Routine Name |
Mark of Introduction |
Purpose |
A00AAF | 18 | Library identification, details of implementation and mark |
A00ACF | 21 | Check availability of a valid licence key |
Routine Name |
Mark of Introduction |
Purpose |
A02AAF | 2 | Square root of complex number |
A02ABF | 2 | Modulus of complex number |
A02ACF | 2 | Quotient of two complex numbers |
Routine Name |
Mark of Introduction |
Purpose |
C02AFF | 14 | All zeros of complex polynomial, modified Laguerre method |
C02AGF | 13 | All zeros of real polynomial, modified Laguerre method |
C02AHF | 14 | All zeros of complex quadratic equation |
C02AJF | 14 | All zeros of real quadratic equation |
C02AKF | 20 | All zeros of real cubic equation |
C02ALF | 20 | All zeros of real quartic equation |
C02AMF | 20 | All zeros of complex cubic equation |
C02ANF | 20 | All zeros of complex quartic equation |
Routine Name |
Mark of Introduction |
Purpose |
C05ADF | 8 | Zero of continuous function in given interval, Bus and Dekker algorithm |
C05AGF | 8 | Zero of continuous function, Bus and Dekker algorithm, from given starting value, binary search for interval |
C05AJF | 8 | Zero of continuous function, continuation method, from a given starting value |
C05AVF | 8 | Binary search for interval containing zero of continuous function (reverse communication) |
C05AXF | 8 | Zero of continuous function by continuation method, from given starting value (reverse communication) |
C05AZF | 7 | Zero in given interval of continuous function by Bus and Dekker algorithm (reverse communication) |
C05NBF | 9 | Solution of system of nonlinear equations using function values only (easy-to-use) |
C05NCF | 9 | Solution of system of nonlinear equations using function values only (comprehensive) |
C05NDF | 14 | Solution of system of nonlinear equations using function values only (reverse communication) |
C05PBF | 9 | Solution of system of nonlinear equations using first derivatives (easy-to-use) |
C05PCF | 9 | Solution of system of nonlinear equations using first derivatives (comprehensive) |
C05PDF/C05PDA | 14 | Solution of system of nonlinear equations using first derivatives (reverse communication) |
C05ZAF | 9 | Check user's routine for calculating first derivatives |
Routine Name |
Mark of Introduction |
Purpose |
C06BAF | 10 | Acceleration of convergence of sequence, Shanks' transformation and epsilon algorithm |
C06DBF | 6 | Sum of a Chebyshev series |
C06EAF | 8 | Single one-dimensional real discrete Fourier transform, no extra workspace |
C06EBF | 8 | Single one-dimensional Hermitian discrete Fourier transform, no extra workspace |
C06ECF | 8 | Single one-dimensional complex discrete Fourier transform, no extra workspace |
C06EKF | 11 | Circular convolution or correlation of two real vectors, no extra workspace |
C06FAF | 8 | Single one-dimensional real discrete Fourier transform, extra workspace for greater speed |
C06FBF | 8 | Single one-dimensional Hermitian discrete Fourier transform, extra workspace for greater speed |
C06FCF | 8 | Single one-dimensional complex discrete Fourier transform, extra workspace for greater speed |
C06FFF | 11 | One-dimensional complex discrete Fourier transform of multi-dimensional data |
C06FJF | 11 | Multi-dimensional complex discrete Fourier transform of multi-dimensional data |
C06FKF | 11 | Circular convolution or correlation of two real vectors, extra workspace for greater speed |
C06FPF | 12 | Multiple one-dimensional real discrete Fourier transforms |
C06FQF | 12 | Multiple one-dimensional Hermitian discrete Fourier transforms |
C06FRF | 12 | Multiple one-dimensional complex discrete Fourier transforms |
C06FUF | 13 | Two-dimensional complex discrete Fourier transform |
C06FXF | 17 | Three-dimensional complex discrete Fourier transform |
C06GBF | 8 | Complex conjugate of Hermitian sequence |
C06GCF | 8 | Complex conjugate of complex sequence |
C06GQF | 12 | Complex conjugate of multiple Hermitian sequences |
C06GSF | 12 | Convert Hermitian sequences to general complex sequences |
C06HAF | 13 | Discrete sine transform |
C06HBF | 13 | Discrete cosine transform |
C06HCF | 13 | Discrete quarter-wave sine transform |
C06HDF | 13 | Discrete quarter-wave cosine transform |
C06LAF | 12 | Inverse Laplace transform, Crump's method |
C06LBF | 14 | Inverse Laplace transform, modified Weeks' method |
C06LCF | 14 | Evaluate inverse Laplace transform as computed by C06LBF |
C06PAF | 19 | Single one-dimensional real and Hermitian complex discrete Fourier transform, using complex data format for Hermitian sequences |
C06PCF | 19 | Single one-dimensional complex discrete Fourier transform, complex data format |
C06PFF | 19 | One-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type) |
C06PJF | 19 | Multi-dimensional complex discrete Fourier transform of multi-dimensional data (using complex data type) |
C06PKF | 19 | Circular convolution or correlation of two complex vectors |
C06PPF | 19 | Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex data format for Hermitian sequences |
C06PQF | 19 | Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex data format for Hermitian sequences |
C06PRF | 19 | Multiple one-dimensional complex discrete Fourier transforms using complex data format |
C06PSF | 19 | Multiple one-dimensional complex discrete Fourier transforms using complex data format and sequences stored as columns |
C06PUF | 19 | Two-dimensional complex discrete Fourier transform, complex data format |
C06PXF | 19 | Three-dimensional complex discrete Fourier transform, complex data format |
C06RAF | 19 | Discrete sine transform (easy-to-use) |
C06RBF | 19 | Discrete cosine transform (easy-to-use) |
C06RCF | 19 | Discrete quarter-wave sine transform (easy-to-use) |
C06RDF | 19 | Discrete quarter-wave cosine transform (easy-to-use) |
Routine Name |
Mark of Introduction |
Purpose |
D01AHF | 8 | One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands |
D01AJF | 8 | One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands |
D01AKF | 8 | One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions |
D01ALF | 8 | One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points |
D01AMF | 2 | One-dimensional quadrature, adaptive, infinite or semi-infinite interval |
D01ANF | 8 | One-dimensional quadrature, adaptive, finite interval, weight function cos(ωx) or sin(ωx) |
D01APF | 8 | One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type |
D01AQF | 8 | One-dimensional quadrature, adaptive, finite interval, weight function 1 / (x-c) , Cauchy principal value (Hilbert transform) |
D01ARF | 10 | One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals |
D01ASF | 13 | One-dimensional quadrature, adaptive, semi-infinite interval, weight function cos(ωx) or sin(ωx) |
D01ATF | 13 | One-dimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines |
D01AUF | 13 | One-dimensional quadrature, adaptive, finite interval, variant of D01AKF efficient on vector machines |
D01BAF | 7 | One-dimensional Gaussian quadrature |
D01BBF | 7 | Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule |
D01BCF | 8 | Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule |
D01BDF | 8 | One-dimensional quadrature, non-adaptive, finite interval |
D01DAF | 5 | Two-dimensional quadrature, finite region |
D01EAF | 12 | Multi-dimensional adaptive quadrature over hyper-rectangle, multiple integrands |
D01FBF | 8 | Multi-dimensional Gaussian quadrature over hyper-rectangle |
D01FCF | 8 | Multi-dimensional adaptive quadrature over hyper-rectangle |
D01FDF | 10 | Multi-dimensional quadrature, Sag–Szekeres method, general product region or n -sphere |
D01GAF | 5 | One-dimensional quadrature, integration of function defined by data values, Gill–Miller method |
D01GBF | 10 | Multi-dimensional quadrature over hyper-rectangle, Monte Carlo method |
D01GCF | 10 | Multi-dimensional quadrature, general product region, number-theoretic method |
D01GDF | 14 | Multi-dimensional quadrature, general product region, number-theoretic method, variant of D01GCF efficient on vector machines |
D01GYF | 10 | Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is prime |
D01GZF | 10 | Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is product of two primes |
D01JAF | 10 | Multi-dimensional quadrature over an n -sphere, allowing for badly behaved integrands |
D01PAF | 10 | Multi-dimensional quadrature over an n -simplex |
Routine Name |
Mark of Introduction |
Purpose |
D02AGF | 2 | ODEs, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined |
D02BGF | 7 | ODEs, IVP, Runge–Kutta–Merson method, until a component attains given value (simple driver) |
D02BHF | 7 | ODEs, IVP, Runge–Kutta–Merson method, until function of solution is zero (simple driver) |
D02BJF | 18 | ODEs, IVP, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver) |
D02CJF | 13 | ODEs, IVP, Adams method, until function of solution is zero, intermediate output (simple driver) |
D02EJF | 12 | ODEs, stiff IVP, BDF method, until function of solution is zero, intermediate output (simple driver) |
D02GAF | 8 | ODEs, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem |
D02GBF | 8 | ODEs, boundary value problem, finite difference technique with deferred correction, general linear problem |
D02HAF | 8 | ODEs, boundary value problem, shooting and matching, boundary values to be determined |
D02HBF | 8 | ODEs, boundary value problem, shooting and matching, general parameters to be determined |
D02JAF | 8 | ODEs, boundary value problem, collocation and least-squares, single n th-order linear equation |
D02JBF | 8 | ODEs, boundary value problem, collocation and least-squares, system of first-order linear equations |
D02KAF | 7 | Second-order Sturm–Liouville problem, regular system, finite range, eigenvalue only |
D02KDF | 7 | Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points |
D02KEF | 8 | Second-order Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points |
D02LAF | 13 | Second-order ODEs, IVP, Runge–Kutta–Nystrom method |
D02LXF | 13 | Second-order ODEs, IVP, setup for D02LAF |
D02LYF | 13 | Second-order ODEs, IVP, diagnostics for D02LAF |
D02LZF | 13 | Second-order ODEs, IVP, interpolation for D02LAF |
D02MVF | 14 | ODEs, IVP, DASSL method, setup for D02M–N routines |
D02MZF | 14 | ODEs, IVP, interpolation for D02M–N routines, natural interpolant |
D02NBF | 12 | Explicit ODEs, stiff IVP, full Jacobian (comprehensive) |
D02NCF | 12 | Explicit ODEs, stiff IVP, banded Jacobian (comprehensive) |
D02NDF | 12 | Explicit ODEs, stiff IVP, sparse Jacobian (comprehensive) |
D02NGF | 12 | Implicit/algebraic ODEs, stiff IVP, full Jacobian (comprehensive) |
D02NHF | 12 | Implicit/algebraic ODEs, stiff IVP, banded Jacobian (comprehensive) |
D02NJF | 12 | Implicit/algebraic ODEs, stiff IVP, sparse Jacobian (comprehensive) |
D02NMF | 12 | Explicit ODEs, stiff IVP (reverse communication, comprehensive) |
D02NNF | 12 | Implicit/algebraic ODEs, stiff IVP (reverse communication, comprehensive) |
D02NRF | 12 | ODEs, IVP, for use with D02M–N routines, sparse Jacobian, enquiry routine |
D02NSF | 12 | ODEs, IVP, for use with D02M–N routines, full Jacobian, linear algebra set up |
D02NTF | 12 | ODEs, IVP, for use with D02M–N routines, banded Jacobian, linear algebra set up |
D02NUF | 12 | ODEs, IVP, for use with D02M–N routines, sparse Jacobian, linear algebra set up |
D02NVF | 12 | ODEs, IVP, BDF method, setup for D02M–N routines |
D02NWF | 12 | ODEs, IVP, Blend method, setup for D02M–N routines |
D02NXF | 12 | ODEs, IVP, sparse Jacobian, linear algebra diagnostics, for use with D02M–N routines |
D02NYF | 12 | ODEs, IVP, integrator diagnostics, for use with D02M–N routines |
D02NZF | 12 | ODEs, IVP, setup for continuation calls to integrator, for use with D02M–N routines |
D02PCF | 16 | ODEs, IVP, Runge–Kutta method, integration over range with output |
D02PDF | 16 | ODEs, IVP, Runge–Kutta method, integration over one step |
D02PVF | 16 | ODEs, IVP, setup for D02PCF and D02PDF |
D02PWF | 16 | ODEs, IVP, resets end of range for D02PDF |
D02PXF | 16 | ODEs, IVP, interpolation for D02PDF |
D02PYF | 16 | ODEs, IVP, integration diagnostics for D02PCF and D02PDF |
D02PZF | 16 | ODEs, IVP, error assessment diagnostics for D02PCF and D02PDF |
D02QFF | 13 | ODEs, IVP, Adams method with root-finding (forward communication, comprehensive) |
D02QGF | 13 | ODEs, IVP, Adams method with root-finding (reverse communication, comprehensive) |
D02QWF | 13 | ODEs, IVP, setup for D02QFF and D02QGF |
D02QXF | 13 | ODEs, IVP, diagnostics for D02QFF and D02QGF |
D02QYF | 13 | ODEs, IVP, root-finding diagnostics for D02QFF and D02QGF |
D02QZF | 13 | ODEs, IVP, interpolation for D02QFF or D02QGF |
D02RAF | 8 | ODEs, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility |
D02SAF | 8 | ODEs, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined |
D02TGF | 8 | n th-order linear ODEs, boundary value problem, collocation and least-squares |
D02TKF | 17 | ODEs, general nonlinear boundary value problem, collocation technique |
D02TVF | 17 | ODEs, general nonlinear boundary value problem, setup for D02TKF |
D02TXF | 17 | ODEs, general nonlinear boundary value problem, continuation facility for D02TKF |
D02TYF | 17 | ODEs, general nonlinear boundary value problem, interpolation for D02TKF |
D02TZF | 17 | ODEs, general nonlinear boundary value problem, diagnostics for D02TKF |
D02XJF | 12 | ODEs, IVP, interpolation for D02M–N routines, natural interpolant |
D02XKF | 12 | ODEs, IVP, interpolation for D02M–N routines, C_{1} interpolant |
D02ZAF | 12 | ODEs, IVP, weighted norm of local error estimate for D02M–N routines |
Routine Name |
Mark of Introduction |
Purpose |
D03EAF | 7 | Elliptic PDE, Laplace's equation, two-dimensional arbitrary domain |
D03EBF | 7 | Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, iterate to convergence |
D03ECF | 8 | Elliptic PDE, solution of finite difference equations by SIP for seven-point three-dimensional molecule, iterate to convergence |
D03EDF | 12 | Elliptic PDE, solution of finite difference equations by a multigrid technique |
D03EEF | 13 | Discretize a second-order elliptic PDE on a rectangle |
D03FAF | 14 | Elliptic PDE, Helmholtz equation, three-dimensional Cartesian co-ordinates |
D03MAF | 7 | Triangulation of plane region |
D03NCF | 20 | Finite difference solution of the Black–Scholes equations |
D03NDF | 20 | Analytic solution of the Black–Scholes equations |
D03NEF | 20 | Compute average values for D03NDF |
D03PCF/D03PCA | 15 | General system of parabolic PDEs, method of lines, finite differences, one space variable |
D03PDF/D03PDA | 15 | General system of parabolic PDEs, method of lines, Chebyshev C^{0} collocation, one space variable |
D03PEF | 16 | General system of first-order PDEs, method of lines, Keller box discretisation, one space variable |
D03PFF | 17 | 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 |
D03PHF/D03PHA | 15 | General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable |
D03PJF/D03PJA | 15 | General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C^{0} collocation, one space variable |
D03PKF | 16 | General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, one space variable |
D03PLF | 17 | 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 |
D03PPF/D03PPA | 16 | General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable |
D03PRF | 16 | General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, remeshing, one space variable |
D03PSF | 17 | 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 |
D03PUF | 17 | Roe's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF |
D03PVF | 17 | Osher's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF |
D03PWF | 18 | Modified HLL Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF |
