# Advice on Replacement Calls¶

The following list gives replacement advice for routines that have either been withdrawn or superseded.

Please contact NAG if you have any questions about how to make appropriate replacements in your code.

`correg`

- Correlation and Regression Analysis¶

### mixeff_hier_init¶

Hierarchical mixed effects regression, initialization function for
`correg.mixeff_hier_reml`

and
`correg.mixeff_hier_ml`

.

Deprecated.

Replaced by `correg.lmm_init`

.

### mixeff_hier_ml¶

Hierarchical mixed effects regression using Maximum Likelihood (ML).

Deprecated.

Replaced by `correg.lmm_fit`

.

### mixeff_hier_reml¶

Hierarchical mixed effects regression using Restricted Maximum Likelihood (REML).

Deprecated.

Replaced by `correg.lmm_fit`

.

### mixeff_ml¶

Linear mixed effects regression using Maximum Likelihood (ML).

Deprecated.

Replaced by `correg.lmm_init`

followed by
`correg.lmm_fit`

.

### mixeff_reml¶

Linear mixed effects regression using Restricted Maximum Likelihood (REML).

Deprecated.

Replaced by `correg.lmm_init`

followed by
`correg.lmm_fit`

.

#### Reason for Replacement¶

None given.

`eigen`

- Eigenvalues and Eigenvectors¶

### withdraw_real_band_geneig¶

Eigenvector of generalized real banded eigenproblem by inverse iteration.

Withdrawn at Mark 27.

Replaced by `sparseig.real_band_solve`

and
`sparseig.real_symm_band_solve`

.

#### Reason for Replacement¶

The replacement functions `sparseig.real_symm_band_solve`

(symmetric case)
and `sparseig.real_band_solve`

(nonsymmetric case)
are threaded for parallel execution in multithreaded implementations.
These functions are based on the ARPACK package and make calls to
BLAS/LAPACK functions. These may be threaded within the vendor library
used by the implementation, which provides an additional opportunity for
multithreaded performance.

### withdraw_real_gen_qu_svd¶

Returns the Householder factorization of a real rectangular matrix. Part or all of the singular value decomposition may also be returned.

Withdrawn at Mark 27.

Replaced by `lapackeig.dgeqrf`

and
`eigen.real_triang_svd`

.

#### Reason for Replacement¶

This function is replaced for multithreaded performance and the ability to benefit from vendor library performance (BLAS/LAPACK).

`fit`

- Curve and Surface Fitting¶

### withdraw_1dmmax¶

Minimax curve fit by polynomials.

Withdrawn at Mark 27.

Replaced by `fit.dim1_minimax_polynomial`

.

#### Reason for Replacement¶

None given.

`glopt`

- Global Optimization of a Function¶

### bnd_mcs_init¶

Initialization function for `glopt.bnd_mcs_solve`

.

Deprecated.

There is no replacement for this function.

### bnd_mcs_optget_char¶

Get the setting of an ‘ON’/’OFF’-valued character option of
`glopt.bnd_mcs_solve`

.

Deprecated.

There is no replacement for this function.

### bnd_mcs_optget_int¶

Get the setting of an integer valued option of
`glopt.bnd_mcs_solve`

.

Deprecated.

There is no replacement for this function.

### bnd_mcs_optget_real¶

Get the setting of a real valued option of `glopt.bnd_mcs_solve`

.

Deprecated.

There is no replacement for this function.

### bnd_mcs_option_check¶

Determine whether an option for `glopt.bnd_mcs_solve`

has been set by you or not.

Deprecated.

There is no replacement for this function.

### bnd_mcs_optset_char¶

Set a single option for `glopt.bnd_mcs_solve`

from an ‘ON’/’OFF’-valued
character argument.

Deprecated.

There is no replacement for this function.

### bnd_mcs_optset_file¶

Supply option values for `glopt.bnd_mcs_solve`

from external file.

Deprecated.

There is no replacement for this function.

### bnd_mcs_optset_int¶

Set a single option for `glopt.bnd_mcs_solve`

from an integer argument.

