Mark 7 Library Contents

a00 – Library Identification

Routine Name	Mark of Introduction	Purpose
a00aac	1	nag_implementation_details Library identification, details of implementation and mark

a02 – Complex Arithmetic

Routine Name	Mark of Introduction	Purpose
a02bac	2	nag_complex Complex number from real and imaginary parts
a02bbc	2	nag_complex_real Real part of a complex number
a02bcc	2	nag_complex_imag Imaginary part of a complex number
a02cac	2	nag_complex_add Addition of two complex numbers
a02cbc	2	nag_complex_subtract Subtraction of two complex numbers
a02ccc	2	nag_complex_multiply Multiplication of two complex numbers
a02cdc	2	nag_complex_divide Quotient of two complex numbers
a02cec	2	nag_complex_negate Negation of a complex number
a02cfc	2	nag_complex_conjg Conjugate of a complex number
a02cgc	2	nag_complex_equal Equality of two complex numbers
a02chc	2	nag_complex_not_equal Inequality of two complex numbers
a02dac	2	nag_complex_arg Argument of a complex number
a02dbc	2	nag_complex_abs Modulus of a complex number
a02dcc	2	nag_complex_sqrt Square root of a complex number
a02ddc	2	nag_complex_i_power Complex number raised to integer power
a02dec	2	nag_complex_r_power Complex number raised to real power
a02dfc	2	nag_complex_c_power Complex number raised to complex power
a02dgc	2	nag_complex_log Complex logarithm
a02dhc	2	nag_complex_exp Complex exponential
a02djc	2	nag_complex_sin Complex sine
a02dkc	2	nag_complex_cos Complex cosine
a02dlc	2	nag_complex_tan Complex tangent

c02 – Zeros of Polynomials

Routine Name	Mark of Introduction	Purpose
c02afc	2	nag_zeros_complex_poly Zeros of a polynomial with complex coefficients
c02agc	2	nag_zeros_real_poly Zeros of a polynomial with real coefficients
c02akc	6	nag_cubic_roots Zeros of a cubic polynomial with real coefficients
c02alc	6	nag_quartic_roots Zeros of a real quartic polynomial with real coefficients

c05 – Roots of One or More Transcendental Equations

Routine Name	Mark of Introduction	Purpose
c05adc	2	nag_zero_cont_func_bd Zero of a continuous function of one variable
c05nbc	2	nag_zero_nonlin_eqns Solution of a system of nonlinear equations (function values only)
c05pbc	2	nag_zero_nonlin_eqns_deriv Solution of a system of nonlinear equations (using first derivatives)
c05sdc	5	nag_zero_cont_func_bd_1 Zero of a continuous function of one variable, thread-safe
c05tbc	5	nag_zero_nonlin_eqns_1 Solution of a system of nonlinear equations (function values only), thread-safe
c05ubc	5	nag_zero_nonlin_eqns_deriv_1 Solution of a system of nonlinear equations (using first derivatives), thread-safe
c05zbc	2	nag_check_deriv Derivative checker for c05pbc
c05zcc	5	nag_check_deriv_1 Derivative checker for c05ubc, thread-safe

c06 – Fourier Transforms

Routine Name	Mark of Introduction	Purpose
c06eac	1	nag_fft_real Single one-dimensional real discrete Fourier transform
c06ebc	1	nag_fft_hermitian Single one-dimensional Hermitian discrete Fourier transform
c06ecc	1	nag_fft_complex Single one-dimensional complex discrete Fourier transform
c06ekc	1	nag_convolution_real Circular convolution or correlation of two real vectors
c06fpc	1	nag_fft_multiple_real Multiple one-dimensional real discrete Fourier transforms
c06fqc	1	nag_fft_multiple_hermitian Multiple one-dimensional Hermitian discrete Fourier transforms
c06frc	1	nag_fft_multiple_complex Multiple one-dimensional complex discrete Fourier transforms
c06fuc	1	nag_fft_2d_complex two-dimensional complex discrete Fourier transform
c06gbc	1	nag_conjugate_hermitian Complex conjugate of Hermitian sequence
c06gcc	1	nag_conjugate_complex Complex conjugate of complex sequence
c06gqc	1	nag_multiple_conjugate_hermitian Complex conjugate of multiple Hermitian sequences
c06gsc	1	nag_multiple_hermitian_to_complex Convert Hermitian sequences to general complex sequences
c06gzc	1	nag_fft_init_trig Initialisation function for other c06 functions
c06hac	2	nag_fft_multiple_sine Discrete sine transform
c06hbc	2	nag_fft_multiple_cosine Discrete cosine transform
c06hcc	2	nag_fft_multiple_qtr_sine Discrete quarter-wave sine transform
c06hdc	2	nag_fft_multiple_qtr_cosine Discrete quarter-wave cosine transform
c06pfc	7	nag_fft_multid_single One-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
c06pjc	7	nag_fft_multid_full Multi-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type)
c06pxc	7	nag_fft_3d Three-dimensional complex discrete Fourier transform, complex data format