D03PXF | 18 | Exact Riemann Solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF |
D03PYF | 15 | PDEs, spatial interpolation with D03PDF/D03PDA or D03PJF/D03PJA |
D03PZF | 15 | PDEs, spatial interpolation with D03PCF/D03PCA, D03PEF, D03PFF, D03PHF/D03PHA, D03PKF, D03PLF, D03PPF/D03PPA, D03PRF or D03PSF |
D03RAF | 18 | General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region |
D03RBF | 18 | General system of second-order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region |
D03RYF | 18 | Check initial grid data in D03RBF |
D03RZF | 18 | Extract grid data from D03RBF |
D03UAF | 7 | Elliptic PDE, solution of finite difference equations by SIP, five-point two-dimensional molecule, one iteration |
D03UBF | 8 | Elliptic PDE, solution of finite difference equations by SIP, seven-point three-dimensional molecule, one iteration |
Routine Name |
Mark of Introduction |
Purpose |
D04AAF | 5 | Numerical differentiation, derivatives up to order 14, function of one real variable |
Routine Name |
Mark of Introduction |
Purpose |
D05AAF | 5 | Linear non-singular Fredholm integral equation, second kind, split kernel |
D05ABF | 6 | Linear non-singular Fredholm integral equation, second kind, smooth kernel |
D05BAF | 14 | Nonlinear Volterra convolution equation, second kind |
D05BDF | 16 | Nonlinear convolution Volterra–Abel equation, second kind, weakly singular |
D05BEF | 16 | Nonlinear convolution Volterra–Abel equation, first kind, weakly singular |
D05BWF | 16 | Generate weights for use in solving Volterra equations |
D05BYF | 16 | Generate weights for use in solving weakly singular Abel-type equations |
Routine Name |
Mark of Introduction |
Purpose |
D06AAF | 20 | Generates a two-dimensional mesh using a simple incremental method |
D06ABF | 20 | Generates a two-dimensional mesh using a Delaunay–Voronoi process |
D06ACF | 20 | Generates a two-dimensional mesh using an Advancing-front method |
D06BAF | 20 | Generates a boundary mesh |
D06CAF | 20 | Uses a barycentering technique to smooth a given mesh |
D06CBF | 20 | Generates a sparsity pattern of a Finite Element matrix associated with a given mesh |
D06CCF | 20 | Renumbers a given mesh using Gibbs method |
D06DAF | 20 | Generates a mesh resulting from an affine transformation of a given mesh |
D06DBF | 20 | Joins together two given adjacent (possibly overlapping) meshes |
Routine Name |
Mark of Introduction |
Purpose |
E01AAF | 1 | Interpolated values, Aitken's technique, unequally spaced data, one variable |
E01ABF | 1 | Interpolated values, Everett's formula, equally spaced data, one variable |
E01AEF | 8 | Interpolating functions, polynomial interpolant, data may include derivative values, one variable |
E01BAF | 8 | Interpolating functions, cubic spline interpolant, one variable |
E01BEF | 13 | Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable |
E01BFF | 13 | Interpolated values, interpolant computed by E01BEF, function only, one variable |
E01BGF | 13 | Interpolated values, interpolant computed by E01BEF, function and first derivative, one variable |
E01BHF | 13 | Interpolated values, interpolant computed by E01BEF, definite integral, one variable |
E01DAF | 14 | Interpolating functions, fitting bicubic spline, data on rectangular grid |
E01RAF | 9 | Interpolating functions, rational interpolant, one variable |
E01RBF | 9 | Interpolated values, evaluate rational interpolant computed by E01RAF, one variable |
E01SAF | 13 | Interpolating functions, method of Renka and Cline, two variables |
E01SBF | 13 | Interpolated values, evaluate interpolant computed by E01SAF, two variables |
E01SGF | 18 | Interpolating functions, modified Shepard's method, two variables |
E01SHF | 18 | Interpolated values, evaluate interpolant computed by E01SGF, function and first derivatives, two variables |
E01TGF | 18 | Interpolating functions, modified Shepard's method, three variables |
E01THF | 18 | Interpolated values, evaluate interpolant computed by E01TGF, function and first derivatives, three variables |
Routine Name |
Mark of Introduction |
Purpose |
E02ACF | 1 | Minimax curve fit by polynomials |
E02ADF | 5 | Least-squares curve fit, by polynomials, arbitrary data points |
E02AEF | 5 | Evaluation of fitted polynomial in one variable from Chebyshev series form (simplified parameter list) |
E02AFF | 5 | Least-squares polynomial fit, special data points (including interpolation) |
E02AGF | 8 | Least-squares polynomial fit, values and derivatives may be constrained, arbitrary data points |
E02AHF | 8 | Derivative of fitted polynomial in Chebyshev series form |
E02AJF | 8 | Integral of fitted polynomial in Chebyshev series form |
E02AKF | 8 | Evaluation of fitted polynomial in one variable from Chebyshev series form |
E02BAF | 5 | Least-squares curve cubic spline fit (including interpolation) |
E02BBF | 5 | Evaluation of fitted cubic spline, function only |
E02BCF | 7 | Evaluation of fitted cubic spline, function and derivatives |
E02BDF | 7 | Evaluation of fitted cubic spline, definite integral |
E02BEF | 13 | Least-squares cubic spline curve fit, automatic knot placement |
E02CAF | 7 | Least-squares surface fit by polynomials, data on lines |
E02CBF | 7 | Evaluation of fitted polynomial in two variables |
E02DAF | 6 | Least-squares surface fit, bicubic splines |
E02DCF | 13 | Least-squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid |
E02DDF | 13 | Least-squares surface fit by bicubic splines with automatic knot placement, scattered data |
E02DEF | 14 | Evaluation of fitted bicubic spline at a vector of points |
E02DFF | 14 | Evaluation of fitted bicubic spline at a mesh of points |
E02GAF | 7 | L_{1} -approximation by general linear function |
E02GBF | 7 | L_{1} -approximation by general linear function subject to linear inequality constraints |
E02GCF | 8 | L_{∞} -approximation by general linear function |
E02RAF | 7 | Padé approximants |
E02RBF | 7 | Evaluation of fitted rational function as computed by E02RAF |
E02ZAF | 6 | Sort two-dimensional data into panels for fitting bicubic splines |
Routine Name |
Mark of Introduction |
Purpose |
E04ABF/E04ABA | 6 | Minimum, function of one variable using function values only |
E04BBF/E04BBA | 6 | Minimum, function of one variable, using first derivative |
E04CCF/E04CCA | 1 | Unconstrained minimum, simplex algorithm, function of several variables using function values only (comprehensive) |
E04DGF/E04DGA | 12 | Unconstrained minimum, preconditioned conjugate gradient algorithm, function of several variables using first derivatives (comprehensive) |
E04DJF/E04DJA | 12 | Supply optional parameter values for E04DGF/E04DGA from external file |
E04DKF/E04DKA | 12 | Supply optional parameter values to E04DGF/E04DGA |
E04FCF | 7 | Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (comprehensive) |
E04FYF | 18 | Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using function values only (easy-to-use) |
E04GBF | 7 | Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm using first derivatives (comprehensive) |
E04GDF | 7 | Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (comprehensive) |
E04GYF | 18 | Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasi-Newton algorithm, using first derivatives (easy-to-use) |
E04GZF | 18 | Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (easy-to-use) |
E04HCF | 6 | Check user's routine for calculating first derivatives of function |
E04HDF | 6 | Check user's routine for calculating second derivatives of function |
E04HEF | 7 | Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (comprehensive) |
E04HYF | 18 | Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm, using second derivatives (easy-to-use) |
E04JYF | 18 | Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using function values only (easy-to-use) |
E04KDF | 6 | Minimum, function of several variables, modified Newton algorithm, simple bounds, using first derivatives (comprehensive) |
E04KYF | 18 | Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using first derivatives (easy-to-use) |
E04KZF | 18 | Minimum, function of several variables, modified Newton algorithm, simple bounds, using first derivatives (easy-to-use) |
E04LBF | 6 | Minimum, function of several variables, modified Newton algorithm, simple bounds, using first and second derivatives (comprehensive) |
E04LYF | 18 | Minimum, function of several variables, modified Newton algorithm, simple bounds, using first and second derivatives (easy-to-use) |
E04MFF/E04MFA | 16 | LP problem (dense) |
E04MGF/E04MGA | 16 | Supply optional parameter values for E04MFF/E04MFA from external file |
E04MHF/E04MHA | 16 | Supply optional parameter values to E04MFF/E04MFA |
E04MZF | 18 | Converts MPSX data file defining LP or QP problem to format required by E04NQF |
E04NCF/E04NCA | 12 | Convex QP problem or linearly-constrained linear least-squares problem (dense) |
E04NDF/E04NDA | 12 | Supply optional parameter values for E04NCF/E04NCA from external file |
E04NEF/E04NEA | 12 | Supply optional parameter values to E04NCF/E04NCA |
E04NFF/E04NFA | 16 | QP problem (dense) |
E04NGF/E04NGA | 16 | Supply optional parameter values for E04NFF/E04NFA from external file |
E04NHF/E04NHA | 16 | Supply optional parameter values to E04NFF/E04NFA |
E04NPF | 21 | Initialization routine for E04NQF |
E04NQF | 21 | LP or QP problem (suitable for sparse problems) |
E04NRF | 21 | Supply optional parameter values for E04NQF from external file |
E04NSF | 21 | Set a single option for E04NQF from a character string |
E04NTF | 21 | Set a single option for E04NQF from an INTEGER argument |
E04NUF | 21 | Set a single option for E04NQF from a double precision argument |
E04NXF | 21 | Get the setting of an INTEGER valued option of E04NQF |
E04NYF | 21 | Get the setting of a double precision valued option of E04NQF |
E04UDF/E04UDA | 12 | Supply optional parameter values for E04UCF/E04UCA or E04UFF/E04UFA from external file |
E04UEF/E04UEA | 12 | Supply optional parameter values to E04UCF/E04UCA or E04UFF/E04UFA |
E04UFF/E04UFA | 18 | Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive) |
E04UGF/E04UGA | 19 | NLP problem (sparse) |
E04UHF/E04UHA | 19 | Supply optional parameter values for E04UGF/E04UGA from external file |
E04UJF/E04UJA | 19 | Supply optional parameter values to E04UGF/E04UGA |
E04UQF/E04UQA | 14 | Supply optional parameter values for E04USF/E04USA from external file |
E04URF/E04URA | 14 | Supply optional parameter values to E04USF/E04USA |
E04USF/E04USA | 20 | Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives (comprehensive) |
E04VGF | 21 | Initialization routine for E04VHF |
E04VHF | 21 | General sparse nonlinear optimizer |
E04VJF | 21 | Determine the pattern of nonzeros in the Jacobian matrix for E04VHF |
E04VKF | 21 | Supply optional parameter values for E04VHF from external file |
E04VLF | 21 | Set a single option for E04VHF from a character string |
E04VMF | 21 | Set a single option for E04VHF from an INTEGER argument |
E04VNF | 21 | Set a single option for E04VHF from a double precision argument |
E04VRF | 21 | Get the setting of an INTEGER valued option of E04VHF |
E04VSF | 21 | Get the setting of a double precision valued option of E04VHF |
E04WBF | 20 | Initialization routine for E04DGA E04MFA E04NCA E04NFA E04UFA E04UGA E04USA |
E04WCF | 21 | Initialization routine for E04WDF |
E04WDF | 21 | Solves the nonlinear programming (NP) problem |
E04WEF | 21 | Supply optional parameter values for E04WDF from external file |
E04WFF | 21 | Set a single option for E04WDF from a character string |
E04WGF | 21 | Set a single option for E04WDF from an INTEGER argument |
E04WHF | 21 | Set a single option for E04WDF from a double precision argument |
E04WJF | 21 | Determine whether an E04WDF option has been set or not |
E04WKF | 21 | Get the setting of an INTEGER valued option of E04WDF |
E04WLF | 21 | Get the setting of a double precision valued option of E04WDF |
E04XAF/E04XAA | 12 | Estimate (using numerical differentiation) gradient and/or Hessian of a function |
E04YAF | 7 | Check user's routine for calculating Jacobian of first derivatives |
E04YBF | 7 | Check user's routine for calculating Hessian of a sum of squares |
E04YCF | 11 | Covariance matrix for nonlinear least-squares problem (unconstrained) |
E04ZCF/E04ZCA | 11 | Check user's routines for calculating first derivatives of function and constraints |
Routine Name |
Mark of Introduction |
Purpose |
F01ABF | 1 | Inverse of real symmetric positive-definite matrix using iterative refinement |
F01ADF | 2 | Inverse of real symmetric positive-definite matrix |
F01BLF | 5 | Pseudo-inverse and rank of real m by n matrix (m≥n) |
F01BRF | 7 | L U factorization of real sparse matrix |
F01BSF | 7 | L U factorization of real sparse matrix with known sparsity pattern |
F01BUF | 7 | U L D L^{T} U^{T} factorization of real symmetric positive-definite band matrix |
F01BVF | 7 | Reduction to standard form, generalized real symmetric-definite banded eigenproblem |
F01CKF | 2 | Matrix multiplication |
F01CRF | 7 | Matrix transposition |
F01CTF | 14 | Sum or difference of two real matrices, optional scaling and transposition |
F01CWF | 14 | Sum or difference of two complex matrices, optional scaling and transposition |
F01LEF | 11 | L U factorization of real tridiagonal matrix |
F01LHF | 13 | L U factorization of real almost block diagonal matrix |
F01MCF | 8 | L D L^{T} factorization of real symmetric positive-definite variable-bandwidth matrix |
F01QGF | 14 | R Q factorization of real m by n upper trapezoidal matrix (m≤n) |
F01QJF | 14 | R Q factorization of real m by n matrix (m≤n) |
F01QKF | 14 | Operations with orthogonal matrices, form rows of Q , after R Q factorization by F01QJF |
F01RGF | 14 | R Q factorization of complex m by n upper trapezoidal matrix (m≤n) |
F01RJF | 14 | R Q factorization of complex m by n matrix (m≤n) |
F01RKF | 14 | Operations with unitary matrices, form rows of Q , after R Q factorization by F01RJF |
F01ZAF | 14 | Convert real matrix between packed triangular and square storage schemes |
F01ZBF | 14 | Convert complex matrix between packed triangular and square storage schemes |
F01ZCF | 14 | Convert real matrix between packed banded and rectangular storage schemes |
F01ZDF | 14 | Convert complex matrix between packed banded and rectangular storage schemes |
Routine Name |
Mark of Introduction |
Purpose |
F02ECF | 17 | Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box) |
F02FJF | 11 | Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box) |
F02GCF | 17 | Selected eigenvalues and eigenvectors of complex nonsymmetric matrix (Black Box) |
F02SDF | 8 | Eigenvector of generalized real banded eigenproblem by inverse iteration |
F02WDF | 8 | Q R factorization, possibly followed by SVD |
F02WUF | 14 | SVD of real upper triangular matrix (Black Box) |
F02XUF | 13 | SVD of complex upper triangular matrix (Black Box) |
Routine Name |
Mark of Introduction |
Purpose |
F03AAF | 1 | Determinant of real matrix (Black Box) |
F03ABF | 1 | Determinant of real symmetric positive-definite matrix (Black Box) |
F03ACF | 1 | Determinant of real symmetric positive-definite band matrix (Black Box) |
F03ADF | 1 | Determinant of complex matrix (Black Box) |
F03AEF | 2 | L L^{T} factorization and determinant of real symmetric positive-definite matrix |
F03AFF | 2 | L U factorization and determinant of real matrix |
Routine Name |
Mark of Introduction |
Purpose |
F04ABF | 2 | Solution of real symmetric positive-definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box) |
F04AEF | 2 | Solution of real simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box) |
F04AFF | 2 | Solution of real symmetric positive-definite simultaneous linear equations using iterative refinement (coefficient matrix already factorized by F03AEF) |