Deprecated.

There is no replacement for this function.

### bnd_mcs_optset_real¶

Set a single option for `glopt.bnd_mcs_solve`

from a real argument.

Deprecated.

There is no replacement for this function.

### bnd_mcs_optset_string¶

Set a single option for `glopt.bnd_mcs_solve`

from a character string.

Deprecated.

There is no replacement for this function.

### bnd_mcs_solve¶

Global optimization by multi-level coordinate search, simple bounds, using function values only.

Deprecated.

Replaced by `glopt.handle_solve_mcs`

.

#### Reason for Replacement¶

A new interface to the Multi-level Coordinate Search (MCS) algorithm to integrate it to the NAG optimization modelling suite has been introduced. This new function gives access to all of the suite facilities and uses the same interface as all compatible solvers, simplifying experimentation significantly.

`lapackeig`

- Least Squares and Eigenvalue Problems (LAPACK)¶

### dgeqpf¶

factorization, with column pivoting, of real general rectangular matrix.

Deprecated.

Replaced by `lapackeig.dgeqp3`

.

### dgges¶

Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors.

Deprecated.

Replaced by `lapackeig.dgges3`

.

### dggev¶

Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.

Deprecated.

Replaced by `lapackeig.dggev3`

.

### dgghrd¶

Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form.

Deprecated.

Replaced by `lapackeig.dgghd3`

.

### dggsvd¶

Computes the generalized singular value decomposition of a real matrix pair.

Deprecated.

Replaced by `lapackeig.dggsvd3`

.

### dggsvp¶

Produces orthogonal matrices that simultaneously reduce the matrix and the matrix to upper triangular form.

Deprecated.

Replaced by `lapackeig.dggsvp3`

.

### zgeqpf¶

factorization, with column pivoting, of complex general rectangular matrix.

Deprecated.

Replaced by `lapackeig.zgeqp3`

.

### zgges¶

Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors.

Deprecated.

Replaced by `lapackeig.zgges3`

.

### zggev¶

Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.

Deprecated.

Replaced by `lapackeig.zggev3`

.

### zgghrd¶

Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form.

Deprecated.

Replaced by `lapackeig.zgghd3`

.

### zggsvd¶

Computes the generalized singular value decomposition of a complex matrix pair.

Deprecated.

Replaced by `lapackeig.zggsvd3`

.

### zggsvp¶

Produces unitary matrices that simultaneously reduce the complex, , matrix and the complex, , matrix to upper triangular form.

Deprecated.

Replaced by `lapackeig.zggsvp3`

.

`linsys`

- Simultaneous Linear Equations¶

### withdraw_real_posdef_solve_1rhs¶

Solution of real symmetric positive definite simultaneous linear equations, one right-hand side using iterative refinement (Black Box).

Withdrawn at Mark 28.3.

Replaced by `lapacklin.dposvx`

.

#### Reason for Replacement¶

This function has been replaced by `lapacklin.dposvx`

for performance. The
replacement function is threaded by NAG and may also be threaded in the
vendor library (BLAS/LAPACK).

### withdraw_real_posdef_solve_ref¶

Solution of real symmetric positive definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box).

Withdrawn at Mark 28.3.

Replaced by `lapacklin.dposvx`

.

#### Reason for Replacement¶

This function has been replaced by `lapacklin.dposvx`

for performance. The
replacement function is threaded by NAG and may also be threaded in the
vendor library (BLAS/LAPACK).

### withdraw_real_square_solve_1rhs¶

Solution of real simultaneous linear equations, one right-hand side using iterative refinement (Black Box).

Withdrawn at Mark 28.3.

Replaced by `lapacklin.dgesvx`

.

#### Reason for Replacement¶

This function has been replaced by `lapacklin.dgesvx`

for performance. The
replacement function is threaded by NAG and may also be threaded in the
vendor library (BLAS/LAPACK).

### withdraw_real_square_solve_ref¶

Solution of real simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box).

Withdrawn at Mark 28.3.

Replaced by `lapacklin.dgesvx`

.