d01 – Quadrature

Routine Name	Mark of Introduction	Purpose
d01ajc	2	nag_1d_quad_gen One-dimensional adaptive quadrature, allowing for badly behaved integrands
d01akc	2	nag_1d_quad_osc One-dimensional adaptive quadrature, suitable for oscillating functions
d01alc	2	nag_1d_quad_brkpts One-dimensional adaptive quadrature, allowing for singularities at specified points
d01amc	2	nag_1d_quad_inf One-dimensional adaptive quadrature over infinite or semi-infinite interval
d01anc	2	nag_1d_quad_wt_trig One-dimensional adaptive quadrature, finite interval, sine or cosine weight functions
d01apc	2	nag_1d_quad_wt_alglog One-dimensional adaptive quadrature, weight function with end-point singularities of algebraic-logarithmic type
d01aqc	2	nag_1d_quad_wt_cauchy One-dimensional adaptive quadrature, weight function 1/(x-c), Cauchy principal value
d01asc	2	nag_1d_quad_inf_wt_trig One-dimensional adaptive quadrature, semi-infinite interval, sine or cosine weight function
d01bac	2	nag_1d_quad_guass One-dimensional Gaussian quadrature rule evaluation
d01fcc	2	nag_multid_quad_adapt Multi-dimensional adaptive quadrature
d01gac	2	nag_1d_quad_vals One-dimensional integration of a function defined by data values only
d01gbc	2	nag_multid_quad_monte_carlo Multi-dimensional quadrature, using Monte Carlo method
d01sjc	5	nag_1d_quad_gen_1 One-dimensional adaptive quadrature, allowing for badly behaved integrands, thread-safe
d01skc	5	nag_1d_quad_osc_1 One-dimensional adaptive quadrature, suitable for oscillating functions, thread-safe
d01slc	5	nag_1d_quad_brkpts_1 One-dimensional adaptive quadrature, allowing for singularities at specified points, thread-safe
d01smc	5	nag_1d_quad_inf_1 One-dimensional adaptive quadrature over infinite or semi-infinite interval, thread-safe
d01snc	5	nag_1d_quad_wt_trig_1 One-dimensional adaptive quadrature, finite interval, sine or cosine weight functions, thread-safe
d01spc	5	nag_1d_quad_wt_alglog_1 One-dimensional adaptive quadrature, weight function with end-point singularities of algebraic-logarithmic type, thread-safe
d01sqc	5	nag_1d_quad_wt_cauchy_1 One-dimensional adaptive quadrature, weight function 1/(x-c), Cauchy principal value, thread-safe
d01ssc	5	nag_1d_quad_inf_wt_trig_1 One-dimensional adaptive quadrature, semi-infinite interval, sine or cosine weight function, thread-safe
d01tac	5	nag_1d_quad_gauss_1 One-dimensional Gaussian quadrature rule evaluation, thread-safe
d01wcc	5	nag_multid_quad_adapt_1 Multi-dimensional adaptive quadrature, thread-safe
d01xbc	5	nag_multid_quad_monte_carlo_1 Multi-dimensional quadrature, using Monte Carlo method, thread-safe

d02 – Ordinary Differential Equations

Routine Name	Mark of Introduction	Purpose
d02cjc	2	nag_ode_ivp_adams_gen Ordinary differential equation solver using a variable-order variable-step Adams method (Black Box)
d02ejc	3	nag_ode_ivp_bdf_gen Ordinary differential equations solver, stiff, initial value problems using the Backward Differentiation Formulae
d02gac	3	nag_ode_bvp_fd_nonlin_fixedbc Ordinary differential equations solver, for simple nonlinear two-point boundary value problems, using a finite difference technique with deferred correction
d02gbc	3	nag_ode_bvp_fd_lin_gen Ordinary differential equations solver, for general linear two-point boundary value problems, using a finite difference technique with deferred correction
d02pcc	3	nag_ode_ivp_rk_range Ordinary differential equations solver, initial value problems over a range using Runge–Kutta methods
d02pdc	3	nag_ode_ivp_rk_onestep Ordinary differential equations solver, initial value problems, one time step using Runge–Kutta methods
d02ppc	3	nag_ode_ivp_rk_free Freeing function for use with the Runge–Kutta suite (d02p functions)
d02pvc	3	nag_ode_ivp_rk_setup Setup function for use with d02pcc and/or d02pdc
d02pwc	3	nag_ode_ivp_rk_reset_tend A function to re-set the end point following a call to d02pdc
d02pxc	3	nag_ode_ivp_rk_interp Ordinary differential equations solver, computes the solution by interpolation anywhere on an integration step taken by d02pdc
d02pzc	3	nag_ode_ivp_rk_errass A function to provide global error assessment during an integration with either d02pcc or d02pdc
d02qfc	2	nag_ode_ivp_adams_roots Ordinary differential equation solver using Adams method (sophisticated use)
d02qwc	2	nag_ode_ivp_adams_setup Setup function for d02qfc
d02qyc	2	nag_ode_ivp_adams_free Freeing function for use with d02qfc
d02qzc	2	nag_ode_ivp_adams_interp Interpolation function for use with d02qfc
d02rac	3	nag_ode_bvp_fd_nonlin_gen Ordinary differential equations solver, for general nonlinear two-point boundary value problems, using a finite difference technique with deferred correction

