Routine Name 
Mark of Introduction 
Purpose 
A00AAF  18  Library identification, details of implementation and mark 
A00ACF  21  Check availability of a valid licence key 
A00ADF  22  Library identification, details of implementation, major and minor marks 
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's method 
C02AGF  13  All zeros of real polynomial, modified Laguerre's 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, Brent algorithm 
C05AGF  8  Zero of continuous function, Brent 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 Brent algorithm (reverse communication) 
C05BAF  22  Real values of Lambert's W function, W(x) 
C05NBF  9  Solution of system of nonlinear equations using function values only (easytouse) 
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) 
C05PBA  22  Solution of system of nonlinear equations using first derivatives (easytouse) 
C05PBF  9  Solution of system of nonlinear equations using first derivatives (easytouse) 
C05PCA  22  Solution of system of nonlinear equations using first derivatives (comprehensive) 
C05PCF  9  Solution of system of nonlinear equations using first derivatives (comprehensive) 
C05PDA  20  Solution of system of nonlinear equations using first derivatives (reverse communication) 
C05PDF  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 onedimensional real discrete Fourier transform, no extra workspace 
C06EBF  8  Single onedimensional Hermitian discrete Fourier transform, no extra workspace 
C06ECF  8  Single onedimensional complex discrete Fourier transform, no extra workspace 
C06EKF  11  Circular convolution or correlation of two real vectors, no extra workspace 
C06FAF  8  Single onedimensional real discrete Fourier transform, extra workspace for greater speed 
C06FBF  8  Single onedimensional Hermitian discrete Fourier transform, extra workspace for greater speed 
C06FCF  8  Single onedimensional complex discrete Fourier transform, extra workspace for greater speed 
C06FFF  11  Onedimensional complex discrete Fourier transform of multidimensional data 
C06FJF  11  Multidimensional complex discrete Fourier transform of multidimensional data 
C06FKF  11  Circular convolution or correlation of two real vectors, extra workspace for greater speed 
C06FPF  12  Multiple onedimensional real discrete Fourier transforms 
C06FQF  12  Multiple onedimensional Hermitian discrete Fourier transforms 
C06FRF  12  Multiple onedimensional complex discrete Fourier transforms 
C06FUF  13  Twodimensional complex discrete Fourier transform 
C06FXF  17  Threedimensional 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 quarterwave sine transform 
C06HDF  13  Discrete quarterwave 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 onedimensional real and Hermitian complex discrete Fourier transform, using complex storage format for Hermitian sequences 
C06PCF  19  Single onedimensional complex discrete Fourier transform, complex data type 
C06PFF  19  Onedimensional complex discrete Fourier transform of multidimensional data (using Complex data type) 
C06PJF  19  Multidimensional complex discrete Fourier transform of multidimensional data (using Complex data type) 
C06PKF  19  Circular convolution or correlation of two complex vectors 
C06PPF  19  Multiple onedimensional real and Hermitian complex discrete Fourier transforms, using complex storage format for Hermitian sequences 
C06PQF  19  Multiple onedimensional real and Hermitian complex discrete Fourier transforms, using complex storage format for Hermitian sequences 
C06PRF  19  Multiple onedimensional complex discrete Fourier transforms using complex data type 
C06PSF  19  Multiple onedimensional complex discrete Fourier transforms using complex data type and sequences stored as columns 
C06PUF  19  Twodimensional complex discrete Fourier transform, complex data type 
C06PXF  19  Threedimensional complex discrete Fourier transform, Complex data type 
C06RAF  19  Discrete sine transform (easytouse) 
C06RBF  19  Discrete cosine transform (easytouse) 
C06RCF  19  Discrete quarterwave sine transform (easytouse) 
C06RDF  19  Discrete quarterwave cosine transform (easytouse) 
Routine Name 
Mark of Introduction 
Purpose 
C09AAF  22  Wavelet filter initialization 
C09CAF  22  onedimensional discrete wavelet transform 
C09CBF  22  onedimensional inverse discrete wavelet transform 
C09CCF  22  onedimensional multilevel discrete wavelet transform 
C09CDF  22  onedimensional inverse multilevel discrete wavelet transform 
Routine Name 
Mark of Introduction 
Purpose 
D01AHF  8  Onedimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for wellbehaved integrands 
D01AJF  8  Onedimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands 
D01AKF  8  Onedimensional quadrature, adaptive, finite interval, method suitable for oscillating functions 
D01ALF  8  Onedimensional quadrature, adaptive, finite interval, allowing for singularities at userspecified breakpoints 
D01AMF  8  Onedimensional quadrature, adaptive, infinite or semiinfinite interval 
D01ANF  8  Onedimensional quadrature, adaptive, finite interval, weight function cos(ωx) or sin(ωx) 
D01APF  8  Onedimensional quadrature, adaptive, finite interval, weight function with endpoint singularities of algebraicologarithmic type 
D01AQF  8  Onedimensional quadrature, adaptive, finite interval, weight function 1 / (x  c), Cauchy principal value (Hilbert transform) 
D01ARF  10  Onedimensional quadrature, nonadaptive, finite interval with provision for indefinite integrals 
D01ASF  13  Onedimensional quadrature, adaptive, semiinfinite interval, weight function cos(ωx) or sin(ωx) 
D01ATF  13  Onedimensional quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines 
D01AUF  13  Onedimensional quadrature, adaptive, finite interval, variant of D01AKF efficient on vector machines 
D01BAF  7  Onedimensional Gaussian quadrature 
D01BBF  7  Precomputed 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  Onedimensional quadrature, nonadaptive, finite interval 
D01DAF  5  Twodimensional quadrature, finite region 
D01EAF

12  Multidimensional adaptive quadrature over hyperrectangle, multiple integrands 
D01FBF  8  Multidimensional Gaussian quadrature over hyperrectangle 
D01FCF  8  Multidimensional adaptive quadrature over hyperrectangle 
D01FDF  10  Multidimensional quadrature, Sag–Szekeres method, general product region or nsphere 
D01GAF  5  Onedimensional quadrature, integration of function defined by data values, Gill–Miller method 
D01GBF  10  Multidimensional quadrature over hyperrectangle, Monte Carlo method 
D01GCF  10  Multidimensional quadrature, general product region, numbertheoretic method 
D01GDF  14  Multidimensional quadrature, general product region, numbertheoretic 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  Multidimensional quadrature over an nsphere, allowing for badly behaved integrands 
D01PAF  10  Multidimensional quadrature over an nsimplex 
Routine Name 
Mark of Introduction 
Purpose 
D02AGF

2  Ordinary differential equations, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined 
D02BGF  7  Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until a component attains given value (simple driver) 
D02BHF  7  Ordinary differential equations, initial value problem, Runge–Kutta–Merson method, until function of solution is zero (simple driver) 
D02BJF

18  Ordinary differential equations, initial value problem, Runge–Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver) 
D02CJF

13  Ordinary differential equations, initial value problem, Adams method, until function of solution is zero, intermediate output (simple driver) 
D02EJF

12  Ordinary differential equations, stiff initial value problem, backward diffential formulae method, until function of solution is zero, intermediate output (simple driver) 
D02GAF

8  Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem 
D02GBF

8  Ordinary differential equations, boundary value problem, finite difference technique with deferred correction, general linear problem 
D02HAF

8  Ordinary differential equations, boundary value problem, shooting and matching, boundary values to be determined 
D02HBF

8  Ordinary differential equations, boundary value problem, shooting and matching, general parameters to be determined 
D02JAF

8  Ordinary differential equations, boundary value problem, collocation and leastsquares, single nthorder linear equation 
D02JBF

8  Ordinary differential equations, boundary value problem, collocation and leastsquares, system of firstorder linear equations 
D02KAF  7  Secondorder Sturm–Liouville problem, regular system, finite range, eigenvalue only 
D02KDF  7  Secondorder Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, userspecified breakpoints 
D02KEF

8  Secondorder Sturm–Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, userspecified breakpoints 
D02LAF

13  Secondorder ordinary differential equations, initial value problem, Runge–Kutta–Nystrom method 
D02LXF  13  Secondorder ordinary differential equations, initial value problem, setup for D02LAF 
D02LYF  13  Secondorder ordinary differential equations, initial value problem, diagnostics for D02LAF 
D02LZF  13  Secondorder ordinary differential equations, initial value problem, interpolation for D02LAF 
D02MCF  22  Implicit ordinary differential equations/DAEs, initial value problem, DASSL method continuation for D02NEF 
D02MVF

14  Ordinary differential equations, initial value problem, DASSL method, setup for D02M–N routines 
D02MWF  22  Implicit ordinary differential equations/DAEs, initial value problem, setup for D02NEF 
D02MZF  14  Ordinary differential equations, initial value problem, interpolation for D02M–N routines, natural interpolant 
D02NBF

12  Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive) 
D02NCF

12  Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive) 
D02NDF

12  Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive) 
D02NEF  22  Implicit ordinary differential equations/DAEs, initial value problem, DASSL method integrator 
D02NGF

12  Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive) 
D02NHF  12  Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive) 
D02NJF

12  Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive) 
D02NMF

12  Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive) 
D02NNF  12  Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive) 
D02NPF  22  Implicit ordinary differential equations/DAEs, initial value problem linear algebra setup routine for D02NEF 
D02NRF  12  Ordinary differential equations, initial value problem, for use with D02M–N routines, sparse Jacobian, enquiry routine 
D02NSF  12  Ordinary differential equations, initial value problem, for use with D02M–N routines, full Jacobian, linear algebra set up 
D02NTF  12  Ordinary differential equations, initial value problem, for use with D02M–N routines, banded Jacobian, linear algebra set up 
D02NUF  12  Ordinary differential equations, initial value problem, for use with D02M–N routines, sparse Jacobian, linear algebra set up 
D02NVF  12  Ordinary differential equations, initial value problem, backward diffential formulae method, setup for D02M–N routines 
D02NWF  12  Ordinary differential equations, initial value problem, Blend method, setup for D02M–N routines 
D02NXF  12  Ordinary differential equations, initial value problem, sparse Jacobian, linear algebra diagnostics, for use with D02M–N routines 
D02NYF  12  Ordinary differential equations, initial value problem, integrator diagnostics, for use with D02M–N routines 
D02NZF  12  Ordinary differential equations, initial value problem, setup for continuation calls to integrator, for use with D02M–N routines 
D02PCF

