old: function [f] = c05ag_f(xx)
...
end
...
[x, a, b, ifail] = c05ag(x, h, eps, eta, 'c05ag_f')
New: function [f, user] = c05au_f(xx, user)
...
end
...
[x, a, b, user, ifail] = c05au(x, h, eps, eta, 'c05au_f')```

### c05aj

Scheduled for withdrawal at Mark 25.
Replaced by nag_roots_contfn_cntin (c05aw).
```Old: function [f] = c05aj_f(xx)
...
end
...
[x, ifail] = c05aj(x, eps, eta, 'c05aj_f', nfmax)
New: function [f, user] = c05aw_f(xx, user)
...
end
...
[x, user, ifail] = c05aw(x, eps, eta, 'c05aw_f', nfmax)```

### c05nb

Scheduled for withdrawal at Mark 25.
Replaced by nag_roots_sys_func_easy (c05qb).
```Old: function  [fvec, iflag] = c05nb_fcn(n, x, iflag)
...
end
...
[x, fvec, ifail] = c05nb('c05nb_fcn', x)
New: function  [fvec, user, iflag] = c05qb_fcn(n, x, user, iflag)
...
end
...
[x, fvec, user, ifail] = c05qb('c05qb_fcn', x)```

### c05nc

Scheduled for withdrawal at Mark 25.
Replaced by nag_roots_sys_func_expert (c05qc).
```Old: function  [fvec, iflag] = c05nc_fcn(n, x, iflag)
...
end
...
[x, fvec, diag, nfev, fjac, r, qtf, ifail] = c05nc('c05nc_fcn', x, ...
ml, mu, diag, mode, nprint, lr)
New: function  [fvec, user, iflag] = c05qc_fcn(n, x, user, iflag)
...
end
...
[x, fvec, diag, nfev, fjac, r, qtf, ifail] = c05qc('c05qc_fcn', x, ...
ml, mu, mode, diag, nprint)```

### c05nd

Scheduled for withdrawal at Mark 25.
Replaced by nag_roots_sys_func_rcomm (c05qd).
```Old: [irevcm, x, fvec, diag, fjac, r, qtf, w, ifail] = c05nd(irevcm, x, fvec, ...
ml, mu, diag, mode, fjac, r, qtf, w)
New: iwsav = zeros(17, 1, 'int64');
rwsav = zeros(4*n + 20, 1);
...
[irevcm, x, fvec, diag, fjac, r, qtf, iwsav, rwsav, ifail] = c05qd(irevcm, x, fvec, ...
ml, mu, mode, diag, fjac, r, qtf, iwsav, rwsav)```

### c05pb

Scheduled for withdrawal at Mark 25.
Replaced by nag_roots_sys_deriv_easy (c05rb).
```Old: function  [fvec, fjac, iflag] = c05pb_fcn(n, x, fvec, fjac, ldfjac, iflag)
...
end
...
[x, fvec, fjac, ifail] = c05pb('c05pb_fcn', x)
New: function  [fvec, fjac, user, iflag] = c05rb_fcn(n, x, fvec, fjac, user, iflag)
...
end
...
[x, fvec, fjac, user, ifail] = c05rb('c05rb_fcn', x)```

### c05pc

Scheduled for withdrawal at Mark 25.
Replaced by nag_roots_sys_deriv_expert (c05rc).
```Old: function  [fvec, fjac, iflag] = c05pc_fcn(n, x, fvec, fjac, ldfjac, iflag)
...
end
...
[x, fvec, fjac, diag, nfev, njev, r, qtf, ifail] = c05pc('c05pc_fcn', x, ...
diag, mode, nprint, lr)
New: function  [fvec, fjac, user, iflag] = c05rc_fcn(n, x, fvec, fjac, user, iflag)
...
end
...
[x, fvec, fjac, diag, nfev, njev, r, qtf, ifail] = c05rc('c05rc_fcn', x, ...
mode, diag, nprint)```

### c05pd

Scheduled for withdrawal at Mark 25.
Replaced by nag_roots_sys_deriv_rcomm (c05rd).
```Old: [irevcm, x, fvec, diag, fjac, r, qtf, w, ifail] = c05pd(irevcm, x, fvec, ...
fjac, diag, mode, r, qtf, w)
New: iwsav = zeros(17, 1, 'int64');
rwsav = zeros(4*n + 10, 1);
...
[irevcm, x, fvec, diag, fjac, r, qtf, iwsav, rwsav, ifail] = c05rd(irevcm, x, fvec, ...
fjac, mode, diag, r, qtf, iwsav, rwsav)```

### c05za

Scheduled for withdrawal at Mark 25.
Replaced by nag_roots_sys_deriv_check (c05zd).
```OLD: [xp, err] = c05za(x, fvec, fjac, fvecp, mode);
NEW: [xp, err, ifail] = c05zd(mode, x, fvec, fjac, fvecp);
```
The array xp will now have dimension n regardless of the value of mode, and likewise err will now have dimension m regardless. The parameter ifail is the standard NAG parameter for error trapping.

## C06 – Summation of Series

### c06db

Scheduled for withdrawal at Mark 25.
Replaced by nag_sum_chebyshev (c06dc).
```Old: for i=1:lx
[result(i)] = c06db(x(i),c,s);
end
New: xmin = -1.0, xmax = 1.0;

if (s == 1 || s == 2 || s == 3)
s_use = s;
else
s_use = 2;
end

[result, ifail] = c06dc(x,xmin,xmax,c,s_use);```
The old function c06db returns a single sum at a time, whereas the new function nag_sum_chebyshev (c06dc) returns a vector of lx values at once. The parameter ifail is the standard NAG parameter for error trapping.

### c06ea

Scheduled for withdrawal at Mark 26.
Replaced by nag_sum_fft_realherm_1d (c06pa).
```Old:[x, ifail] = c06ea(x)
New:[x, ifail] = c06pa('f', x, n)
```
The output values x are stored in a different order with real and imaginary parts stored contiguously. The mapping of output elements is as follows:
• x(2 × i)x(i)${\mathbf{x}}\left(2×\mathit{i}\right)←\mathrm{x}\left(\mathit{i}\right)$, for i = 0,1,,n / 2$\mathit{i}=0,1,\dots ,{\mathbf{n}}/2$ and
x(2 + i + 1)x(ni)${\mathbf{x}}\left(2+\mathit{i}+1\right)←{\mathbf{x}}\left({\mathbf{n}}-\mathit{i}\right)$, for i = 1,2,,(n + 1) / 2$\mathit{i}=1,2,\dots ,\left({\mathbf{n}}+1\right)/2$.

### c06eb

Scheduled for withdrawal at Mark 26.
Replaced by nag_sum_fft_realherm_1d (c06pa).
```Old: [x, ifail] = c06eb(x)
New: [x, ifail] = c06pa('b', x, n);
```
x(0 : n + 1)${\mathbf{x}}\left(0:{\mathbf{n}}+1\right)$ has been extended by 2$2$ elements from the original x(0 : n1)${\mathbf{x}}\left(0:{\mathbf{n}}-1\right)$. The input values of x are stored in a different order with real and imaginary parts stored contiguously. Also nag_sum_fft_realherm_1d (c06pa) performs the inverse transform without the need to first conjugate. If prior conjugation of original array x is assumed then the mapping of input elements is:
• x(2 × i)x(i)${\mathbf{x}}\left(2×\mathit{i}\right)←\mathrm{x}\left(\mathit{i}\right)$, for i = 0,1,,n / 2$\mathit{i}=0,1,\dots ,{\mathbf{n}}/2$ and
x(2 × i + 1)x(ni)${\mathbf{x}}\left(2×\mathit{i}+1\right)←{\mathbf{x}}\left({\mathbf{n}}-\mathit{i}\right)$, for i = 1,2,,(n1) / 2$\mathit{i}=1,2,\dots ,\left({\mathbf{n}}-1\right)/2$.

### c06ec

Scheduled for withdrawal at Mark 26.
Replaced by nag_sum_fft_complex_1d (c06pc).
```Old: [x, y, ifail] = c06ec(x, y)
New: [z, ifail] = c06pc('f', z);
```
z is a complex array of length n such that z(i) = complex(x(i),y(i))$\text{z}\left(\mathit{i}\right)=\mathrm{complex}\left(\text{x}\left(\mathit{i}\right),\text{y}\left(\mathit{i}\right)\right)$, for i = 0,1,n1$\mathit{i}=0,1,\dots {\mathbf{n}}-1$ on input and output.

### c06ek

Scheduled for withdrawal at Mark 26.
Replaced by nag_sum_convcorr_real (c06fk).
```Old: [x, y, ifail] = c06ek(job, x, y)
New: [x, y, ifail] = c06fk(job, x, y)
```

### c06fr

Scheduled for withdrawal at Mark 26.
Replaced by nag_sum_fft_complex_1d_multi_col (c06ps).
```Old: [x, y, trig, ifail] = c06fr(m, n, x, y, init, trig)
New: [z, ifail] = c06pr('f', m, n, complex(x,y))
x = real(z)
y = imag(z)
```

### c06fu

Scheduled for withdrawal at Mark 26.
Replaced by nag_sum_fft_complex_2d (c06pu).
```Old: [x, y, trigm, trign, ifail] = c06fu(m, n, x, y, init, trigm, trign)
New: [z, ifail] = c06pr('f', m, n, complex(x, y));
x = real(z)
y = imag(z)
```

### c06gb

Scheduled for withdrawal at Mark 26.
There is no replacement for this routine.

### c06gc

Scheduled for withdrawal at Mark 26.
There is no replacement for this routine.

### c06gq

Scheduled for withdrawal at Mark 26.
There is no replacement for this routine.

### c06gs

Scheduled for withdrawal at Mark 26.
There is no replacement for this routine.

### c06ha

Scheduled for withdrawal at Mark 26.
Replaced by nag_sum_fft_real_sine_simple (c06ra).
```Old: [x, trig, ifail] = c06ha(m, n, x, init, trig)
New: y(1:m*(n-1)) = x(1:m*(n-1))
[y, ifail] = c06ra(m, n, y)
x = y(1:m*n)
```
where y$\mathrm{y}$ is a real array of lengths m × (n + 2)$\mathrm{m}×\left(\mathrm{n}+2\right)$.

### c06hb

Scheduled for withdrawal at Mark 26.
Replaced by nag_sum_fft_real_sine_simple (c06ra).
```Old: [x, trig, ifail] = c06hb(m, n, x, init, trig)
New: y(1:m*(n+1)) = x(1:m*(n+1))
[y, ifail] = c06rb(m, n, y)
x = y(1:m*(n+1)
```

### c06hc

Scheduled for withdrawal at Mark 26.
Replaced by nag_sum_fft_real_qtrsine_simple (c06rc).
```Old: [x, trig, ifail] = c06hc(direct, m, n, x, init, trig)
New: y(1:m*n) = x(1:m*n)
[y, ifail] = c06ra(m, n, y)
x = y(1:m*n)
```
where y$\mathrm{y}$ is a real array of length m × (n + 2)$\mathrm{m}×\left(\mathrm{n}+2\right)$.