#### Reason for Replacement¶

This function has been replaced by `lapacklin.dgesvx`

for performance. The
replacement function is threaded by NAG and may also be threaded in the
vendor library (BLAS/LAPACK).

`ode`

- Ordinary Differential Equations¶

### withdraw_bvp_coll_nlin¶

Ordinary differential equations, general nonlinear boundary value problem, collocation technique.

Withdrawn at Mark 27.

Replaced by `ode.bvp_coll_nlin_solve`

.

#### Reason for Replacement¶

This replacement was made primarily for reasons of threadsafety.

`omp`

- OpenMP Utilities¶

### get_nested¶

Tests the status of nested OpenMP parallelism.

Scheduled for withdrawal at Mark 31.3.

Replaced by `omp.get_max_active_levels`

.

#### Reason for Replacement¶

None given.

### set_nested¶

Enables or disables nested OpenMP parallelism.

Scheduled for withdrawal at Mark 31.3.

Replaced by `omp.set_max_active_levels`

.

#### Reason for Replacement¶

None given.

`opt`

- Minimizing or Maximizing a Function¶

### bounds_bobyqa_func¶

Bound constrained minimum, model-based algorithm, using function values only.

Deprecated.

Replaced by `opt.handle_solve_dfno`

and
`opt.handle_solve_dfno_rcomm`

.

#### Reason for Replacement¶

`opt.handle_solve_dfno`

and `opt.handle_solve_dfno_rcomm`

are a part of the new NAG optimization modelling suite (see the E04 Introduction) which allows you to define and solve various problems in a uniform manner. They also offer various algorithmic additions, such as a performance improvement on noisy problems, a possibility to progress towards the solution earlier than after initial function evaluations, heuristic stopping criteria, recovery from unavailable function evaluations, and various other algorithmic updates and tuning. In addition, `opt.handle_solve_dfno_rcomm`

offers a reverse communication interface (see the E04 Introduction) which might be useful in some environments or if you can parallelize your function evaluations.

### lsq_uncon_quasi_deriv_comp¶

Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (comprehensive).

Deprecated.

Replaced by `opt.handle_solve_bxnl`

.

#### Reason for Replacement¶

`opt.handle_solve_bxnl`

is part of the new NAG optimization modelling suite (see the E04 Introduction), therefore the definition of the nonlinear residual function values and gradients need to be split into two separate subroutines. `opt.handle_solve_bxnl`

offers a significant improvement in performance over `opt.lsq_uncon_quasi_deriv_comp`

as well as additional functionality, such as the addition of variable bounds and user-evaluation recovery, amongst many others.

### lsq_uncon_quasi_deriv_easy¶

Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use).

Deprecated.

Replaced by `opt.handle_solve_bxnl`

.

#### Reason for Replacement¶

`opt.handle_solve_bxnl`

is part of the new NAG optimization modelling suite (see the E04 Introduction), therefore the definition of the nonlinear residual function values and gradients need to be split into two separate subroutines. `opt.handle_solve_bxnl`

is a modern replacement for `opt.lsq_uncon_quasi_deriv_easy`

and offers additional functionality, such as the addition of variable bounds and user-evaluation recovery, amongst many others.

### nlp1_sparse_option_file¶

Supply option values for `opt.nlp1_sparse_solve`

from external file.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

This was an option setting function for `opt.nlp1_sparse_solve`

which has been superseded by `opt.handle_solve_ssqp`

. `opt.handle_solve_ssqp`

is part of the NAG optimization modelling suite (see the E04 Introduction) which uses the option setting facilities common to that suite.

### nlp1_sparse_option_string¶

Supply option values to `opt.nlp1_sparse_solve`

from a character string.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

This was an option setting function for `opt.nlp1_sparse_solve`

which has been superseded by `opt.handle_solve_ssqp`

. `opt.handle_solve_ssqp`

is part of the NAG optimization modelling suite (see the E04 Introduction) which uses the option setting facilities common to that suite.