16  Ordinary differential equations, initial value problem, Runge–Kutta method, integration over range with output 
D02PDF

16  Ordinary differential equations, initial value problem, Runge–Kutta method, integration over one step 
D02PVF  16  Ordinary differential equations, initial value problem, setup for D02PCF and D02PDF 
D02PWF

16  Ordinary differential equations, initial value problem, resets end of range for D02PDF 
D02PXF

16  Ordinary differential equations, initial value problem, interpolation for D02PDF 
D02PYF  16  Ordinary differential equations, initial value problem, integration diagnostics for D02PCF and D02PDF 
D02PZF

16  Ordinary differential equations, initial value problem, error assessment diagnostics for D02PCF and D02PDF 
D02QFF  13  Ordinary differential equations, initial value problem, Adams method with rootfinding (forward communication, comprehensive) 
D02QGF

13  Ordinary differential equations, initial value problem, Adams method with rootfinding (reverse communication, comprehensive) 
D02QWF  13  Ordinary differential equations, initial value problem, setup for D02QFF and D02QGF 
D02QXF  13  Ordinary differential equations, initial value problem, diagnostics for D02QFF and D02QGF 
D02QYF  13  Ordinary differential equations, initial value problem, rootfinding diagnostics for D02QFF and D02QGF 
D02QZF

13  Ordinary differential equations, initial value problem, interpolation for D02QFF or D02QGF 
D02RAF

8  Ordinary differential equations, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility 
D02SAF

8  Ordinary differential equations, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined 
D02TGF

8  nthorder linear ordinary differential equations, boundary value problem, collocation and leastsquares 
D02TKF

17  Ordinary differential equations, general nonlinear boundary value problem, collocation technique 
D02TVF

17  Ordinary differential equations, general nonlinear boundary value problem, setup for D02TKF 
D02TXF

17  Ordinary differential equations, general nonlinear boundary value problem, continuation facility for D02TKF 
D02TYF

17  Ordinary differential equations, general nonlinear boundary value problem, interpolation for D02TKF 
D02TZF

17  Ordinary differential equations, general nonlinear boundary value problem, diagnostics for D02TKF 
D02XJF  12  Ordinary differential equations, initial value problem, interpolation for D02M–N routines, natural interpolant 
D02XKF  12  Ordinary differential equations, initial value problem, interpolation for D02M–N routines, C_{1} interpolant 
D02ZAF  12  Ordinary differential equations, initial value problem, weighted norm of local error estimate for D02M–N routines 
Routine Name 
Mark of Introduction 
Purpose 
D03EAF  7  Elliptic PDE, Laplace's equation, twodimensional arbitrary domain 
D03EBF

7  Elliptic PDE, solution of finite difference equations by SIP, fivepoint twodimensional molecule, iterate to convergence 
D03ECF

8  Elliptic PDE, solution of finite difference equations by SIP for sevenpoint threedimensional molecule, iterate to convergence 
D03EDF

12  Elliptic PDE, solution of finite difference equations by a multigrid technique 
D03EEF

13  Discretize a secondorder elliptic PDE on a rectangle 
D03FAF  14  Elliptic PDE, Helmholtz equation, threedimensional Cartesian coordinates 
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 
D03PCA  20  General system of parabolic PDEs, method of lines, finite differences, one space variable 
D03PCF

15  General system of parabolic PDEs, method of lines, finite differences, one space variable 
D03PDA  20  General system of parabolic PDEs, method of lines, Chebyshev C^{0} collocation, one space variable 
D03PDF

15  General system of parabolic PDEs, method of lines, Chebyshev C^{0} collocation, one space variable 
D03PEF

16  General system of firstorder PDEs, method of lines, Keller box discretisation, one space variable 
D03PFF  17  General system of convectiondiffusion PDEs with source terms in conservative form, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable 
D03PHA  20  General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable 
D03PHF

15  General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable 
D03PJA  20  General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C^{0} collocation, one space variable 
D03PJF

15  General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C^{0} collocation, one space variable 
D03PKF

16  General system of firstorder PDEs, coupled DAEs, method of lines, Keller box discretisation, one space variable 
D03PLF

17  General system of convectiondiffusion 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 
D03PPA  20  General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable 
D03PPF

16  General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable 
D03PRF

16  General system of firstorder PDEs, coupled DAEs, method of lines, Keller box discretisation, remeshing, one space variable 
D03PSF

17  General system of convectiondiffusion 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 secondorder PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region 
D03RBF  18  General system of secondorder 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, fivepoint twodimensional molecule, one iteration 
D03UBF

8  Elliptic PDE, solution of finite difference equations by SIP, sevenpoint threedimensional 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 nonsingular Fredholm integral equation, second kind, split kernel 
D05ABF  6  Linear nonsingular 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 Abeltype equations 
Routine Name 
Mark of Introduction 
Purpose 
D06AAF  20  Generates a twodimensional mesh using a simple incremental method 
D06ABF  20  Generates a twodimensional mesh using a Delaunay–Voronoi process 
D06ACF  20  Generates a twodimensional mesh using an Advancingfront 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, monotonicitypreserving, 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  Leastsquares 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  Leastsquares polynomial fit, special data points (including interpolation) 
E02AGF

8  Leastsquares 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  Leastsquares 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  Leastsquares cubic spline curve fit, automatic knot placement 
E02CAF

7  Leastsquares surface fit by polynomials, data on lines parallel to one independent coordinate axis 
E02CBF  7  Evaluation of fitted polynomial in two variables 
E02DAF

6  Leastsquares surface fit, bicubic splines 
E02DCF

13  Leastsquares surface fit by bicubic splines with automatic knot placement, data on rectangular grid 
E02DDF

13  Leastsquares 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 twodimensional data into panels for fitting bicubic splines 
Routine Name 
Mark of Introduction 
Purpose 
E04ABA  20  Minimum, function of one variable using function values only 
E04ABF  6  Minimum, function of one variable using function values only 
E04BBA  20  Minimum, function of one variable, using first derivative 
E04BBF  6  Minimum, function of one variable, using first derivative 
E04CBF

22  Unconstrained minimization using simplex algorithm, function of several variables using function values only 
E04CCA  20  Unconstrained minimum, simplex algorithm, function of several variables using function values only (comprehensive) 
E04CCF  1  Unconstrained minimum, simplex algorithm, function of several variables using function values only (comprehensive) 
E04DGA  20  Unconstrained minimum, preconditioned conjugate gradient algorithm, function of several variables using first derivatives (comprehensive) 
E04DGF  12  Unconstrained minimum, preconditioned conjugate gradient algorithm, function of several variables using first derivatives (comprehensive) 
E04DJA  20  Supply optional parameter values for E04DGF/E04DGA from external file 
E04DJF  12  Supply optional parameter values for E04DGF/E04DGA from external file 
E04DKA  20  Supply optional parameter values to E04DGF/E04DGA 
E04DKF  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 (easytouse) 
E04GBF  7  Unconstrained minimum of a sum of squares, combined Gauss–Newton and quasiNewton 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 quasiNewton algorithm, using first derivatives (easytouse) 
E04GZF  18  Unconstrained minimum of a sum of squares, combined Gauss–Newton and modified Newton algorithm using first derivatives (easytouse) 
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 (easytouse) 
E04JYF  18  Minimum, function of several variables, quasiNewton algorithm, simple bounds, using function values only (easytouse) 
E04KDF  6  Minimum, function of several variables, modified Newton algorithm, simple bounds, using first derivatives (comprehensive) 
E04KYF  18  Minimum, function of several variables, quasiNewton algorithm, simple bounds, using first derivatives (easytouse) 
E04KZF  18  Minimum, function of several variables, modified Newton algorithm, simple bounds, using first derivatives (easytouse) 
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 (easytouse) 
E04MFA  20  LP problem (dense) 
E04MFF  16  LP problem (dense) 
E04MGA  20  Supply optional parameter values for E04MFF/E04MFA from external file 
E04MGF  16  Supply optional parameter values for E04MFF/E04MFA from external file 
E04MHA  20  Supply optional parameter values to E04MFF/E04MFA 
E04MHF  16  Supply optional parameter values to E04MFF/E04MFA 
E04MZF  18  Converts MPSX data file defining LP or QP problem to format required by E04NKF/E04NKA 
E04NCA  20  Convex QP problem or linearlyconstrained linear leastsquares problem (dense) 
E04NCF  12  Convex QP problem or linearlyconstrained linear leastsquares problem (dense) 
E04NDA  20  Supply optional parameter values for E04NCF/E04NCA from external file 
E04NDF  12  Supply optional parameter values for E04NCF/E04NCA from external file 
E04NEA  20  Supply optional parameter values to E04NCF/E04NCA 
E04NEF  12  Supply optional parameter values to E04NCF/E04NCA 
E04NFA  20  QP problem (dense) 
E04NFF  16  QP problem (dense) 
E04NGA  20  Supply optional parameter values for E04NFF/E04NFA from external file 
E04NGF  16  Supply optional parameter values for E04NFF/E04NFA from external file 
E04NHA  20  Supply optional parameter values to E04NFF/E04NFA 
E04NHF  16  Supply optional parameter values to E04NFF/E04NFA 
E04NKA  20  LP or QP problem (sparse) 
E04NKF  18  LP or QP problem (sparse) 
E04NLA  20  Supply optional parameter values for E04NKF/E04NKA from external file 
E04NLF  18  Supply optional parameter values for E04NKF/E04NKA from external file 
E04NMA  20  Supply optional parameter values to E04NKF/E04NKA 
E04NMF  18  Supply optional parameter values to E04NKF/E04NKA 
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 real argument 
E04NXF  21  Get the setting of an integer valued option of E04NQF 
E04NYF  21  Get the setting of a real valued option of E04NQF 
E04UCA  20  Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (comprehensive) 
E04UCF  12  Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (comprehensive) 
E04UDA  20  Supply optional parameter values for E04UCF/E04UCA or E04UFF/E04UFA from external file 
E04UDF  12  Supply optional parameter values for E04UCF/E04UCA or E04UFF/E04UFA from external file 
E04UEA  20  Supply optional parameter values to E04UCF/E04UCA or E04UFF/E04UFA 
E04UEF  12  Supply optional parameter values to E04UCF/E04UCA or E04UFF/E04UFA 
E04UFA  20  Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive) 
E04UFF  18  Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally first derivatives (reverse communication, comprehensive) 
E04UGA  20  NLP problem (sparse) 
E04UGF  19  NLP problem (sparse) 
E04UHA  20  Supply optional parameter values for E04UGF/E04UGA from external file 
E04UHF  19  Supply optional parameter values for E04UGF/E04UGA from external file 
E04UJA  20  Supply optional parameter values to E04UGF/E04UGA 
E04UJF  19  Supply optional parameter values to E04UGF/E04UGA 
E04UQA  20  Supply optional parameter values for E04USF/E04USA from external file 
E04UQF  14  Supply optional parameter values for E04USF/E04USA from external file 
E04URA  20  Supply optional parameter values to E04USF/E04USA 
E04URF  14  Supply optional parameter values to E04USF/E04USA 
E04USA  20  Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally first derivatives (comprehensive) 
E04USF  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 real argument 
E04VRF  21  Get the setting of an integer valued option of E04VHF 
E04VSF  21  Get the setting of a real valued option of E04VHF 
E04WBF  20  Initialization routine for E04DGA, E04MFA, E04NCA, E04NFA, E04UFA, E04UGA and 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 real argument 
E04WKF  21  Get the setting of an integer valued option of E04WDF 
E04WLF  21  Get the setting of a real valued option of E04WDF 
E04XAA  20  Estimate (using numerical differentiation) gradient and/or Hessian of a function 
E04XAF  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 leastsquares problem (unconstrained) 
E04ZCA  20  Check user's routines for calculating first derivatives of function and constraints 
E04ZCF  11  Check user's routines for calculating first derivatives of function and constraints 
Routine Name 
Mark of Introduction 
Purpose 
E05JAF  22  Initialization routine for E05JBF 
E05JBF