### c06hd

Scheduled for withdrawal at Mark 26.
Replaced by nag_sum_fft_real_qtrcosine_simple (c06rd).
```Old: [x, trig, ifail] = c06hd(direct, m, n, x, init, trig)
New: y(1:m*n) = x(1:m*n)
[y, ifail] = c06ra(m, n, y)
x = y(1:m*n)```
where y$\mathrm{y}$ is a real array of length m × (n + 2)$\mathrm{m}×\left(\mathrm{n}+2\right)$.

### d01ba

Scheduled for withdrawal at Mark 26.
```  Old: [result, ifail] = d01ba(d01xxx, a, b, n, @fun)

function [f] = fun(x)
f = ...
New: % set key according to quadrature formula
% key =  0 : (d01xxx='d01baz')
% key = -3 : (d01xxx='d01bay')
% key = -4 : (d01xxx='d01baw')
% key = -5 : (d01xxx='d01bax')
% key = abs(key) for normal weights
key = 0
[result, user, ifail] = d01ua(key, a, b, n, @f, 'user', user)
function [fv, iflag, user] = f(x, nx, iflag, user)
% see example below
...
fv = ...
```
user can be used to pass information to the user-supplied function f.
iflag is an integer which you may use to force an immediate exit from nag_quad_1d_gauss_vec (d01ua) in case of an error in the user-supplied function f.
f may be used to call the original FUN as follows, although it may be more efficient to recode the integrand.
```  function [fv, iflag, user] = f(x, nx, iflag, user)
fv = fun(x)
```

### d01bb

Scheduled for withdrawal at Mark 26.
```Old: [weight, abscis, ifail] = d01bb('d01xxx', a, b, itype, n)
New: [weight, abscis, ifail] = d01tb(key, a, b, n)
```
The supplied functions d01xxx and the parameter itype have been combined into a single parameter key. key < 0${\mathbf{key}}<0$ is equivalent to ITYPE = 1$\text{ITYPE}=1$ (adjusted weights). key > 0${\mathbf{key}}>0$ is equivalent to itype = 0$\mathrm{itype}=0$ (normal weights). |key|$|{\mathbf{key}}|$ indicates the quadrature rule.
• |key| = 0$|{\mathbf{key}}|=0$ : Gauss–Legendre (d01xxx = 'd01baz'$\mathbf{d01xxx}='\mathrm{d01baz}'$)
• |key| = 3$|{\mathbf{key}}|=3$ : Gauss–Laguerre (d01xxx = 'd01bax'$\mathbf{d01xxx}='\mathrm{d01bax}'$)
• |key| = 4$|{\mathbf{key}}|=4$ : Gauss–Hermite (d01xxx = 'd01baw'$\mathbf{d01xxx}='\mathrm{d01baw}'$)
• |key| = 5$|{\mathbf{key}}|=5$ : Rational Gauss (d01xxx = 'd01bay'$\mathbf{d01xxx}='\mathrm{d01bay}'$)

## D02 – Ordinary Differential Equations

### d02pc

Scheduled for withdrawal at Mark 26.
Replaced by nag_ode_ivp_rkts_range (d02pe) and associated D02P functions.
```Old: [work, ifail] = d02pv(tstart, ystart, tend, tol, thres, ...
...
[tgot, ygot, ypgot, ymax, work, ifail] = ...
d02pc(@f, neq, twant, ygot, ymax, work)
New: if not(errass)
method = -method
end
[iwsav, rwsav, ifail] = ...
d02pq(tstart, tend, yinit, tol, thresh, method)
...
[tgot, ygot, ypgot, ymax, user, iwsav, rwsav, ifail] = ...
d02pe(@f2, twant, ygot, ymax, iwsav, rwsav)
```
iuser is available to allow you to pass information to the user defined function f2.
The definition of f2 can use the original function f as follows:
```function [yp, user] = f2(t, n, y, user)
yp = f(t, y)
```

### d02pd

Scheduled for withdrawal at Mark 26.
Replaced by nag_ode_ivp_rkts_onestep (d02pf) and associated D02P functions.
```Old: [work, ifail] = d02pv(tstart, ystart, tend, tol, thresh, ...
[tnow, ynow, ypnow, work, ifail] = d02pd(@f, neq, work)

New: if not(errass)
method = -method
end
[iwsav, rwsav, ifail] = ...
d02pq(tstart, tend, yinit, tol, thresh, method)
[tnow, ynow, ypnow, user, iwsav, rwsav, ifail] = ...
d02pf(@f2, n, iwsav, rwsav);
```
user is available to allow you to pass information to the user defined function f2.
The definition of f2 can use the original function f as follows:
```function [yp, user] = f(t, n, y, user)
yp = f(t, y)
```

### d02pv

Scheduled for withdrawal at Mark 26.
Replaced by nag_ode_ivp_rkts_setup (d02pq).
See d02pc, d02pd for further information.

### d02pw

Scheduled for withdrawal at Mark 26.
Replaced by nag_ode_ivp_rkts_reset_tend (d02pr).
```Old: [ifail] = d02pw(tendnu)
New: [iwsav, rwsav, ifail] = d02pr(tendnu, iwsav, rwsav)
```
iwsav and rwsav are arrays returned by nag_ode_ivp_rkts_setup (d02pq).

### d02px

Scheduled for withdrawal at Mark 26.
Replaced by nag_ode_ivp_rkts_interp (d02ps).
```Old: [ywant, ypwant, work, wrkint, ifail] = ...
d02px(neq, twant, reqest, nwant, @f, work, wrkint)
New: if (reqest=='S' .or. reqest=='s')
ideriv = int64(0)
elseif (reqest=='D' .or. reqest=='d')
ideriv = int64(1)
else
ideriv = int64(2)
end
[ywant, ypwant, wcomm, user, iwsav, rwsav, ifail] = ...
d02ps(n, twant(j), ideriv, nwant, @f2, workint, iwsav, rwsav)
```
iwsav and rwsav are arrays returned by nag_ode_ivp_rkts_setup (d02pq).
user is available to allow you to pass information to the user defined function f2.
The definition of f2 can use the original function f as follows:
```function [yp, user] = f2(t, n, y, user)
yp = f(t, y)
```

### d02py

Scheduled for withdrawal at Mark 26.
Replaced by nag_ode_ivp_rkts_diag (d02pt).
```Old: [totfcn, stpcst, waste, stpsok, hnext, ifail] = d02py
New: [fevals, stepcost, waste, stepsok, hnext, iwsav, ifail] = ...
d02pt(iwsav, rwsav)
```
iwsav and rwsav are arrays returned by nag_ode_ivp_rkts_setup (d02pq).

### d02pz

Scheduled for withdrawal at Mark 26.
Replaced by nag_ode_ivp_rkts_errass (d02pu).
```Old: [rmserr, errmax, terrmx, ifail] = d02pz(n, work)
New: [rmserr, errmax, terrmx, iwsav, rwsav, ifail] = ...
d02pu(n, iwsav, rwsav)
```
n must be unchanged from that passed to nag_ode_ivp_rkts_setup (d02pq).
iwsav and rwsav are arrays returned by nag_ode_ivp_rkts_setup (d02pq).

## E04 – Minimizing or Maximizing a Function

### e04cc

Withdrawn at Mark 24.
Replaced by nag_opt_uncon_simplex (e04cb).
```Old: [x, f, user, ifail] = e04cc(x, tol, funct, monit2, maxcal, 'n', n, 'user', user)
New: [x, f, user, ifail] = e04cb(x, tolf, tolx, funct, monit3, maxcal, 'n', n, 'user', user) ```
The new function can be derived from the old as follows:
```function user = monit3(fmin, fmax, sim, n, ncall, serror, vratio, user)
user = monit2(fmin,fmax,sim,n,n+1,ncall,user);
% Add code here to monitor the values of serror and vratio, if necessary```

### e04un

Withdrawn at Mark 22.
Replaced by nag_opt_lsq_gencon_deriv (e04us).
The specification of the subroutine objfun must also be changed as follows:
```Old: [iter, istate, c, cjac, f, fjac, clamda, objf, r, x, user, ...
ifail] = ...
e04un(a, bl, bu, y, confun, objfun, istate, cjac, fjac, clamda, r, ...
x, 'm', m, 'n', n, 'nclin', nclin, 'ncnln', ncnln, 'user', user)
New: [iter, istate, c, cjac, f, fjac, clamda, objf, r, x, user, ...
lwsav, iwsav, rwsav, ifail] = ...
e04us(a, bl, bu, y, confun, objfun, istate, cjac, fjac, clamda, r, ...
x, lwsav, iwsav, rwsav, 'm', m, 'n', n, 'nclin', nclin, ...
'ncnln', ncnln, 'user', user)```
The specification of the subroutine objfun must also be changed as follows:
```Old: [mode, f, fjac, user] = objfun(mode, m, n, ldfj, x, fjac, nstate, user)
New: [mode, f, fjac, user] = objfun(mode, m, n, ldfj, needfi, x, fjac, nstate, user) ```
See the function documents for further information.

### e04zc

Withdrawn at Mark 24.
There is no replacement for this routine.

## F02 – Eigenvalues and Eigenvectors

### f02bj

Withdrawn at Mark 23.
Replaced by nag_lapack_dggev (f08wa).
```Old: [a, b, alfr, alfi, beta, v, iter, ifail] = f02bj(a, b, eps1, matv, 'n', n);
New: if matv
jobvr = 'v';
else
jobvr = 'n';
end
[a, b, alfr, alfi, beta, vl, vr, info] = f08wa('n', jobvr, a, b, 'n', n);```

### f02ea

Withdrawn at Mark 23.
Replaced by nag_lapack_dgees (f08pa).
```Old: [a, wr, wi, z, ifail] = f02ea(job, a, 'n', n)
New: if (job == 'n')
jobvs = 'n';
else
jobvs = 'v';
end
[a, sdim, wr, wi, vs, info] = f08pa(jobvs, 'n', select, a, 'n', n);

function [result] = select(wr, wi)
result = true;```

### f02eb

Withdrawn at Mark 23.
Replaced by nag_lapack_dgeev (f08na).
```Old: [a, wr, wi, vr, vi, ifail] = f02eb(job, a, 'n', n);
New: if (job == 'n')
jobvr = 'n';
else
jobvr = 'v';
end
[a, wr, wi, vl, vr, info] = f08na('n', jobvr, a, 'n', n);  ```
Note that Eigenvector information is stored differently in vr. See the function documents for further details.

### f02fa

Withdrawn at Mark 23.
Replaced by nag_lapack_dsyev (f08fa).
```Old: [a, w, ifail] = f02fa(job, uplo, a, 'n', n);
New: [a, w, info] = f08fa(jobz, uplo, a, 'n', n);```

### f02fc

Withdrawn at Mark 23.
Replaced by nag_lapack_dsyevx (f08fb).
```Old: [a, m, w, z, ifail] = f02fc(job, range, uplo, a, wl, wu, il, iu, mest, 'n', n);
New: [a, m, w, z, jfail, info] = f08fb(job, range, uplo, a, wl, wu, il, iu, abstol, 'n', n);```

### f02fd

Withdrawn at Mark 23.
Replaced by nag_lapack_dsygv (f08sa).
```Old: [a, b, w, ifail] = f02fd(itype, job, uplo, a, b, 'n', n);
New: [a, b, w, info] = f08sa(itype, job, uplo, a, b, 'n', n);```

### f02fh

Withdrawn at Mark 23.
Replaced by nag_lapack_dsbgv (f08ua).
```Old: [a, b, d, ifail] = f02fh(ma, a, mb, b, 'n', n);
New: [a, b, d, z, info] = f08ua('n', 'u', ma, mb, a, b, 'n', n);```
The order of eigenvalues in d changes from descending to ascending.