F04AGF | 2 | Solution of real symmetric positive-definite simultaneous linear equations (coefficient matrix already factorized by F03AEF) |
F04AHF | 2 | Solution of real simultaneous linear equations using iterative refinement (coefficient matrix already factorized by F03AFF) |
F04AJF | 2 | Solution of real simultaneous linear equations (coefficient matrix already factorized by F03AFF) |
F04AMF | 2 | Least-squares solution of m real equations in n unknowns, rank = n , m ≥ n using iterative refinement (Black Box) |
F04ASF | 4 | Solution of real symmetric positive-definite simultaneous linear equations, one right-hand side using iterative refinement (Black Box) |
F04ATF | 4 | Solution of real simultaneous linear equations, one right-hand side using iterative refinement (Black Box) |
F04AXF | 7 | Solution of real sparse simultaneous linear equations (coefficient matrix already factorized) |
F04BAF | 21 | Computes the solution and error-bound to a real system of linear equations |
F04BBF | 21 | Computes the solution and error-bound to a real banded system of linear equations |
F04BCF | 21 | Computes the solution and error-bound to a real tridiagonal system of linear equations |
F04BDF | 21 | Computes the solution and error-bound to a real symmetric positive-definite system of linear equations |
F04BEF | 21 | Computes the solution and error-bound to a real symmetric positive-definite system of linear equations, packed storage |
F04BFF | 21 | Computes the solution and error-bound to a real symmetric positive-definite banded system of linear equations |
F04BGF | 21 | Computes the solution and error-bound to a real symmetric positive-definite tridiagonal system of linear equations |
F04BHF | 21 | Computes the solution and error-bound to a real symmetric system of linear equations |
F04BJF | 21 | Computes the solution and error-bound to a real symmetric system of linear equations, packed storage |
F04CAF | 21 | Computes the solution and error-bound to a complex system of linear equations |
F04CBF | 21 | Computes the solution and error-bound to a complex banded system of linear equations |
F04CCF | 21 | Computes the solution and error-bound to a complex tridiagonal system of linear equations |
F04CDF | 21 | Computes the solution and error-bound to a complex Hermitian positive-definite system of linear equations |
F04CEF | 21 | Computes the solution and error-bound to a complex Hermitian positive-definite system of linear equations, packed storage |
F04CFF | 21 | Computes the solution and error-bound to a complex Hermitian positive-definite banded system of linear equations |
F04CGF | 21 | Computes the solution and error-bound to a complex Hermitian positive-definite tridiagonal system of linear equations |
F04CHF | 21 | Computes the solution and error-bound to a complex Hermitian system of linear equations |
F04CJF | 21 | Computes the solution and error-bound to a complex Hermitian system of linear equations, packed storage |
F04DHF | 21 | Computes the solution and error-bound to a complex symmetric system of linear equations |
F04DJF | 21 | Computes the solution and error-bound to a complex symmetric system of linear equations, packed storage. |
F04FEF | 15 | Solution of the Yule–Walker equations for real symmetric positive-definite Toeplitz matrix, one right-hand side |
F04FFF | 15 | Solution of real symmetric positive-definite Toeplitz system, one right-hand side |
F04JGF | 8 | Least-squares (if rank = n ) or minimal least-squares (if rank < n ) solution of m real equations in n unknowns, rank ≤ n , m ≥ n |
F04LEF | 11 | Solution of real tridiagonal simultaneous linear equations (coefficient matrix already factorized by F01LEF) |
F04LHF | 13 | Solution of real almost block diagonal simultaneous linear equations (coefficient matrix already factorized by F01LHF) |
F04MCF | 8 | Solution of real symmetric positive-definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by F01MCF) |
F04MEF | 15 | Update solution of the Yule–Walker equations for real symmetric positive-definite Toeplitz matrix |
F04MFF | 15 | Update solution of real symmetric positive-definite Toeplitz system |
F04QAF | 11 | Sparse linear least-squares problem, m real equations in n unknowns |
F04YAF | 11 | Covariance matrix for linear least-squares problems, m real equations in n unknowns |
F04YCF | 13 | Norm estimation (for use in condition estimation), real matrix |
F04ZCF | 13 | Norm estimation (for use in condition estimation), complex matrix |
Routine Name |
Mark of Introduction |
Purpose |
F05AAF | 5 | Gram–Schmidt orthogonalisation of n vectors of order m |
Routine Name |
Mark of Introduction |
Purpose |
F06AAF (DROTG) | 12 | Generate real plane rotation |
F06BAF | 12 | Generate real plane rotation, storing tangent |
F06BCF | 12 | Recover cosine and sine from given real tangent |
F06BEF | 12 | Generate real Jacobi plane rotation |
F06BHF | 12 | Apply real similarity rotation to 2 by 2 symmetric matrix |
F06BLF | 12 | Compute quotient of two real scalars, with overflow flag |
F06BMF | 12 | Compute Euclidean norm from scaled form |
F06BNF | 12 | Compute square root of (a^{2}+b^{2}) , real a and b |
F06BPF | 12 | Compute eigenvalue of 2 by 2 real symmetric matrix |
F06CAF | 12 | Generate complex plane rotation, storing tangent, real cosine |
F06CBF | 12 | Generate complex plane rotation, storing tangent, real sine |
F06CCF | 12 | Recover cosine and sine from given complex tangent, real cosine |
F06CDF | 12 | Recover cosine and sine from given complex tangent, real sine |
F06CHF | 12 | Apply complex similarity rotation to 2 by 2 Hermitian matrix |
F06CLF | 12 | Compute quotient of two complex scalars, with overflow flag |
F06DBF | 12 | Broadcast scalar into integer vector |
F06DFF | 12 | Copy integer vector |
F06EAF (DDOT) | 12 | Dot product of two real vectors |
F06ECF (DAXPY) | 12 | Add scalar times real vector to real vector |
F06EDF (DSCAL) | 12 | Multiply real vector by scalar |
F06EFF (DCOPY) | 12 | Copy real vector |
F06EGF (DSWAP) | 12 | Swap two real vectors |
F06EJF (DNRM2) | 12 | Compute Euclidean norm of real vector |
F06EKF (DASUM) | 12 | Sum absolute values of real vector elements |
F06EPF (DROT) | 12 | Apply real plane rotation |
F06ERF (DDOTI) | 14 | Dot product of two real sparse vectors |
F06ETF (DAXPYI) | 14 | Add scalar times real sparse vector to real sparse vector |
F06EUF (DGTHR) | 14 | Gather real sparse vector |
F06EVF (DGTHRZ) | 14 | Gather and set to zero real sparse vector |
F06EWF (DSCTR) | 14 | Scatter real sparse vector |
F06EXF (DROTI) | 14 | Apply plane rotation to two real sparse vectors |
F06FAF | 12 | Compute cosine of angle between two real vectors |
F06FBF | 12 | Broadcast scalar into real vector |
F06FCF | 12 | Multiply real vector by diagonal matrix |
F06FDF | 12 | Multiply real vector by scalar, preserving input vector |
F06FEF (DRSCL) | 21 | Multiply real vector by reciprocal of scalar |
F06FGF | 12 | Negate real vector |
F06FJF | 12 | Update Euclidean norm of real vector in scaled form |
F06FKF | 12 | Compute weighted Euclidean norm of real vector |
F06FLF | 12 | Elements of real vector with largest and smallest absolute value |
F06FPF | 12 | Apply real symmetric plane rotation to two vectors |
F06FQF | 12 | Generate sequence of real plane rotations |
F06FRF | 12 | Generate real elementary reflection, NAG style |
F06FSF | 12 | Generate real elementary reflection, LINPACK style |
F06FTF | 12 | Apply real elementary reflection, NAG style |
F06FUF | 12 | Apply real elementary reflection, LINPACK style |
F06GAF (ZDOTU) | 12 | Dot product of two complex vectors, unconjugated |
F06GBF (ZDOTC) | 12 | Dot product of two complex vectors, conjugated |
F06GCF (ZAXPY) | 12 | Add scalar times complex vector to complex vector |
F06GDF (ZSCAL) | 12 | Multiply complex vector by complex scalar |
F06GFF (ZCOPY) | 12 | Copy complex vector |
F06GGF (ZSWAP) | 12 | Swap two complex vectors |
F06GRF (ZDOTUI) | 14 | Dot product of two complex sparse vector, unconjugated |
F06GSF (ZDOTCI) | 14 | Dot product of two complex sparse vector, conjugated |
F06GTF (ZAXPYI) | 14 | Add scalar times complex sparse vector to complex sparse vector |
F06GUF (ZGTHR) | 14 | Gather complex sparse vector |
F06GVF (ZGTHRZ) | 14 | Gather and set to zero complex sparse vector |
F06GWF (ZSCTR) | 14 | Scatter complex sparse vector |
F06HBF | 12 | Broadcast scalar into complex vector |
F06HCF | 12 | Multiply complex vector by complex diagonal matrix |
F06HDF | 12 | Multiply complex vector by complex scalar, preserving input vector |
F06HGF | 12 | Negate complex vector |
F06HPF | 12 | Apply complex plane rotation |
F06HQF | 12 | Generate sequence of complex plane rotations |
F06HRF | 12 | Generate complex elementary reflection |
F06HTF | 12 | Apply complex elementary reflection |
F06JDF (ZDSCAL) | 12 | Multiply complex vector by real scalar |
F06JJF (DZNRM2) | 12 | Compute Euclidean norm of complex vector |
F06JKF (DZASUM) | 12 | Sum absolute values of complex vector elements |
F06JLF (IDAMAX) | 12 | Index, real vector element with largest absolute value |
F06JMF (IZAMAX) | 12 | Index, complex vector element with largest absolute value |
F06KCF | 12 | Multiply complex vector by real diagonal matrix |
F06KDF | 12 | Multiply complex vector by real scalar, preserving input vector |
F06KEF (ZDRSCL) | 21 | Multiply complex vector by reciprocal of real scalar |
F06KFF | 12 | Copy real vector to complex vector |
F06KJF | 12 | Update Euclidean norm of complex vector in scaled form |
F06KLF | 12 | Last non-negligible element of real vector |
F06KPF | 12 | Apply real plane rotation to two complex vectors |
F06PAF (DGEMV) | 12 | Matrix-vector product, real rectangular matrix |
F06PBF (DGBMV) | 12 | Matrix-vector product, real rectangular band matrix |
F06PCF (DSYMV) | 12 | Matrix-vector product, real symmetric matrix |
F06PDF (DSBMV) | 12 | Matrix-vector product, real symmetric band matrix |
F06PEF (DSPMV) | 12 | Matrix-vector product, real symmetric packed matrix |
F06PFF (DTRMV) | 12 | Matrix-vector product, real triangular matrix |
F06PGF (DTBMV) | 12 | Matrix-vector product, real triangular band matrix |
F06PHF (DTPMV) | 12 | Matrix-vector product, real triangular packed matrix |
F06PJF (DTRSV) | 12 | System of equations, real triangular matrix |
F06PKF (DTBSV) | 12 | System of equations, real triangular band matrix |
F06PLF (DTPSV) | 12 | System of equations, real triangular packed matrix |
F06PMF (DGER) | 12 | Rank-1 update, real rectangular matrix |
F06PPF (DSYR) | 12 | Rank-1 update, real symmetric matrix |
F06PQF (DSPR) | 12 | Rank-1 update, real symmetric packed matrix |
F06PRF (DSYR2) | 12 | Rank-2 update, real symmetric matrix |
F06PSF (DSPR2) | 12 | Rank-2 update, real symmetric packed matrix |
F06QFF | 13 | Matrix copy, real rectangular or trapezoidal matrix |
F06QHF | 13 | Matrix initialization, real rectangular matrix |
F06QJF | 13 | Permute rows or columns, real rectangular matrix, permutations represented by an integer array |
F06QKF | 13 | Permute rows or columns, real rectangular matrix, permutations represented by a real array |
F06QMF | 13 | Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations |
F06QPF | 13 | Q R factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix |
F06QQF | 13 | Q R factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row |
F06QRF | 13 | Q R or R Q factorization by sequence of plane rotations, real upper Hessenberg matrix |
F06QSF | 13 | Q R or R Q factorization by sequence of plane rotations, real upper spiked matrix |
F06QTF | 13 | Q R factorization of U Z or R Q factorization of Z U , U real upper triangular, Z a sequence of plane rotations |
F06QVF | 13 | Compute upper Hessenberg matrix by sequence of plane rotations, real upper triangular matrix |
F06QWF | 13 | Compute upper spiked matrix by sequence of plane rotations, real upper triangular matrix |
F06QXF | 13 | Apply sequence of plane rotations, real rectangular matrix |
F06RAF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, real general matrix |
F06RBF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, real band matrix |
F06RCF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, real symmetric matrix |
F06RDF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage |
F06REF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, real symmetric band matrix |
F06RJF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix |
F06RKF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage |
F06RLF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, real triangular band matrix |
F06RMF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, real Hessenberg matrix |
F06RNF | 21 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, real tridiagonal matrix |
F06RPF | 21 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix |
F06SAF (ZGEMV) | 12 | Matrix-vector product, complex rectangular matrix |
F06SBF (ZGBMV) | 12 | Matrix-vector product, complex rectangular band matrix |
F06SCF (ZHEMV) | 12 | Matrix-vector product, complex Hermitian matrix |
F06SDF (ZHBMV) | 12 | Matrix-vector product, complex Hermitian band matrix |
F06SEF (ZHPMV) | 12 | Matrix-vector product, complex Hermitian packed matrix |
F06SFF (ZTRMV) | 12 | Matrix-vector product, complex triangular matrix |
F06SGF (ZTBMV) | 12 | Matrix-vector product, complex triangular band matrix |
F06SHF (ZTPMV) | 12 | Matrix-vector product, complex triangular packed matrix |
F06SJF (ZTRSV) | 12 | System of equations, complex triangular matrix |
F06SKF (ZTBSV) | 12 | System of equations, complex triangular band matrix |
F06SLF (ZTPSV) | 12 | System of equations, complex triangular packed matrix |
F06SMF (ZGERU) | 12 | Rank-1 update, complex rectangular matrix, unconjugated vector |
F06SNF (ZGERC) | 12 | Rank-1 update, complex rectangular matrix, conjugated vector |
F06SPF (ZHER) | 12 | Rank-1 update, complex Hermitian matrix |
F06SQF (ZHPR) | 12 | Rank-1 update, complex Hermitian packed matrix |
F06SRF (ZHER2) | 12 | Rank-2 update, complex Hermitian matrix |
F06SSF (ZHPR2) | 12 | Rank-2 update, complex Hermitian packed matrix |
F06TAF (ZSYMV) | 21 | Matrix-vector product, complex symmetric matrix |
F06TBF (ZSYR) | 21 | Rank-1 update, complex symetric matrix |
F06TCF (ZSPMV) | 21 | Matrix-vector product, complex symmetric packed matrix |
F06TDF (ZSPR) | 21 | Rank-1 update, complex symetric packed matrix |
F06TFF | 13 | Matrix copy, complex rectangular or trapezoidal matrix |
F06THF | 13 | Matrix initialization, complex rectangular matrix |
F06TMF | 13 | Unitary similarity transformation of Hermitian matrix as a sequence of plane rotations |
F06TPF | 13 | Q R factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix |
F06TQF | 13 | Q R × k factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row |
F06TRF | 13 | Q R or R Q factorization by sequence of plane rotations, complex upper Hessenberg matrix |
F06TSF | 13 | Q R or R Q factorization by sequence of plane rotations, complex upper spiked matrix |
F06TTF | 13 | Q R factorization of U Z or R Q factorization of Z U , U complex upper triangular, Z a sequence of plane rotations |
F06TVF | 13 | Compute upper Hessenberg matrix by sequence of plane rotations, complex upper triangular matrix |
F06TWF | 13 | Compute upper spiked matrix by sequence of plane rotations, complex upper triangular matrix |
F06TXF | 13 | Apply sequence of plane rotations, complex rectangular matrix, real cosine and complex sine |
F06TYF | 13 | Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine |
F06UAF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex general matrix |
F06UBF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex band matrix |
F06UCF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex Hermitian matrix |