22  Global optimization by multilevel coordinate search, simple bounds, using function values only 
E05JCF

22  Supply optional parameter values for E05JBF from external file 
E05JDF  22  Set a single optional parameter for E05JBF from a character string 
E05JEF  22  Set a single optional parameter for E05JBF from an ‘ON’/‘OFF’valued character argument 
E05JFF  22  Set a single optional parameter for E05JBF from an integer argument 
E05JGF  22  Set a single optional parameter for E05JBF from a real argument 
E05JHF  22  Determine whether an optional parameter for E05JBF has been set by you or not 
E05JJF  22  Get the setting of an ‘ON’/‘OFF’valued character optional parameter of E05JBF 
E05JKF  22  Get the setting of an Integer valued optional parameter of E05JBF 
E05JLF  22  Get the setting of a real valued optional parameter of E05JBF 
Routine Name 
Mark of Introduction 
Purpose 
F01ABF  1  Inverse of real symmetric positivedefinite matrix using iterative refinement 
F01ADF  2  Inverse of real symmetric positivedefinite matrix 
F01BLF  5  Pseudoinverse and rank of realm by n matrix (m ≥ n) 
F01BRF  7  LU factorization of real sparse matrix 
F01BSF  7  LU factorization of real sparse matrix with known sparsity pattern 
F01BUF  7  ULDL^{T}U^{T} factorization of real symmetric positivedefinite band matrix 
F01BVF  7  Reduction to standard form, generalized real symmetricdefinite 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 
F01ECF  22  Real matrix exponential 
F01LEF  11  LU factorization of real tridiagonal matrix 
F01LHF  13  LU factorization of real almost block diagonal matrix 
F01MCF  8  LDL^{T} factorization of real symmetric positivedefinite variablebandwidth matrix 
F01QGF  14  RQ factorization of realm by n upper trapezoidal matrix (m ≤ n) 
F01QJF  14  RQ factorization of realm by n matrix (m ≤ n) 
F01QKF  14  Operations with orthogonal matrices, form rows of Q, after RQ factorization by F01QJF 
F01RGF  14  RQ factorization of complex m by n upper trapezoidal matrix (m ≤ n) 
F01RJF  14  RQ factorization of complex m by n matrix (m ≤ n) 
F01RKF  14  Operations with unitary matrices, form rows of Q, after RQ 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 
F02BJF  6  Computes all eigenvalues and, optionally, eigenvectors of generalized eigenproblem by QZ algorithm, real matrices (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02EAF  16  All eigenvalues and Schur factorization of real general matrix (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02EBF  16  All eigenvalues and eigenvectors of real general matrix (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02ECF  17  Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box) 
F02FAF  16  Computes all eigenvalues and, optionally, eigenvectors of real symmetric matrix (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02FCF  17  Selected eigenvalues and optionally eigenvectors of real symmetric matrix (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02FDF  16  All eigenvalues and eigenvectors of real symmetricdefinite generalized problem (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02FHF  11  All eigenvalues of generalized banded real symmetricdefinite eigenproblem (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02FJF  11  Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box) 
F02GAF  16  All eigenvalues and Schur factorization of complex general matrix (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02GBF  16  Computes all eigenvalues and, optionally, eigenvectors of complex general matrix (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02GCF  17  Selected eigenvalues and eigenvectors of complex nonsymmetric matrix (Black Box) 
F02GJF  8  Computes all eigenvalues and, optionally, eigenvectors of generalized complex eigenproblem by QZ algorithm (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02HAF  16  All eigenvalues and eigenvectors of complex Hermitian matrix (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02HCF  17  Selected eigenvalues and eigenvectors of complex Hermitian matrix (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02HDF  16  All eigenvalues and eigenvectors of complex Hermitiandefinite generalized problem (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02SDF  8  Eigenvector of generalized real banded eigenproblem by inverse iteration 
F02WDF  8  QR factorization, possibly followed by SVD 
F02WEF  13  SVD of real matrix (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F02WGF  22  Computes leading terms in the singular value decomposition of a real general matrix; also computes corresponding left and right singular vectors 
F02WUF  14  SVD of real upper triangular matrix (Black Box) 
F02XEF  13  SVD of complex matrix (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
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 positivedefinite matrix (Black Box) 
F03ACF  1  Determinant of real symmetric positivedefinite band matrix (Black Box) 
F03ADF  1  Determinant of complex matrix (Black Box) 
F03AEF  2  LL^{T} factorization and determinant of real symmetric positivedefinite matrix 
F03AFF  2  LU factorization and determinant of real matrix 
Routine Name 
Mark of Introduction 
Purpose 
F04AAF  2  Solution of real simultaneous linear equations with multiple righthand sides (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F04ABF  2  Solution of real symmetric positivedefinite simultaneous linear equations with multiple righthand sides using iterative refinement (Black Box) 
F04ACF  2  Solution of real symmetric positivedefinite banded simultaneous linear equations with multiple righthand sides (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F04ADF  2  Solution of complex simultaneous linear equations with multiple righthand sides (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F04AEF  2  Solution of real simultaneous linear equations with multiple righthand sides using iterative refinement (Black Box) 
F04AFF  2  Solution of real symmetric positivedefinite simultaneous linear equations using iterative refinement (coefficient matrix already factorized by F03AEF) 
F04AGF  2  Solution of real symmetric positivedefinite 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  Leastsquares solution of mreal equations in n unknowns, rank = n, m ≥ n using iterative refinement (Black Box) 
F04ARF  4  Solution of real simultaneous linear equations, one righthand side (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F04ASF  4  Solution of real symmetric positivedefinite simultaneous linear equations, one righthand side using iterative refinement (Black Box) 
F04ATF  4  Solution of real simultaneous linear equations, one righthand 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 errorbound to a real system of linear equations 
F04BBF  21  Computes the solution and errorbound to a real banded system of linear equations 
F04BCF  21  Computes the solution and errorbound to a real tridiagonal system of linear equations 
F04BDF  21  Computes the solution and errorbound to a real symmetric positivedefinite system of linear equations 
F04BEF  21  Computes the solution and errorbound to a real symmetric positivedefinite system of linear equations, packed storage 
F04BFF  21  Computes the solution and errorbound to a real symmetric positivedefinite banded system of linear equations 
F04BGF  21  Computes the solution and errorbound to a real symmetric positivedefinite tridiagonal system of linear equations 
F04BHF  21  Computes the solution and errorbound to a real symmetric system of linear equations 
F04BJF  21  Computes the solution and errorbound to a real symmetric system of linear equations, packed storage 
F04CAF  21  Computes the solution and errorbound to a complex system of linear equations 
F04CBF  21  Computes the solution and errorbound to a complex banded system of linear equations 
F04CCF  21  Computes the solution and errorbound to a complex tridiagonal system of linear equations 
F04CDF  21  Computes the solution and errorbound to a complex Hermitian positivedefinite system of linear equations 
F04CEF  21  Computes the solution and errorbound to a complex Hermitian positivedefinite system of linear equations, packed storage 
F04CFF  21  Computes the solution and errorbound to a complex Hermitian positivedefinite banded system of linear equations 
F04CGF  21  Computes the solution and errorbound to a complex Hermitian positivedefinite tridiagonal system of linear equations 
F04CHF  21  Computes the solution and errorbound to a complex Hermitian system of linear equations 
F04CJF  21  Computes the solution and errorbound to a complex Hermitian system of linear equations, packed storage 
F04DHF  21  Computes the solution and errorbound to a complex symmetric system of linear equations 
F04DJF  21  Computes the solution and errorbound to a complex symmetric system of linear equations, packed storage. 
F04EAF  11  Solution of real tridiagonal simultaneous linear equations, one righthand side (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F04FAF  11  Solution of real symmetric positivedefinite tridiagonal simultaneous linear equations, one righthand side (Black Box) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F04FEF  15  Solution of the Yule–Walker equations for real symmetric positivedefinite Toeplitz matrix, one righthand side 
F04FFF  15  Solution of real symmetric positivedefinite Toeplitz system, one righthand side 
F04JAF  8  Minimal leastsquares solution of mreal equations in n unknowns, rank ≤ n, m ≥ n Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F04JDF  8  Minimal leastsquares solution of mreal equations in n unknowns, rank ≤ m, m ≤ n Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F04JGF  8  Leastsquares (if rank = n) or minimal leastsquares (if rank < n) solution of mreal equations in n unknowns, m ≥ n 