### f02ga

Withdrawn at Mark 23.
Replaced by nag_lapack_zgees (f08pn).
```Old: [a, w, z, ifail] = f02ga(job, a, 'n', n);
New: if (job == 'n')
jobvs = 'n';
else
jobvs = 'v';
end
[a, sdim, w, z, info] = f08pn(jobvs, 'n', select, a, 'n', n);

function [result] = select(c)
result = true;```

### f02gb

Withdrawn at Mark 23.
Replaced by nag_lapack_zgeev (f08nn).
```Old: [a, w, v, ifail] = f02gb(job, a, 'n', n);
New: [a, w, vl, v, info] = f08nn('n', job, a, 'n', n);```

### f02gj

Withdrawn at Mark 23.
Replaced by nag_lapack_zggev (f08wn).
```Old: [ar, ai, br, bi, alfr, alfi, beta, vr, vi, iter, ifail] = ...
f02gj(ar, ai, br, bi, eps1, matv, 'n', n);
New: if matv
jobvr = 'v';
else
jobvr = 'n';
end
[a, b, alpha, beta1, vl, v, info] = ...
f08wn('n', jobvr, complex(ar,ai), complex(br,bi), 'n', n);
% Note that the results are single complex objects, rather than the
% real, imaginary pairs returned by f02gj```
Note that the separated double and imaginary parts of input and output data in f02gj has been replaced by combined complex types in nag_lapack_zggev (f08wn).

### f02ha

Withdrawn at Mark 23.
Replaced by nag_lapack_zheev (f08fn).
```Old: [a, w, ifail] = f02ha(job, uplo, a, 'n', n);
New: [a, w, info] = f08fn(job, uplo, a, 'n', n);```

### f02hc

Withdrawn at Mark 23.
Replaced by nag_lapack_zheevx (f08fp).
```Old: [a, m, w, z, ifail] = f02hc(job, range, uplo, a, wl, wu, il, iu, mest, 'n', n);
New: [a, m, w, z, jfail, info] = f08fp(job, range, uplo, a, wl, wu, il, iu, abstol, 'n', n); ```

### f02hd

Withdrawn at Mark 23.
Replaced by nag_lapack_zhegv (f08sn).
```Old: [a, b, w, ifail] = f02hd(itype, job, uplo, a, b, 'n', n);
New: [a, b, w, info] = f08sn(itype, job, uplo, a, b, 'n', n);```

### f02we

Withdrawn at Mark 23.
Replaced by nag_lapack_dgesvd (f08kb).
```Old: [a, b, q, sv, pt, work, ifail] = f02we(a, b, wantq, wantp, 'm', m, 'n', n, 'ncolb', ncolb);
New: if wantq
jobu = 'a';
else
jobu = 'n';
end
if wantp
jobvt = 'a';
else
jobvt = 'n';
end
[a, sv, u, pt, info] = f08kb(jobu, jobvt, a, 'm', m, 'n', n);```
Please note that the facility to return QTB${Q}^{\mathrm{T}}B$ is not provided so arguments wantb$\mathrm{wantb}$ and b$\mathrm{b}$ are not required. Instead, nag_lapack_dgesvd (f08kb) has an option to return the entire m * m${\mathbf{m}}*{\mathbf{m}}$ orthogonal matrix Q$Q$, referred to as u${\mathbf{u}}$ in its documentation, through its 8th argument.

### f02xe

Withdrawn at Mark 23.
Replaced by nag_lapack_zgesvd (f08kp).
```Old: [a, b, q, sv, ph, rwork, ifail] = f02xe(a, b, wantq, wantp, 'm', m, 'n', n, 'ncolb', ncolb);
New: if wantq
jobu = 'a';
else
jobu = 'n';
end
if wantp
jobvt = 'a';
else
jobvt = 'n';
end
[a, sv, q, ph, info] = f08kp(jobu, jobvt, a, 'm', m, 'n', n);```
Please note that the facility to return QHB${Q}^{\mathrm{H}}B$ is not provided so arguments wantb$\mathrm{wantb}$ and b$\mathrm{b}$ are not required. Instead, nag_lapack_zgesvd (f08kp) has an option to return the entire m * m${\mathbf{m}}*{\mathbf{m}}$ unitary matrix Q$Q$, referred to as u${\mathbf{u}}$ in its documentation, through its 8th argument.

## F03 – Determinants

### f03aa

Scheduled for withdrawal at Mark 25.
Replaced by nag_lapack_dgetrf (f07ad) and nag_det_real_gen (f03ba).
```OLD: [a, det, ifail] = f03aa(a);
NEW: ...
[d, id, ifail] = f03ba(a, ipiv);
det = d*2^id;
```

### f03ab

Scheduled for withdrawal at Mark 25.
Replaced by nag_lapack_dpotrf (f07fd) and nag_det_real_sym (f03bf).
```OLD: [a, det, ifail] = f03ab(a);
NEW: ...
[a, info] = f07fd('u', a);
[d, id, ifail] = f03bf(a);
det = d*2^id;
```
Note: the upper triangular part of A$A$, stored in a, has been replaced here by its Cholesky factorization; the lower triangular part of A$A$ can be used and overwritten by replacing 'u' by 'l' in the call to nag_lapack_dpotrf (f07fd) above.

### f03ac

Scheduled for withdrawal at Mark 25.
Replaced by nag_lapack_dpbtrf (f07hd) and nag_det_real_band_sym (f03bh).
```OLD: [det, rl, ifail] = f03ac(a, m);
NEW: ...
[ab, info] = f07hd('l', kd, ab);
[d, id, ifail] = f03bh('l', kd, ab);
det = d*2^id;`
```
Note: the storage of A$A$ in arrays a and ab is different. In fact ab(i,j) = a(j,i)${\mathbf{ab}}\left(\mathit{i},\mathit{j}\right)=\mathrm{a}\left(\mathit{j},\mathit{i}\right)$, for i = 1,2,,m$\mathit{i}=1,2,\dots ,m$ and j = max (1,im),,,i$\mathit{j}=\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,i-m\right),,\dots ,i$ which conforms to the LAPACK banded storage scheme. The factorization is returned in ab rather than in a separate array (rl). The upper part of matrix A$A$ can also be stored in ab on input to nag_lapack_dpbtrf (f07hd).

Scheduled for withdrawal at Mark 25.
Replaced by nag_lapack_zgetrf (f07ar) and nag_det_complex_gen (f03bn).
```OLD: [a, detr, deti, ifail] = f03ad(a);
New: ...
[a, ipiv, info] = f07ar(a);
[d, id, ifail] = f03bn(a, ipiv);
detr = real(d)*2^id;
deti = imag(d)*2^id;
```
Note: the real and imaginary parts of the determinant are independently scaled.

### f03ae

Scheduled for withdrawal at Mark 25.
Replaced by nag_lapack_dpotrf (f07fd) and nag_det_real_sym (f03bf).
```OLD: [a, p, d1, id, ifail] = f03ae(a);
NEW: ...
[a, info] = f07fd('u', a);
[d, id, ifail] = f03bf(a);
```
Note: the upper triangular part of A$A$, stored in a, has been replaced here by its Cholesky factorization; the lower triangular part of A$A$ can be used and overwritten by replacing uplo = 'U'${\mathbf{uplo}}=\text{'U'}$ by uplo = 'L'${\mathbf{uplo}}=\text{'L'}$ in the call to nag_lapack_dpotrf (f07fd) above.

### f03af

Scheduled for withdrawal at Mark 25.
Replaced by nag_lapack_dgetrf (f07ad) and nag_det_real_gen (f03ba).
```OLD: [a, d1, id, p, ifail] = f03af(epsilon, a);
NEW: ...
[d, id, ifail] = f03ba(a, ipiv);
```
Note: real array p has been replaced by the integer array ipiv for holding the pivots of the factorization.

## F04 – Simultaneous Linear Equations

### f04aa

Withdrawn at Mark 23.
Replaced by nag_lapack_dgesv (f07aa).
```Old: [a, c, ifail] = f04aa(a, b, 'n', n, 'm', m);
New: [a, ipiv, b, info] = f07aa(a, b, 'n', n, 'nrhs_p', nrhs_p);```
Note that the answer is now in b.

### f04ac

Withdrawn at Mark 23.
Replaced by nag_lapack_dpbsv (f07ha).
```Old: [c, rl, ifail] = f04ac(a, b, m, 'n', n, 'ir', ir, 'm1', m1);
New: [ab, b, info] = f07ha('u', n, ab, b, 'n', n, 'nrhs_p', nrhs_p) ;```
Note that a and ab are stored differently. With the 'U' option, ab may be regarded as the transpose of a. Note also that the answer is now stored in b.

Withdrawn at Mark 23.
Replaced by nag_lapack_zgesv (f07an).
```Old: [a, c, ifail] = f04ad(a, b, 'n', n, 'm', m);
New: [a, ipiv, b, info] = f07an(a, b, 'n', n, 'nrhs_p', nrhs_p);```
Note that the answer is now in b.

### f04af

Scheduled for withdrawal at Mark 25.
There is no replacement for this routine.
The factorization and solution of a positive definite linear system can be handled by calls to functions from Chapter F07, e.g., nag_lapack_dposvx (f07fb).
For example:
```OLD: ...
[a, p, d1, id, ifail] = f03ae(a);
[x, bb, k, ifail] = f04af(a, p, b, epsilon);
NEW: ...
[a, af, equed, s, b, x, rcond, ferr, berr, info] = ...
f07fb('e', 'u', a, af, 'y', s, b);
[d, id, ifail] = f03bf(a);
```

### f04ag

Scheduled for withdrawal at Mark 25.
There is no replacement for this routine.
The factorization and solution of a positive definite linear system can be handled by calls to functions from Chapter F07, e.g., nag_lapack_dposv (f07fa).
For example:
```OLD: ...
[a, p, d1, id, ifail] = f03ae(a);
[x] = f04ag(a, p, b);
NEW: ...
[a, b, info] = f07fa('u', a, b);
[d, id, ifail] = f03bf(a);
```

### f04ah

Scheduled for withdrawal at Mark 25.
There is no replacement for this routine.
The factorization and solution of a real general linear system can be handled by calls to functions from the Chapter F07, e.g., nag_lapack_dgesvx (f07ab).
For example:
```OLD: ...
[a, d1, id, p, ifail] = f03af(epsilon, a);
[x, bb, k, ifail] = f04ah(a, aa, p, b, epsilon);
NEW: ...
[a, af, ipiv, equed, r, c, b, x, rcond, ferr, berr, work, info] = ...
f07ab('equil', 'no trans', a, af, ipiv, 'yes', r, c, b);
[d, id, ifail] = f03ba(a, ipiv);
```

### f04aj

Scheduled for withdrawal at Mark 25.
There is no replacement for this routine.
The factorization and solution of a real general linear system can be handled by calls to functions from Chapter F07, e.g., nag_lapack_dgesv (f07aa).
For example:
```OLD: ...
[a, d1, id, p, ifail] = f03af(epsilon, a);
[b] = f04aj(a, p, b);
NEW: ...
[a, ipiv, bOut, info] = f07aa(a, b);
[d, id, ifail] = f03ba(a, ipiv);
```

### f04ar

Withdrawn at Mark 23.
Replaced by nag_lapack_dgesv (f07aa).
```Old: [a, c, ifail] = f04ar(a, b, 'n', n);
New; [a, ipiv, b, info] = f07aa(a, b, 'n', n, 'nrhs_p', nrhs_p);```
Note that the answer is now in b.

### f04ea

Withdrawn at Mark 23.
Replaced by nag_lapack_dgtsv (f07ca).
```Old: [d, du, dl, b, ifail] = f04ea(d, du, dl, b, 'n', n);
New: [dl, d, du, b, info] = f07ca(dl(2), d, du(2), b, 'n', n, 'nrhs_p', nrhs_p);```
Note that the answer is now in b.

### f04fa

Withdrawn at Mark 23.
Replaced by nag_lapack_dptsv (f07ja), or nag_lapack_dpttrf (f07jd) and nag_lapack_dpttrs (f07je).
```Old: [d, e, b, ifail] = f04fa(job, d, e, b, 'n', n);
[d, e, info] = f07jd(d, e, 'n', n);
New: if (job == 0)
[d, e, b, info] = f07ja(d, e, b, 'n', n, 'nrhs_p', nrhs_p);
else
% [d, e, info] = f07jd(d, e, 'n', n);
[b, info] = f07je(d, e, b, 'n', n, 'nrhs_p', nrhs_p);
end```
Note that the answer is now in b.

### f04ja

Withdrawn at Mark 23.
Replaced by nag_lapack_dgelss (f08ka).
```Old: [a, b, sigma, irank, work, ifail] = f04ja(a, b, tol, lwork, 'm', m, 'n', n);
New: [a, b, s, rank, info] = f08ka(a, b, rcond, 'm', m, 'n', n, 'nrhs_p', nrhs_p);```
Note that the answer is now in b, singular values are in s instead of work, and the standard error is not computed.

### f04jd

Withdrawn at Mark 23.
Replaced by nag_lapack_dgelss (f08ka).
```Old: [a, b, sigma, irank, work, ifail] = f04jd(a, b, tol, lwork, 'm', m, 'n', n);
New: [a, b, s, irank, info] = f08ka(a, b, rcond, 'm', m, 'n', n, 'nrhs_p', nrhs_p);```
Note that the answer is now in b, singular values are in s instead of work, and the standard error is not computed.