d03 – Partial Differential Equations

Routine Name	Mark of Introduction	Purpose
d03ncc	7	nag_pde_bs_1d Finite difference solution of the Black–Scholes equations
d03ndc	7	nag_pde_bs_1d_analytic Analytic solution of the Black–Scholes equations
d03nec	7	nag_pde_bs_1d_means Compute average values for d03ndc
d03pcc	7	nag_pde_parab_1d_fd General system of parabolic PDEs, method of lines, finite differences, one space variable
d03pdc	7	nag_pde_parab_1d_coll General system of parabolic PDEs, method of lines, Chebyshev C⁰ collocation, one space variable
d03pec	7	nag_pde_parab_1d_keller General system of first-order PDEs, method of lines, Keller box discretisation, one space variable
d03pfc	7	nag_pde_parab_1d_cd General system of convection-diffusion PDEs with source terms in conservative form, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
d03phc	7	nag_pde_parab_1d_fd_ode General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable
d03pjc	7	nag_pde_parab_1d_coll_ode General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C⁰ collocation, one space variable
d03pkc	7	nag_pde_parab_1d_keller_ode General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, one space variable
d03plc	7	nag_pde_parab_1d_cd_ode General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable
d03ppc	7	nag_pde_parab_1d_fd_ode_remesh General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
d03prc	7	nag_pde_parab_1d_keller_ode_remesh General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, remeshing, one space variable
d03psc	7	nag_pde_parab_1d_cd_ode_remesh General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, remeshing, one space variable
d03puc	7	nag_pde_parab_1d_euler_roe Roe's approximate Riemann solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pvc	7	nag_pde_parab_1d_euler_osher Osher's approximate Riemann solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pwc	7	nag_pde_parab_1d_euler_hll Modified HLL Riemann solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pxc	7	nag_pde_parab_1d_euler_exact Exact Riemann Solver for Euler equations in conservative form, for use with d03pfc, d03plc and d03psc
d03pyc	7	nag_pde_interp_1d_coll PDEs, spatial interpolation with d03pdc or d03pjc
d03pzc	7	nag_pde_interp_1d_fd PDEs, spatial interpolation with d03pcc, d03pec, d03pfc, d03phc, d03pkc, d03plc, d03ppc, d03prc or d03psc

d06 – Mesh Generation

Routine Name	Mark of Introduction	Purpose
d06aac	7	nag_mesh2d_inc Generates a two-dimensional mesh using a simple incremental method
d06abc	7	nag_mesh2d_delaunay Generates a two-dimensional mesh using a Delaunay–Voronoi process
d06acc	7	nag_mesh2d_front Generates a two-dimensional mesh using an Advancing-front method
d06bac	7	nag_mesh2d_bound Generates a boundary mesh
d06cac	7	nag_mesh2d_smooth Uses a barycentering technique to smooth a given mesh
d06cbc	7	nag_mesh2d_sparse Generates a sparsity pattern of a Finite Element matrix associated with a given mesh
d06ccc	7	nag_mesh2d_renum Renumbers a given mesh using Gibbs method
d06dac	7	nag_mesh2d_trans Generates a mesh resulting from an affine transformation of a given mesh
d06dbc	7	nag_mesh2d_join Joins together two given adjacent (possibly overlapping) meshes

e01 – Interpolation

Routine Name	Mark of Introduction	Purpose
e01aec	7	nag_1d_cheb_interp Interpolating functions, polynomial interpolant, data may include derivative values, one variable
e01bac	2	nag_1d_spline_interpolant Interpolating function, cubic spline interpolant, one variable
e01bec	1	nag_monotonic_interpolant Interpolating function, monotonicity-preserving, piecewise cubic Hermite, one variable
e01bfc	1	nag_monotonic_evaluate Evaluation of interpolant computed by e01bec, function only
e01bgc	2	nag_monotonic_deriv Evaluation of interpolant computed by e01bec, function and first derivative
e01bhc	2	nag_monotonic_intg Evaluation of interpolant computed by e01bec, definite integral
e01dac	2	nag_2d_spline_interpolant Interpolating function, bicubic spline interpolant, two variables
e01rac	7	nag_1d_ratnl_interp Interpolating functions, rational interpolant, one variable
e01rbc	7	nag_1d_ratnl_eval Interpolated values, evaluate rational interpolant computed by e01rac, one variable
e01sac	3	nag_2d_scat_interpolant A function to generate a two-dimensional surface interpolating a set of data points, using either the method of Renka and Cline or the modified Shepard's method
e01sbc	3	nag_2d_scat_eval A function to evaluate, at a set of points, the two-dimensional interpolant function generated by e01sac
e01szc	3	nag_2d_scat_free Freeing function for use with e01sbc
e01tgc	7	nag_3d_shep_interp Interpolating functions, modified Shepard's method, three variables
e01thc	7	nag_3d_shep_eval Interpolated values, evaluate interpolant computed by e01tgc, function and first derivatives, three variables