F04JLF  17  Real general Gauss–Markov linear model (including weighted leastsquares) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F04JMF  17  Equalityconstrained real linear leastsquares problem Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F04KLF  17  Complex general Gauss–Markov linear model (including weighted leastsquares) Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
F04KMF  17  Equalityconstrained complex linear leastsquares problem Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
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 positivedefinite variablebandwidth simultaneous linear equations (coefficient matrix already factorized by F01MCF) 
F04MEF  15  Update solution of the Yule–Walker equations for real symmetric positivedefinite Toeplitz matrix 
F04MFF  15  Update solution of real symmetric positivedefinite Toeplitz system 
F04QAF  11  Sparse linear leastsquares problem, mreal equations in n unknowns 
F04YAF  11  Covariance matrix for linear leastsquares problems, mreal 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  12  DROTG 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}), reala 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  12  DDOT Dot product of two real vectors 
F06ECF  12  DAXPY Add scalar times real vector to real vector 
F06EDF  12  DSCAL Multiply real vector by scalar 
F06EFF  12  DCOPY Copy real vector 
F06EGF  12  DSWAP Swap two real vectors 
F06EJF  12  DNRM2 Compute Euclidean norm of real vector 
F06EKF  12  DASUM Sum absolute values of real vector elements 
F06EPF  12  DROT Apply real plane rotation 
F06ERF  14  DDOTI Dot product of two real sparse vectors 
F06ETF  14  DAXPYI Add scalar times real sparse vector to real sparse vector 
F06EUF  14  DGTHR Gather real sparse vector 
F06EVF  14  DGTHRZ Gather and set to zero real sparse vector 
F06EWF  14  DSCTR Scatter real sparse vector 
F06EXF  14  DROTI 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  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  12  ZDOTU Dot product of two complex vectors, unconjugated 
F06GBF  12  ZDOTC Dot product of two complex vectors, conjugated 
F06GCF  12  ZAXPY Add scalar times complex vector to complex vector 
F06GDF  12  ZSCAL Multiply complex vector by complex scalar 
F06GFF  12  ZCOPY Copy complex vector 
F06GGF  12  ZSWAP Swap two complex vectors 
F06GRF  14  ZDOTUI Dot product of two complex sparse vector, unconjugated 
F06GSF  14  ZDOTCI Dot product of two complex sparse vector, conjugated 
F06GTF  14  ZAXPYI Add scalar times complex sparse vector to complex sparse vector 
F06GUF  14  ZGTHR Gather complex sparse vector 
F06GVF  14  ZGTHRZ Gather and set to zero complex sparse vector 
F06GWF  14  ZSCTR 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 
F06HMF  21  ZROT Apply plane rotation with real cosine and complex sine 
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  12  ZDSCAL Multiply complex vector by real scalar 
F06JJF  12  DZNRM2 Compute Euclidean norm of complex vector 
F06JKF  12  DZASUM Sum absolute values of complex vector elements 
F06JLF  12  IDAMAX Index, real vector element with largest absolute value 
F06JMF  12  IZAMAX 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  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 nonnegligible element of real vector 
F06KPF  12  Apply real plane rotation to two complex vectors 
F06PAF  12  DGEMV Matrixvector product, real rectangular matrix 
F06PBF  12  DGBMV Matrixvector product, real rectangular band matrix 
F06PCF  12  DSYMV Matrixvector product, real symmetric matrix 
F06PDF  12  DSBMV Matrixvector product, real symmetric band matrix 
F06PEF  12  DSPMV Matrixvector product, real symmetric packed matrix 
F06PFF  12  DTRMV Matrixvector product, real triangular matrix 
F06PGF  12  DTBMV Matrixvector product, real triangular band matrix 
F06PHF  12  DTPMV Matrixvector product, real triangular packed matrix 
F06PJF  12  DTRSV System of equations, real triangular matrix 
F06PKF  12  DTBSV System of equations, real triangular band matrix 
F06PLF  12  DTPSV System of equations, real triangular packed matrix 
F06PMF  12  DGER Rank1 update, real rectangular matrix 
F06PPF  12  DSYR Rank1 update, real symmetric matrix 
F06PQF  12  DSPR Rank1 update, real symmetric packed matrix 
F06PRF  12  DSYR2 Rank2 update, real symmetric matrix 
F06PSF  12  DSPR2 Rank2 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  QR factorization by sequence of plane rotations, rank1 update of real upper triangular matrix 
F06QQF  13  QR factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row 
F06QRF  13  QR or RQ factorization by sequence of plane rotations, real upper Hessenberg matrix 
F06QSF  13  QR or RQ factorization by sequence of plane rotations, real upper spiked matrix 
F06QTF  13  QR factorization of UP or RQ factorization of PU, Ureal upper triangular, P 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  1norm, ∞norm, Frobenius norm, largest absolute element, real general matrix 
F06RBF  15  1norm, ∞norm, Frobenius norm, largest absolute element, real band matrix 
F06RCF  15  1norm, ∞norm, Frobenius norm, largest absolute element, real symmetric matrix 
F06RDF  15  1norm, ∞norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage 
F06REF  15  1norm, ∞norm, Frobenius norm, largest absolute element, real symmetric band matrix 
F06RJF  15  1norm, ∞norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix 
F06RKF  15  1norm, ∞norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage 
F06RLF  15  1norm, ∞norm, Frobenius norm, largest absolute element, real triangular band matrix 
F06RMF  15  1norm, ∞norm, Frobenius norm, largest absolute element, real Hessenberg matrix 
F06RNF  21  1norm, ∞norm, Frobenius norm, largest absolute element, real tridiagonal matrix 
F06RPF  21  1norm, ∞norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix 
F06SAF  12  ZGEMV Matrixvector product, complex rectangular matrix 
F06SBF  12  ZGBMV Matrixvector product, complex rectangular band matrix 
F06SCF  12  ZHEMV Matrixvector product, complex Hermitian matrix 
F06SDF  12  ZHBMV Matrixvector product, complex Hermitian band matrix 
F06SEF  12  ZHPMV Matrixvector product, complex Hermitian packed matrix 
F06SFF  12  ZTRMV Matrixvector product, complex triangular matrix 
F06SGF  12  ZTBMV Matrixvector product, complex triangular band matrix 
F06SHF  12  ZTPMV Matrixvector product, complex triangular packed matrix 
F06SJF  12  ZTRSV System of equations, complex triangular matrix 
F06SKF  12  ZTBSV System of equations, complex triangular band matrix 
F06SLF  12  ZTPSV System of equations, complex triangular packed matrix 
F06SMF  12  ZGERU Rank1 update, complex rectangular matrix, unconjugated vector 
F06SNF  12  ZGERC Rank1 update, complex rectangular matrix, conjugated vector 
F06SPF  12  ZHER Rank1 update, complex Hermitian matrix 
F06SQF  12  ZHPR Rank1 update, complex Hermitian packed matrix 
F06SRF  12  ZHER2 Rank2 update, complex Hermitian matrix 
F06SSF  12  ZHPR2 Rank2 update, complex Hermitian packed matrix 
F06TAF  21  Matrixvector product, complex symmetric matrix 
F06TBF  21  Rank1 update, complex symmetric matrix 
F06TCF  21  Matrixvector product, complex symmetric packed matrix 
F06TDF  21  Rank1 update, complex symmetric 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  QR factorization by sequence of plane rotations, rank1 update of complex upper triangular matrix 
F06TQF  13  QR × k factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row 
F06TRF  13  QR or RQ factorization by sequence of plane rotations, complex upper Hessenberg matrix 
F06TSF  13  QR or RQ factorization by sequence of plane rotations, complex upper spiked matrix 
F06TTF  13  QR factorization of UP or RQ factorization of PU, U complex upper triangular, P 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  1norm, ∞norm, Frobenius norm, largest absolute element, complex general matrix 
F06UBF  15  1norm, ∞norm, Frobenius norm, largest absolute element, complex band matrix 
F06UCF  15  1norm, ∞norm, Frobenius norm, largest absolute element, complex Hermitian matrix 
F06UDF  15  1norm, ∞norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage 
F06UEF  15  1norm, ∞norm, Frobenius norm, largest absolute element, complex Hermitian band matrix 
F06UFF  15  1norm, ∞norm, Frobenius norm, largest absolute element, complex symmetric matrix 
F06UGF  15  1norm, ∞norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage 
F06UHF  15  1norm, ∞norm, Frobenius norm, largest absolute element, complex symmetric band matrix 
F06UJF  15  1norm, ∞norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix 
F06UKF  15  1norm, ∞norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage 
F06ULF  15  1norm, ∞norm, Frobenius norm, largest absolute element, complex triangular band matrix 
F06UMF  15  1norm, ∞norm, Frobenius norm, largest absolute element, complex Hessenberg matrix 
F06UNF  21  1norm, ∞norm, Frobenius norm, largest absolute element, complex tridiagonal matrix 
F06UPF  21  1norm, ∞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  14  DGEMM Matrixmatrix product, two real rectangular matrices 
F06YCF  14  DSYMM Matrixmatrix product, one real symmetric matrix, one real rectangular matrix 
F06YFF  14  DTRMM Matrixmatrix product, one real triangular matrix, one real rectangular matrix 
F06YJF  14  DTRSM Solves a system of equations with multiple righthand sides, real triangular coefficient matrix 
F06YPF  14  DSYRK Rankk update of a real symmetric matrix 
F06YRF  14  DSYR2K Rank2k update of a real symmetric matrix 
F06ZAF  14  ZGEMM Matrixmatrix product, two complex rectangular matrices 
F06ZCF  14  ZHEMM Matrixmatrix product, one complex Hermitian matrix, one complex rectangular matrix 
F06ZFF  14  ZTRMM Matrixmatrix product, one complex triangular matrix, one complex rectangular matrix 
F06ZJF  14  ZTRSM Solves system of equations with multiple righthand sides, complex triangular coefficient matrix 
F06ZPF  14  ZHERK Rankk update of a complex Hermitian matrix 
F06ZRF  14  ZHER2K Rank2k update of a complex Hermitian matrix 
F06ZTF  14  ZSYMM Matrixmatrix product, one complex symmetric matrix, one complex rectangular matrix 
F06ZUF  14  ZSYRK Rankk update of a complex symmetric matrix 