### f04jl

Withdrawn at Mark 23.
Replaced by nag_lapack_dggglm (f08zb).
```Old: [a, b, d, x, y, ifail] = f04jl(a, b, d, 'm', m, 'n', n, 'p', p);
New: [a, b, d, x, y, info] = f08zb(a, b, d, 'm', m, 'n', n, 'p', p);```

### f04jm

Withdrawn at Mark 23.
Replaced by nag_lapack_dgglse (f08za).
```Old: [a, b, c, d, x, ifail] = f04jm(a, b, c, d, 'm', m, 'n', n, 'p', p);
New: [a, b, c, d, x, info] = f08za(a, b, c, d, 'm', m, 'n', n, 'p', p);```

### f04kl

Withdrawn at Mark 23.
Replaced by nag_lapack_zggglm (f08zp).
```Old: [a, b, d, x, y, ifail] = f04kl(a, b, d, 'm', m, 'n', n, 'p', p);
New: [a, b, d, x, y, info] = f08zp(a, b, d, 'm', m, 'n', n, 'p', p);```

### f04km

Withdrawn at Mark 23.
Replaced by nag_lapack_zgglse (f08zn).
```Old: [a, b, c, d, x, ifail] = f04km(a, b, c, d, 'm', m, 'n', n, 'p', p);
New: [a, b, c, d, x, info] = f08zn(a, b, c, d, 'm', m, 'n', n, 'p', p);```

### f04yc

Scheduled for withdrawal at Mark 26.
Replaced by nag_linsys_real_gen_norm_rcomm (f04yd).
```Old: [icase, x, estnrm, work, iwork, ifail] = ...
f04yc(icase, x, estnrm, work, iwork)
New: [irevcm, x, y, estnrm, work, iwork, ifail] = ...
f04yd(irevcm, x, y, estnrm, seed, work, iwork)
```
nag_linsys_real_gen_norm_rcomm (f04yd) returns an estimate of the 1$1$-norm of a rectangular M × N$M×N$ matrix, whereas f04yc only works with square matrices. The real array X, which was previously used to return matrix–vector products to f04yc, has been replaced with two real arrays x(ldx, * )${\mathbf{x}}\left({\mathbf{ldx}},*\right)$ and y(ldy, * )${\mathbf{y}}\left({\mathbf{ldy}},*\right)$ which are used to return matrix-matrix products to nag_linsys_real_gen_norm_rcomm (f04yd). Here, ldxn${\mathbf{ldx}}\ge {\mathbf{n}}$, ldym${\mathbf{ldy}}\ge {\mathbf{m}}$ and the second dimensions of x and y are at least of size t, where you can choose parameter t. The sizes of the workspace arrays work and iwork have been increased to m × t${\mathbf{m}}×{\mathbf{t}}$ and 2 × n + 5 × t + 20$2×{\mathbf{n}}+5×{\mathbf{t}}+20$ respectively. The integer seed provides a seed for the random number generator used by nag_linsys_real_gen_norm_rcomm (f04yd). The integer icase has been replaced by irevcm, which can take the values 0$0$, 1$1$ or 2$2$. See the function documentation for nag_linsys_real_gen_norm_rcomm (f04yd) further details about the reverse communication interface.

### f04zc

Scheduled for withdrawal at Mark 26.
Replaced by nag_linsys_complex_gen_norm_rcomm (f04zd).
```Old: [icase, x, estnrm, work, ifail] = f04zc(icase, x, estnrm, work)
New: [irevcm, x, y, estnrm, work, rwork, iwork, ifail] = ...
f04zd(irevcm, x, y, estnrm, seed, work, rwork, iwork)
```
nag_linsys_complex_gen_norm_rcomm (f04zd) returns an estimate of the 1$1$norm of a rectangular M × N$M×N$ matrix, whereas f04zc only works with square matrices. The complex array X, which was previously used to return matrix–vector products to f04zc, has been replaced with two complex arrays x(ldx, * )${\mathbf{x}}\left({\mathbf{ldx}},*\right)$ and y(ldy, * )${\mathbf{y}}\left({\mathbf{ldy}},*\right)$ which are used to return matrix-matrix products to nag_linsys_complex_gen_norm_rcomm (f04zd). Here, ldxn${\mathbf{ldx}}\ge {\mathbf{n}}$, ldym${\mathbf{ldy}}\ge {\mathbf{m}}$ and the second dimensions of x and y are at least of size t, where you can choose the parameter t. The sizes of the workspace arrays work and iwork have been increased to m × t${\mathbf{m}}×{\mathbf{t}}$ and 2 × n + 5 × t + 20$2×{\mathbf{n}}+5×{\mathbf{t}}+20$ respectively and there is an additional real workspace array rwork of size 2 × n$2×{\mathbf{n}}$. The integer seed provides a seed for the random number generator used by nag_linsys_complex_gen_norm_rcomm (f04zd). The integer icase has been replaced by irevcm, which can take the values 0$0$, 1$1$ or 2$2$. See the function documentation for nag_linsys_complex_gen_norm_rcomm (f04zd) for further details about the reverse communication interface.

## F11 – Large Scale Linear Systems

### f11ga

Withdrawn at Mark 22.
Replaced by nag_sparse_real_symm_basic_setup (f11gd).
```Old: [lwreq, ifail] = f11ga(method, precon, n, tol, maxitn, anorm, sigmax, ...
maxits, monit, 'sigcmp', sigcmp, 'norm_p', norm_p, ...
'weight', weight, 'iterm', iterm, 'sigtol', sigtol)
New: [lwreq, work, ifail] = f11gd(method, precon, n, tol, maxitn, anorm, sigmax, ...
maxits, monit, 'sigcmp', sigcmp, 'norm_p', norm_p, ...
'weight', weight, 'iterm', iterm, 'sigtol', sigtol) ```
nag_sparse_real_symm_basic_setup (f11gd) returns an additional parameter, work.
See the function document for further information.

### f11gb

Withdrawn at Mark 22.
Replaced by nag_sparse_real_symm_basic_solver (f11ge).
```Old: [irevcm, u, v, work, ifail] = f11gb(irevcm, u, v, work, 'n', n, 'lwork', lwork)
New: [irevcm, u, v, work, ifail] = f11ge(irevcm, u, v, wgt, work);```
wgt must be a one-dimensional double array of length at least n $n$ (the order of the matrix) if weights are to be used in the termination criterion, and 1 $1$ otherwise. Note that the call to nag_sparse_real_symm_basic_solver (f11ge) requires the weights to be supplied in wgt(1 : n) ${\mathbf{wgt}}\left(1:n\right)$ rather than work(1 : n) ${\mathbf{work}}\left(1:n\right)$.

### f11gc

Withdrawn at Mark 22.
Replaced by nag_sparse_real_symm_basic_diag (f11gf).
```Old: [itn, stplhs, stprhs, anorm, sigmax, its, sigerr, ifail] = f11gc();
New: [itn, stplhs, stprhs, anorm, sigmax, its, sigerr, ifail] = f11gf(work);```
nag_sparse_real_symm_basic_diag (f11gf) takes an additional parameter, work.
See the function document for further information.

## G01 – Simple Calculations on Statistical Data

### g01aa

Scheduled for withdrawal at Mark 26.
Replaced by nag_stat_summary_onevar (g01at).
```Old: [xmean, s2, s3, s4, xmin, xmax, iwt, wtsum, ifail] = g01aa(x)
New: pn = int64(0)
[pn, xmean, xsd, xskew, xkurt, xmin, xmax, rcomm, ifail] = ...
g01at(x, pn, rcomm)
iwt = pn
wtsum = rcomm(1)
```

## G05 – Random Number Generators

### g05ca

Withdrawn at Mark 22.
Replaced by nag_rand_dist_uniform01 (g05sa).
```Old: for i=1:n
x(i) = g05ca;
end
New: [state, x, ifail] = g05sa(n, state);```
The integer array state in the call to nag_rand_dist_uniform01 (g05sa) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_uniform01 (g05sa) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_uniform01 (g05sa) is likely to be different from those produced by g05ca.

### g05cb

Withdrawn at Mark 22.
Replaced by nag_rand_init_repeat (g05kf).
```Old: g05cb(ii);
New: genid = int64(ii);
subid = int64(1);
seed  = [int64(1)];
[state, ifail] = g05kf(genid, subid, seed);```
The integer array state in the call to nag_rand_init_repeat (g05kf) contains information on the base generator being used. The base generator is chosen via the integer parameters genid and subid. The required length of the array state depends on the base generator chosen. Due to changes in the underlying code a sequence of values produced by using a random number generator initialized via a call to nag_rand_init_repeat (g05kf) is likely to be different from a sequence produced by a generator initialized by g05cb, even if the same value for ii is used.

### g05cc

Withdrawn at Mark 22.
Replaced by nag_rand_init_nonrepeat (g05kg).
```Old: g05cc;
New: genid = int64(1);
subid = int64(1);
[state, ifail] = g05kg(genid, subid);```
The integer array state in the call to nag_rand_init_nonrepeat (g05kg) contains information on the base generator being used. The base generator is chosen via the integer parameters genid and subid.

### g05cf

Withdrawn at Mark 22.
.
```Old: [ia, xi, ifail] = g05cf(ni, nx);
New: cstate = state;```
The state of the base generator for the group of functions nag_rand_init_repeat (g05kf), nag_rand_init_nonrepeat (g05kg), nag_rand_init_leapfrog (g05kh), nag_rand_init_skipahead (g05kj), nag_rand_permute (g05nc), nag_rand_sample (g05nd), nag_rand_times_garch_asym1 (g05pd)nag_rand_matrix_2waytable (g05pz), nag_rand_copula_students_t (g05rc)nag_rand_multivar_normal (g05rz), g05s and g05t can be saved by simply creating a local copy of the array state. The first element of the state array contains the number of elements that are used by the random number generating functions, therefore either this number of elements can be copied, or the whole array (as defined in the calling program).

### g05cg

Withdrawn at Mark 22.
.
```Old: [ifail] = g05cg(ia, xa, 'ni', ni, 'nx', nx)
New: lstate = cstate(1);
state(1:lstate) = cstate(1:lstate);```
The state of the base generator for the group of functions nag_rand_init_repeat (g05kf), nag_rand_init_nonrepeat (g05kg), nag_rand_init_leapfrog (g05kh), nag_rand_init_skipahead (g05kj), nag_rand_permute (g05nc), nag_rand_sample (g05nd), nag_rand_times_garch_asym1 (g05pd)nag_rand_matrix_2waytable (g05pz), nag_rand_copula_students_t (g05rc)nag_rand_multivar_normal (g05rz), g05s and g05t can be restored by simply copying back the previously saved copy of the state array. The first element of the state array contains the number of elements that are used by the random number generating functions, therefore either this number of elements can be copied, or the whole array (as defined in the calling program).

### g05da

Withdrawn at Mark 22.
Replaced by nag_rand_dist_uniform (g05sq).
```Old: for i=1:n
x(i) = g05da(aa,bb);
end
New: [a, b] = sort([aa, bb]);
[state, x, ifail] = g05sq(n, a, b, state);```
The old function g05da returns a single variate at a time, whereas the new function nag_rand_dist_uniform (g05sq) returns a vector of n values in one go. In nag_rand_dist_uniform (g05sq) the minimum value must be held in the parameter a and the maximum in parameter b, therefore a < b${\mathbf{a}}<{\mathbf{b}}$. This was not the case for the equivalent parameters in g05da.
The integer array state in the call to nag_rand_dist_uniform (g05sq) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_uniform (g05sq) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_uniform (g05sq) is likely to be different from those produced by g05da.

### g05db

Withdrawn at Mark 22.
Replaced by nag_rand_dist_exp (g05sf).
```Old: for i=1:n
x(i) = g05db(a);
end
New: [state, x, ifail] = g05sf(n, abs(a), state);```
The old function g05db returns a single variate at a time, whereas the new function nag_rand_dist_exp (g05sf) returns a vector of n values in one go. In nag_rand_dist_exp (g05sf) parameter a must be non-negative, this was not the case for the equivalent parameter in g05db.
The integer array state in the call to nag_rand_dist_exp (g05sf) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_exp (g05sf) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_exp (g05sf) is likely to be different from those produced by g05db.