e02 – Curve and Surface Fitting

Routine Name	Mark of Introduction	Purpose
e02adc	5	nag_1d_cheb_fit Computes the coefficients of a Chebyshev series polynomial for arbitrary data
e02aec	5	nag_1d_cheb_eval Evaluates the coefficients of a Chebyshev series polynomial
e02afc	5	nag_1d_cheb_interp_fit Computes the coefficients of a Chebyshev series polynomial for interpolated data
e02agc	7	nag_1d_cheb_fit_constr Least-squares polynomial fit, values and derivatives may be constrained, arbitrary data points
e02ahc	7	nag_1d_cheb_deriv Derivative of fitted polynomial in Chebyshev series form
e02ajc	7	nag_1d_cheb_intg Integral of fitted polynomial in Chebyshev series form
e02akc	7	nag_1d_cheb_eval2 Evaluation of fitted polynomial in one variable from Chebyshev series form
e02bac	2	nag_1d_spline_fit_knots Least-squares curve cubic spline fit (including interpolation), one variable
e02bbc	2	nag_1d_spline_evaluate Evaluation of fitted cubic spline, function only
e02bcc	2	nag_1d_spline_deriv Evaluation of fitted cubic spline, function and derivatives
e02bdc	2	nag_1d_spline_intg Evaluation of fitted cubic spline, definite integral
e02bec	2	nag_1d_spline_fit Least-squares cubic spline curve fit, automatic knot placement, one variable
e02cac	7	nag_2d_cheb_fit_lines Least-squares surface fit by polynomials, data on lines
e02cbc	7	nag_2d_cheb_eval Evaluation of fitted polynomial in two variables
e02dcc	2	nag_2d_spline_fit_grid Least-squares bicubic spline fit with automatic knot placement, two variables (rectangular grid)
e02ddc	2	nag_2d_spline_fit_scat Least-squares bicubic spline fit with automatic knot placement, two variables (scattered data)
e02dec	2	nag_2d_spline_eval Evaluation of bicubic spline, at a set of points
e02dfc	2	nag_2d_spline_eval_rect Evaluation of bicubic spline, at a mesh of points
e02gac	7	nag_lone_fit L₁-approximation by general linear function
e02gcc	7	nag_linf_fit L_∞-approximation by general linear function
e02rac	7	nag_1d_pade Padé-approximants
e02rbc	7	nag_1d_pade_eval Evaluation of fitted rational function as computed by e02rac

e04 – Minimizing or Maximizing a Function

Routine Name	Mark of Introduction	Purpose
e04abc	5	nag_opt_one_var_no_deriv Minimizes a function of one variable, using function values only
e04bbc	5	nag_opt_one_var_deriv Minimizes a function of one variable, requires first derivatives
e04ccc	4	nag_opt_simplex Unconstrained minimization using simplex algorithm
e04dgc	2	nag_opt_conj_grad Unconstrained minimization using conjugate gradients
e04fcc	2	nag_opt_lsq_no_deriv Unconstrained nonlinear least squares (no derivatives required)
e04gbc	2	nag_opt_lsq_deriv Unconstrained nonlinear least squares (first derivatives required)
e04hcc	2	nag_opt_check_deriv Derivative checker for use with e04kbc
e04hdc	5	nag_opt_check_2nd_deriv Checks second derivatives of a user-defined function
e04jbc	2	nag_opt_bounds_no_deriv Bound constrained nonlinear minimization (no derivatives required)
e04kbc	2	nag_opt_bounds_deriv Bound constrained nonlinear minimization (first derivatives required)
e04lbc	5	nag_opt_bounds_2nd_deriv Solves bound constrained problems (first and second derivatives required)
e04mfc	2	nag_opt_lp Linear programming
e04myc	5	nag_opt_sparse_mps_free Free memory allocated by e04mzc
e04mzc	5	nag_opt_sparse_mps_read Read MPSX data for sparse LP or QP problem from a file
e04ncc	5	nag_opt_lin_lsq Solves linear least-squares and convex quadratic programming problems (non-sparse)
e04nfc	2	nag_opt_qp Quadratic programming
e04nkc	5	nag_opt_sparse_convex_qp Solves sparse linear programming or convex quadratic programming problems
e04ucc	4	nag_opt_nlp Minimization with nonlinear constraints using a sequential QP method
e04ugc	6	nag_opt_nlp_sparse NLP problem (sparse)
e04unc	5	nag_opt_nlin_lsq Solves nonlinear least-squares problems using the sequential QP method
e04xac	5	nag_opt_estimate_deriv Computes an approximation to the gradient vector and/or the Hessian matrix for use with e04ucc and other nonlinear optimization functions
e04xxc	2	nag_opt_init Initialisation function for option setting
e04xyc	2	nag_opt_read Read options from a text file
e04xzc	2	nag_opt_free Memory freeing function for use with option setting
e04yac	2	nag_opt_lsq_check_deriv Least-squares derivative checker for use with e04gbc
e04ycc	2	nag_opt_lsq_covariance Covariance matrix for nonlinear least-squares

f01 – Matrix Factorizations

Routine Name	Mark of Introduction	Purpose
f01bnc	1	nag_complex_cholesky UU^H factorization of complex Hermitian positive-definite matrix
f01mcc	1	nag_real_cholesky_skyline LDL^T factorization of real symmetric positive-definite variable-bandwidth (skyline) matrix
f01qcc	1	nag_real_qr QR factorization of real m by n matrix (m ≥ n)
f01qdc	1	nag_real_apply_q Compute QB or Q^T B after factorization by f01qcc
f01qec	1	nag_real_form_q Form columns of Q after factorization by f01qcc
f01rcc	1	nag_complex_qr QR factorization of complex m by n matrix (m≥ n)
f01rdc	1	nag_complex_apply_q Compute QB or Q^H B after factorization by f01rcc
f01rec	1	nag_complex_form_q Form columns of Q after factorization by f01rcc