F06ZWF  14  ZSYR2K Rank2k update of a complex symmetric matrix 
Routine Name 
Mark of Introduction 
Purpose 
F07AAF  21  DGESV Computes the solution to a real system of linear equations 
F07ABF  21  DGESVX Uses the LU factorization to compute the solution, errorbound and condition estimate for a real system of linear equations 
F07ACF  22  DSGESV Mixed precision real system solver 
F07ADF  15  DGETRF LU factorization of realm by n matrix 
F07AEF  15  DGETRS Solution of real system of linear equations, multiple righthand sides, matrix already factorized by F07ADF (DGETRF) 
F07AFF  21  DGEEQU Computes row and column scalings intended to equilibrate a general real matrix and reduce its condition number 
F07AGF  15  DGECON Estimate condition number of real matrix, matrix already factorized by F07ADF (DGETRF) 
F07AHF  15  DGERFS Refined solution with error bounds of real system of linear equations, multiple righthand sides 
F07AJF  15  DGETRI Inverse of real matrix, matrix already factorized by F07ADF (DGETRF) 
F07ANF  21  ZGESV Computes the solution to a complex system of linear equations 
F07APF  21  ZGESVX Uses the LU factorization to compute the solution, errorbound and condition estimate for a complex system of linear equations 
F07AQF  22  ZCGESV Mixed precision complex system solver 
F07ARF  15  ZGETRF LU factorization of complex m by n matrix 
F07ASF  15  ZGETRS Solution of complex system of linear equations, multiple righthand sides, matrix already factorized by F07ARF (ZGETRF) 
F07ATF  21  ZGEEQU Computes row and column scalings intended to equilibrate a general complex matrix and reduce its condition number 
F07AUF  15  ZGECON Estimate condition number of complex matrix, matrix already factorized by F07ARF (ZGETRF) 
F07AVF  15  ZGERFS Refined solution with error bounds of complex system of linear equations, multiple righthand sides 
F07AWF  15  ZGETRI Inverse of complex matrix, matrix already factorized by F07ARF (ZGETRF) 
F07BAF  21  DGBSV Computes the solution to a real banded system of linear equations 
F07BBF  21  DGBSVX Uses the LU factorization to compute the solution, errorbound and condition estimate for a real banded system of linear equations 
F07BDF  15  DGBTRF LU factorization of realm by n band matrix 
F07BEF  15  DGBTRS Solution of real band system of linear equations, multiple righthand sides, matrix already factorized by F07BDF (DGBTRF) 
F07BFF  21  DGBEQU Computes row and column scalings intended to equilibrate a real banded matrix and reduce its condition number 
F07BGF  15  DGBCON Estimate condition number of real band matrix, matrix already factorized by F07BDF (DGBTRF) 
F07BHF  15  DGBRFS Refined solution with error bounds of real band system of linear equations, multiple righthand sides 
F07BNF  21  ZGBSV Computes the solution to a complex banded system of linear equations 
F07BPF  21  ZGBSVX Uses the LU factorization to compute the solution, errorbound and condition estimate for a complex banded system of linear equations 
F07BRF  15  ZGBTRF LU factorization of complex m by n band matrix 
F07BSF  15  ZGBTRS Solution of complex band system of linear equations, multiple righthand sides, matrix already factorized by F07BRF (ZGBTRF) 
F07BTF  21  ZGBEQU Computes row and column scalings intended to equilibrate a complex banded matrix and reduce its condition number 
F07BUF  15  ZGBCON Estimate condition number of complex band matrix, matrix already factorized by F07BRF (ZGBTRF) 
F07BVF  15  ZGBRFS Refined solution with error bounds of complex band system of linear equations, multiple righthand sides 
F07CAF  21  DGTSV Computes the solution to a real tridiagonal system of linear equations 
F07CBF  21  DGTSVX Uses the LU factorization to compute the solution, errorbound and condition estimate for a real tridiagonal system of linear equations 
F07CDF  21  DGTTRF LU factorization of real tridiagonal matrix 
F07CEF  21  DGTTRS Solves a real tridiagonal system of linear equations using the LU factorization computed by F07CDF (DGTTRF) 
F07CGF  21  DGTCON Estimates the reciprocal of the condition number of a real tridiagonal matrix using the LU factorization computed by F07CDF (DGTTRF) 
F07CHF  21  DGTRFS Refined solution with error bounds of real tridiagonal system of linear equations, multiple righthand sides 
F07CNF  21  ZGTSV Computes the solution to a complex tridiagonal system of linear equations 
F07CPF  21  ZGTSVX Uses the LU factorization to compute the solution, errorbound and condition estimate for a complex tridiagonal system of linear equations 
F07CRF  21  ZGTTRF LU factorization of complex tridiagonal matrix 
F07CSF  21  ZGTTRS Solves a complex tridiagonal system of linear equations using the LU factorization computed by F07CDF (DGTTRF) 
F07CUF  21  ZGTCON Estimates the reciprocal of the condition number of a complex tridiagonal matrix using the LU factorization computed by F07CDF (DGTTRF) 
F07CVF  21  ZGTRFS Refined solution with error bounds of complex tridiagonal system of linear equations, multiple righthand sides 
F07FAF  21  DPOSV Computes the solution to a real symmetric positivedefinite system of linear equations 
F07FBF  21  DPOSVX Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a real symmetric positivedefinite system of linear equations 
F07FDF  15  DPOTRF Cholesky factorization of real symmetric positivedefinite matrix 
F07FEF  15  DPOTRS Solution of real symmetric positivedefinite system of linear equations, multiple righthand sides, matrix already factorized by F07FDF (DPOTRF) 
F07FFF  21  DPOEQU Computes row and column scalings intended to equilibrate a real symmetric positivedefinite matrix and reduce its condition number 
F07FGF  15  DPOCON Estimate condition number of real symmetric positivedefinite matrix, matrix already factorized by F07FDF (DPOTRF) 
F07FHF  15  DPORFS Refined solution with error bounds of real symmetric positivedefinite system of linear equations, multiple righthand sides 
F07FJF  15  DPOTRI Inverse of real symmetric positivedefinite matrix, matrix already factorized by F07FDF (DPOTRF) 
F07FNF  21  ZPOSV Computes the solution to a complex Hermitian positivedefinite system of linear equations 
F07FPF  21  ZPOSVX Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a complex Hermitian positivedefinite system of linear equations 
F07FRF  15  ZPOTRF Cholesky factorization of complex Hermitian positivedefinite matrix 
F07FSF  15  ZPOTRS Solution of complex Hermitian positivedefinite system of linear equations, multiple righthand sides, matrix already factorized by F07FRF (ZPOTRF) 
F07FTF  21  ZPOEQU Computes row and column scalings intended to equilibrate a complex Hermitian positivedefinite matrix and reduce its condition number 
F07FUF  15  ZPOCON Estimate condition number of complex Hermitian positivedefinite matrix, matrix already factorized by F07FRF (ZPOTRF) 
F07FVF  15  ZPORFS Refined solution with error bounds of complex Hermitian positivedefinite system of linear equations, multiple righthand sides 
F07FWF  15  ZPOTRI Inverse of complex Hermitian positivedefinite matrix, matrix already factorized by F07FRF (ZPOTRF) 
F07GAF  21  DPPSV Computes the solution to a real symmetric positivedefinite system of linear equations, packed storage 
F07GBF  21  DPPSVX Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a real symmetric positivedefinite system of linear equations, packed storage 
F07GDF  15  DPPTRF Cholesky factorization of real symmetric positivedefinite matrix, packed storage 
F07GEF  15  DPPTRS Solution of real symmetric positivedefinite system of linear equations, multiple righthand sides, matrix already factorized by F07GDF (DPPTRF), packed storage 
F07GFF  21  DPPEQU Computes row and column scalings intended to equilibrate a real symmetric positivedefinite matrix and reduce its condition number, packed storage 
F07GGF  15  DPPCON Estimate condition number of real symmetric positivedefinite matrix, matrix already factorized by F07GDF (DPPTRF), packed storage 
F07GHF  15  DPPRFS Refined solution with error bounds of real symmetric positivedefinite system of linear equations, multiple righthand sides, packed storage 
F07GJF  15  DPPTRI Inverse of real symmetric positivedefinite matrix, matrix already factorized by F07GDF (DPPTRF), packed storage 
F07GNF  21  ZPPSV Computes the solution to a complex Hermitian positivedefinite system of linear equations, packed storage 
F07GPF  21  ZPPSVX Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a complex Hermitian positivedefinite system of linear equations, packed storage 
F07GRF  15  ZPPTRF Cholesky factorization of complex Hermitian positivedefinite matrix, packed storage 
F07GSF  15  ZPPTRS Solution of complex Hermitian positivedefinite system of linear equations, multiple righthand sides, matrix already factorized by F07GRF (ZPPTRF), packed storage 
F07GTF  21  ZPPEQU Computes row and column scalings intended to equilibrate a complex Hermitian positivedefinite matrix and reduce its condition number, packed storage 
F07GUF  15  ZPPCON Estimate condition number of complex Hermitian positivedefinite matrix, matrix already factorized by F07GRF (ZPPTRF), packed storage 
F07GVF  15  ZPPRFS Refined solution with error bounds of complex Hermitian positivedefinite system of linear equations, multiple righthand sides, packed storage 
F07GWF  15  ZPPTRI Inverse of complex Hermitian positivedefinite matrix, matrix already factorized by F07GRF (ZPPTRF), packed storage 
F07HAF  21  DPBSV Computes the solution to a real symmetric positivedefinite banded system of linear equations 
F07HBF  21  DPBSVX Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a real symmetric positivedefinite banded system of linear equations 
F07HDF  15  DPBTRF Cholesky factorization of real symmetric positivedefinite band matrix 
F07HEF  15  DPBTRS Solution of real symmetric positivedefinite band system of linear equations, multiple righthand sides, matrix already factorized by F07HDF (DPBTRF) 
F07HFF  21  DPBEQU Computes row and column scalings intended to equilibrate a real symmetric positivedefinite banded matrix and reduce its condition number 