### nlp1_sparse_solve¶

Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

A modern Sequential Quadratic Programming (SQP) algorithm that uses the NAG optimization modelling suite (see the E04 Introduction) has been introduced. This new function `opt.handle_solve_ssqp`

has access to all of the suite facilities and uses the same interface as all compatible solvers.

### nlp2_sparse_init¶

Initialization function for `opt.nlp2_sparse_solve`

.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

This was an initialization function for `opt.nlp2_sparse_solve`

which has been superseded by `opt.handle_solve_ssqp`

. `opt.handle_solve_ssqp`

is part of the NAG optimization modelling suite (see the E04 Introduction) which uses the initialization facilities common to that suite.

### nlp2_sparse_jacobian¶

Determine the pattern of nonzeros in the Jacobian matrix for
`opt.nlp2_sparse_solve`

.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

This was a sparsity structure defining function for `opt.nlp2_sparse_solve`

which has been superseded by `opt.handle_solve_ssqp`

. `opt.handle_solve_ssqp`

is part of the NAG optimization modelling suite (see the E04 Introduction) which uses the problem defining facilities common to that suite.

### nlp2_sparse_option_double_get¶

Get the setting of a real valued option of `opt.nlp2_sparse_solve`

.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

This was an option getting function for `opt.nlp2_sparse_solve`

which has been superseded by `opt.handle_solve_ssqp`

. `opt.handle_solve_ssqp`

is part of the NAG optimization modelling suite (see the E04 Introduction) which uses the option getting facilities common to that suite.

### nlp2_sparse_option_double_set¶

Set a single option for `opt.nlp2_sparse_solve`

from a real argument.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

This was an option setting function for `opt.nlp2_sparse_solve`

which has been superseded by `opt.handle_solve_ssqp`

. `opt.handle_solve_ssqp`

is part of the NAG optimization modelling suite (see the E04 Introduction) which uses the option setting facilities common to that suite.

### nlp2_sparse_option_file¶

Supply option values for `opt.nlp2_sparse_solve`

from external file.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

This was an option setting function for `opt.nlp2_sparse_solve`

which has been superseded by `opt.handle_solve_ssqp`

. `opt.handle_solve_ssqp`

is part of the NAG optimization modelling suite (see the E04 Introduction) which uses the option setting facilities common to that suite.

### nlp2_sparse_option_integer_get¶

Get the setting of an integer valued option of
`opt.nlp2_sparse_solve`

.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

This was an option getting function for `opt.nlp2_sparse_solve`

which has been superseded by `opt.handle_solve_ssqp`

. `opt.handle_solve_ssqp`

is part of the NAG optimization modelling suite (see the E04 Introduction) which uses the option getting facilities common to that suite.

### nlp2_sparse_option_integer_set¶

Set a single option for `opt.nlp2_sparse_solve`

from an integer argument.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

This was an option setting function for `opt.nlp2_sparse_solve`

which has been superseded by `opt.handle_solve_ssqp`

. `opt.handle_solve_ssqp`

is part of the NAG optimization modelling suite (see the E04 Introduction) which uses the option setting facilities common to that suite.

### nlp2_sparse_option_string¶

Set a single option for `opt.nlp2_sparse_solve`

from a character string.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

`opt.nlp2_sparse_solve`

which has been superseded by `opt.handle_solve_ssqp`

. `opt.handle_solve_ssqp`

is part of the NAG optimization modelling suite (see the E04 Introduction) which uses the option setting facilities common to that suite.

### nlp2_sparse_solve¶

Nonlinear programming (NLP), sparse, active-set SQP method, using function values and optionally first derivatives, recommended.

Deprecated.

Replaced by `opt.handle_solve_ssqp`

.

#### Reason for Replacement¶

A modern Sequential Quadratic Programming (SQP) algorithm that uses the NAG optimization modelling suite (see the E04 Introduction) has been introduced. This new function `opt.handle_solve_ssqp`

has access to all of the suite facilities and uses the same interface as all compatible solvers.

### qpconvex1_sparse_mps¶

Read MPS data file defining LP or QP problem, deprecated.

Deprecated.

Replaced by `opt.miqp_mps_read`

.