### g05dc

Withdrawn at Mark 22.
Replaced by nag_rand_dist_logistic (g05sl).
```Old: for  i=1:n
x(i) = g05dc(a,b);
end
New: [state, x, ifail] = g05sl(n, a, abs(b), state);```
The old function g05dc returns a single variate at a time, whereas the new function nag_rand_dist_logistic (g05sl) returns a vector of n values in one go. In nag_rand_dist_logistic (g05sl) the spread (parameter a) must be positive, this was not the case for the equivalent parameters in g05dc.
The integer array state in the call to nag_rand_dist_logistic (g05sl) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_logistic (g05sl) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_logistic (g05sl) is likely to be different from those produced by g05dc.

### g05dd

Withdrawn at Mark 22.
Replaced by nag_rand_dist_normal (g05sk).
```Old: for i=1:n
x(i) = g05dd(xmu, sd);
end
New: [state, x, ifail] = g05sk(n, xmu, sd^2, state);```
The old function g05dd returns a single variate at a time, whereas the new function nag_rand_dist_normal (g05sk) returns a vector of n values in one go. nag_rand_dist_normal (g05sk) expects the variance of the Normal distribution (parameter var), compared to g05dd which expected the standard deviation.
The integer array state in the call to nag_rand_dist_normal (g05sk) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_normal (g05sk) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_normal (g05sk) is likely to be different from those produced by g05dd.

### g05de

Withdrawn at Mark 22.
Replaced by nag_rand_dist_lognormal (g05sm).
```Old: for i=1:n
x(i) = g05de(xmu, sd);
end
New: [state, x, ifail] = g05sm(n, xmu, sd^2, state);```
The old function g05de returns a single variate at a time, whereas the new function nag_rand_dist_lognormal (g05sm) returns a vector of n values in one go. nag_rand_dist_lognormal (g05sm) expects the variance of the corresponding Normal distribution (parameter var), compared to g05de which expected the standard deviation.
The integer array state in the call to nag_rand_dist_lognormal (g05sm) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_lognormal (g05sm) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_lognormal (g05sm) is likely to be different from those produced by g05de.

### g05df

Withdrawn at Mark 22.
Replaced by nag_rand_dist_cauchy (g05sc).
```Old: for i=1:n
x(i) = g05df(xmed, b);
end
New: [state, x, ifail] = g05sc(n, xmed, abs(b), state);```
The old function g05df returns a single variate at a time, whereas the new function nag_rand_dist_cauchy (g05sc) returns a vector of n values in one go. nag_rand_dist_cauchy (g05sc) expects the semi-interquartile range (parameter semiqr) to be non-negative, this was not the case for the equivalent parameter in g05df.
The integer array state in the call to nag_rand_dist_cauchy (g05sc) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_cauchy (g05sc) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_cauchy (g05sc) is likely to be different from those produced by g05df.

### g05dh

Withdrawn at Mark 22.
Replaced by nag_rand_dist_chisq (g05sd).
```Old: for i=1:n
[x(i), ifail] = g05dh(df);
end
New: [state, x, ifail] = g05sd(n, df, state);```
The old function g05dh returns a single variate at a time, whereas the new function nag_rand_dist_chisq (g05sd) returns a vector of n values in one go.
The integer array state in the call to nag_rand_dist_chisq (g05sd) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_chisq (g05sd) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_chisq (g05sd) is likely to be different from those produced by g05dh.

### g05dj

Withdrawn at Mark 22.
Replaced by nag_rand_dist_students_t (g05sn).
```Old: for i=1:n
[x(i), ifail] = g05dj(df);
end
New: [state, x, ifail] = g05sn(n, df, state);```
The old function g05dj returns a single variate at a time, whereas the new function nag_rand_dist_students_t (g05sn) returns a vector of n values in one go.
The integer array state in the call to nag_rand_dist_students_t (g05sn) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_students_t (g05sn) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_students_t (g05sn) is likely to be different from those produced by g05dj.

### g05dk

Withdrawn at Mark 22.
Replaced by nag_rand_dist_f (g05sh).
```Old: for i=1:n
[x(i), ifail] = g05df(df1, df2);
end
New: [state, x, ifail] = g05sh(n, df1, df2, state);```
The old function g05dk returns a single variate at a time, whereas the new function nag_rand_dist_f (g05sh) returns a vector of n values in one go.
The integer array state in the call to nag_rand_dist_f (g05sh) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_f (g05sh) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_f (g05sh) is likely to be different from those produced by g05dk.

### g05dp

Withdrawn at Mark 22.
Replaced by nag_rand_dist_weibull (g05ss).
```Old: for i=1:n
[x(i), ifail] = g05pd(a, b);
end
New: [state, x, ifail] = g05ss(n, a, b, state);```
The old function g05dp returns a single variate at a time, whereas the new function nag_rand_dist_weibull (g05ss) returns a vector of n values in one go.
The integer array state in the call to nag_rand_dist_weibull (g05ss) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_weibull (g05ss) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_weibull (g05ss) is likely to be different from those produced by g05dp.

### g05dr

Withdrawn at Mark 22.
Replaced by nag_rand_int_poisson_varmean (g05tk).
```Old: for i=1:n
[x(i), ifail] = g05dr(lambda);
end
New: [r, state, x, ifail] = g05tj(int64(3), n, lambda, r, state);```
The old function g05dr returns a single variate at a time, whereas the new function nag_rand_int_poisson (g05tj) returns a vector of n values in one go. For efficiency, the new function can make use of a reference vector, r. If, as in this case, the integer parameter mode is set to 3, the real reference vector r is not referenced.
The integer array state in the call to nag_rand_int_poisson (g05tj) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_int_poisson (g05tj) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_int_poisson (g05tj) is likely to be different from those produced by g05dr.

### g05dy

Withdrawn at Mark 22.
Replaced by nag_rand_int_uniform (g05tl).
```Old: for i=1:n
x(i) = g05dy(aa, bb);
end
New: [a, b] = sort([aa, bb]);
[state, x, ifail] = g05tl(n, a, b, state);```
The old function g05dy returns a single variate at a time, whereas the new function nag_rand_int_uniform (g05tl) returns a vector of n values in one go. In nag_rand_int_uniform (g05tl) the minimum value must be held in the parameter a and the maximum in parameter b, therefore ab${\mathbf{a}}\le {\mathbf{b}}$. This was not the case for the equivalent parameters in g05dy.
The integer array state in the call to nag_rand_int_uniform (g05tl) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_int_uniform (g05tl) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_int_uniform (g05tl) is likely to be different from those produced by g05dy.

### g05dz

Withdrawn at Mark 22.
Replaced by nag_rand_logical (g05tb).
```Old: for i=1:n
x(i) = g05dz(pp);
end
New: p = max(0, min(pp, 1));
[state, x, ifail] = g05tb(n, p, state);```
The old function g05dz returns a single variate at a time, whereas the new function nag_rand_logical (g05tb) returns a vector of n values in one go. The double parameter p in nag_rand_logical (g05tb) must not be less than zero or greater than one, this was not the case for the equivalent parameter in g05dz.
The integer array state in the call to nag_rand_logical (g05tb) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_logical (g05tb) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_logical (g05tb) is likely to be different from those produced by g05dz.

### g05ea

Withdrawn at Mark 22.
Replaced by nag_rand_multivar_normal (g05rz).
```Old: [r1, ifail] = g05ea(xmu, c, eps, lr1, 'n', m);
New: [r, state, x, ifail] = g05rz(int64(0), n, xmu, c, r, state, 'm', m, 'lr', lr);```
The old function g05ea sets up a reference vector for use by g05ez. The functionality of both these functions has been combined into the single new function nag_rand_multivar_normal (g05rz). Setting mode = 0${\mathbf{mode}}=0$ in the call to nag_rand_multivar_normal (g05rz) only sets up the double reference vector r and hence mimics the functionality of g05ea.
The length of the double reference vector, r, in nag_rand_multivar_normal (g05rz) must be at least m × (m + 1) + 1${\mathbf{m}}×\left({\mathbf{m}}+1\right)+1$. In contrast to the equivalent parameter in g05ea, this array must be allocated in the calling program.

### g05eb

Withdrawn at Mark 22.
Replaced by nag_rand_int_uniform (g05tl).
There is no direct replacement for function g05eb. g05eb sets up a reference vector for use by g05ey, this reference vector is no longer required. The replacement function for g05ey is nag_rand_int_uniform (g05tl).

### g05ec

Withdrawn at Mark 22.
Replaced by nag_rand_int_poisson (g05tj).
```Old: [r1, ifail] = g05ec(lambda, lr1);
for i=1:n
x(i) = g05ey(r1);
end
New: [r, state, x, ifail] = g05tj(int64(2), n, lambda, r, state);```
The old function g05ec sets up a reference vector for use by g05ey. The replacement function nag_rand_int_poisson (g05tj) is now used to both set up a reference vector and generate the required variates. Setting mode = 0${\mathbf{mode}}=0$ in the call to nag_rand_int_poisson (g05tj) sets up the double reference vector r and hence mimics the functionality of g05ec. Setting mode = 1${\mathbf{mode}}=1$ generates a series of variates from a reference vector mimicking the functionality of g05ey for this particular distribution. Setting mode = 2${\mathbf{mode}}=2$ initializes the reference vector and generates the variates in one go.
The function g05ey returns a single variate at a time, whereas the new function nag_rand_int_poisson (g05tj) returns a vector of n values in one go.
The length of the double reference vector, r, in nag_rand_int_poisson (g05tj), must be allocated in the calling program in contrast to the equivalent parameter in g05ec, see the documentation for more details.
The integer array state in the call to nag_rand_int_poisson (g05tj) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_int_poisson (g05tj) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_int_poisson (g05tj) is likely to be different from those produced by a combination of g05ec and g05ey.

### g05ed

Withdrawn at Mark 22.
Replaced by nag_rand_int_binomial (g05ta).
```Old: [r1, ifail] = g05ed(m, p, lr1);
for i=1:n
x(i) = g05ey(r1);
end
New: [r, state, x, ifail] = g05ta(int64(2), n, m, p, r, state);```
The old function g05ed sets up a reference vector for use by g05ey. The replacement function nag_rand_int_binomial (g05ta) is now used to both set up a reference vector and generate the required variates. Setting mode = 0${\mathbf{mode}}=0$ in the call to nag_rand_int_binomial (g05ta) sets up the double reference vector r and hence mimics the functionality of g05ed. Setting mode = 1${\mathbf{mode}}=1$ generates a series of variates from a reference vector mimicking the functionality of g05ey for this particular distribution. Setting mode = 2${\mathbf{mode}}=2$ initializes the reference vector and generates the variates in one go.
The function g05ey returns a single variate at a time, whereas the new function nag_rand_int_binomial (g05ta) returns a vector of n values in one go.
The length of the double reference vector, r, in nag_rand_int_binomial (g05ta), needs to be a different length from the equivalent parameter in g05ed, see the documentation for more details.
The integer array state in the call to nag_rand_int_binomial (g05ta) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_int_binomial (g05ta) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_int_binomial (g05ta) is likely to be different from those produced by a combination of g05ed and g05ey.

### g05ee

Withdrawn at Mark 22.
Replaced by nag_rand_int_negbin (g05th).
```Old: [r1, ifail] = g05ee(m, p, lr1);
for i=1:n
x(i) = g05ey(r1);
end
New: [r, state, x, ifail] = g05th(int64(2), n, m, p, r, state);```
The old function g05ee sets up a reference vector for use by g05ey. The replacement function nag_rand_int_negbin (g05th) is now used to both set up a reference vector and generate the required variates. Setting mode = 0${\mathbf{mode}}=0$ in the call to nag_rand_int_negbin (g05th) sets up the double reference vector r and hence mimics the functionality of g05ee. Setting mode = 1${\mathbf{mode}}=1$ generates a series of variates from a reference vector mimicking the functionality of g05ey for this particular distribution. Setting mode = 2${\mathbf{mode}}=2$ initializes the reference vector and generates the variates in one go.
The function g05ey returns a single variate at a time, whereas the new function nag_rand_int_negbin (g05th) returns a vector of n values in one go.
The length of the double reference vector, r, in nag_rand_int_negbin (g05th), needs to be a different length from the equivalent parameter in g05ee, see the documentation for nag_rand_int_negbin (g05th) for more details.
The integer array state in the call to nag_rand_int_negbin (g05th) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_int_negbin (g05th) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_int_negbin (g05th) is likely to be different from those produced by a combination of g05ee and g05ey.

### g05ef

Withdrawn at Mark 22.
Replaced by nag_rand_int_hypergeom (g05te).
```Old: [r1, ifail] = g05ef(ns, m, np, lr1);
for i=1:n
x(i) = g05ey(r1);
end
New: [r, state, x, ifail] = g05te(int64(2), n, ns, np, m, r, state);```
The old function g05ef sets up a reference vector for use by g05ey. The replacement function nag_rand_int_hypergeom (g05te) is now used to both set up a reference vector and generate the required variates. Setting mode = 0${\mathbf{mode}}=0$ in the call to nag_rand_int_hypergeom (g05te) sets up the double reference vector r and hence mimics the functionality of g05ef. Setting mode = 1${\mathbf{mode}}=1$ generates a series of variates from a reference vector mimicking the functionality of g05ey for this particular distribution. Setting mode = 2${\mathbf{mode}}=2$ initializes the reference vector and generates the variates in one go.
The function g05ey returns a single variate at a time, whereas the new function nag_rand_int_hypergeom (g05te) returns a vector of n values in one go.
The length of the double reference vector, r, in nag_rand_int_hypergeom (g05te), needs to be a different length from the equivalent parameter in g05ef, see the documentation for more details.
The integer array state in the call to nag_rand_int_hypergeom (g05te) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_int_hypergeom (g05te) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_int_hypergeom (g05te) is likely to be different from those produced by a combination of g05ef and g05ey.