F07HGF  15  DPBCON Estimate condition number of real symmetric positivedefinite band matrix, matrix already factorized by F07HDF (DPBTRF) 
F07HHF  15  DPBRFS Refined solution with error bounds of real symmetric positivedefinite band system of linear equations, multiple righthand sides 
F07HNF  21  ZPBSV Computes the solution to a complex Hermitian positivedefinite banded system of linear equations 
F07HPF  21  ZPBSVX Uses the Cholesky factorization to compute the solution, errorbound and condition estimate for a complex Hermitian positivedefinite banded system of linear equations 
F07HRF  15  ZPBTRF Cholesky factorization of complex Hermitian positivedefinite band matrix 
F07HSF  15  ZPBTRS Solution of complex Hermitian positivedefinite band system of linear equations, multiple righthand sides, matrix already factorized by F07HRF (ZPBTRF) 
F07HTF  21  ZPBEQU Computes row and column scalings intended to equilibrate a complex Hermitian positivedefinite banded matrix and reduce its condition number 
F07HUF  15  ZPBCON Estimate condition number of complex Hermitian positivedefinite band matrix, matrix already factorized by F07HRF (ZPBTRF) 
F07HVF  15  ZPBRFS Refined solution with error bounds of complex Hermitian positivedefinite band system of linear equations, multiple righthand sides 
F07JAF  21  DPTSV Computes the solution to a real symmetric positivedefinite tridiagonal system of linear equations 
F07JBF  21  DPTSVX Uses the modified Cholesky factorization to compute the solution, errorbound and condition estimate for a real symmetric positivedefinite tridiagonal system of linear equations 
F07JDF  21  DPTTRF Computes the modified Cholesky factorization of a real symmetric positivedefinite tridiagonal matrix 
F07JEF  21  DPTTRS Solves a real symmetric positivedefinite tridiagonal system using the modified Cholesky factorization computed by F07JDF (DPTTRF) 
F07JGF  21  DPTCON Computes the reciprocal of the condition number of a real symmetric positivedefinite tridiagonal system using the modified Cholesky factorization computed by F07JDF (DPTTRF) 
F07JHF  21  DPTRFS Refined solution with error bounds of real symmetric positivedefinite tridiagonal system of linear equations, multiple righthand sides 
F07JNF  21  ZPTSV Computes the solution to a complex Hermitian positivedefinite tridiagonal system of linear equations 
F07JPF  21  ZPTSVX Uses the modified Cholesky factorization to compute the solution, errorbound and condition estimate for a complex Hermitian positivedefinite tridiagonal system of linear equations 
F07JRF  21  ZPTTRF Computes the modified Cholesky factorization of a complex Hermitian positivedefinite tridiagonal matrix 
F07JSF  21  ZPTTRS Solves a complex Hermitian positivedefinite tridiagonal system using the modified Cholesky factorization computed by F07JRF (ZPTTRF) 
F07JUF  21  ZPTCON Computes the reciprocal of the condition number of a complex Hermitian positivedefinite tridiagonal system using the modified Cholesky factorization computed by F07JRF (ZPTTRF) 
F07JVF  21  ZPTRFS Refined solution with error bounds of complex Hermitian positivedefinite tridiagonal system of linear equations, multiple righthand sides 
F07MAF  21  DSYSV Computes the solution to a real symmetric system of linear equations 
F07MBF  21  DSYSVX Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations 
F07MDF  15  DSYTRF Bunch–Kaufman factorization of real symmetric indefinite matrix 
F07MEF  15  DSYTRS Solution of real symmetric indefinite system of linear equations, multiple righthand sides, matrix already factorized by F07MDF (DSYTRF) 
F07MGF  15  DSYCON Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF (DSYTRF) 
F07MHF  15  DSYRFS Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple righthand sides 
F07MJF  15  DSYTRI Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF (DSYTRF) 
F07MNF  21  ZHESV Computes the solution to a complex Hermitian system of linear equations 
F07MPF  21  ZHESVX Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations 
F07MRF  15  ZHETRF Bunch–Kaufman factorization of complex Hermitian indefinite matrix 
F07MSF  15  ZHETRS Solution of complex Hermitian indefinite system of linear equations, multiple righthand sides, matrix already factorized by F07MRF (ZHETRF) 
F07MUF  15  ZHECON Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF (ZHETRF) 
F07MVF  15  ZHERFS Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple righthand sides 
F07MWF  15  ZHETRI Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07MRF (ZHETRF) 
F07NNF  21  ZSYSV Computes the solution to a complex symmetric system of linear equations 
F07NPF  21  ZSYSVX Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations 
F07NRF  15  ZSYTRF Bunch–Kaufman factorization of complex symmetric matrix 
F07NSF  15  ZSYTRS Solution of complex symmetric system of linear equations, multiple righthand sides, matrix already factorized by F07NRF (ZSYTRF) 
F07NUF  15  ZSYCON Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF (ZSYTRF) 
F07NVF  15  ZSYRFS Refined solution with error bounds of complex symmetric system of linear equations, multiple righthand sides 
F07NWF  15  ZSYTRI Inverse of complex symmetric matrix, matrix already factorized by F07NRF (ZSYTRF) 
F07PAF  21  DSPSV Computes the solution to a real symmetric system of linear equations, packed storage 
F07PBF  21  DSPSVX Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage 
F07PDF  15  DSPTRF Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage 
F07PEF  15  DSPTRS Solution of real symmetric indefinite system of linear equations, multiple righthand sides, matrix already factorized by F07PDF (DSPTRF), packed storage 
F07PGF  15  DSPCON Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF (DSPTRF), packed storage 
F07PHF  15  DSPRFS Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple righthand sides, packed storage 
F07PJF  15  DSPTRI Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF (DSPTRF), packed storage 
F07PNF  21  ZHPSV Computes the solution to a complex Hermitian system of linear equations, packed storage 
F07PPF  21  ZHPSVX Uses the diagonal pivoting factorization to compute the solution to a complex Hermitian system of linear equations, packed storage 
F07PRF  15  ZHPTRF Bunch–Kaufman factorization of complex Hermitian indefinite matrix, packed storage 
F07PSF  15  ZHPTRS Solution of complex Hermitian indefinite system of linear equations, multiple righthand sides, matrix already factorized by F07PRF (ZHPTRF), packed storage 
F07PUF  15  ZHPCON Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF (ZHPTRF), packed storage 
F07PVF  15  ZHPRFS Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple righthand sides, packed storage 
F07PWF  15  ZHPTRI Inverse of complex Hermitian indefinite matrix, matrix already factorized by F07PRF (ZHPTRF), packed storage 
F07QNF  21  ZSPSV Computes the solution to a complex symmetric system of linear equations, packed storage 
F07QPF  21  ZSPSVX Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations, packed storage 
F07QRF  15  ZSPTRF Bunch–Kaufman factorization of complex symmetric matrix, packed storage 
F07QSF  15  ZSPTRS Solution of complex symmetric system of linear equations, multiple righthand sides, matrix already factorized by F07QRF (ZSPTRF), packed storage 
F07QUF  15  ZSPCON Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF (ZSPTRF), packed storage 
F07QVF  15  ZSPRFS Refined solution with error bounds of complex symmetric system of linear equations, multiple righthand sides, packed storage 
F07QWF  15  ZSPTRI Inverse of complex symmetric matrix, matrix already factorized by F07QRF (ZSPTRF), packed storage 
F07TEF  15  DTRTRS Solution of real triangular system of linear equations, multiple righthand sides 
F07TGF  15  DTRCON Estimate condition number of real triangular matrix 
F07THF  15  DTRRFS Error bounds for solution of real triangular system of linear equations, multiple righthand sides 
F07TJF  15  DTRTRI Inverse of real triangular matrix 
F07TSF  15  ZTRTRS Solution of complex triangular system of linear equations, multiple righthand sides 
F07TUF  15  ZTRCON Estimate condition number of complex triangular matrix 
F07TVF  15  ZTRRFS Error bounds for solution of complex triangular system of linear equations, multiple righthand sides 
F07TWF  15  ZTRTRI Inverse of complex triangular matrix 
F07UEF  15  DTPTRS Solution of real triangular system of linear equations, multiple righthand sides, packed storage 
F07UGF  15  DTPCON Estimate condition number of real triangular matrix, packed storage 
F07UHF  15  DTPRFS Error bounds for solution of real triangular system of linear equations, multiple righthand sides, packed storage 
F07UJF  15  DTPTRI Inverse of real triangular matrix, packed storage 
F07USF  15  ZTPTRS Solution of complex triangular system of linear equations, multiple righthand sides, packed storage 
F07UUF  15  ZTPCON Estimate condition number of complex triangular matrix, packed storage 
F07UVF  15  ZTPRFS Error bounds for solution of complex triangular system of linear equations, multiple righthand sides, packed storage 
F07UWF  15  ZTPTRI Inverse of complex triangular matrix, packed storage 
F07VEF  15  DTBTRS Solution of real band triangular system of linear equations, multiple righthand sides 
F07VGF  15  DTBCON Estimate condition number of real band triangular matrix 
F07VHF  15  DTBRFS Error bounds for solution of real band triangular system of linear equations, multiple righthand sides 
F07VSF  15  ZTBTRS Solution of complex band triangular system of linear equations, multiple righthand sides 
F07VUF  15  ZTBCON Estimate condition number of complex band triangular matrix 
F07VVF  15  ZTBRFS Error bounds for solution of complex band triangular system of linear equations, multiple righthand sides 
Routine Name 
Mark of Introduction 
Purpose 
F08AAF  21  DGELS Solves an overdetermined or underdetermined real linear system 
F08AEF  16  DGEQRF QR factorization of real general rectangular matrix 