#### Reason for Replacement¶

None given.

### uncon_conjgrd_comp¶

Unconstrained minimum, preconditioned conjugate gradient algorithm, using first derivatives (comprehensive).

Deprecated.

Replaced by `opt.handle_solve_bounds_foas`

.

#### Reason for Replacement¶

The new solver `opt.handle_solve_bounds_foas`

is part of the NAG optimization modelling suite(see the E04 Introduction), therefore the definition of the objective function values and gradients need to be split into two separate subroutines. `opt.handle_solve_bounds_foas`

offers a significant improvement in performance over `opt.uncon_conjgrd_comp`

as well as additional functionality, such as the addition of variable bounds and monitoring.

### uncon_conjgrd_option_file¶

Supply option values for `opt.uncon_conjgrd_comp`

from external file.

Deprecated.

There is no replacement for this function.

### uncon_conjgrd_option_string¶

Supply option values to `opt.uncon_conjgrd_comp`

from a character string.

Deprecated.

There is no replacement for this function.

`pde`

- Partial Differential Equations¶

### withdraw_2d_gen_order2_checkgrid¶

Check initial grid data in `pde.dim2_gen_order2_rectilinear`

.

Withdrawn at Mark 27.

There is no replacement for this function.

`quad`

- Quadrature¶

### dim1_fin_bad¶

One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands (single abscissa interface).

Scheduled for withdrawal at Mark 31.3.

Replaced by `quad.dim1_fin_general`

.

#### Reason for Replacement¶

`quad.dim1_fin_general`

provides thread safety in
passing of data to user-supplied function. `quad.dim1_fin_general`

also requires the
user-supplied function to calculate a vector of
abscissae at once for greater efficiency and returns additional
information on the computation (in the arrays and
.

### dim1_fin_bad_vec¶

One-dimensional quadrature, adaptive, finite interval, variant of
`quad.dim1_fin_bad`

efficient on vector machines.

Scheduled for withdrawal at Mark 31.3.

Replaced by `quad.dim1_fin_general`

.

#### Reason for Replacement¶

`quad.dim1_fin_general`

provides thread safety in
passing of data to user-supplied function. `quad.dim1_fin_general`

also returns additional
information on the computation (in the arrays and
.

### dim1_fin_osc¶

One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions (single abscissa interface).

Scheduled for withdrawal at Mark 31.3.

Replaced by `quad.dim1_fin_osc_fn`

.

#### Reason for Replacement¶

`quad.dim1_fin_osc_fn`

provides thread safety in
passing of data to user-supplied function. `quad.dim1_fin_osc_fn`

also requires the
user-supplied function to calculate a vector of
abscissae at once for greater efficiency and returns additional
information on the computation (in the arrays and
.

### dim1_fin_osc_vec¶

One-dimensional quadrature, adaptive, finite interval, variant of
`quad.dim1_fin_osc`

efficient on vector machines.

Scheduled for withdrawal at Mark 31.3.

Replaced by `quad.dim1_fin_osc_fn`

.

#### Reason for Replacement¶

`quad.dim1_fin_osc_fn`

provides thread safety in
passing of data to user-supplied function. `quad.dim1_fin_osc_fn`

also returns additional
information on the computation (in the arrays and
.

### dim1_fin_sing¶

One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points (single abscissa interface).

Scheduled for withdrawal at Mark 31.3.

Replaced by `quad.dim1_fin_brkpts`

.

#### Reason for Replacement¶

`quad.dim1_fin_brkpts`

provides thread safety in
passing of data to user-supplied function. `quad.dim1_fin_brkpts`

also requires the
user-supplied function to calculate a vector of
abscissae at once for greater efficiency and returns additional
information on the computation (in the arrays and
.

### dim1_inf¶

One-dimensional quadrature, adaptive, infinite or semi-infinite interval.

Scheduled for withdrawal at Mark 31.3.

Replaced by `quad.dim1_inf_general`

.