F06UDF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage |
F06UEF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex Hermitian band matrix |
F06UFF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex symmetric matrix |
F06UGF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage |
F06UHF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex symmetric band matrix |
F06UJF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix |
F06UKF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage |
F06ULF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex triangular band matrix |
F06UMF | 15 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex Hessenberg matrix |
F06UNF | 21 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex tridiagonal matrix |
F06UPF | 21 | 1 -norm, ∞ -norm, Frobenius norm, largest absolute element, complex Hermitian tridiagonal matrix |
F06VJF | 13 | Permute rows or columns, complex rectangular matrix, permutations represented by an integer array |
F06VKF | 13 | Permute rows or columns, complex rectangular matrix, permutations represented by a real array |
F06VXF | 13 | Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine |
F06YAF (DGEMM) | 14 | Matrix-matrix product, two real rectangular matrices |
F06YCF (DSYMM) | 14 | Matrix-matrix product, one real symmetric matrix, one real rectangular matrix |
F06YFF (DTRMM) | 14 | Matrix-matrix product, one real triangular matrix, one real rectangular matrix |
F06YJF (DTRSM) | 14 | Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix |
F06YPF (DSYRK) | 14 | Rank- k update of a real symmetric matrix |
F06YRF (DSYR2K) | 14 | Rank- 2 k update of a real symmetric matrix |
F06ZAF (ZGEMM) | 14 | Matrix-matrix product, two complex rectangular matrices |
F06ZCF (ZHEMM) | 14 | Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix |
F06ZFF (ZTRMM) | 14 | Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix |
F06ZJF (ZTRSM) | 14 | Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix |
F06ZPF (ZHERK) | 14 | Rank- k update of a complex Hermitian matrix |
F06ZRF (ZHER2K) | 14 | Rank- 2 k update of a complex Hermitian matrix |
F06ZTF (ZSYMM) | 14 | Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix |
F06ZUF (ZSYRK) | 14 | Rank- k update of a complex symmetric matrix |
F06ZWF (ZSYR2K) | 14 | Rank- 2 k update of a complex symmetric matrix |
Routine Name |
Mark of Introduction |
Purpose |
F07AAF (DGESV) | 21 | Computes the solution to a real system of linear equations |
F07ABF (DGESVX) | 21 | Uses the L U factorization to compute the solution, error-bound and condition estimate for a real system of linear equations |
F07ADF (DGETRF) | 15 | L U factorization of real m by n matrix |
F07AEF (DGETRS) | 15 | Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07ADF (DGETRF) |
F07AFF (DGEEQU) | 21 | Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number |
F07AGF (DGECON) | 15 | Estimate condition number of real matrix, matrix already factorized by F07ADF (DGETRF) |
F07AHF (DGERFS) | 15 | Refined solution with error bounds of real system of linear equations, multiple right-hand sides |
F07AJF (DGETRI) | 15 | Inverse of real matrix, matrix already factorized by F07ADF (DGETRF) |
F07ANF (ZGESV) | 21 | Computes the solution to a complex system of linear equations |
F07APF (ZGESVX) | 21 | Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex system of linear equations |
F07ARF (ZGETRF) | 15 | L U factorization of complex m by n matrix |
F07ASF (ZGETRS) | 15 | Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF (ZGETRF) |
F07ATF (ZGEEQU) | 21 | Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number |
F07AUF (ZGECON) | 15 | Estimate condition number of complex matrix, matrix already factorized by F07ARF (ZGETRF) |
F07AVF (ZGERFS) | 15 | Refined solution with error bounds of complex system of linear equations, multiple right-hand sides |
F07AWF (ZGETRI) | 15 | Inverse of complex matrix, matrix already factorized by F07ARF (ZGETRF) |
F07BAF (DGBSV) | 21 | Computes the solution to a real banded system of linear equations |
F07BBF (DGBSVX) | 21 | Uses the L U factorization to compute the solution, error-bound and condition estimate for a real banded system of linear equations |
F07BDF (DGBTRF) | 15 | L U factorization of real m by n band matrix |
F07BEF (DGBTRS) | 15 | Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF (DGBTRF) |
F07BFF (DGBEQU) | 21 | Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number |
F07BGF (DGBCON) | 15 | Estimate condition number of real band matrix, matrix already factorized by F07BDF (DGBTRF) |
F07BHF (DGBRFS) | 15 | Refined solution with error bounds of real band system of linear equations, multiple right-hand sides |
F07BNF (ZGBSV) | 21 | Computes the solution to a complex banded system of linear equations |
F07BPF (ZGBSVX) | 21 | Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex banded system of linear equations |
F07BRF (ZGBTRF) | 15 | L U factorization of complex m by n band matrix |
F07BSF (ZGBTRS) | 15 | Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF (ZGBTRF) |
F07BTF (ZGBEQU) | 21 | Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number |
F07BUF (ZGBCON) | 15 | Estimate condition number of complex band matrix, matrix already factorized by F07BRF (ZGBTRF) |
F07BVF (ZGBRFS) | 15 | Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides |
F07CAF (DGTSV) | 21 | Computes the solution to a real tridiagonal system of linear equations |
F07CBF (DGTSVX) | 21 | Uses the L U factorization to compute the solution, error-bound and condition estimate for a real tridiagonal system of linear equations |
F07CDF (DGTTRF) | 21 | L U factorization of real tridiagonal matrix |
F07CEF (DGTTRS) | 21 | Solves a real tridiagonal system of linear equations using the L U factorization computed by F07CDF (DGTTRF) |
F07CGF (DGTCON) | 21 | Estimates the reciprocal of the condition number of a real tridiagonal matrix using the L U factorization computed by F07CDF (DGTTRF) |
F07CHF (DGTRFS) | 21 | Refined solution with error bounds of real tridiagonal system of linear equations, multiple right-hand sides |
F07CNF (ZGTSV) | 21 | Computes the solution to a complex tridiagonal system of linear equations |
F07CPF (ZGTSVX) | 21 | Uses the L U factorization to compute the solution, error-bound and condition estimate for a complex tridiagonal system of linear equations |
F07CRF (ZGTTRF) | 21 | L U factorization of complex tridiagonal matrix |
F07CSF (ZGTTRS) | 21 | Solves a complex tridiagonal system of linear equations using the L U factorization computed by F07CDF (DGTTRF) |
F07CUF (ZGTCON) | 21 | Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the L U factorization computed by F07CDF (DGTTRF) |
F07CVF (ZGTRFS) | 21 | Refined solution with error bounds of complex tridiagonal system of linear equations, multiple right-hand sides |
F07FAF (DPOSV) | 21 | Computes the solution to a real symmetric positive-definite system of linear equations |
F07FBF (DPOSVX) | 21 | Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite system of linear equations |
F07FDF (DPOTRF) | 15 | Cholesky factorization of real symmetric positive-definite matrix |
F07FEF (DPOTRS) | 15 | Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF (DPOTRF) |
F07FFF (DPOEQU) | 21 | Computes row and column scalings intended to equilibrate a real symmetric positive-definite matrix and reduce its condition number |
F07FGF (DPOCON) | 15 | Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07FDF (DPOTRF) |
F07FHF (DPORFS) | 15 | Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides |
F07FJF (DPOTRI) | 15 | Inverse of real symmetric positive-definite matrix, matrix already factorized by F07FDF (DPOTRF) |
F07FNF (ZPOSV) | 21 | Computes the solution to a complex Hermitian positive-definite system of linear equations |
F07FPF (ZPOSVX) | 21 | Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite system of linear equations |
F07FRF (ZPOTRF) | 15 | Cholesky factorization of complex Hermitian positive-definite matrix |
F07FSF (ZPOTRS) | 15 | Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRF (ZPOTRF) |
F07FTF (ZPOEQU) | 21 | Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite matrix and reduce its condition number |
F07FUF (ZPOCON) | 15 | Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07FRF (ZPOTRF) |
F07FVF (ZPORFS) | 15 | Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides |
F07FWF (ZPOTRI) | 15 | Inverse of complex Hermitian positive-definite matrix, matrix already factorized by F07FRF (ZPOTRF) |
F07GAF (DPPSV) | 21 | Computes the solution to a real symmetric positive-definite system of linear equations, packed storage |
F07GBF (DPPSVX) | 21 | Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite system of linear equations, packed storage |
F07GDF (DPPTRF) | 15 | Cholesky factorization of real symmetric positive-definite matrix, packed storage |
F07GEF (DPPTRS) | 15 | Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF (DPPTRF), packed storage |
F07GFF (DPPEQU) | 21 | Computes row and column scalings intended to equilibrate a real symmetric positive-definite matrix and reduce its condition number, packed storage |
F07GGF (DPPCON) | 15 | Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07GDF (DPPTRF), packed storage |
F07GHF (DPPRFS) | 15 | Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides, packed storage |
F07GJF (DPPTRI) | 15 | Inverse of real symmetric positive-definite matrix, matrix already factorized by F07GDF (DPPTRF), packed storage |
F07GNF (ZPPSV) | 21 | Computes the solution to a complex Hermitian positive-definite system of linear equations, packed storage |
F07GPF (ZPPSVX) | 21 | Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite system of linear equations, packed storage |
F07GRF (ZPPTRF) | 15 | Cholesky factorization of complex Hermitian positive-definite matrix, packed storage |
F07GSF (ZPPTRS) | 15 | Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GRF (ZPPTRF), packed storage |
F07GTF (ZPPEQU) | 21 | Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite matrix and reduce its condition number, packed storage |
F07GUF (ZPPCON) | 15 | Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07GRF (ZPPTRF), packed storage |
F07GVF (ZPPRFS) | 15 | Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, packed storage |
F07GWF (ZPPTRI) | 15 | Inverse of complex Hermitian positive-definite matrix, matrix already factorized by F07GRF (ZPPTRF), packed storage |
F07HAF (DPBSV) | 21 | Computes the solution to a real symmetric positive-definite banded system of linear equations |
F07HBF (DPBSVX) | 21 | Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite banded system of linear equations |
F07HDF (DPBTRF) | 15 | Cholesky factorization of real symmetric positive-definite band matrix |
F07HEF (DPBTRS) | 15 | Solution of real symmetric positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF (DPBTRF) |
F07HFF (DPBEQU) | 21 | Computes row and column scalings intended to equilibrate a real symmetric positive-definite banded matrix and reduce its condition number |
F07HGF (DPBCON) | 15 | Estimate condition number of real symmetric positive-definite band matrix, matrix already factorized by F07HDF (DPBTRF) |
F07HHF (DPBRFS) | 15 | Refined solution with error bounds of real symmetric positive-definite band system of linear equations, multiple right-hand sides |
F07HNF (ZPBSV) | 21 | Computes the solution to a complex Hermitian positive-definite banded system of linear equations |
F07HPF (ZPBSVX) | 21 | Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite banded system of linear equations |
F07HRF (ZPBTRF) | 15 | Cholesky factorization of complex Hermitian positive-definite band matrix |
F07HSF (ZPBTRS) | 15 | Solution of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HRF (ZPBTRF) |
F07HTF (ZPBEQU) | 21 | Computes row and column scalings intended to equilibrate a complex Hermitian positive-definite banded matrix and reduce its condition number |
F07HUF (ZPBCON) | 15 | Estimate condition number of complex Hermitian positive-definite band matrix, matrix already factorized by F07HRF (ZPBTRF) |
F07HVF (ZPBRFS) | 15 | Refined solution with error bounds of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides |
F07JAF (DPTSV) | 21 | Computes the solution to a real symmetric positive-definite tridiagonal system of linear equations |
F07JBF (DPTSVX) | 21 | Uses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive-definite tridiagonal system of linear equations |
F07JDF (DPTTRF) | 21 | Computes the modified Cholesky factorization of a real symmetric positive-definite tridiagonal matrix |
F07JEF (DPTTRS) | 21 | Solves a real symmetric positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JDF (DPTTRF) |
F07JGF (DPTCON) | 21 | Computes the reciprocal of the condition number of a real symmetric positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JDF (DPTTRF) |
F07JHF (DPTRFS) | 21 | Refined solution with error bounds of real symmetric positive-definite tridiagonal system of linear equations, multiple right-hand sides |
F07JNF (ZPTSV) | 21 | Computes the solution to a complex Hermitian positive-definite tridiagonal system of linear equations |
F07JPF (ZPTSVX) | 21 | Uses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a complex Hermitian positive-definite tridiagonal system of linear equations |
F07JRF (ZPTTRF) | 21 | Computes the modified Cholesky factorization of a complex Hermitian positive-definite tridiagonal matrix |
F07JSF (ZPTTRS) | 21 | Solves a complex Hermitian positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JRF (ZPTTRF) |
F07JUF (ZPTCON) | 21 | Computes the reciprocal of the condition number of a complex Hermitian positive-definite tridiagonal system using the modified Cholesky factorization computed by F07JRF (ZPTTRF) |
F07JVF (ZPTRFS) | 21 | Refined solution with error bounds of complex Hermitian positive-definite tridiagonal system of linear equations, multiple right-hand sides |
F07MAF (DSYSV) | 21 | Computes the solution to a real symmetric system of linear equations |
F07MBF (DSYSVX) | 21 | Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations |
F07MDF (DSYTRF) | 15 | Bunch–Kaufman factorization of real symmetric indefinite matrix |
F07MEF (DSYTRS) | 15 | Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF (DSYTRF) |
F07MGF (DSYCON) | 15 | Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF (DSYTRF) |
F07MHF (DSYRFS) | 15 | Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides |
F07MJF (DSYTRI) | 15 | Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF (DSYTRF) |
F07MNF (ZHESV) | 21 | Computes the solution to a complex Hermitian system of linear equations |
F07MPF (ZHESVX) | 21 | Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations |
F07MRF (ZHETRF) | 15 | Bunch–Kaufman factorization of complex Hermitian indefinite matrix |
F07MSF (ZHETRS) | 15 | Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MRF (ZHETRF) |
F07MUF (ZHECON) | 15 | Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF (ZHETRF) |
F07MVF (ZHERFS) | 15 | Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides |
F07MWF (ZHETRI) | 15 | Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MRF (ZHETRF) |
F07NNF (ZSYSV) | 21 | Computes the solution to a complex symmetric system of linear equations |
F07NPF (ZSYSVX) | 21 | Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations |
F07NRF (ZSYTRF) | 15 | Bunch–Kaufman factorization of complex symmetric matrix |
F07NSF (ZSYTRS) | 15 | Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF (ZSYTRF) |
F07NUF (ZSYCON) | 15 | Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF (ZSYTRF) |
F07NVF (ZSYRFS) | 15 | Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides |
F07NWF (ZSYTRI) | 15 | Inverse of complex symmetric matrix, matrix already factorized by F07NRF (ZSYTRF) |
F07PAF (DSPSV) | 21 | Computes the solution to a real symmetric system of linear equations, packed storage |
F07PBF (DSPSVX) | 21 | Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage |
F07PDF (DSPTRF) | 15 | Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage |
F07PEF (DSPTRS) | 15 | Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF (DSPTRF), packed storage |
F07PGF (DSPCON) | 15 | Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF (DSPTRF), packed storage |
F07PHF (DSPRFS) | 15 | Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage |
F07PJF (DSPTRI) | 15 | Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF (DSPTRF), packed storage |
F07PNF (ZHPSV) | 21 | Computes the solution to a complex Hermitian system of linear equations, packed storage |
F07PPF (ZHPSVX) | 21 | Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations, packed storage |
F07PRF (ZHPTRF) | 15 | Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage |
F07PSF (ZHPTRS) | 15 | Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PRF (ZHPTRF), packed storage |
F07PUF (ZHPCON) | 15 | Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF (ZHPTRF), packed storage |
F07PVF (ZHPRFS) | 15 | Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage |
F07PWF (ZHPTRI) | 15 | Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PRF (ZHPTRF), packed storage |
F07QNF (ZSPSV) | 21 | Computes the solution to a complex symmetric system of linear equations, packed storage |
F07QPF (ZSPSVX) | 21 | Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations, packed storage |
F07QRF (ZSPTRF) | 15 | Bunch–Kaufman factorization of complex symmetric matrix, packed storage |
F07QSF (ZSPTRS) | 15 | Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF (ZSPTRF), packed storage |
F07QUF (ZSPCON) | 15 | Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF (ZSPTRF), packed storage |
F07QVF (ZSPRFS) | 15 | Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage |
F07QWF (ZSPTRI) | 15 | Inverse of complex symmetric matrix, matrix already factorized by F07QRF (ZSPTRF), packed storage |
F07TEF (DTRTRS) | 15 | Solution of real triangular system of linear equations, multiple right-hand sides |
F07TGF (DTRCON) | 15 | Estimate condition number of real triangular matrix |
F07THF (DTRRFS) | 15 | Error bounds for solution of real triangular system of linear equations, multiple right-hand sides |
F07TJF (DTRTRI) | 15 | Inverse of real triangular matrix |
F07TSF (ZTRTRS) | 15 | Solution of complex triangular system of linear equations, multiple right-hand sides |
F07TUF (ZTRCON) | 15 | Estimate condition number of complex triangular matrix |
F07TVF (ZTRRFS) | 15 | Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides |
F07TWF (ZTRTRI) | 15 | Inverse of complex triangular matrix |
F07UEF (DTPTRS) | 15 | Solution of real triangular system of linear equations, multiple right-hand sides, packed storage |
F07UGF (DTPCON) | 15 | Estimate condition number of real triangular matrix, packed storage |
F07UHF (DTPRFS) | 15 | Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage |
F07UJF (DTPTRI) | 15 | Inverse of real triangular matrix, packed storage |
F07USF (ZTPTRS) | 15 | Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage |
F07UUF (ZTPCON) | 15 | Estimate condition number of complex triangular matrix, packed storage |
F07UVF (ZTPRFS) | 15 | Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage |
F07UWF (ZTPTRI) | 15 | Inverse of complex triangular matrix, packed storage |
F07VEF (DTBTRS) | 15 | Solution of real band triangular system of linear equations, multiple right-hand sides |
F07VGF (DTBCON) | 15 | Estimate condition number of real band triangular matrix |
F07VHF (DTBRFS) | 15 | Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides |
F07VSF (ZTBTRS) | 15 | Solution of complex band triangular system of linear equations, multiple right-hand sides |
F07VUF (ZTBCON) | 15 | Estimate condition number of complex band triangular matrix |
F07VVF (ZTBRFS) | 15 | Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides |
Routine Name |
Mark of Introduction |
Purpose |
F08AAF (DGELS) | 21 | Solves an overdetermined or underdetermined real linear system |
F08AEF (DGEQRF) | 16 | Q R factorization of real general rectangular matrix |
F08AFF (DORGQR) | 16 | Form all or part of orthogonal Q from Q R factorization determined by F08AEF (DGEQRF) or F08BEF (DGEQPF) |
F08AGF (DORMQR) | 16 | Apply orthogonal transformation determined by F08AEF (DGEQRF) or F08BEF (DGEQPF) |
F08AHF (DGELQF) | 16 | L Q factorization of real general rectangular matrix |
F08AJF (DORGLQ) | 16 | Form all or part of orthogonal Q from L Q factorization determined by F08AHF (DGELQF) |
F08AKF (DORMLQ) | 16 | Apply orthogonal transformation determined by F08AHF (DGELQF) |
F08ANF (ZGELS) | 21 | Solves an overdetermined or underdetermined complex linear system |
F08ASF (ZGEQRF) | 16 | Q R factorization of complex general rectangular matrix |
F08ATF (ZUNGQR) | 16 | Form all or part of unitary Q from Q R factorization determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF) |
F08AUF (ZUNMQR) | 16 | Apply unitary transformation determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF) |
F08AVF (ZGELQF) | 16 | L Q factorization of complex general rectangular matrix |
F08AWF (ZUNGLQ) | 16 | Form all or part of unitary Q from L Q factorization determined by F08AVF (ZGELQF) |
F08AXF (ZUNMLQ) | 16 | Apply unitary transformation determined by F08AVF (ZGELQF) |
F08BAF (DGELSY) | 21 | Computes the minimum-norm solution to a real linear least-squares problem |
F08BEF (DGEQPF) | 16 | Q R factorization of real general rectangular matrix with column pivoting |
F08BFF (DGEQP3) | 21 | Q R factorization of real general rectangular matrix with column pivoting, using BLAS-3 |
F08BHF (DTZRZF) | 21 | Reduces a real upper trapezoidal matrix to upper triangular form |
F08BKF (DORMRZ) | 21 | Apply orthogonal transformation determined by F08BHF (DTZRZF) |
F08BNF (ZGELSY) | 21 | Computes the minimum-norm solution to a complex linear least-squares problem |
F08BSF (ZGEQPF) | 16 | Q R factorization of complex general rectangular matrix with column pivoting |
F08BTF (ZGEQP3) | 21 | Q R factorization of complex general rectangular matrix with column pivoting, using BLAS-3 |
F08BVF (ZTZRZF) | 21 | Reduces a complex upper trapezoidal matrix to upper triangular form |
F08BXF (ZUNMRZ) | 21 | Apply unitary transformation determined by F08BVF (ZTZRZF) |
F08CEF (DGEQLF) | 21 | Q L factorization of real general rectangular matrix |
F08CFF (DORGQL) | 21 | Form all or part of orthogonal Q from Q L factorization determined by F08CEF (DGEQLF) |
F08CGF (DORMQL) | 21 | Apply orthogonal transformation determined by F08CEF (DGEQLF) |
F08CHF (DGERQF) | 21 | R Q factorization of real general rectangular matrix |
F08CJF (DORGRQ) | 21 | Form all or part of orthogonal Q from R Q factorization determined by F08CHF (DGERQF) |
F08CKF (DORMRQ) | 21 | Apply orthogonal transformation determined by F08CHF (DGERQF) |
F08CSF (ZGEQLF) | 21 | Q L factorization of complex general rectangular matrix |
F08CTF (ZUNGQL) | 21 | Form all or part of orthogonal Q from Q L factorization determined by F08CSF (ZGEQLF) |
F08CUF (ZUNMQL) | 21 | Apply unitary transformation determined by F08CSF (ZGEQLF) |
F08CVF (ZGERQF) | 21 | R Q factorization of complex general rectangular matrix |
F08CWF (ZUNGRQ) | 21 | Form all or part of orthogonal Q from R Q factorization determined by F08CVF (ZGERQF) |
F08CXF (ZUNMRQ) | 21 | Apply unitary transformation determined by F08CVF (ZGERQF) |
F08FAF (DSYEV) | 21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
F08FBF (DSYEVX) | 21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
F08FCF (DSYEVD) | 19 | All eigenvalues and optionally all eigenvectors of real symmetric matrix (divide-and-conquer) |
F08FDF (DSYEVR) | 21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) |
F08FEF (DSYTRD) | 16 | Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form |
F08FFF (DORGTR) | 16 | Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD) |
F08FGF (DORMTR) | 16 | Apply orthogonal transformation determined by F08FEF (DSYTRD) |
F08FLF (DDISNA) | 21 | Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix |
F08FNF (ZHEEV) | 21 | Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
F08FPF (ZHEEVX) | 21 | Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
F08FQF (ZHEEVD) | 19 | All eigenvalues and optionally all eigenvectors of complex Hermitian matrix (divide-and-conquer) |
F08FRF (ZHEEVR) | 21 | Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) |
F08FSF (ZHETRD) | 16 | Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form |
F08FTF (ZUNGTR) | 16 | Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD) |
F08FUF (ZUNMTR) | 16 | Apply unitary transformation matrix determined by F08FSF (ZHETRD) |
F08GAF (DSPEV) | 21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
F08GBF (DSPEVX) | 21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
F08GCF (DSPEVD) | 19 | All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer) |
F08GEF (DSPTRD) | 16 | Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage |
F08GFF (DOPGTR) | 16 | Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD) |
F08GGF (DOPMTR) | 16 | Apply orthogonal transformation determined by F08GEF (DSPTRD) |
F08GNF (ZHPEV) | 21 | Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
F08GPF (ZHPEVX) | 21 | Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
F08GQF (ZHPEVD) | 19 | All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer) |
F08GSF (ZHPTRD) | 16 | Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage |
F08GTF (ZUPGTR) | 16 | Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD) |
F08GUF (ZUPMTR) | 16 | Apply unitary transformation matrix determined by F08GSF (ZHPTRD) |
F08HAF (DSBEV) | 21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
F08HBF (DSBEVX) | 21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
F08HCF (DSBEVD) | 19 | All eigenvalues and optionally all eigenvectors of real symmetric band matrix (divide-and-conquer) |
F08HEF (DSBTRD) | 16 | Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form |
F08HNF (ZHBEV) | 21 | Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
F08HPF (ZHBEVX) | 21 | Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
F08HQF (ZHBEVD) | 19 | All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix (divide-and-conquer) |
F08HSF (ZHBTRD) | 16 | Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form |
F08JAF (DSTEV) | 21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
F08JBF (DSTEVX) | 21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
F08JCF (DSTEVD) | 19 | All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer) |
F08JDF (DSTEVR) | 21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations) |
F08JEF (DSTEQR) | 16 | All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit Q L or Q R |
F08JFF (DSTERF) | 16 | All eigenvalues of real symmetric tridiagonal matrix, root-free variant of Q L or Q R |
F08JGF (DPTEQR) | 16 | All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix |
F08JHF (DSTEDC) | 21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer) |
F08JJF (DSTEBZ) | 16 | Selected eigenvalues of real symmetric tridiagonal matrix by bisection |
F08JKF (DSTEIN) | 16 | Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array |
F08JLF (DSTEGR) | 21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations) |
F08JSF (ZSTEQR) | 16 | All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit Q L or Q R |
F08JUF (ZPTEQR) | 16 | All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix |
F08JVF (ZSTEDC) | 21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer) |
F08JXF (ZSTEIN) | 16 | Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array |
F08JYF (ZSTEGR) | 21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations) |
F08KAF (DGELSS) | 21 | Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition |
F08KBF (DGESVD) | 21 | Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors |
F08KCF (DGELSD) | 21 | Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition (divide-and-conquer) |
F08KDF (DGESDD) | 21 | Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer) |
F08KEF (DGEBRD) | 16 | Orthogonal reduction of real general rectangular matrix to bidiagonal form |
F08KFF (DORGBR) | 16 | Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD) |
F08KGF (DORMBR) | 16 | Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD) |
F08KNF (ZGELSS) | 21 | Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition |
F08KPF (ZGESVD) | 21 | Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors |
F08KQF (ZGELSD) | 21 | Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition (divide-and-conquer) |
F08KRF (ZGESDD) | 21 | Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer) |
F08KSF (ZGEBRD) | 16 | Unitary reduction of complex general rectangular matrix to bidiagonal form |
F08KTF (ZUNGBR) | 16 | Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD) |
F08KUF (ZUNMBR) | 16 | Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD) |
F08LEF (DGBBRD) | 19 | Reduction of real rectangular band matrix to upper bidiagonal form |
F08LSF (ZGBBRD) | 19 | Reduction of complex rectangular band matrix to upper bidiagonal form |
F08MDF (DBDSDC) | 21 | Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer) |
F08MEF (DBDSQR) | 16 | SVD of real bidiagonal matrix reduced from real general matrix |
F08MSF (ZBDSQR) | 16 | SVD of real bidiagonal matrix reduced from complex general matrix |
F08NAF (DGEEV) | 21 | Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix |
F08NBF (DGEEVX) | 21 | Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors |
F08NEF (DGEHRD) | 16 | Orthogonal reduction of real general matrix to upper Hessenberg form |
F08NFF (DORGHR) | 16 | Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) |
F08NGF (DORMHR) | 16 | Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) |
F08NHF (DGEBAL) | 16 | Balance real general matrix |
F08NJF (DGEBAK) | 16 | Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (DGEBAL) |
F08NNF (ZGEEV) | 21 | Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix |
F08NPF (ZGEEVX) | 21 | Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors |
F08NSF (ZGEHRD) | 16 | Unitary reduction of complex general matrix to upper Hessenberg form |
F08NTF (ZUNGHR) | 16 | Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) |
F08NUF (ZUNMHR) | 16 | Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) |
F08NVF (ZGEBAL) | 16 | Balance complex general matrix |
F08NWF (ZGEBAK) | 16 | Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (ZGEBAL) |
F08PAF (DGEES) | 21 | Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors |
F08PBF (DGEESX) | 21 | Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues |
F08PEF (DHSEQR) | 16 | Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix |
F08PKF (DHSEIN) | 16 | Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration |
F08PNF (ZGEES) | 21 | Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors |
F08PPF (ZGEESX) | 21 | Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues |
F08PSF (ZHSEQR) | 16 | Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix |
F08PXF (ZHSEIN) | 16 | Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration |
F08QFF (DTREXC) | 16 | Reorder Schur factorization of real matrix using orthogonal similarity transformation |
F08QGF (DTRSEN) | 16 | Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
F08QHF (DTRSYL) | 16 | Solve real Sylvester matrix equation A X + X B = C , A and B are upper quasi-triangular or transposes |
F08QKF (DTREVC) | 16 | Left and right eigenvectors of real upper quasi-triangular matrix |
F08QLF (DTRSNA) | 16 | Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix |
F08QTF (ZTREXC) | 16 | Reorder Schur factorization of complex matrix using unitary similarity transformation |
F08QUF (ZTRSEN) | 16 | Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
F08QVF (ZTRSYL) | 16 | Solve complex Sylvester matrix equation A X + X B = C , A and B are upper triangular or conjugate-transposes |
F08QXF (ZTREVC) | 16 | Left and right eigenvectors of complex upper triangular matrix |
F08QYF (ZTRSNA) | 16 | Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix |
F08SAF (DSYGV) | 21 | Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
F08SBF (DSYGVX) | 21 | Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
F08SCF (DSYGVD) | 21 | Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer) |
F08SEF (DSYGST) | 16 | Reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FDF (DPOTRF) |
F08SNF (ZHEGV) | 21 | Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
F08SPF (ZHEGVX) | 21 | Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
F08SQF (ZHEGVD) | 21 | Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer) |
F08SSF (ZHEGST) | 16 | Reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , B factorized by F07FRF (ZPOTRF) |
F08TAF (DSPGV) | 21 | Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |
F08TBF (DSPGVX) | 21 | Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |
F08TCF (DSPGVD) | 21 | Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer) |
F08TEF (DSPGST) | 16 | Reduction to standard form of real symmetric-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GDF (DPPTRF) |
F08TNF (ZHPGV) | 21 | Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |
F08TPF (ZHPGVX) | 21 | Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |
F08TQF (ZHPGVD) | 21 | Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer) |
F08TSF (ZHPGST) | 16 | Reduction to standard form of complex Hermitian-definite generalized eigenproblem A x = λ B x , A B x = λ x or B A x = λ x , packed storage, B factorized by F07GRF (ZPPTRF) |
F08UAF (DSBGV) | 21 | Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
F08UBF (DSBGVX) | 21 | Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
F08UCF (DSBGVD) | 21 | Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer) |
F08UEF (DSBGST) | 19 | Reduction of real symmetric-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A |
F08UFF (DPBSTF) | 19 | Computes a split Cholesky factorization of real symmetric positive-definite band matrix A |
F08UNF (ZHBGV) | 21 | Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
F08UPF (ZHBGVX) | 21 | Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
F08UQF (ZHBGVD) | 21 | Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer) |
F08USF (ZHBGST) | 19 | Reduction of complex Hermitian-definite banded generalized eigenproblem A x = λ B x to standard form C y = λ y , such that C has the same bandwidth as A |
F08UTF (ZPBSTF) | 19 | Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A |
F08VAF (DGGSVD) | 21 | Computes the generalized singular value decomposition of a real matrix pair |
F08VEF (DGGSVP) | 21 | Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair |
F08VNF (ZGGSVD) | 21 | Computes the generalized singular value decomposition of a complex matrix pair |
F08VSF (ZGGSVP) | 21 | Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair |
F08WAF (DGGEV) | 21 | Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |
F08WBF (DGGEVX) | 21 | Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors |
F08WEF (DGGHRD) | 20 | Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |
F08WHF (DGGBAL) | 20 | Balance a pair of real general matrices |
F08WJF (DGGBAK) | 20 | Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF (DGGBAL) |
F08WNF (ZGGEV) | 21 | Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |
F08WPF (ZGGEVX) | 21 | Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors |
F08WSF (ZGGHRD) | 20 | Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |
F08WVF (ZGGBAL) | 20 | Balance a pair of complex general matrices |
F08WWF (ZGGBAK) | 20 | Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF (ZGGBAL) |
F08XAF (DGGES) | 21 | 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 |
F08XBF (DGGESX) | 21 | 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; also, optionally, computes reciprocal condition numbers for selected eigenvalues |
F08XEF (DHGEQZ) | 20 | Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices |
F08XNF (ZGGES) | 21 | 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 |
F08XPF (ZGGESX) | 21 | 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; also, optionally, computes reciprocal condition numbers for selected eigenvalues |
F08XSF (ZHGEQZ) | 20 | Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices |
F08YEF (DTGSJA) | 21 | Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair |
F08YFF (DTGEXC) | 21 | Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation |
F08YGF (DTGSEN) | 21 | Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces |
F08YHF (DTGSYL) | 21 | Solves the real-valued generalized Sylvester equation |
F08YKF (DTGEVC) | 20 | Left and right eigenvectors of a pair of real upper quasi-triangular matrices |
F08YLF (DTGSNA) | 21 | Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form |
F08YSF (ZTGSJA) | 21 | Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair |
F08YTF (ZTGEXC) | 21 | Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation |
F08YUF (ZTGSEN) | 21 | Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces |
F08YVF (ZTGSYL) | 21 | Solves the complex generalized Sylvester equation |
F08YXF (ZTGEVC) | 20 | Left and right eigenvectors of a pair of complex upper triangular matrices |
F08YYF (ZTGSNA) | 21 | Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form |
F08ZAF (DGGLSE) | 21 | Solves the real linear equality-constrained least-squares (LSE) problem |
F08ZBF (DGGGLM) | 21 | Solves a real general Gauss–Markov linear model (GLM) problem |
F08ZEF (DGGQRF) | 21 | Computes a generalized Q R factorization of a real matrix pair |
F08ZFF (DGGRQF) | 21 | Computes a generalized R Q factorization of a real matrix pair |
F08ZNF (ZGGLSE) | 21 | Solves the complex linear equality-constrained least-squares (LSE) problem |
F08ZPF (ZGGGLM) | 21 | Solves a complex general Gauss–Markov linear model (GLM) problem |
F08ZSF (ZGGQRF) | 21 | Computes a generalized Q R factorization of a complex matrix pair |
F08ZTF (ZGGRQF) | 21 | Computes a generalized R Q factorization of a complex matrix pair |
Routine Name |
Mark of Introduction |
Purpose |
F11BDF | 19 | Real sparse nonsymmetric linear systems, setup for F11BEF |
F11BEF | 19 | Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method |
F11BFF | 19 | Real sparse nonsymmetric linear systems, diagnostic for F11BEF |
F11BRF | 19 | Complex sparse non-Hermitian linear systems, setup for F11BSF |
F11BSF | 19 | Complex sparse non-Hermitian linear systems, preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method |
F11BTF | 19 | Complex sparse non-Hermitian linear systems, diagnostic for F11BSF |
F11DAF | 18 | Real sparse nonsymmetric linear systems, incomplete L U factorization |
F11DBF | 18 | Solution of linear system involving incomplete L U preconditioning matrix generated by F11DAF |
F11DCF | 18 | Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DAF |
F11DDF | 18 | Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse nonsymmetric matrix |
F11DEF | 18 | Solution of real sparse nonsymmetric linear system, RGMRES, CGS, Bi-CGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box) |
F11DKF | 20 | Real sparse nonsymmetric linear systems, line Jacobi preconditioner |
F11DNF | 19 | Complex sparse non-Hermitian linear systems, incomplete L U factorization |
F11DPF | 19 | Solution of complex linear system involving incomplete L U preconditioning matrix generated by F11DNF |
F11DQF | 19 | Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, preconditioner computed by F11DNF (Black Box) |
F11DRF | 19 | Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse non-Hermitian matrix |
F11DSF | 19 | Solution of complex sparse non-Hermitian linear system, RGMRES, CGS, Bi-CGSTAB or TFQMR method, Jacobi or SSOR preconditioner Black Box |
F11DXF | 20 | Complex sparse nonsymmetric linear systems, line Jacobi preconditioner |
F11GDF | 20 | Real sparse symmetric linear systems, setup for F11GEF |
F11GEF | 20 | Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos |
F11GFF | 20 | Real sparse symmetric linear systems, diagnostic for F11GEF |
F11GRF | 20 | Complex sparse Hermitian linear systems, setup for F11GSF |
F11GSF | 20 | Complex sparse Hermitian linear systems, preconditioned conjugate gradient or Lanczos |
F11GTF | 20 | Complex sparse Hermitian linear systems, diagnostic for F11GSF |
F11JAF | 17 | Real sparse symmetric matrix, incomplete Cholesky factorization |
F11JBF | 17 | Solution of linear system involving incomplete Cholesky preconditioning matrix generated by F11JAF |
F11JCF | 17 | Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box) |
F11JDF | 17 | Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix |
F11JEF | 17 | Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box) |
F11JNF | 19 | Complex sparse Hermitian matrix, incomplete Cholesky factorization |
F11JPF | 19 | Solution of complex linear system involving incomplete Cholesky preconditioning matrix generated by F11JNF |
F11JQF | 19 | Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JNF (Black Box) |
F11JRF | 19 | Solution of linear system involving preconditioning matrix generated by applying SSOR to complex sparse Hermitian matrix |
F11JSF | 19 | Solution of complex sparse Hermitian linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box) |
F11MDF | 21 | Real sparse nonsymmetric linear systems, setup for F11MEF |
F11MEF | 21 | L U factorization of real sparse matrix |
F11MFF | 21 | Solution of real sparse simultaneous linear equations (coefficient matrix already factorized) |
F11MGF | 21 | Estimate condition number of real matrix, matrix already factorized by F11MEF |
F11MHF | 21 | Refined solution with error bounds of real system of linear equations, multiple right-hand sides |
F11MKF | 21 | Real sparse nonsymmetric matrix matrix multiply, compressed column storage |
F11MLF | 21 | 1 -norm, ∞ -norm, largest absolute element, real general matrix |
F11MMF | 21 | Real sparse nonsymmetric linear systems, diagnostic for F11MEF |
F11XAF | 18 | Real sparse nonsymmetric matrix vector multiply |
F11XEF | 17 | Real sparse symmetric matrix vector multiply |
F11XNF | 19 | Complex sparse non-Hermitian matrix vector multiply |
F11XSF | 19 | Complex sparse Hermitian matrix vector multiply |
F11ZAF | 18 | Real sparse nonsymmetric matrix reorder routine |
F11ZBF | 17 | Real sparse symmetric matrix reorder routine |
F11ZNF | 19 | Complex sparse non-Hermitian matrix reorder routine |
F11ZPF | 19 | Complex sparse Hermitian matrix reorder routine |
Routine Name |
Mark of Introduction |
Purpose |
F12AAF | 21 | Initialization routine for (F12ABF) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem |
F12ABF | 21 | Implements a reverse communication interface for the Implicitly Restarted Arnoldi iteration for computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric sparse (standard or generalized) eigenproblem |
F12ACF | 21 | Returns the converged approximations (as determined by F12ABF) to eigenvalues of a real nonsymmetric sparse (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace |
F12ADF | 21 | Set a single option from a string (F12ABF/F12ACF/F12AGF) |
F12AEF | 21 | Provides monitoring information for F12ABF |
F12AFF | 21 | Initialization routine for (F12AGF) computing selected eigenvalues and, optionally, eigenvectors of a real nonsymmetric banded (standard or generalized) eigenproblem |
F12AGF | 21 | Computes approximations to selected eigenvalues of a real nonsymmetric banded (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace |
F12ANF | 21 | Initialization routine for (F12APF) computing selected eigenvalues and, optionally, eigenvectors of a complex sparse (standard or generalized) eigenproblem |
F12APF | 21 | Implements a reverse communication interface for the Implicitly Restarted Arnoldi iteration for computing selected eigenvalues and, optionally, eigenvectors of a complex sparse (standard or generalized) eigenproblem |
F12AQF | 21 | Returns the converged approximations (as determined by F12ABF) to eigenvalues of a complex sparse (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace |
F12ARF | 21 | Set a single option from a string (F12APF/F12AQF) |
F12ASF | 21 | Provides monitoring information for F12APF |
F12FAF | 21 | Initialization routine for (F12FBF) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem |
F12FBF | 21 | Implements a reverse communication interface for the Implicitly Restarted Arnoldi iteration for computing selected eigenvalues and, optionally, eigenvectors of a real symmetric sparse (standard or generalized) eigenproblem |
F12FCF | 21 | Returns the converged approximations (as determined by F12ABF) to eigenvalues of a real symmetric sparse (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace |
F12FDF | 21 | Set a single option from a string (F12FBF/F12FCF/F12FGF) |
F12FEF | 21 | Provides monitoring information for F12FBF |
F12FFF | 21 | Initialization routine for (F12FGF) computing selected eigenvalues and, optionally, eigenvectors of a real symmetric banded (standard or generalized) eigenproblem |
F12FGF | 21 | Computes approximations to selected eigenvalues of a real symmetric banded (standard or generalized) eigenproblem and, optionally, the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace |
Routine Name |
Mark of Introduction |
Purpose |
G01AAF | 4 | Mean, variance, skewness, kurtosis, etc., one variable, from raw data |
G01ABF | 4 | Mean, variance, skewness, kurtosis, etc., two variables, from raw data |
G01ADF | 4 | Mean, variance, skewness, kurtosis, etc., one variable, from frequency table |
G01AEF | 4 | Frequency table from raw data |
G01AFF | 4 | Two-way contingency table analysis, with χ^{2} /Fisher's exact test |
G01AGF | 8 | Lineprinter scatterplot of two variables |
G01AHF | 8 | Lineprinter scatterplot of one variable against Normal scores |
G01AJF | 10 | Lineprinter histogram of one variable |
G01ALF | 14 | Computes a five-point summary (median, hinges and extremes) |
G01ARF | 14 | Constructs a stem and leaf plot |
G01ASF | 14 | Constructs a box and whisker plot |
G01BJF | 13 | Binomial distribution function |
G01BKF | 13 | Poisson distribution function |
G01BLF | 13 | Hypergeometric distribution function |
G01DAF | 8 | Normal scores, accurate values |
G01DBF | 12 | Normal scores, approximate values |
G01DCF | 12 | Normal scores, approximate variance-covariance matrix |
G01DDF | 12 | Shapiro and Wilk's W test for Normality |
G01DHF | 15 | Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores |
G01EAF | 15 | Computes probabilities for the standard Normal distribution |
G01EBF | 14 | Computes probabilities for Student's t -distribution |
G01ECF | 14 | Computes probabilities for χ^{2} distribution |
G01EDF | 14 | Computes probabilities for F -distribution |
G01EEF | 14 | Computes upper and lower tail probabilities and probability density function for the beta distribution |
G01EFF | 14 | Computes probabilities for the gamma distribution |
G01EMF | 15 | Computes probability for the Studentized range statistic |
G01EPF | 15 | Computes bounds for the significance of a Durbin–Watson statistic |
G01ERF | 16 | Computes probability for von Mises distribution |
G01ETF | 21 | Landau distribution function Φ (λ) |
G01EUF | 21 | Vavilov distribution function Φ_{V} ( λ ; κ ,β^{2}) |
G01EYF | 14 | Computes probabilities for the one-sample Kolmogorov–Smirnov distribution |