### g05eg

Withdrawn at Mark 22.
Replaced by nag_rand_times_arma (g05ph).
```Old: [r, var, ifail] = g05eg(e, a, b, nr, 'na', na, 'nb', nb)
New: theta = zeros(iq, 1);
avar = b(1)^2;
if avar > 0
for i=1:nb-1
theta(i) = -b(i+1)/b(1);
end
end
mode = int64(0);
[r, state, var, x, ifail] = g05ph(mode, n, e, na, a, nb-1, theta, avar, r, state);```
The double vector theta must be of length at least iq = nb1${\mathbf{iq}}=\mathrm{nb}-1$.
The old function g05eg sets up a reference vector for use by g05ew. The replacement function nag_rand_times_arma (g05ph) is now used to both set up a reference vector and generate the required variates. Setting mode = 0${\mathbf{mode}}=0$ in the call to nag_rand_times_arma (g05ph) sets up the double reference vector r and hence mimics the functionality of g05eg. When mode = 0${\mathbf{mode}}=0$, the integer array state in the call to nag_rand_times_arma (g05ph) need not be set.

### g05eh

Withdrawn at Mark 22.
Replaced by nag_rand_permute (g05nc).
```Old: [index, ifail] = g05eh(index, 'n', n);
New: [index, state, ifail] = g05nc(index, state, 'n', n);```
The integer array state in the call to nag_rand_permute (g05nc) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_permute (g05nc) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_permute (g05nc) is likely to be different from those produced by g05eh.

### g05ej

Withdrawn at Mark 22.
Replaced by nag_rand_sample (g05nd).
```Old: [iz, ifail] = g05ej(ia, m, 'n', n);
New: [iz, state, ifail] = g05nd(ia, m, state, 'n', n);```
The integer array state in the call to nag_rand_sample (g05nd) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_sample (g05nd) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_sample (g05nd) is likely to be different from those produced by g05ej.

### g05ew

Withdrawn at Mark 22.
Replaced by nag_rand_times_arma (g05ph).
```Old: [r, var, ifail] = g05eg(e, a, b, nr, 'na', na, 'nb', nb)
for i=1:n
[x(i), ifail] = g05ew(r);
end
New: theta = zeros(iq, 1);
avar = b(1)^2;
if avar > 0
for i=1:nb-1
theta(i) = -b(i+1)/b(1);
end
end
mode = int64(2);
[r, state, var, x, ifail] = g05ph(mode, n, e, na, a, nb-1, theta, avar, r,
state);
```
The double vector theta must be of length at least iq = nb1${\mathbf{iq}}=\mathrm{nb}-1$.
The old function g05eg sets up a reference vector for use by g05ew. The replacement function nag_rand_times_arma (g05ph) is now used to both set up a reference vector and generate the required variates. Setting the integer parameter mode to 0 in the call to nag_rand_times_arma (g05ph) sets up the double reference vector r and hence mimics the functionality of g05eg. Setting mode to 1 generates a series of variates from a reference vector mimicking the functionality of g05ew. Setting mode to 2 initializes the reference vector and generates the variates in one go.
The integer array state in the call to nag_rand_times_arma (g05ph) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_times_arma (g05ph) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_times_arma (g05ph) is likely to be different from those produced by g05eg.

### g05ex

Withdrawn at Mark 22.
Replaced by nag_rand_int_general (g05td).
```Old: [r1, ifail] = g05ex(p, ip1, itype, lr1, 'np', np)
for i=1:n
x(i) = g05ey(r1);
end
New: mode = int64(2);
[r, state, x, ifail] = g05td(mode, n, p, ip1, itype, r, state, 'np', np);```
The old function g05ex sets up a reference vector for use by g05ey. The replacement function nag_rand_int_general (g05td) is now used to both set up a reference vector and generate the required variates. Setting mode = 0${\mathbf{mode}}=0$ in the call to nag_rand_int_general (g05td) sets up the double reference vector r and hence mimics the functionality of g05ex. Setting mode = 1${\mathbf{mode}}=1$ generates a series of variates from a reference vector mimicking the functionality of g05ey for this particular distribution. Setting mode = 2${\mathbf{mode}}=2$ initializes the reference vector and generates the variates in one go.
The function g05ey returns a single variate at a time, whereas the new function nag_rand_int_general (g05td) returns a vector of n values in one go.
The length of the double reference vector, r, in nag_rand_int_general (g05td) must be allocated in the calling program in contrast to the equivalent parameter in g05ex, see the documentation for more details.
The integer array state in the call to nag_rand_int_general (g05td) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_int_general (g05td) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_int_general (g05td) is likely to be different from those produced by a combination of g05ex, g05ey.

### g05ey

Withdrawn at Mark 22.
Replaced by nag_rand_int_general (g05td).
There is no direct replacement function for g05ey.
g05ey is designed to generate random draws from a distribution defined by a reference vector. These reference vectors are created by other functions in Chapter G05, for example g05eb, which have themselves been superseded. In order to replace a call to g05ey you must identify which NAG function generated the reference vector being used and look up its replacement. For example, to replace a call to g05ey preceded by a call to g05eb, as in:
```    [r, ifail] = g05eb(m, n, nr);
x = g05ey(r);```
you would need to look at the replacement function for g05eb.

### g05ez

Withdrawn at Mark 22.
Replaced by nag_rand_multivar_normal (g05rz).
```Old: [r1, ifail] = g05ea(xmu, c, eps, lr1, 'n', n);
for i=1:n
[x(i,1:m), ifail] = g05ez(m, r);
end
New: mode = int64(2);
[r, state, x, ifail] = g05rz(mode, n, xmu, c, r, state, 'm', m, 'lr', lr);```
The old function g05ea sets up a reference vector for use by g05ez. The functionality of both these functions has been combined into the single new function nag_rand_multivar_normal (g05rz). Setting mode = 2${\mathbf{mode}}=2$ in the call to nag_rand_multivar_normal (g05rz) sets up the double reference vector r and generates the draws from the multivariate Normal distribution in one go.
The old function g05ez returns a single (m-dimensional vector) draw from the multivariate Normal distribution at a time, whereas the new function nag_rand_multivar_normal (g05rz) returns an n by m matrix of n draws in one go.
The integer array state in the call to nag_rand_multivar_normal (g05rz) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_multivar_normal (g05rz) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_multivar_normal (g05rz) is likely to be different from those produced by g05ez.

### g05fa

Withdrawn at Mark 22.
Replaced by nag_rand_dist_uniform (g05sq).
```Old: [x] = g05fa(aa, bb, n);
New: [a, b] = sort([aa, bb]);
[state, x, ifail] = g05sq(n, a, b, state);```
In nag_rand_dist_uniform (g05sq) the minimum value must be held in the parameter A and the maximum in parameter b, therefore ab${\mathbf{a}}\le {\mathbf{b}}$. This was not the case for the equivalent parameters in g05fa.
The integer array state in the call to nag_rand_dist_uniform (g05sq) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_uniform (g05sq) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_uniform (g05sq) is likely to be different from those produced by g05fa.

### g05fb

Withdrawn at Mark 22.
Replaced by nag_rand_dist_exp (g05sf).
```Old: x = g05fb(a, n);
New: [state, x, ifail] = g05sf(n, abs(a), state);```
In nag_rand_dist_exp (g05sf) parameter a must be non-negative, this was not the case for the equivalent parameter in g05fb.
The integer array state in the call to nag_rand_dist_exp (g05sf) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_exp (g05sf) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_exp (g05sf) is likely to be different from those produced by g05fb.

### g05fd

Withdrawn at Mark 22.
Replaced by nag_rand_dist_normal (g05sk).
```Old: x = g05fd(xmu, sd, n);
New: var = sd^2;
[state, x, ifail] = g05sk(n, xmu, var, state);```
nag_rand_dist_normal (g05sk) expects the variance of the Normal distribution (parameter var), compared to g05fd which expected the standard deviation.
The integer array state in the call to nag_rand_dist_normal (g05sk) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_normal (g05sk) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_normal (g05sk) is likely to be different from those produced by g05fd.

### g05fe

Withdrawn at Mark 22.
Replaced by nag_rand_dist_beta (g05sb).
```Old: [x, ifail] = g05fe(a, b, n);
New: [state, x, ifail] = g05sb(n, a, b, state);```
The integer array state in the call to nag_rand_dist_beta (g05sb) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_beta (g05sb) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_beta (g05sb) is likely to be different from those produced by g05fe.

### g05ff

Withdrawn at Mark 22.
Replaced by nag_rand_dist_gamma (g05sj).
```Old: [x, ifail] = g05ff(a, b, n);
New: [state, x, ifail] = g05sj(n, a, b, state);```
The integer array state in the call to nag_rand_dist_gamma (g05sj) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_gamma (g05sj) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_gamma (g05sj) is likely to be different from those produced by g05ff.

### g05fs

Withdrawn at Mark 22.
Replaced by nag_rand_dist_vonmises (g05sr).
```Old: [x, ifail] = g05sf(vk, n);
New: [state, x, ifail] = g05sr(n, vk, state);```
The integer array state in the call to nag_rand_dist_vonmises (g05sr) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_dist_vonmises (g05sr) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_dist_vonmises (g05sr) is likely to be different from those produced by g05fs.

### g05ga

Withdrawn at Mark 22.
Replaced by nag_rand_matrix_orthog (g05px).
```Old: [a, ifail] = g05ga(side, init, m, a, 'n', n);
New: [state, a, ifail] = g05px(side, init, state, a, 'm', m, 'n', n);```
The integer array state in the call to nag_rand_matrix_orthog (g05px) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_matrix_orthog (g05px) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_matrix_orthog (g05px) is likely to be different from those produced by g05ga.

### g05gb

Withdrawn at Mark 22.
Replaced by nag_rand_matrix_corr (g05py).
```Old: [c, ifail] = g05gb(d, 'n', n, 'eps', eps);
New: [state, c, ifail] = g05py(d, state, 'n', n, 'eps', eps) ```
The integer array state in the call to nag_rand_matrix_corr (g05py) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_matrix_corr (g05py) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_matrix_corr (g05py) is likely to be different from those produced by g05gb.