#### Reason for Replacement¶

`quad.dim1_inf_general`

provides thread safety in
passing of data to user-supplied function. `quad.dim1_inf_general`

also requires the
user-supplied function to calculate a vector of
abscissae at once for greater efficiency and returns additional
information on the computation (in the arrays and
.

### withdraw_1d_gen_vec_multi_diagnostic¶

Diagnostic function for `quad.dim1_gen_vec_multi_rcomm`

.

Withdrawn at Mark 28.3.

There is no replacement for this function.

#### Reason for Replacement¶

This function has been withdrawn as a separate diagnostic function is not required.

### withdraw_dim1_gauss_wgen¶

Old function for calculating weights and abscissae for Gaussian
quadrature rules, replaced by `quad.dim1_gauss_wgen`

.

Scheduled for withdrawal at Mark 31.3.

Replaced by `quad.dim1_gauss_wgen`

.

#### Reason for Replacement¶

None given.

`smooth`

- Smoothing in Statistics¶

### withdraw_kerndens_gauss¶

Kernel density estimate using Gaussian kernel.

Withdrawn at Mark 27.

Replaced by `smooth.kerndens_gauss`

.

#### Reason for Replacement¶

The replacement routine introduces new functionality with respect to the automatic selection of a suitable window width.

#### Replacement Pseudocode¶

Old code:

```
# First call:
usefft = False
comm = {}
ns = ...
fft = np.empty(ns)
kg = withdraw_kerndens_gauss(
x, window, slo, shi, usefft, fft, comm,
)
# Subsequent call(s):
usefft = True
kg = withdraw_kerndens_gauss(
x, window, slo, shi, usefft, kg.fft, comm,
)
```

New code:

```
# First call:
comm = {}
ns = ...
kg = kerndens_gauss(
x, comm, wtype=1, window=window, slo=slo, shi=shi, ns=ns,
)
# Subsequent call(s):
kg = kerndens_gauss(
x, comm, wtype=1, window=window, ns=ns,
)
```

`stat`

- Simple Calculations on Statistical Data¶

### withdraw_plot_histogram¶

Lineprinter histogram of one variable.

Withdrawn at Mark 27.

There is no replacement for this function.

#### Reason for Replacement¶

Frequency tables generated by `stat.frequency_table`

provide equivalent
information.

### withdraw_plot_scatter_2var¶

Lineprinter scatterplot of two variables.

Withdrawn at Mark 27.

There is no replacement for this function.

### withdraw_plot_scatter_normal¶

Lineprinter scatterplot of one variable against Normal scores.

Withdrawn at Mark 27.

There is no replacement for this function.

`sum`

- Summation of Series¶

### withdraw_fft_hermitian_1d_multi_rfmt¶

Multiple one-dimensional Hermitian discrete Fourier transforms.

Scheduled for withdrawal at Mark 30.2.

Replaced by `sum.fft_realherm_1d_multi_row`

or
`sum.fft_realherm_1d_multi_col`

.

#### Reason for Replacement¶

`sum.fft_realherm_1d_multi_col`

provides a
simpler interface for both forward and backward transforms.
`sum.fft_realherm_1d_multi_row`

returns real
sequences in row order at the expense of efficiency.

### withdraw_fft_real_1d_multi_rfmt¶

Multiple one-dimensional real discrete Fourier transforms.

Scheduled for withdrawal at Mark 30.2.

Replaced by `sum.fft_realherm_1d_multi_row`

or
`sum.fft_realherm_1d_multi_col`

.

#### Reason for Replacement¶

`sum.fft_realherm_1d_multi_col`

provides a
simpler interface for both forward and backward transforms.
`sum.fft_realherm_1d_multi_row`

retains original
input ordering at the expense of efficiency.

`zeros`

- Zeros of Polynomials¶

### poly_complex¶

All zeros of complex polynomial, modified Laguerre’s method.

Deprecated.

Replaced by `zeros.poly_complex_fpml`

.

#### Reason for Replacement¶

None given.

### poly_real¶

All zeros of real polynomial, modified Laguerre’s method.

Deprecated.

Replaced by `zeros.poly_real_fpml`

.

#### Reason for Replacement¶

None given.