f02 – Eigenvalues and Eigenvectors

Routine Name	Mark of Introduction	Purpose
f02aac	1	nag_real_symm_eigenvalues All eigenvalues of real symmetric matrix
f02abc	1	nag_real_symm_eigensystem All eigenvalues and eigenvectors of real symmetric matrix
f02adc	1	nag_real_symm_general_eigenvalues All eigenvalues of generalized real symmetric-definite eigenproblem
f02aec	1	nag_real_symm_general_eigensystem All eigenvalues and eigenvectors of generalized real symmetric-definite eigenproblem
f02afc	1	nag_real_eigenvalues All eigenvalues of real matrix
f02agc	1	nag_real_eigensystem All eigenvalues and eigenvectors of real matrix
f02awc	2	nag_hermitian_eigenvalues All eigenvalues of complex Hermitian matrix
f02axc	2	nag_hermitian_eigensystem All eigenvalues and eigenvectors of complex Hermitian matrix
f02bjc	2	nag_real_general_eigensystem All eigenvalues and optionally eigenvectors of real generalized eigenproblem, by QZ algorithm
f02ecc	5	nag_real_eigensystem_sel Computes selected eigenvalues and eigenvectors of a real general matrix
f02gcc	5	nag_complex_eigensystem_sel Computes selected eigenvalues and eigenvectors of a complex general matrix
f02wec	1	nag_real_svd SVD of real matrix
f02xec	1	nag_complex_svd SVD of complex matrix

f03 – Determinants

Routine Name	Mark of Introduction	Purpose
f03aec	1	nag_real_cholesky LL^T factorization and determinant of real symmetric positive-definite matrix
f03afc	1	nag_real_lu LU factorization and determinant of real matrix
f03ahc	1	nag_complex_lu LU factorization and determinant of complex matrix

f04 – Simultaneous Linear Equations

Routine Name	Mark of Introduction	Purpose
f04adc	1	nag_complex_lin_eqn_mult_rhs Approximate solution of complex simultaneous linear equations with multiple right-hand sides
f04agc	1	nag_real_cholesky_solve_mult_rhs Approximate solution of real symmetric positive-definite simultaneous linear equations (coefficient matrix already factorized by f03aec)
f04ajc	1	nag_real_lu_solve_mult_rhs Approximate solution of real simultaneous linear equations (coefficient matrix already factorized by f03afc)
f04akc	1	nag_complex_lu_solve_mult_rhs Approximate solution of complex simultaneous linear equations (coefficient matrix already factorized by f03ahc)
f04arc	1	nag_real_lin_eqn Approximate solution of real simultaneous linear equations, one right-hand side
f04awc	1	nag_hermitian_lin_eqn_mult_rhs Approximate solution of complex Hermitian positive-definite simultaneous linear equations (coefficient matrix already factorized by f01bnc)
f04mcc	1	nag_real_cholesky_skyline_solve Approximate solution of real symmetric positive-definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by f01mcc)

f06 – Linear Algebra Support Functions

Routine Name	Mark of Introduction	Purpose
f06pac	3	dgemv Matrix-vector product, real rectangular matrix
f06pbc	3	dgbmv Matrix-vector product, real rectangular band matrix
f06pcc	3	dsymv Matrix-vector product, real symmetric matrix
f06pdc	3	dsbmv Matrix-vector product, real symmetric band matrix
f06pec	3	dspmv Matrix-vector product, real symmetric packed matrix
f06pfc	3	dtrmv Matrix-vector product, real triangular matrix
f06pgc	3	dtbmv Matrix-vector product, real triangular band matrix
f06phc	3	dtpmv Matrix-vector product, real triangular packed matrix
f06pjc	3	dtrsv System of equations, real triangular matrix
f06pkc	3	dtbsv System of equations, real triangular band matrix
f06plc	3	dtpsv System of equations, real triangular packed matrix
f06pmc	3	dger Rank-1 update, real rectangular matrix
f06ppc	3	dsyr Rank-1 update, real symmetric matrix
f06pqc	3	dspr Rank-1 update, real symmetric packed matrix
f06prc	3	dsyr2 Rank-2 update, real symmetric matrix
f06psc	3	dspr2 Rank-2 update, real symmetric packed matrix
f06sac	3	zgemv Matrix-vector product, complex rectangular matrix
f06sbc	3	zgbmv Matrix-vector product, complex rectangular band matrix
f06scc	3	zhemv Matrix-vector product, complex Hermitian matrix
f06sdc	3	zhbmv Matrix-vector product, complex Hermitian band matrix
f06sec	3	zhpmv Matrix-vector product, complex Hermitian packed matrix
f06sfc	3	ztrmv Matrix-vector product, complex triangular matrix
f06sgc	3	ztbmv Matrix-vector product, complex triangular band matrix
f06shc	3	ztpmv Matrix-vector product, complex triangular packed matrix
f06sjc	3	ztrsv System of equations, complex triangular matrix
f06skc	3	ztbsv System of equations, complex triangular band matrix
f06slc	3	ztpsv System of equations, complex triangular packed matrix
f06smc	3	zgeru Rank-1 update, complex rectangular matrix, unconjugated vector
f06snc	3	zgerc Rank-1 update, complex rectangular matrix, conjugated vector
f06spc	3	zher Rank-1 update, complex Hermitian matrix
f06sqc	3	zhpr Rank-1 update, complex Hermitian packed matrix
f06src	3	zher2 Rank-2 update, complex Hermitian matrix
f06ssc	3	zhpr2 Rank-2 update, complex Hermitian packed matrix
f06yac	3	dgemm Matrix-matrix product, two real rectangular matrices
f06ycc	3	dsymm Matrix-matrix product, one real symmetric matrix, one real rectangular matrix
f06yfc	3	dtrmm Matrix-matrix product, one real triangular matrix, one real rectangular matrix
f06yjc	3	dtrsm Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix
f06ypc	3	dsyrk Rank-k update of a real symmetric matrix
f06yrc	3	dsyr2k Rank-2k update of a real symmetric matrix
f06zac	3	zgemm Matrix-matrix product, two complex rectangular matrices
f06zcc	3	zhemm Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix
f06zfc	3	ztrmm Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix
f06zjc	3	ztrsm Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix
f06zpc	3	zherk Rank-k update of a complex Hermitian matrix
f06zrc	3	zher2k Rank-2k update of a complex Hermitian matrix
f06ztc	3	zsymm Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix
f06zuc	3	zsyrk Rank-k update of a complex symmetric matrix
f06zwc	3	zsyr2k Rank-2k update of a complex symmetric matrix

f07 – Linear Equations (LAPACK)

A list of the LAPACK equivalent names is included in f07 Chapter Introduction.