### g05hd

Withdrawn at Mark 22.
Replaced by nag_rand_times_mv_varma (g05pj).
```Old: [w, ref, ifail] = g05hd(mode, ip, iq, mean, par, qq, n, ref, 'k', k, 'lpar', lpar, 'lref', lref)
New: if mode = 'c'
imode = int64(0);
else
imode = int64(1);
end
ll = 0;
for l=1:ip
for i=1:k
for j=1:k
ll = ll+1;
phi(i, j, l) = par(ll);
end
end
end
for l=1:iq-1
for i=1:k
for j=1:k
ll = ll+1;
theta(i, j, l) = par(ll);
end
end
end
xmean = zeros(k, 1);
if mean = 'm'
xmean = par(ll+1:ll+k+1);
end
[ref, state, x, ifail] = g05pj(imode, n, xmean, ip, phi, iq, theta, ...
qq, ref, state, 'k', k, 'lr', lr) ```
The integer parameter imode should be set to 0, 1 or 3 in place of the parameter mode having settings of 'S', 'C' or 'R' respectively. The double array phi should have length at least max (1,ip × (k × k)) $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{ip}}×\left({\mathbf{k}}×{\mathbf{k}}\right)\right)$; if dimensioned as phi(k,k,ip) ${\mathbf{phi}}\left({\mathbf{k}},{\mathbf{k}},{\mathbf{ip}}\right)$ (as in the above example) then phi (i,j,l) ${\mathbf{phi}}\left(i,j,l\right)$ will contain the element par ((l1) × k × k + (i1) × k + j) $\mathrm{par}\left(\left(l-1\right)×k×k+\left(i-1\right)×k+j\right)$. The double array theta should have length at least max (1,iq × (k × k)) $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{iq}}×\left({\mathbf{k}}×{\mathbf{k}}\right)\right)$; if dimensioned as theta (k,k,iq) ${\mathbf{theta}}\left({\mathbf{k}},{\mathbf{k}},{\mathbf{iq}}\right)$ (as in the above example) then theta (i,j,l) ${\mathbf{theta}}\left(i,j,l\right)$ will contain the element par (ip × k × k + (l1) × k × k + (i1) × k + j) $\mathrm{par}\left(\mathrm{ip}×k×k+\left(l-1\right)×k×k+\left(i-1\right)×k+j\right)$. The double array xmean should have length at least k; if mean = 'M' $\mathrm{mean}=\text{'M'}$ then xmean (i) ${\mathbf{xmean}}\left(i\right)$ will contain the element par (ip + iq × k × k + i) $\mathrm{par}\left(\mathrm{ip}+\mathrm{iq}×k×k+i\right)$, otherwise xmean should contain an array of zero values.
The integer array state in the call to nag_rand_times_mv_varma (g05pj) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_times_mv_varma (g05pj) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_times_mv_varma (g05pj) is likely to be different from those produced by g05hd.

### g05hk

Withdrawn at Mark 24.
Replaced by nag_rand_times_garch_asym1 (g05pd).
```Old: [ht, et, rvec, iseed, rwsav, ifail] = g05hk(dist, num, ip, iq, theta, gamma, df, fcall, rvec, igen, iseed, rwsav)
New: [ht, et, r, state, ifail] = g05pd(dist, num, ip, iq, theta, gamma, df, fcall, r, state, 'lr', lr)```
The integer array state in the call to nag_rand_times_garch_asym1 (g05pd) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_times_garch_asym1 (g05pd) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_times_garch_asym1 (g05pd) is likely to be different from those produced by g05hk.

### g05hl

Withdrawn at Mark 24.
Replaced by nag_rand_times_garch_asym2 (g05pe).
```Old: [ht, et, rvec, iseed, rwsav, ifail] = g05hl(dist, num, ip, iq, theta, gamma, df, fcall, rvec, igen, iseed, rwsav);
New: [ht, et, r, state, ifail] = g05pe(dist, num, ip, iq, theta, gamma, df, fcall, r, state, 'lr', lr);```
The integer array state in the call to nag_rand_times_garch_asym2 (g05pe) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_times_garch_asym2 (g05pe) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_times_garch_asym2 (g05pe) is likely to be different from those produced by g05hl.

### g05hm

Withdrawn at Mark 24.
Replaced by nag_rand_times_garch_gjr (g05pf).
```Old: [ht, et, rvec, iseed, rwsav, ifail] = g05hm(dist, num, ip, iq, theta, gamma, df, fcall, rvec, igen, iseed, rwsav);
New: [ht, et, r, state, ifail] = g05pf(dist, num, ip, iq, theta, gamma, df, fcall, r, state, 'lr', lr); ```
The integer array state in the call to nag_rand_times_garch_gjr (g05pf) contains information on the base generator being used. This array must have been initialized prior to calling nag_rand_times_garch_gjr (g05pf) with a call to either nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg). Due to changes in the underlying code the sequence of values produced by nag_rand_times_garch_gjr (g05pf) is likely to be different from those produced by g05hm.

### g05hn

Withdrawn at Mark 24.
Replaced by nag_rand_times_garch_exp (g05pg).
```Old: [ht, et, rvec, iseed, rwsav, ifail] = g05hn(dist, num, ip, iq, theta, df, fcall, rvec, igen, iseed, rwsav);
New: [ht, et, r, state, ifail] = g05pg(dist, num, ip, iq, theta, df, fcall, r, state, 'lr', lr);```

### g05ka

Withdrawn at Mark 24.
Replaced by nag_rand_dist_uniform01 (g05sa).
```Old: for i=1:n
[x(i), iseed] = g05ka(igen, iseed);
end
New: [state, x, ifail] = g05sa(n, state);```
The old function g05ka returns a single variate at a time, whereas the new function nag_rand_dist_uniform01 (g05sa) returns a vector of n values in one go.

### g05kb

Withdrawn at Mark 24.
Replaced by nag_rand_init_repeat (g05kf).
```Old: [igen, iseed] = g05kb(igen, iseed);
New: if (igen == 0)
[state, ifail] = g05kf(int23(1), int64(1), iseed, 'lseed', lseed);
else
[state, ifail] = g05kf(int64(1), igen, iseed, 'lseed', lseed);
end```

### g05kc

Withdrawn at Mark 24.
Replaced by nag_rand_init_nonrepeat (g05kg).
```Old: [igen, iseed] = g05kc(igen);
New: if (igen == 0)
[state, ifail] = g05kg(int64(1), int64(1));
else
[state, ifail] = g05kg(int64(2), igen);
end```

### g05ke

Withdrawn at Mark 24.
Replaced by nag_rand_logical (g05tb).
```Old: for i=1:n
[x(i), iseed, ifail] = g05ke(p, igen, iseed);
end
New: [state, x, ifail] = g05tb(n, p, state);```
The old function g05ke returns a single variate at a time, whereas the new function nag_rand_logical (g05tb) returns a vector of n values in one go.

### g05la

Withdrawn at Mark 24.
Replaced by nag_rand_dist_normal (g05sk).
```Old: [x, iseed, ifail] = g05la(xmu, var, n, igen, iseed);
New: [state, x, ifail] = g05sk(n, xmu, var, state);```

### g05lb

Withdrawn at Mark 24.
Replaced by nag_rand_dist_students_t (g05sn).
```Old: [x, iseed, ifail] = g05lb(df, n, igen, iseed);
New: [state, x, ifail] = g05sn(n, df, state);```

### g05lc

Withdrawn at Mark 24.
Replaced by nag_rand_dist_chisq (g05sd).
```Old: [x, iseed, ifail] = g05lc(df, n, igen, iseed);
New: [state, x, ifail] = g05sd(n, df, state);```

### g05ld

Withdrawn at Mark 24.
Replaced by nag_rand_dist_f (g05sh).
```Old: [x, iseed, ifail] = g05ld(df1, df2, n, igen, iseed);
New: [state, x, ifail] = g05sh(n, df1, df2, state);```

### g05le

Withdrawn at Mark 24.
Replaced by nag_rand_dist_beta (g05sb).
```Old: [x, iseed, ifail] = g05le(a, b, n, igen, iseed);
New: [state, x, ifail] = g05sb(n, a, b, state);```

### g05lf

Withdrawn at Mark 24.
Replaced by nag_rand_dist_gamma (g05sj).
```Old: [x, iseed, ifail] = g05lf(a, b, n, igen, iseed);
New: [state, x, ifail] = g05sj(n, a, b, state);```

### g05lg

Withdrawn at Mark 24.
Replaced by nag_rand_dist_uniform (g05sq).
```Old: [x, iseed, ifail] = g05lg(a, b, n, igen, iseed);
New: [state, x, ifail] = g05sq(n, a, b, state);```

### g05lh

Withdrawn at Mark 24.
Replaced by nag_rand_dist_triangular (g05sp).
```Old: [x, iseed, ifail] = g05lh(xmin, xmax, xmed, n, igen, iseed);
New: [state, x, ifail] = g05sp(n, xmin, xmed, xmax, state);```

### g05lj

Withdrawn at Mark 24.
Replaced by nag_rand_dist_exp (g05sf).
```Old: [x, iseed, ifail] = g05lj(a, n, igen, iseed);
New: [state, x, ifail] = g05sf(n, a, state);```

### g05lk

Withdrawn at Mark 24.
Replaced by nag_rand_dist_lognormal (g05sm).
```Old: [x, iseed, ifail] = g05lk(xmu, var, n, igen, iseed);
New: [state, x, ifail] = g05sm(n, xmu, var, state);```

### g05ll

Withdrawn at Mark 24.
Replaced by nag_rand_dist_gamma (g05sj).
```Old: [x, iseed, ifail] = g05ll(xmed, semiqr, n, igen, iseed);
New: [state, x, ifail] = g05sc(n, xmed, semiqr, state);```

### g05lm

Withdrawn at Mark 24.
Replaced by nag_rand_dist_weibull (g05ss).
```Old: [x, iseed, ifail] = g05lm(a, b, n, igen, iseed);
New: [state, x, ifail] = g05ss(n, a, b, state);```

### g05ln

Withdrawn at Mark 24.
Replaced by nag_rand_dist_logistic (g05sl).
```Old: [x, iseed, ifail] = g05ln(a, b, n, igen, iseed);
New: [state, x, ifail] = g05sl(n, a, b, state);```

### g05lp

Withdrawn at Mark 24.
Replaced by nag_rand_dist_vonmises (g05sr).
```Old: [x, iseed, ifail] = g05lp(vk, n, igen, iseed);
New: [state, x, ifail] = g05sr(n, vk, state);```

### g05lq

Withdrawn at Mark 24.
Replaced by nag_rand_dist_expmix (g05sg).
```Old: [x, iseed, ifail] = g05lq(a, wgt, n, igen, iseed, 'nmix', nmix);
New: [state, x, ifail] = g05sg(n, a, wgt, state, 'nmix', nmix);```

### g05lx

Withdrawn at Mark 24.
Replaced by nag_rand_multivar_students_t (g05ry).
```Old: [x, iseed, r, ifail] = g05lx(mode, df, xmu, c, n, igen, iseed, r, 'm', m, 'lr', lr);
New: [r, state, x, ifail] = g05ry(mode, n, df, xmu, c, r, state, 'm', m, 'lr', lr);```

### g05ly

Withdrawn at Mark 24.
Replaced by nag_rand_multivar_normal (g05rz).
```Old: [x, iseed, r, ifail] = g05ly(mode, xmu, c, n, igen, iseed, r, 'm', m, 'lr', lr);
New: [r, state, x, ifail] = g05rz(mode, n, xmu, c, r, state, 'm', m, 'lr', lr);```

### g05lz

Withdrawn at Mark 24.
Replaced by nag_rand_multivar_normal (g05rz).
```Old: [x, iseed, r, ifail] = g05lz(mode, xmu, c, igen, iseed, r, 'n', n);
New: n = int64(1);
[r, state, x, ifail] = g05rz(mode, n, xmu, c, r, state, 'm', m, 'lr', lr); ```

### g05ma

Withdrawn at Mark 24.
Replaced by nag_rand_int_uniform (g05tl).
```Old: [x, iseed, ifail] = g05ma(a, b, n, igen, iseed);
New: [state, x, ifail] = g05tl(n, a, b, state);```

### g05mb

Withdrawn at Mark 24.
Replaced by nag_rand_int_geom (g05tc).
```Old: [x, iseed, r, ifail] = g05mb(mode, p, n, igen, iseed, r);
New: [r, state, x, ifail] = g05tc(mode, n, p, r, state);```
g05mb returned the number of trials required to get the first success, whereas nag_rand_int_geom (g05tc) returns the number of failures before the first success, therefore the value returned by nag_rand_int_geom (g05tc) is one less than the equivalent value returned from g05mb.

### g05mc

Withdrawn at Mark 24.
Replaced by nag_rand_int_negbin (g05th).
```Old: [x, iseed, r, ifail] = g05mc(mode, m, p, n, igen, iseed, r);
New: [r, state, x, ifail] = g05th(mode, n, m, p, r, state);```