F08AFF  16  DORGQR Form all or part of orthogonal Q from QR factorization determined by F08AEF (DGEQRF) or F08BEF (DGEQPF) 
F08AGF  16  DORMQR Apply orthogonal transformation determined by F08AEF (DGEQRF) or F08BEF (DGEQPF) 
F08AHF  16  DGELQF LQ factorization of real general rectangular matrix 
F08AJF  16  DORGLQ Form all or part of orthogonal Q from LQ factorization determined by F08AHF (DGELQF) 
F08AKF  16  DORMLQ Apply orthogonal transformation determined by F08AHF (DGELQF) 
F08ANF  21  ZGELS Solves an overdetermined or underdetermined complex linear system 
F08ASF  16  ZGEQRF QR factorization of complex general rectangular matrix 
F08ATF  16  ZUNGQR Form all or part of unitary Q from QR factorization determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF) 
F08AUF  16  ZUNMQR Apply unitary transformation determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF) 
F08AVF  16  ZGELQF LQ factorization of complex general rectangular matrix 
F08AWF  16  ZUNGLQ Form all or part of unitary Q from LQ factorization determined by F08AVF (ZGELQF) 
F08AXF  16  ZUNMLQ Apply unitary transformation determined by F08AVF (ZGELQF) 
F08BAF  21  DGELSY Computes the minimumnorm solution to a real linear leastsquares problem 
F08BEF  16  DGEQPF QR factorization of real general rectangular matrix with column pivoting 
F08BFF  21  DGEQP3 QR factorization of real general rectangular matrix with column pivoting, using BLAS3 
F08BHF  21  DTZRZF Reduces a real upper trapezoidal matrix to upper triangular form 
F08BKF  21  DORMRZ Apply orthogonal transformation determined by F08BHF (DTZRZF) 
F08BNF  21  ZGELSY Computes the minimumnorm solution to a complex linear leastsquares problem 
F08BSF  16  ZGEQPF QR factorization of complex general rectangular matrix with column pivoting 
F08BTF  21  ZGEQP3 QR factorization of complex general rectangular matrix with column pivoting, using BLAS3 
F08BVF  21  ZTZRZF Reduces a complex upper trapezoidal matrix to upper triangular form 
F08BXF  21  ZUNMRZ Apply unitary transformation determined by F08BVF (ZTZRZF) 
F08CEF  21  DGEQLF QL factorization of real general rectangular matrix 
F08CFF  21  DORGQL Form all or part of orthogonal Q from QL factorization determined by F08CEF (DGEQLF) 
F08CGF  21  DORMQL Apply orthogonal transformation determined by F08CEF (DGEQLF) 
F08CHF  21  DGERQF RQ factorization of real general rectangular matrix 
F08CJF  21  DORGRQ Form all or part of orthogonal Q from RQ factorization determined by F08CHF (DGERQF) 
F08CKF  21  DORMRQ Apply orthogonal transformation determined by F08CHF (DGERQF) 
F08CSF  21  ZGEQLF QL factorization of complex general rectangular matrix 
F08CTF  21  ZUNGQL Form all or part of orthogonal Q from QL factorization determined by F08CSF (ZGEQLF) 
F08CUF  21  ZUNMQL Apply unitary transformation determined by F08CSF (ZGEQLF) 
F08CVF  21  ZGERQF RQ factorization of complex general rectangular matrix 
F08CWF  21  ZUNGRQ Form all or part of orthogonal Q from RQ factorization determined by F08CVF (ZGERQF) 
F08CXF  21  ZUNMRQ Apply unitary transformation determined by F08CVF (ZGERQF) 
F08FAF  21  DSYEV Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix 
F08FBF  21  DSYEVX Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix 
F08FCF  19  DSYEVD Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divideandconquer) 
F08FDF  21  DSYEVR Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) 
F08FEF  16  DSYTRD Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form 
F08FFF  16  DORGTR Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD) 
F08FGF  16  DORMTR Apply orthogonal transformation determined by F08FEF (DSYTRD) 
F08FLF  21  DDISNA 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  21  ZHEEV Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix 
F08FPF  21  ZHEEVX Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix 
F08FQF  19  ZHEEVD Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divideandconquer) 
F08FRF  21  ZHEEVR Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) 
F08FSF  16  ZHETRD Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form 
F08FTF  16  ZUNGTR Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD) 
F08FUF  16  ZUNMTR Apply unitary transformation matrix determined by F08FSF (ZHETRD) 
F08GAF  21  DSPEV Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage 
F08GBF  21  DSPEVX Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage 
F08GCF  19  DSPEVD Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divideandconquer) 
F08GEF  16  DSPTRD Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage 
F08GFF  16  DOPGTR Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD) 
F08GGF  16  DOPMTR Apply orthogonal transformation determined by F08GEF (DSPTRD) 
F08GNF  21  ZHPEV Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage 
F08GPF  21  ZHPEVX Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage 
F08GQF  19  ZHPEVD Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divideandconquer) 
F08GSF  16  ZHPTRD Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage 
F08GTF  16  ZUPGTR Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD) 
F08GUF  16  ZUPMTR Apply unitary transformation matrix determined by F08GSF (ZHPTRD) 
F08HAF  21  DSBEV Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix 
F08HBF  21  DSBEVX Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix 
F08HCF  19  DSBEVD Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divideandconquer) 
F08HEF  16  DSBTRD Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form 
F08HNF  21  ZHBEV Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix 
F08HPF  21  ZHBEVX Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix 
F08HQF  19  ZHBEVD Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divideandconquer) 
F08HSF  16  ZHBTRD Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form 
F08JAF  21  DSTEV Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix 
F08JBF  21  DSTEVX Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix 
F08JCF  19  DSTEVD Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divideandconquer) 
F08JDF  21  DSTEVR Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations) 
F08JEF  16  DSTEQR All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm 
F08JFF  16  DSTERF All eigenvalues of real symmetric tridiagonal matrix, rootfree variant of the QL or QR algorithm 
F08JGF  16  DPTEQR Computes all eigenvalues and eigenvectors of real symmetric positivedefinite tridiagonal matrix, reduced from real symmetric positivedefinite matrix 
F08JHF  21  DSTEDC Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divideandconquer) 
F08JJF  16  DSTEBZ Selected eigenvalues of real symmetric tridiagonal matrix by bisection 
F08JKF  16  DSTEIN Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array 
F08JLF  21  DSTEGR Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations) 
F08JSF  16  ZSTEQR All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm 
F08JUF  16  ZPTEQR Computes all eigenvalues and eigenvectors of real symmetric positivedefinite tridiagonal matrix, reduced from complex Hermitian positivedefinite matrix 
F08JVF  21  ZSTEDC Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divideandconquer) 
F08JXF  16  ZSTEIN Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array 
F08JYF  21  ZSTEGR 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  21  DGELSS Computes the minimumnorm solution to a real linear leastsquares problem using singular value decomposition 
F08KBF  21  DGESVD Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors 
F08KCF  21  DGELSD Computes the minimumnorm solution to a real linear leastsquares problem using singular value decomposition (divideandconquer) 
F08KDF  21  DGESDD Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divideandconquer) 
F08KEF  16  DGEBRD Orthogonal reduction of real general rectangular matrix to bidiagonal form 
F08KFF  16  DORGBR Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD) 
F08KGF  16  DORMBR Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD) 
F08KNF  21  ZGELSS Computes the minimumnorm solution to a complex linear leastsquares problem using singular value decomposition 
F08KPF  21  ZGESVD Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors 
F08KQF  21  ZGELSD Computes the minimumnorm solution to a complex linear leastsquares problem using singular value decomposition (divideandconquer) 
F08KRF  21  ZGESDD Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divideandconquer) 
F08KSF  16  ZGEBRD Unitary reduction of complex general rectangular matrix to bidiagonal form 
F08KTF  16  ZUNGBR Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD) 
F08KUF  16  ZUNMBR Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD) 
F08LEF  19  DGBBRD Reduction of real rectangular band matrix to upper bidiagonal form 
F08LSF  19  ZGBBRD Reduction of complex rectangular band matrix to upper bidiagonal form 
F08MDF  21  DBDSDC Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divideandconquer) 
F08MEF  16  DBDSQR SVD of real bidiagonal matrix reduced from real general matrix 
F08MSF  16  ZBDSQR SVD of real bidiagonal matrix reduced from complex general matrix 
F08NAF  21  DGEEV Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix 
F08NBF  21  DGEEVX 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  16  DGEHRD Orthogonal reduction of real general matrix to upper Hessenberg form 
F08NFF  16  DORGHR Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) 
F08NGF  16  DORMHR Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) 
F08NHF  16  DGEBAL Balance real general matrix 
F08NJF  16  DGEBAK Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (DGEBAL) 
F08NNF  21  ZGEEV Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix 
F08NPF  21  ZGEEVX 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  16  ZGEHRD Unitary reduction of complex general matrix to upper Hessenberg form 
F08NTF  16  ZUNGHR Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) 
F08NUF  16  ZUNMHR Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) 
F08NVF  16  ZGEBAL Balance complex general matrix 