G01EZF | 14 | Computes probabilities for the two-sample Kolmogorov–Smirnov distribution |
G01FAF | 15 | Computes deviates for the standard Normal distribution |
G01FBF | 14 | Computes deviates for Student's t -distribution |
G01FCF | 14 | Computes deviates for the χ^{2} distribution |
G01FDF | 14 | Computes deviates for the F -distribution |
G01FEF | 14 | Computes deviates for the beta distribution |
G01FFF | 14 | Computes deviates for the gamma distribution |
G01FMF | 15 | Computes deviates for the Studentized range statistic |
G01FTF | 21 | Landau inverse function Ψ (x) |
G01GBF | 14 | Computes probabilities for the non-central Student's t -distribution |
G01GCF | 14 | Computes probabilities for the non-central χ^{2} distribution |
G01GDF | 14 | Computes probabilities for the non-central F -distribution |
G01GEF | 14 | Computes probabilities for the non-central beta distribution |
G01HAF | 14 | Computes probability for the bivariate Normal distribution |
G01HBF | 15 | Computes probabilities for the multivariate Normal distribution |
G01JCF | 14 | Computes probability for a positive linear combination of χ^{2} variables |
G01JDF | 15 | Computes lower tail probability for a linear combination of (central) χ^{2} variables |
G01MBF | 15 | Computes reciprocal of Mills' Ratio |
G01MTF | 21 | Landau density function φ (λ) |
G01MUF | 21 | Vavilov density function φ_{V} ( λ ; κ ,β^{2}) |
G01NAF | 16 | Cumulants and moments of quadratic forms in Normal variables |
G01NBF | 16 | Moments of ratios of quadratic forms in Normal variables, and related statistics |
G01PTF | 21 | Landau first moment function Φ_{1} (x) |
G01QTF | 21 | Landau second moment function Φ_{2} (x) |
G01RTF | 21 | Landau derivative function φ ′ (λ) |
G01ZUF | 21 | Initialization routine for G01MUF and G01EUF |
Routine Name |
Mark of Introduction |
Purpose |
G02BAF | 4 | Pearson product-moment correlation coefficients, all variables, no missing values |
G02BBF | 4 | Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values |
G02BCF | 4 | Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values |
G02BDF | 4 | Correlation-like coefficients (about zero), all variables, no missing values |
G02BEF | 4 | Correlation-like coefficients (about zero), all variables, casewise treatment of missing values |
G02BFF | 4 | Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values |
G02BGF | 4 | Pearson product-moment correlation coefficients, subset of variables, no missing values |
G02BHF | 4 | Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values |
G02BJF | 4 | Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values |
G02BKF | 4 | Correlation-like coefficients (about zero), subset of variables, no missing values |
G02BLF | 4 | Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values |
G02BMF | 4 | Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values |
G02BNF | 4 | Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data |
G02BPF | 4 | Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data |
G02BQF | 4 | Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data |
G02BRF | 4 | Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data |
G02BSF | 4 | Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values |
G02BTF | 14 | Update a weighted sum of squares matrix with a new observation |
G02BUF | 14 | Computes a weighted sum of squares matrix |
G02BWF | 14 | Computes a correlation matrix from a sum of squares matrix |
G02BXF | 14 | Computes (optionally weighted) correlation and covariance matrices |
G02BYF | 17 | Computes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by G02BXF |
G02CAF | 4 | Simple linear regression with constant term, no missing values |
G02CBF | 4 | Simple linear regression without constant term, no missing values |
G02CCF | 4 | Simple linear regression with constant term, missing values |
G02CDF | 4 | Simple linear regression without constant term, missing values |
G02CEF | 4 | Service routines for multiple linear regression, select elements from vectors and matrices |
G02CFF | 4 | Service routines for multiple linear regression, re-order elements of vectors and matrices |
G02CGF | 4 | Multiple linear regression, from correlation coefficients, with constant term |
G02CHF | 4 | Multiple linear regression, from correlation-like coefficients, without constant term |
G02DAF | 14 | Fits a general (multiple) linear regression model |
G02DCF | 14 | Add/delete an observation to/from a general linear regression model |
G02DDF | 14 | Estimates of linear parameters and general linear regression model from updated model |
G02DEF | 14 | Add a new independent variable to a general linear regression model |
G02DFF | 14 | Delete an independent variable from a general linear regression model |
G02DGF | 14 | Fits a general linear regression model to new dependent variable |
G02DKF | 14 | Estimates and standard errors of parameters of a general linear regression model for given constraints |
G02DNF | 14 | Computes estimable function of a general linear regression model and its standard error |
G02EAF | 14 | Computes residual sums of squares for all possible linear regressions for a set of independent variables |
G02ECF | 14 | Calculates R^{2} and C_{P} values from residual sums of squares |
G02EEF | 14 | Fits a linear regression model by forward selection |
G02EFF | 21 | Stepwise linear regression |
G02FAF | 14 | Calculates standardized residuals and influence statistics |
G02FCF | 15 | Computes Durbin–Watson test statistic |
G02GAF | 14 | Fits a generalized linear model with Normal errors |
G02GBF | 14 | Fits a generalized linear model with binomial errors |
G02GCF | 14 | Fits a generalized linear model with Poisson errors |
G02GDF | 14 | Fits a generalized linear model with gamma errors |
G02GKF | 14 | Estimates and standard errors of parameters of a general linear model for given constraints |
G02GNF | 14 | Computes estimable function of a generalized linear model and its standard error |
G02HAF | 13 | Robust regression, standard M -estimates |
G02HBF | 13 | Robust regression, compute weights for use with G02HDF |
G02HDF | 13 | Robust regression, compute regression with user-supplied functions and weights |
G02HFF | 13 | Robust regression, variance-covariance matrix following G02HDF |
G02HKF | 14 | Calculates a robust estimation of a correlation matrix, Huber's weight function |
G02HLF | 14 | Calculates a robust estimation of a correlation matrix, user-supplied weight function plus derivatives |
G02HMF | 14 | Calculates a robust estimation of a correlation matrix, user-supplied weight function |
G02JAF | 21 | Linear mixed effects regression using Restricted Maximum Likelihood (REML) |
G02JBF | 21 | Linear mixed effects regression using Maximum Likelihood (ML) |
Routine Name |
Mark of Introduction |
Purpose |
G03AAF | 14 | Performs principal component analysis |
G03ACF | 14 | Performs canonical variate analysis |
G03ADF | 14 | Performs canonical correlation analysis |
G03BAF | 15 | Computes orthogonal rotations for loading matrix, generalized orthomax criterion |
G03BCF | 15 | Computes Procrustes rotations |
G03CAF | 15 | Computes maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations |
G03CCF | 15 | Computes factor score coefficients (for use after G03CAF) |
G03DAF | 15 | Computes test statistic for equality of within-group covariance matrices and matrices for discriminant analysis |
G03DBF | 15 | Computes Mahalanobis squared distances for group or pooled variance-covariance matrices (for use after G03DAF) |
G03DCF | 15 | Allocates observations to groups according to selected rules (for use after G03DAF) |
G03EAF | 16 | Computes distance matrix |
G03ECF | 16 | Hierarchical cluster analysis |
G03EFF | 16 | K -means cluster analysis |
G03EHF | 16 | Constructs dendrogram (for use after G03ECF) |
G03EJF | 16 | Computes cluster indicator variable (for use after G03ECF) |
G03FAF | 17 | Performs principal co-ordinate analysis, classical metric scaling |
G03FCF | 17 | Performs non-metric (ordinal) multidimensional scaling |
G03ZAF | 15 | Produces standardized values ( z -scores) for a data matrix |
Routine Name |
Mark of Introduction |
Purpose |
G04AGF | 8 | Two-way analysis of variance, hierarchical classification, subgroups of unequal size |
G04BBF | 16 | Analysis of variance, randomized block or completely randomized design, treatment means and standard errors |
G04BCF | 17 | Analysis of variance, general row and column design, treatment means and standard errors |
G04CAF | 16 | Analysis of variance, complete factorial design, treatment means and standard errors |
G04DAF | 17 | Computes sum of squares for contrast between means |
G04DBF | 17 | Computes confidence intervals for differences between means computed by G04BBF or G04BCF |
G04EAF | 17 | Computes orthogonal polynomials or dummy variables for factor/classification variable |
Routine Name |
Mark of Introduction |
Purpose |
G05HKF | 20 | Univariate time series, generate n terms of either a symmetric GARCH process or a GARCH process with asymmetry of the form (ε_{ t - 1 }+γ)^{2} |
G05HLF | 20 | Univariate time series, generate n terms of a GARCH process with asymmetry of the form (|ε_{ t - 1 }|+γε_{ t - 1 })^{2} |
G05HMF | 20 | Univariate time series, generate n terms of an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process |
G05HNF | 20 | Univariate time series, generate n terms of an exponential GARCH (EGARCH) process |
G05KAF | 20 | Pseudo-random real numbers, uniform distribution over (0,1), seeds and generator number passed explicitly |
G05KBF | 20 | Initialize seeds of a given generator for random number generating routines (that pass seeds explicitly) to give a repeatable sequence |
G05KCF | 20 | Initialize seeds of a given generator for random number generating routines (that pass seeds expicitly) to give non-repeatable sequence |
G05KEF | 20 | Pseudo-random logical (boolean) value, seeds and generator number passed explicitly |
G05LAF | 20 | Generates a vector of random numbers from a Normal distribution, seeds and generator number passed explicitly |
G05LBF | 20 | Generates a vector of random numbers from a Student's t -distribution, seeds and generator number passed explicitly |
G05LCF | 20 | Generates a vector of random numbers from a χ^{2} distribution, seeds and generator number passed explicitly |
G05LDF | 20 | Generates a vector of random numbers from an F -distribution, seeds and generator number passed explicitly |
G05LEF | 20 | Generates a vector of random numbers from a β distribution, seeds and generator number passed explicitly |
G05LFF | 20 | Generates a vector of random numbers from a γ distribution, seeds and generator number passed explicitly |
G05LGF | 20 | Generates a vector of random numbers from a uniform distribution, seeds and generator number passed explicitly |
G05LHF | 20 | Generates a vector of random numbers from a triangular distribution, seeds and generator number passed explicitly |
G05LJF | 20 | Generates a vector of random numbers from an exponential distribution, seeds and generator number passed explicitly |
G05LKF | 20 | Generates a vector of random numbers from a lognormal distribution, seeds and generator number passed explicitly |
G05LLF | 20 | Generates a vector of random numbers from a Cauchy distribution, seeds and generator number passed explicitly |
G05LMF | 20 | Generates a vector of random numbers from a Weibull distribution, seeds and generator number passed explicitly |
G05LNF | 20 | Generates a vector of random numbers from a logistic distribution, seeds and generator number passed explicitly |
G05LPF | 20 | Generates a vector of random numbers from a von Mises distribution, seeds and generator number passed explicitly |
G05LQF | 20 | Generates a vector of random numbers from an exponential mixture distribution, seeds and generator number passed explicitly |
G05LXF | 21 | Generates a matrix of random numbers from a multivariate Student's t -distribution, seeds and generator passed explicitly |
G05LYF | 21 | Generates a matrix of random numbers from a multivariate Normal distribution, seeds and generator passed explicitly |
G05LZF | 20 | Generates a vector of random numbers from a multivariate Normal distribution, seeds and generator number passed explicitly |
G05MAF | 20 | Generates a vector of random integers from a uniform distribution, seeds and generator number passed explicitly |
G05MBF | 20 | Generates a vector of random integers from a geometric distribution, seeds and generator number passed explicitly |
G05MCF | 20 | Generates a vector of random integers from a negative binomial distribution, seeds and generator number passed explicitly |
G05MDF | 20 | Generates a vector of random integers from a logarithmic distribution, seeds and generator number passed explicitly |
G05MEF | 20 | Generates a vector of random integers from a Poisson distribution with varying mean, seeds and generator number passed explicitly |
G05MJF | 20 | Generates a vector of random integers from a binomial distribution, seeds and generator number passed explicitly |
G05MKF | 20 | Generates a vector of random integers from a Poisson distribution, seeds and generator number passed explicitly |
G05MLF | 20 | Generates a vector of random integers from a hypergeometric distribution, seeds and generator number passed explicitly |
G05MRF | 20 | Generates a vector of random integers from a multinomial distribution, seeds and generator number passed explicitly |
G05MZF | 20 | Generates a vector of random integers from a general discrete distribution, seeds and generator number passed explicitly |
G05NAF | 20 | Pseudo-random permutation of an integer vector |
G05NBF | 20 | Pseudo-random sample from an integer vector |
G05PAF | 20 | Generates a realisation of a time series from an ARMA model |
G05PCF | 20 | Generates a realisation of a multivariate time series from a VARMA model |
G05QAF | 20 | Computes a random orthogonal matrix |
G05QBF | 20 | Computes a random correlation matrix |
G05QDF | 20 | Generates a random table matrix |
G05RAF | 21 | Generates a matrix of random numbers from a Gaussian Copula, seeds and generator passed explicitly |
G05RBF | 21 | Generates a matrix of random numbers from a Student's t -Copula, seeds and generator passed explicitly |
G05YCF | 21 | Initializes the Faure generator (G05YDF/G05YJF/G05YKF) |
G05YDF | 21 | Generates a sequence of quasi-random numbers using Faure's method |
G05YEF | 21 | Initializes the Sobol generator (G05YFF/G05YJF/G05YKF) |
G05YFF | 21 | Generates a sequence of quasi-random numbers using Sobol's method |
G05YGF | 21 | Initializes the Neiderreiter generator (G05YHF/G05YJF/G05YKF) |
G05YHF | 21 | Generates a sequence of quasi-random numbers using Neiderreiter's method |
G05YJF | 21 | Generates a Normal quasi-random number sequence using Faure's, Sobol's or Neiderreiter's method |
G05YKF | 21 | Generates a log-Normal quasi-random number sequence using Faure's, Sobol's or Neiderreiter's method |
Routine Name |
Mark of Introduction |
Purpose |
G07AAF | 15 | Computes confidence interval for the parameter of a binomial distribution |
G07ABF | 15 | Computes confidence interval for the parameter of a Poisson distribution |
G07BBF | 15 | Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data |
G07BEF | 15 | Computes maximum likelihood estimates for parameters of the Weibull distribution |
G07CAF | 15 | Computes t -test statistic for a difference in means between two Normal populations, confidence interval |
G07DAF | 13 | Robust estimation, median, median absolute deviation, robust standard deviation |
G07DBF | 13 | Robust estimation, M -estimates for location and scale parameters, standard weight functions |