### g05md

Withdrawn at Mark 24.
Replaced by nag_rand_int_log (g05tf).
```Old: [x, iseed, r, ifail] = g05md(mode, a, n, igen, iseed, r);
New: [r, state, x, ifail] = g05tf(mode, n, a, r, state);```

### g05me

Withdrawn at Mark 24.
Replaced by nag_rand_int_poisson_varmean (g05tk).
```Old: [x, iseed, ifail] = g05me(vlamda, igen, iseed, 'm', m);
New: [state, x, ifail] = g05tk(vlamda, state, 'm', m);```

### g05mj

Withdrawn at Mark 24.
Replaced by nag_rand_int_binomial (g05ta).
```Old: [x, iseed, r, ifail] = g05mj(mode, m, p, n, igen, iseed, r);
New: [r, state, x, ifail] = g05ta(mode, n, m, p, r, state);```

### g05mk

Withdrawn at Mark 24.
Replaced by nag_rand_int_poisson (g05tj).
```Old: [x, iseed, r, ifail] = g05mk(mode, lambda, n, igen, iseed, r);
New: [r, state, x, ifail] = g05tj(mode, n, lambda, r, state);```

### g05ml

Withdrawn at Mark 24.
Replaced by nag_rand_int_hypergeom (g05te).
```Old: [x, iseed, r, ifail] = g05ml(mode, ns, np, m, n, igen, iseed, r);
New: [r, state, x, ifail] = g05te(mode, n, ns, np, m, r, state);```

### g05mr

Withdrawn at Mark 24.
Replaced by nag_rand_int_multinomial (g05tg).
```Old: [x, iseed, r, ifail] = g05mr(mode, m, p, n, igen, iseed, r, 'k', k);
New: [r, state, x, ifail] = g05tg(mode, n, m, p, r, state, 'k', k);```

### g05mz

Withdrawn at Mark 24.
Replaced by nag_rand_int_general (g05td).
```Old: [x, iseed, r, ifail] = g05mz(mode, p, ip1, itype, n, igen, iseed, r, 'np', np);
New: [r, state, x, ifail] = g05td(mode, n, p, ip1, itype, r, state, 'np', np);```

### g05na

Withdrawn at Mark 24.
Replaced by nag_rand_permute (g05nc).
```Old: [index, iseed, ifail] = g05na(index, igen, iseed, 'n', n);
New: [index, state, ifail] = g05nc(index, state, 'n', n);```

### g05nb

Withdrawn at Mark 24.
Replaced by nag_rand_sample (g05nd).
```Old: [isampl, iseed, ifail] = g05nb(ipop, m, igen, iseed, 'n', n);
New: [isampl, state, ifail] = g05nd(ipop, m, state, 'n', n);```

### g05pa

Withdrawn at Mark 24.
Replaced by nag_rand_times_arma (g05ph).
```Old: [var, x, iseed, r, ifail] = g05pa(mode, xmean, phi, theta, avar, n, igen, iseed, r, 'ip', ip, 'iq', iq);
New: [r, state, var, x, ifail] = g05ph(mode, n, xmean, ip, phi, iq, theta, avar, r, state);```

### g05pc

Withdrawn at Mark 24.
Replaced by nag_rand_times_mv_varma (g05pj).
```Old: [x, iseed, r, ifail] = g05pc(mode, xmean, ip, phi, iq, theta, var, n, igen, iseed, r, 'k', k);
New: [r, state, x, ifail] = g05pj(mode, n, xmean, ip, phi, iq, theta, var, r, state, 'k', k, 'lr', lr);```

### g05qa

Withdrawn at Mark 24.
Replaced by nag_rand_matrix_orthog (g05px).
```Old: [a, iseed, ifail] = g05qa(side, init, a, igen, iseed, 'm', m, 'n', n);
New: [state, a, ifail] = g05px(side, init, state, a, 'm', m, 'n', n);```

### g05qb

Withdrawn at Mark 24.
Replaced by nag_rand_matrix_corr (g05py).
```Old: [c, iseed, ifail] = g05qb(d, igen, iseed, 'n', n, 'eps', eps);
New: [state, c, ifail] = g05py(d, state, 'n', n, 'eps', eps)```

### g05qd

Withdrawn at Mark 24.
Replaced by nag_rand_matrix_2waytable (g05pz).
```Old: [x, iseed, r, ifail] = g05qd(mode, totr, totc, igen, iseed, r, 'nrow', nrow, 'ncol', ncol, 'nr', nr);
New: [r, state, x, ifail] = g05pz(mode, totr, totc, r, state, 'nrow', nrow, 'ncol', ncol, 'lr', lr);```

### g05ra

Withdrawn at Mark 24.
Replaced by nag_rand_copula_normal (g05rd).
```Old: [x, iseed, r, ifail] = g05ra(mode, c, n, igen, iseed, r, 'm', m, 'lr', lr);
New: [r, state, x, ifail] = g05rd(mode, n, c, r, state, 'm', m, 'lr', lr);```

### g05rb

Withdrawn at Mark 24.
Replaced by nag_rand_copula_students_t (g05rc).
```Old: [x, iseed, r, ifail] = g05rb(mode, df, c, n, igen, iseed, r, 'm', m, 'lr', lr);
New: [r, state, x, ifail] = g05rc(mode, n, df, c, r, state, 'm', m, 'lr', lr);```

### g05ya

Withdrawn at Mark 23.
Replaced by nag_rand_quasi_init (g05yl) and nag_rand_quasi_uniform (g05ym).
 Faure quasi-random numbers ```Old: [quas, iref, ifail] = g05ya(true, 'f', iskip, idim, iref); New: [iref, ifail] = g05yl(int64(4), idim, iskip);``````Old: [quas, iref, ifail] = g05ya(false, 'f', iskip, idim, iref); New: [quas, iref, ifail] = g05ym(int64(1), int64(2), iref);``` Sobol quasi-random numbers ```Old: [quas, iref, ifail] = g05ya(true, 's', iskip, idim, iref); New: [iref, ifail] = g05yl(int64(2), idim, iskip);``````Old: [quas, iref, ifail] = g05ya(false, 's', iskip, idim, iref); New: [quas, iref, ifail] = g05ym(int64(1), int64(2), iref);``` Neiderreiter quasi-random numbers ```Old: [quas, iref, ifail] = g05ya(true, 'n', iskip, idim, iref); New: [iref, ifail] = g05yl(int64(3), idim, iskip);``````Old: [quas, iref, ifail] = g05ya(false, 'n', iskip, idim, iref); New: [quas, iref, ifail] = g05ym(int64(1), int64(2), iref);```

### g05yb

Withdrawn at Mark 23.
Replaced by nag_rand_quasi_init (g05yl) and either nag_rand_quasi_normal (g05yj) or nag_rand_quasi_lognormal (g05yk).
This function has been replaced by a suite of functions consisting of the relevant initialization function followed by one of two possible generator functions.
 Faure quasi-random numbers with Gaussian probability: ```Old: [quasi, iref, ifail] = g05yb(true, 'f', false, mean, std, iskip, iref, 'idim', idim); New: [iref, ifail] = g05yl(int64(4), idim, iskip);``````Old: [quasi, iref, ifail] = g05yb(false, 'f', false, mean, std, iskip, iref, 'idim', idim); New: [quasi, iref, ifail] = g05yj(mean, std, n, iref);``` Sobol quasi-random numbers with Gaussian probability: ```Old: [quasi, iref, ifail] = g05yb(true, 's', false, mean, std, iskip, iref, 'idim', idim); New: [iref, ifail] = g05yl(int64(2), idim, iskip);``````Old: [quasi, iref, ifail] = g05yb(false, 's', false, mean, std, iskip, iref, 'idim', idim); New: [quasi, iref, ifail] = g05yj(mean, std, n, iref);``` Neiderreiter quasi-random numbers with Gaussian probability: ```Old: [quasi, iref, ifail] = g05yb(true, 'n', false, mean, std, iskip, iref, 'idim', idim); New: [iref, ifail] = g05yl(int64(3), idim, iskip);``````Old: [quasi, iref, ifail] = g05yb(false, 'n', false, mean, std, iskip, iref, 'idim', idim); New: [quasi, iref, ifail] = g05yj(mean, std, n, iref);``` Faure quasi-random numbers with log Normal probability: ```Old: [quasi, iref, ifail] = g05yb(true, 'f', true, mean, std, iskip, iref, 'idim', idim); New: [iref, ifail] = g05yl(int64(4), idim, iskip);``````Old: [quasi, iref, ifail] = g05yb(false, 'f', true, mean, std, iskip, iref, 'idim', idim); New: [quasi, iref, ifail] = g05yk(mean, std, n, iref);``` Sobol quasi-random numbers with log Normal probability: ```Old: [quasi, iref, ifail] = g05yb(true, 's', true, mean, std, iskip, iref, 'idim', idim); New: [iref, ifail] = g05yl(int64(2), idim, iskip);``````Old: [quasi, iref, ifail] = g05yb(false, 's', true, mean, std, iskip, iref, 'idim', idim); New: [quasi, iref, ifail] = g05yk(mean, std, n, iref);``` Neiderreiter quasi-random numbers with log Normal probability: ```Old: [quasi, iref, ifail] = g05yb(true, 'n', true, mean, std, iskip, iref, 'idim', idim); New: [iref, ifail] = g05yl(int64(3), idim, iskip);``````Old: [quasi, iref, ifail] = g05yb(false, 'n', true, mean, std, iskip, iref, 'idim', idim); New: [quasi, iref, ifail] = g05yk(mean, std, n, iref);```

### g05yc

Withdrawn at Mark 24.
Replaced by nag_rand_quasi_init (g05yl).
```Old: [iref, ifail] = g05yc(idim);
New: [iref, ifail] = g05yl(int64(4), idim, iskip);```

### g05yd

Withdrawn at Mark 24.
Replaced by nag_rand_quasi_uniform (g05ym).
```Old: [quasi, iref, ifail] = g05yd(n, iref);
New: [quas, iref, ifail] = g05ym(n, rcord, iref);```

### g05ye

Withdrawn at Mark 24.
Replaced by nag_rand_quasi_init (g05yl).
```Old: [iref, ifail] = g05ye(idim, iskip);
New: [iref, ifail] = g05yl(int64(2), idim, iskip);```

### g05yf

Withdrawn at Mark 24.
Replaced by nag_rand_quasi_uniform (g05ym).
```Old: [quasi, iref, ifail] = g05yf(n, iref);
New: [quas, iref, ifail] = g05ym(n, rcord, iref);```

### g05yg

Withdrawn at Mark 24.
Replaced by nag_rand_quasi_init (g05yl).
```Old: [iref, ifail] = g05yg(idim, iskip);
New: [iref, ifail] = g05yl(int64(3), idim, iskip);```

### g05yh

Withdrawn at Mark 24.
Replaced by nag_rand_quasi_uniform (g05ym).
```Old: [quasi, iref, ifail] = g05yh(n, iref);
New: [quas, iref, ifail] = g05ym(n, rcord, iref);```

### g05za

Withdrawn at Mark 22.
There is no replacement for this routine.

## G13 – Time Series Analysis

### g13dc

Withdrawn at Mark 24.
Replaced by nag_tsa_multi_varma_estimate (g13dd).
```Old: [par, qq, niter, rlogl, v, g, cm, ifail] = ...
g13dc(ip, iq, mean, par, qq, w, parhld, exact, iprint, cgetol, ishow, ...
'k', k, 'n', n, 'npar', npar, 'maxcal', maxcal)
New: [par, qq, niter, rlogl, v, g, cm, ifail] = ...
g13dd(ip, iq, mean, par, qq, w, parhld, exact, iprint, cgetol, ishow, ...
'k', k, 'n', n, 'npar', npar, 'maxcal', maxcal) ```
This replacement is caused by changes in the underlying Fortran interface (removal of workspace arguments) which have no effect on the MATLAB toolbox interface.

## X02 – Machine Constants

### x02da

Withdrawn at Mark 24.
There is no replacement for this routine.

### x02dj

Withdrawn at Mark 24.
There is no replacement for this routine.

Chapter Contents
NAG Toolbox

© The Numerical Algorithms Group Ltd, Oxford, UK. 2009–2013