Routine Name	Mark of Introduction	Purpose
f07adc	7	nag_dgetrf LU factorization of real m by n matrix
f07aec	7	nag_dgetrs Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by f07adc
f07agc	7	nag_dgecon Estimate condition number of real matrix, matrix already factorized by f07adc
f07ahc	7	nag_dgerfs Refined solution with error bounds of real system of linear equations, multiple right-hand sides
f07ajc	7	nag_dgetri Inverse of real matrix, matrix already factorized by f07adc
f07arc	7	nag_zgetrf LU factorization of complex m by n matrix
f07asc	7	nag_zgetrs Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by f07arc
f07auc	7	nag_zgecon Estimate condition number of complex matrix, matrix already factorized by f07arc
f07avc	7	nag_zgerfs Refined solution with error bounds of complex system of linear equations, multiple right-hand sides
f07awc	7	nag_zgetri Inverse of complex matrix, matrix already factorized by f07arc
f07bdc	7	nag_dgbtrf LU factorization of real m by n band matrix
f07bec	7	nag_dgbtrs Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by f07bdc
f07bgc	7	nag_dgbcon Estimate condition number of real band matrix, matrix already factorized by f07bdc
f07bhc	7	nag_dgbrfs Refined solution with error bounds of real band system of linear equations, multiple right-hand sides
f07brc	7	nag_zgbtrf LU factorization of complex m by n band matrix
f07bsc	7	nag_zgbtrs Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by f07brc
f07buc	7	nag_zgbcon Estimate condition number of complex band matrix, matrix already factorized by f07brc
f07bvc	7	nag_zgbrfs Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides
f07fdc	7	nag_dpotrf Cholesky factorization of real symmetric positive-definite matrix
f07fec	7	nag_dpotrs Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by f07fdc
f07fgc	7	nag_dpocon Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by f07fdc
f07fhc	7	nag_dporfs Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides
f07fjc	7	nag_dpotri Inverse of real symmetric positive-definite matrix, matrix already factorized by f07fdc
f07frc	7	nag_zpotrf Cholesky factorization of complex Hermitian positive-definite matrix
f07fsc	7	nag_zpotrs Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by f07frc
f07fuc	7	nag_zpocon Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by f07frc
f07fvc	7	nag_zporfs Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides
f07fwc	7	nag_zpotri Inverse of complex Hermitian positive-definite matrix, matrix already factorized by f07frc
f07gdc	7	nag_dpptrf Cholesky factorization of real symmetric positive-definite matrix, packed storage
f07gec	7	nag_dpptrs Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by f07gdc, packed storage
f07ggc	7	nag_dppcon Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by f07gdc, packed storage
f07ghc	7	nag_dpprfs Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides, packed storage
f07gjc	7	nag_dpptri Inverse of real symmetric positive-definite matrix, matrix already factorized by f07gdc, packed storage
f07grc	7	nag_zpptrf Cholesky factorization of complex Hermitian positive-definite matrix, packed storage
f07gsc	7	nag_zpptrs Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by f07grc, packed storage
f07guc	7	nag_zppcon Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by f07grc, packed storage
f07gvc	7	nag_zpprfs Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, packed storage
f07gwc	7	nag_zpptri Inverse of complex Hermitian positive-definite matrix, matrix already factorized by f07grc, packed storage
f07hdc	7	nag_dpbtrf Cholesky factorization of real symmetric positive-definite band matrix
f07hec	7	nag_dpbtrs Solution of real symmetric positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by f07hdc
f07hgc	7	nag_dpbcon Estimate condition number of real symmetric positive-definite band matrix, matrix already factorized by f07hdc
f07hhc	7	nag_dpbrfs Refined solution with error bounds of real symmetric positive-definite band system of linear equations, multiple right-hand sides
f07hrc	7	nag_zpbtrf Cholesky factorization of complex Hermitian positive-definite band matrix
f07hsc	7	nag_zpbtrs Solution of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by f07hrc
f07huc	7	nag_zpbcon Estimate condition number of complex Hermitian positive-definite band matrix, matrix already factorized by f07hrc
f07hvc	7	nag_zpbrfs Refined solution with error bounds of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides
f07mdc	7	nag_dsytrf Bunch–Kaufman factorization of real symmetric indefinite matrix