G07DCF | 13 | Robust estimation, M -estimates for location and scale parameters, user-defined weight functions |
G07DDF | 14 | Computes a trimmed and winsorized mean of a single sample with estimates of their variance |
G07EAF | 16 | Robust confidence intervals, one-sample |
G07EBF | 16 | Robust confidence intervals, two-sample |
Routine Name |
Mark of Introduction |
Purpose |
G08AAF | 8 | Sign test on two paired samples |
G08ACF | 8 | Median test on two samples of unequal size |
G08AEF | 8 | Friedman two-way analysis of variance on k matched samples |
G08AFF | 8 | Kruskal–Wallis one-way analysis of variance on k samples of unequal size |
G08AGF | 14 | Performs the Wilcoxon one-sample (matched pairs) signed rank test |
G08AHF | 14 | Performs the Mann–Whitney U test on two independent samples |
G08AJF | 14 | Computes the exact probabilities for the Mann–Whitney U statistic, no ties in pooled sample |
G08AKF | 14 | Computes the exact probabilities for the Mann–Whitney U statistic, ties in pooled sample |
G08ALF | 15 | Performs the Cochran Q test on cross-classified binary data |
G08BAF | 8 | Mood's and David's tests on two samples of unequal size |
G08CBF | 14 | Performs the one-sample Kolmogorov–Smirnov test for standard distributions |
G08CCF | 14 | Performs the one-sample Kolmogorov–Smirnov test for a user-supplied distribution |
G08CDF | 14 | Performs the two-sample Kolmogorov–Smirnov test |
G08CGF | 14 | Performs the χ^{2} goodness of fit test, for standard continuous distributions |
G08DAF | 8 | Kendall's coefficient of concordance |
G08EAF | 14 | Performs the runs up or runs down test for randomness |
G08EBF | 14 | Performs the pairs (serial) test for randomness |
G08ECF | 14 | Performs the triplets test for randomness |
G08EDF | 14 | Performs the gaps test for randomness |
G08RAF | 12 | Regression using ranks, uncensored data |
G08RBF | 12 | Regression using ranks, right-censored data |
Routine Name |
Mark of Introduction |
Purpose |
G10ABF | 16 | Fit cubic smoothing spline, smoothing parameter given |
G10ACF | 16 | Fit cubic smoothing spline, smoothing parameter estimated |
G10BAF | 16 | Kernel density estimate using Gaussian kernel |
G10CAF | 16 | Compute smoothed data sequence using running median smoothers |
G10ZAF | 16 | Reorder data to give ordered distinct observations |
Routine Name |
Mark of Introduction |
Purpose |
G11AAF | 16 | χ^{2} statistics for two-way contingency table |
G11BAF | 17 | Computes multiway table from set of classification factors using selected statistic |
G11BBF | 17 | Computes multiway table from set of classification factors using given percentile/quantile |
G11BCF | 17 | Computes marginal tables for multiway table computed by G11BAF or G11BBF |
G11CAF | 19 | Returns parameter estimates for the conditional analysis of stratified data |
G11SAF | 12 | Contingency table, latent variable model for binary data |
G11SBF | 12 | Frequency count for G11SAF |
Routine Name |
Mark of Introduction |
Purpose |
G12AAF | 15 | Computes Kaplan–Meier (product-limit) estimates of survival probabilities |
G12BAF | 17 | Fits Cox's proportional hazard model |
G12ZAF | 19 | Creates the risk sets associated with the Cox proportional hazards model for fixed covariates |
Routine Name |
Mark of Introduction |
Purpose |
G13AAF | 9 | Univariate time series, seasonal and non-seasonal differencing |
G13ABF | 9 | Univariate time series, sample autocorrelation function |
G13ACF | 9 | Univariate time series, partial autocorrelations from autocorrelations |
G13ADF | 9 | Univariate time series, preliminary estimation, seasonal ARIMA model |
G13AEF | 9 | Univariate time series, estimation, seasonal ARIMA model (comprehensive) |
G13AFF | 9 | Univariate time series, estimation, seasonal ARIMA model (easy-to-use) |
G13AGF | 9 | Univariate time series, update state set for forecasting |
G13AHF | 9 | Univariate time series, forecasting from state set |
G13AJF | 10 | Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model |
G13ASF | 13 | Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF |
G13AUF | 14 | Computes quantities needed for range-mean or standard deviation-mean plot |
G13BAF | 10 | Multivariate time series, filtering (pre-whitening) by an ARIMA model |
G13BBF | 11 | Multivariate time series, filtering by a transfer function model |
G13BCF | 10 | Multivariate time series, cross-correlations |
G13BDF | 11 | Multivariate time series, preliminary estimation of transfer function model |
G13BEF | 11 | Multivariate time series, estimation of multi-input model |
G13BGF | 11 | Multivariate time series, update state set for forecasting from multi-input model |
G13BHF | 11 | Multivariate time series, forecasting from state set of multi-input model |
G13BJF | 11 | Multivariate time series, state set and forecasts from fully specified multi-input model |
G13CAF | 10 | Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window |
G13CBF | 10 | Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window |
G13CCF | 10 | Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window |
G13CDF | 10 | Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window |
G13CEF | 10 | Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra |
G13CFF | 10 | Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra |
G13CGF | 10 | Multivariate time series, noise spectrum, bounds, impulse response function and its standard error |
G13DBF | 11 | Multivariate time series, multiple squared partial autocorrelations |
G13DCF | 12 | Multivariate time series, estimation of VARMA model |
G13DJF | 15 | Multivariate time series, forecasts and their standard errors |
G13DKF | 15 | Multivariate time series, updates forecasts and their standard errors |
G13DLF | 15 | Multivariate time series, differences and/or transforms |
G13DMF | 15 | Multivariate time series, sample cross-correlation or cross-covariance matrices |
G13DNF | 15 | Multivariate time series, sample partial lag correlation matrices, χ^{2} statistics and significance levels |
G13DPF | 16 | Multivariate time series, partial autoregression matrices |
G13DSF | 13 | Multivariate time series, diagnostic checking of residuals, following G13DCF |
G13DXF | 15 | Calculates the zeros of a vector autoregressive (or moving average) operator |
G13EAF | 17 | Combined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter |
G13EBF | 17 | Combined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter |
G13FAF | 20 | Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form (ε_{ t - 1 }+γ)^{2} |
G13FBF | 20 | Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form (ε_{ t - 1 }+γ)^{2} |
G13FCF | 20 | Univariate time series, parameter estimation for a GARCH process with asymmetry of the form (|ε_{ t - 1 }|+γε_{ t - 1 })^{2} |
G13FDF | 20 | Univariate time series, forecast function for a GARCH process with asymmetry of the form (|ε_{ t - 1 }|+γε_{ t - 1 })^{2} |
G13FEF | 20 | Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process |
G13FFF | 20 | Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process |
G13FGF | 20 | Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process |
G13FHF | 20 | Univariate time series, forecast function for an exponential GARCH (EGARCH) process |
Routine Name |
Mark of Introduction |
Purpose |
H02BBF | 14 | Integer LP problem (dense) |
H02BFF | 16 | Interpret MPSX data file defining IP or LP problem, optimize and print solution |
H02BUF | 16 | Convert MPSX data file defining IP or LP problem to format required by H02BBF or E04MFF/E04MFA |
H02BVF | 16 | Print IP or LP solutions with user specified names for rows and columns |
H02BZF | 15 | Integer programming solution, supplies further information on solution obtained by H02BBF |
H02CBF | 19 | Integer QP problem (dense) |
H02CCF | 19 | Read optional parameter values for H02CBF from external file |
H02CDF | 19 | Supply optional parameter values to H02CBF |
H02CEF | 19 | Integer LP or QP problem (sparse) |
H02CFF | 19 | Read optional parameter values for H02CEF from external file |
H02CGF | 19 | Supply optional parameter values to H02CEF |
H03ABF | 4 | Transportation problem, modified ‘stepping stone’ method |
H03ADF | 18 | Shortest path problem, Dijkstra's algorithm |
Routine Name |
Mark of Introduction |
Purpose |
M01CAF | 12 | Sort a vector, real numbers |
M01CBF | 12 | Sort a vector, integer numbers |
M01CCF | 12 | Sort a vector, character data |
M01DAF | 12 | Rank a vector, real numbers |
M01DBF | 12 | Rank a vector, integer numbers |
M01DCF | 12 | Rank a vector, character data |
M01DEF | 12 | Rank rows of a matrix, real numbers |
M01DFF | 12 | Rank rows of a matrix, integer numbers |
M01DJF | 12 | Rank columns of a matrix, real numbers |
M01DKF | 12 | Rank columns of a matrix, integer numbers |
M01DZF | 12 | Rank arbitrary data |
M01EAF | 12 | Rearrange a vector according to given ranks, real numbers |
M01EBF | 12 | Rearrange a vector according to given ranks, integer numbers |
M01ECF | 12 | Rearrange a vector according to given ranks, character data |
M01EDF | 19 | Rearrange a vector according to given ranks, complex numbers |
M01ZAF | 12 | Invert a permutation |
M01ZBF | 12 | Check validity of a permutation |
M01ZCF | 12 | Decompose a permutation into cycles |
Routine Name |
Mark of Introduction |
Purpose |
P01ABF | 12 | Return value of error indicator/terminate with error message |
Routine Name |
Mark of Introduction |
Purpose |
S01BAF | 14 | ln(1+x) |
S01EAF | 14 | Complex exponential, e^{z} |
S07AAF | 1 | tanx |
S09AAF | 1 | arcsinx |
S09ABF | 3 | arccosx |
S10AAF | 3 | tanhx |
S10ABF | 4 | sinhx |
S10ACF | 4 | coshx |
S11AAF | 4 | arctanhx |
S11ABF | 4 | arcsinhx |
S11ACF | 4 | arccoshx |
S13AAF | 1 | Exponential integral E_{1} (x) |
S13ACF | 2 | Cosine integral Ci(x) |
S13ADF | 5 | Sine integral Si(x) |
S14AAF | 1 | Gamma function |
S14ABF | 8 | Log Gamma function |
S14ACF | 14 | ψ (x) - lnx |
S14ADF | 14 | Scaled derivatives of ψ (x) |
S14AEF | 20 | Polygamma function ψ^{(n)} (x) for real x |
S14AFF | 20 | Polygamma function ψ^{(n)} (z) for complex z |
S14AGF | 21 | Logarithm of the Gamma function lnΓ (z) |
S14BAF | 14 | Incomplete Gamma functions P (a,x) and Q (a,x) |
S15ABF | 3 | Cumulative Normal distribution function P (x) |
S15ACF | 4 | Complement of cumulative Normal distribution function Q (x) |
S15ADF | 4 | Complement of error function erfc(x) |
S15AEF | 4 | Error function erf(x) |
S15AFF | 7 | Dawson's integral |
S15DDF | 14 | Scaled complex complement of error function, exp(-z^{2}) erfc(-iz) |
S17ACF | 1 | Bessel function Y_{0} (x) |
S17ADF | 1 | Bessel function Y_{1} (x) |
S17AEF | 5 | Bessel function J_{0} (x) |
S17AFF | 5 | Bessel function J_{1} (x) |
S17AGF | 8 | Airy function Ai(x) |
S17AHF | 8 | Airy function Bi(x) |
S17AJF | 8 | Airy function Ai^{′} (x) |
S17AKF | 8 | Airy function Bi ′ (x) |
S17ALF | 20 | Zeros of Bessel functions J_{α} (x) , J_{α} ′ (x) , Y_{α} (x) or Y_{α} ′ (x) |
S17DCF | 13 | Bessel functions Y_{ ν + a } (z) , real a ≥ 0 , complex z , ν = 0 , 1 , 2 , … |
S17DEF | 13 | Bessel functions J_{ ν + a } (z) , real a ≥ 0 , complex z , ν = 0 , 1 , 2 , … |
S17DGF | 13 | Airy functions Ai(z) and Ai ′ (z) , complex z |
S17DHF | 13 | Airy functions Bi(z) and Bi ′ (z) , complex z |
S17DLF | 13 | Hankel functions H_{ ν + a }^{(j)} (z) , j = 1 , 2 , real a ≥ 0 , complex z , ν = 0 , 1 , 2 , … |
S18ACF | 1 | Modified Bessel function K_{0} (x) |
S18ADF | 1 | Modified Bessel function K_{1} (x) |
S18AEF | 5 | Modified Bessel function I_{0} (x) |
S18AFF | 5 | Modified Bessel function I_{1} (x) |
S18CCF | 10 | Scaled modified Bessel function e^{x} K_{0} (x) |
S18CDF | 10 | Scaled modified Bessel function e^{x} K_{1} (x) |
S18CEF | 10 | Scaled modified Bessel function e^{ - |x| } I_{0} (x) |
S18CFF | 10 | Scaled modified Bessel function e^{ - |x| } I_{1} (x) |
S18DCF | 13 | Modified Bessel functions K_{ ν + a } (z) , real a ≥ 0 , complex z , ν = 0 , 1 , 2 , … |
S18DEF | 13 | Modified Bessel functions I_{ ν + a } (z) , real a ≥ 0 , complex z , ν = 0 , 1 , 2 , … |
S18GKF | 21 | Bessel function of the 1st kind J_{ α ± n } (z) |
S19AAF | 11 | Kelvin function berx |
S19ABF | 11 | Kelvin function beix |
S19ACF | 11 | Kelvin function kerx |
S19ADF | 11 | Kelvin function keix |
S20ACF | 5 | Fresnel integral S (x) |
S20ADF | 5 | Fresnel integral C (x) |
S21BAF | 8 | Degenerate symmetrised elliptic integral of 1st kind R_{C} (x,y) |
S21BBF | 8 | Symmetrised elliptic integral of 1st kind R_{F} (x,y,z) |
S21BCF | 8 | Symmetrised elliptic integral of 2nd kind R_{D} (x,y,z) |
S21BDF | 8 | Symmetrised elliptic integral of 3rd kind R_{J} (x,y,z,r) |
S21CAF | 15 | Jacobian elliptic functions sn, cn and dn of real argument |
S21CBF | 20 | Jacobian elliptic functions sn, cn and dn of complex argument |
S21CCF | 20 | Jacobian theta functions θ_{k} (x,q) of real argument |
S21DAF | 20 | General elliptic integral of 2nd kind F (z, k ′ ,a,b) of complex argument |
S22AAF | 20 | Legendre functions of 1st kind P_{n}^{m} (x) or P_{n}^{m} (x) |
Routine Name |
Mark of Introduction |
Purpose |
X01AAF | 5 | Provides the mathematical constant π |
X01ABF | 5 | Provides the mathematical constant γ (Euler's Constant) |
Routine Name |
Mark of Introduction |
Purpose |
X02AHF | 9 | The largest permissible argument for sin and cos |
X02AJF | 12 | The machine precision |
X02AKF | 12 | The smallest positive model number |
X02ALF | 12 | The largest positive model number |
X02AMF | 12 | The safe range parameter |
X02ANF | 15 | The safe range parameter for complex floating-point arithmetic |
X02BBF | 5 | The largest representable integer |
X02BEF | 5 | The maximum number of decimal digits that can be represented |
X02BHF | 12 | The floating-point model parameter, b |
X02BJF | 12 | The floating-point model parameter, p |
X02BKF | 12 | The floating-point model parameter e_{min} |
X02BLF | 12 | The floating-point model parameter e_{max} |
X02DAF | 8 | Switch for taking precautions to avoid underflow |
X02DJF | 12 | The floating-point model parameter ROUNDS |
Routine Name |
Mark of Introduction |
Purpose |
X03AAF | 5 | Real inner product added to initial value, basic/additional precision |
X03ABF | 5 | Complex inner product added to initial value, basic/additional precision |
Routine Name |
Mark of Introduction |
Purpose |
X04AAF | 7 | Return or set unit number for error messages |
X04ABF | 7 | Return or set unit number for advisory messages |
X04ACF | 19 | Open unit number for reading, writing or appending, and associate unit with named file |
X04ADF | 19 | Close file associated with given unit number |
X04BAF | 12 | Write formatted record to external file |
X04BBF | 12 | Read formatted record from external file |
X04CAF | 14 | Print real general matrix (easy-to-use) |
X04CBF | 14 | Print real general matrix (comprehensive) |
X04CCF | 14 | Print real packed triangular matrix (easy-to-use) |
X04CDF | 14 | Print real packed triangular matrix (comprehensive) |
X04CEF | 14 | Print real packed banded matrix (easy-to-use) |
X04CFF | 14 | Print real packed banded matrix (comprehensive) |
X04DAF | 14 | Print complex general matrix (easy-to-use) |
X04DBF | 14 | Print complex general matrix (comprehensive) |
X04DCF | 14 | Print complex packed triangular matrix (easy-to-use) |
X04DDF | 14 | Print complex packed triangular matrix (comprehensive) |
X04DEF | 14 | Print complex packed banded matrix (easy-to-use) |
X04DFF | 14 | Print complex packed banded matrix (comprehensive) |
X04EAF | 14 | Print integer matrix (easy-to-use) |
X04EBF | 14 | Print integer matrix (comprehensive) |
Routine Name |
Mark of Introduction |
Purpose |
X05AAF | 14 | Return date and time as an array of integers |
X05ABF | 14 | Convert array of integers representing date and time to character string |
X05ACF | 14 | Compare two character strings representing date and time |
X05BAF | 14 | Return the CPU time |