f07mec	7	nag_dsytrs Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07mdc
f07mgc	7	nag_dsycon Estimate condition number of real symmetric indefinite matrix, matrix already factorized by f07mdc
f07mhc	7	nag_dsyrfs Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides
f07mjc	7	nag_dsytri Inverse of real symmetric indefinite matrix, matrix already factorized by f07mdc
f07mrc	7	nag_zhetrf Bunch–Kaufman factorization of complex Hermitian indefinite matrix
f07msc	7	nag_zhetrs Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07mrc
f07muc	7	nag_zhecon Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by f07mrc
f07mvc	7	nag_zherfs Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides
f07mwc	7	nag_zhetri Inverse of complex Hermitian indefinite matrix, matrix already factorized by f07mrc
f07nrc	7	nag_zsytrf Bunch–Kaufman factorization of complex symmetric matrix
f07nsc	7	nag_zsytrs Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by f07nrc
f07nuc	7	nag_zsycon Estimate condition number of complex symmetric matrix, matrix already factorized by f07nrc
f07nvc	7	nag_zsyrfs Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides
f07nwc	7	nag_zsytri Inverse of complex symmetric matrix, matrix already factorized by f07nrc
f07pdc	7	nag_dsptrf Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage
f07pec	7	nag_dsptrs Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07pdc, packed storage
f07pgc	7	nag_dspcon Estimate condition number of real symmetric indefinite matrix, matrix already factorized by f07pdc, packed storage
f07phc	7	nag_dsprfs Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage
f07pjc	7	nag_dsptri Inverse of real symmetric indefinite matrix, matrix already factorized by f07pdc, packed storage
f07prc	7	nag_zhptrf Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage
f07psc	7	nag_zhptrs Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by f07prc, packed storage
f07puc	7	nag_zhpcon Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by f07prc, packed storage
f07pvc	7	nag_zhprfs Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage
f07pwc	7	nag_zhptri Inverse of complex Hermitian indefinite matrix, matrix already factorized by f07prc, packed storage
f07qrc	7	nag_zsptrf Bunch–Kaufman factorization of complex symmetric matrix, packed storage
f07qsc	7	nag_zsptrs Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by f07qrc, packed storage
f07quc	7	nag_zspcon Estimate condition number of complex symmetric matrix, matrix already factorized by f07qrc, packed storage
f07qvc	7	nag_zsprfs Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage
f07qwc	7	nag_zsptri Inverse of complex symmetric matrix, matrix already factorized by f07qrc, packed storage
f07tec	7	nag_dtrtrs Solution of real triangular system of linear equations, multiple right-hand sides
f07tgc	7	nag_dtrcon Estimate condition number of real triangular matrix
f07thc	7	nag_dtrrfs Error bounds for solution of real triangular system of linear equations, multiple right-hand sides
f07tjc	7	nag_dtrtri Inverse of real triangular matrix
f07tsc	7	nag_ztrtrs Solution of complex triangular system of linear equations, multiple right-hand sides
f07tuc	7	nag_ztrcon Estimate condition number of complex triangular matrix
f07tvc	7	nag_ztrrfs Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
f07twc	7	nag_ztrtri Inverse of complex triangular matrix
f07uec	7	nag_dtptrs Solution of real triangular system of linear equations, multiple right-hand sides, packed storage
f07ugc	7	nag_dtpcon Estimate condition number of real triangular matrix, packed storage
f07uhc	7	nag_dtprfs Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage
f07ujc	7	nag_dtptri Inverse of real triangular matrix, packed storage
f07usc	7	nag_ztptrs Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
f07uuc	7	nag_ztpcon Estimate condition number of complex triangular matrix, packed storage
f07uvc	7	nag_ztprfs Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage
f07uwc	7	nag_ztptri Inverse of complex triangular matrix, packed storage
f07vec	7	nag_dtbtrs Solution of real band triangular system of linear equations, multiple right-hand sides
f07vgc	7	nag_dtbcon Estimate condition number of real band triangular matrix
f07vhc	7	nag_dtbrfs Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
f07vsc	7	nag_ztbtrs Solution of complex band triangular system of linear equations, multiple right-hand sides
f07vuc	7	nag_ztbcon Estimate condition number of complex band triangular matrix
f07vvc	7	nag_ztbrfs Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides

f08 – Least-squares and Eigenvalue Problems (LAPACK)

A list of the LAPACK equivalent names is included in f08 Chapter Introduction.

Routine Name	Mark of Introduction	Purpose
f08aec	7	nag_dgeqrf QR factorization of real general rectangular matrix
f08afc	7	nag_dorgqr Form all or part of orthogonal Q from QR factorization determined by f08aec or f08bec
f08agc	7	nag_dormqr Apply orthogonal transformation determined by f08aec or f08bec
f08ahc	7	nag_dgelqf LQ factorization of real general rectangular matrix
f08ajc	7	nag_dorglq Form all or part of orthogonal Q from LQ factorization determined by f08ahc
f08akc	7	nag_dormlq Apply orthogonal transformation determined by f08ahc
f08asc	7	nag_zgeqrf QR factorization of complex general rectangular matrix
f08atc	7	nag_zungqr Form all or part of unitary Q from QR factorization determined by f08asc or f08bsc
f08auc	7	nag_zunmqr Apply unitary transformation determined by f08asc or f08bsc
f08avc	7	nag_zgelqf LQ factorization of complex general rectangular matrix
f08awc	7	nag_zunglq Form all or part of unitary Q from LQ factorization determined by f08avc
f08axc	7	nag_zunmlq Apply unitary transformation determined by f08avc
f08bec	7	nag_dgeqpf QR factorization of real general rectangular matrix with column pivoting
f08bsc	7	nag_zgeqpf QR factorization of complex general rectangular matrix with column pivoting
f08fcc	7	nag_dsyevd All eigenvalues and optionally all eigenvectors of real symmetric matrix, using divide and conquer
f08fec	7	nag_dsytrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
f08ffc	7	nag_dorgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fec
f08fgc	7	nag_dormtr Apply orthogonal transformation determined by f08fec
f08fqc	7	nag_zheevd All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, using divide and conquer
f08fsc	7	nag_zhetrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
f08ftc	7	nag_zungtr Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsc
f08fuc	7	nag_zunmtr Apply unitary transformation matrix determined by f08fsc
f08gcc	7	nag_dspevd All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage, using divide and conquer
f08gec	7	nag_dsptrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
f08gfc	7	nag_dopgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gec
f08ggc	7	nag_dopmtr Apply orthogonal transformation determined by f08gec
f08gqc	7	nag_zhpevd All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage, using divide and conquer
f08gsc	7	nag_zhptrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
f08gtc	7	nag_zupgtr Generate unitary transformation matrix from reduction to tridiagonal form determined by f08gsc
f08guc	7	nag_zupmtr Apply unitary transformation matrix determined by f08gsc
f08hcc	7	nag_dsbevd All eigenvalues and optionally all eigenvectors of real symmetric band matrix, using divide and conquer
f08hec	7	nag_dsbtrd Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
f08hqc	7	nag_zhbevd All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix, using divide and conquer
f08hsc	7	nag_zhbtrd Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
f08jcc	7	nag_dstevd All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix, using divide and conquer
f08jec	7	nag_dsteqr All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR
f08jfc	7	nag_dsterf All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR
f08jgc	7	nag_dpteqr All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix
f08jjc	7	nag_dstebz Selected eigenvalues of real symmetric tridiagonal matrix by bisection
f08jkc	7	nag_dstein Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
f08jsc	7	nag_zsteqr All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR
f08juc	7	nag_zpteqr All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix
f08jxc	7	nag_zstein Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
f08kec	7	nag_dgebrd Orthogonal reduction of real general rectangular matrix to bidiagonal form
f08kfc	7	nag_dorgbr Generate orthogonal transformation matrices from reduction to bidiagonal form determined by f08kec
f08kgc	7	nag_dormbr Apply orthogonal transformations from reduction to bidiagonal form determined by f08kec
f08ksc	7	nag_zgebrd Unitary reduction of complex general rectangular matrix to bidiagonal form
f08ktc	7	nag_zungbr Generate unitary transformation matrices from reduction to bidiagonal form determined by f08ksc
f08kuc	7	nag_zunmbr Apply unitary transformations from reduction to bidiagonal form determined by f08ksc
f08lec	7	nag_dgbbrd Reduction of real rectangular band matrix to upper bidiagonal form
f08lsc	7	nag_zgbbrd Reduction of complex rectangular band matrix to upper bidiagonal form
f08mec	7	nag_dbdsqr SVD of real bidiagonal matrix reduced from real general matrix
f08msc	7	nag_zbdsqr SVD of real bidiagonal matrix reduced from complex general matrix
f08nec	7	nag_dgehrd Orthogonal reduction of real general matrix to upper Hessenberg form
f08nfc	7	nag_dorghr Generate orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec
f08ngc	7	nag_dormhr Apply orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec
f08nhc	7	nag_dgebal Balance real general matrix
f08njc	7	nag_dgebak Transform eigenvectors of real balanced matrix to those of original matrix supplied to f08nhc
f08nsc	7	nag_zgehrd Unitary reduction of complex general matrix to upper Hessenberg form
f08ntc	7	nag_zunghr Generate unitary transformation matrix from reduction to Hessenberg form determined by f08nsc
f08nuc	7	nag_zunmhr Apply unitary transformation matrix from reduction to Hessenberg form determined by f08nsc
f08nvc	7	nag_zgebal Balance complex general matrix
f08nwc	7	nag_zgebak Transform eigenvectors of complex balanced matrix to those of original matrix supplied to f08nvc
f08pec	7	nag_dhseqr Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
f08pkc	7	nag_dhsein Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
f08psc	7	nag_zhseqr Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
f08pxc	7	nag_zhsein Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
f08qfc	7	nag_dtrexc Reorder Schur factorization of real matrix using orthogonal similarity transformation
f08qgc	7	nag_dtrsen Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
f08qhc	7	nag_dtrsyl Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes
f08qkc	7	nag_dtrevc Left and right eigenvectors of real upper quasi-triangular matrix
f08qlc	7	nag_dtrsna Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
f08qtc	7	nag_ztrexc Reorder Schur factorization of complex matrix using unitary similarity transformation
f08quc	7	nag_ztrsen Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
f08qvc	7	nag_ztrsyl Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes
f08qxc	7	nag_ztrevc Left and right eigenvectors of complex upper triangular matrix
f08qyc	7	nag_ztrsna Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
f08sec	7	nag_dsygst Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by f07fdc
f08ssc	7	nag_zhegst Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by f07frc
f08tec	7	nag_dspgst Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by f07gdc
f08tsc	7	nag_zhpgst Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by f07grc
f08uec	7	nag_dsbgst Reduction of real symmetric-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A
f08ufc	7	nag_dpbstf Computes a split Cholesky factorization of real symmetric positive-definite band matrix A
f08usc	7	nag_zhbgst Reduction of complex Hermitian-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A
f08utc	7	nag_zpbstf Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A
f08wec	7	nag_dgghrd Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
f08whc	7	nag_dggbal Balance a pair of real general matrices
f08wjc	7	nag_dggbak Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08whc
f08wsc	7