F08NWF  16  ZGEBAK Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (ZGEBAL) 
F08PAF  21  DGEES Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors 
F08PBF  21  DGEESX 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  16  DHSEQR Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix 
F08PKF  16  DHSEIN Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration 
F08PNF  21  ZGEES Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors 
F08PPF  21  ZGEESX 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  16  ZHSEQR Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix 
F08PXF  16  ZHSEIN Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration 
F08QFF  16  DTREXC Reorder Schur factorization of real matrix using orthogonal similarity transformation 
F08QGF  16  DTRSEN Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities 
F08QHF  16  DTRSYL Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasitriangular or transposes 
F08QKF  16  DTREVC Left and right eigenvectors of real upper quasitriangular matrix 
F08QLF  16  DTRSNA Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasitriangular matrix 
F08QTF  16  ZTREXC Reorder Schur factorization of complex matrix using unitary similarity transformation 
F08QUF  16  ZTRSEN Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities 
F08QVF  16  ZTRSYL Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugatetransposes 
F08QXF  16  ZTREVC Left and right eigenvectors of complex upper triangular matrix 
F08QYF  16  ZTRSNA Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix 
F08SAF  21  DSYGV Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem 
F08SBF  21  DSYGVX Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem 
F08SCF  21  DSYGVD Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem (divideandconquer) 
F08SEF  16  DSYGST Reduction to standard form of real symmetricdefinite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, B factorized by F07FDF (DPOTRF) 
F08SNF  21  ZHEGV Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem 
F08SPF  21  ZHEGVX Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem 
F08SQF  21  ZHEGVD Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem (divideandconquer) 
F08SSF  16  ZHEGST Reduction to standard form of complex Hermitiandefinite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, B factorized by F07FRF (ZPOTRF) 
F08TAF  21  DSPGV Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem, packed storage 
F08TBF  21  DSPGVX Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem, packed storage 
F08TCF  21  DSPGVD Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite eigenproblem, packed storage (divideandconquer) 
F08TEF  16  DSPGST Reduction to standard form of real symmetricdefinite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, packed storage, B factorized by F07GDF (DPPTRF) 
F08TNF  21  ZHPGV Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem, packed storage 
F08TPF  21  ZHPGVX Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem, packed storage 
F08TQF  21  ZHPGVD Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem, packed storage (divideandconquer) 
F08TSF  16  ZHPGST Reduction to standard form of complex Hermitiandefinite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, packed storage, B factorized by F07GRF (ZPPTRF) 
F08UAF  21  DSBGV Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetricdefinite eigenproblem 
F08UBF  21  DSBGVX Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetricdefinite eigenproblem 
F08UCF  21  DSBGVD Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetricdefinite eigenproblem (divideandconquer) 
F08UEF  19  DSBGST Reduction of real symmetricdefinite banded generalized eigenproblem Ax = λBx to standard form Cy = λy, such that C has the same bandwidth as A 
F08UFF  19  DPBSTF Computes a split Cholesky factorization of real symmetric positivedefinite band matrix A 
F08UNF  21  ZHBGV Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitiandefinite eigenproblem 
F08UPF  21  ZHBGVX Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitiandefinite eigenproblem 
F08UQF  21  ZHBGVD Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitiandefinite eigenproblem (divideandconquer) 
F08USF  19  ZHBGST Reduction of complex Hermitiandefinite banded generalized eigenproblem Ax = λBx to standard form Cy = λy, such that C has the same bandwidth as A 
F08UTF  19  ZPBSTF Computes a split Cholesky factorization of complex Hermitian positivedefinite band matrix A 
F08VAF  21  DGGSVD Computes the generalized singular value decomposition of a real matrix pair 
F08VEF  21  DGGSVP Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair 
F08VNF  21  ZGGSVD Computes the generalized singular value decomposition of a complex matrix pair 
F08VSF  21  ZGGSVP Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair 
F08WAF  21  DGGEV Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors 
F08WBF  21  DGGEVX 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  20  DGGHRD Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form 
F08WHF  20  DGGBAL Balance a pair of real general matrices 
F08WJF  20  DGGBAK Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF (DGGBAL) 
F08WNF  21  ZGGEV Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors 
F08WPF  21  ZGGEVX 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  20  ZGGHRD Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form 
F08WVF  20  ZGGBAL Balance a pair of complex general matrices 
F08WWF  20  ZGGBAK Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF (ZGGBAL) 
F08XAF  21  DGGES Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors 
F08XBF  21  DGGESX 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  20  DHGEQZ Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices 
F08XNF  21  ZGGES Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors 
F08XPF  21  ZGGESX 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  20  ZHGEQZ Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices 
F08YEF  21  DTGSJA Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair 
F08YFF  21  DTGEXC Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation 
F08YGF  21  DTGSEN 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  21  DTGSYL Solves the realvalued generalized Sylvester equation 
F08YKF  20  DTGEVC Left and right eigenvectors of a pair of real upper quasitriangular matrices 
F08YLF  21  DTGSNA Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form 
F08YSF  21  ZTGSJA Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair 
F08YTF  21  ZTGEXC Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation 
F08YUF  21  ZTGSEN 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  21  ZTGSYL Solves the complex generalized Sylvester equation 
F08YXF  20  ZTGEVC Left and right eigenvectors of a pair of complex upper triangular matrices 
F08YYF  21  ZTGSNA Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form 
F08ZAF  21  DGGLSE Solves the real linear equalityconstrained leastsquares (LSE) problem 
F08ZBF  21  DGGGLM Solves a real general Gauss–Markov linear model (GLM) problem 
F08ZEF  21  DGGQRF Computes a generalized QR factorization of a real matrix pair 
F08ZFF  21  DGGRQF Computes a generalized RQ factorization of a real matrix pair 
F08ZNF  21  ZGGLSE Solves the complex linear equalityconstrained leastsquares (LSE) problem 
F08ZPF  21  ZGGGLM Solves a complex general Gauss–Markov linear model (GLM) problem 
F08ZSF  21  ZGGQRF Computes a generalized QR factorization of a complex matrix pair 
F08ZTF  21  ZGGRQF Computes a generalized RQ 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, BiCGSTAB or TFQMR method 
F11BFF  19  Real sparse nonsymmetric linear systems, diagnostic for F11BEF 
F11BRF  19  Complex sparse nonHermitian linear systems, setup for F11BSF 
F11BSF  19  Complex sparse nonHermitian linear systems, preconditioned RGMRES, CGS, BiCGSTAB or TFQMR method 
F11BTF  19  Complex sparse nonHermitian linear systems, diagnostic for F11BSF 
F11DAF  18  Real sparse nonsymmetric linear systems, incomplete LU factorization 
F11DBF  18  Solution of linear system involving incomplete LU preconditioning matrix generated by F11DAF 
F11DCF  18  Solution of real sparse nonsymmetric linear system, RGMRES, CGS, BiCGSTAB 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, BiCGSTAB, or TFQMR method, Jacobi or SSOR preconditioner (Black Box) 
F11DKF  20  Real sparse nonsymmetric linear systems, line Jacobi preconditioner 
F11DNF  19  Complex sparse nonHermitian linear systems, incomplete LU factorization 
F11DPF  19  Solution of complex linear system involving incomplete LU preconditioning matrix generated by F11DNF 
F11DQF  19  Solution of complex sparse nonHermitian linear system, RGMRES, CGS, BiCGSTAB 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 nonHermitian matrix 
F11DSF  19  Solution of complex sparse nonHermitian linear system, RGMRES, CGS, BiCGSTAB 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  LU 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 righthand sides 
F11MKF  21  Real sparse nonsymmetric matrixmatrix multiply, compressed column storage 
F11MLF  21  1norm, ∞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 nonHermitian 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 nonHermitian 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 F12APF) 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 F12FBF) 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 
F16DLF  22  Sum elements of integer vector 
F16DNF  22  Maximum value and location, integer vector 
F16DPF  22  Minimum value and location, integer vector 
F16DQF  22  Maximum absolute value and location, integer vector 
F16DRF  22  Minimum absolute value and location, integer vector 
F16EHF  22  BLAS_DWAXPBY Real scaled vector addition preserving input 
F16ELF  22  BLAS_DSUM Sum elements of real vector 
F16GHF  22  BLAS_ZWAXPBY Complex scaled vector addition preserving input 
F16GLF  22  BLAS_ZSUM Sum elements of complex vector 
F16JNF  22  BLAS_DMAX_VAL Maximum value and location, real vector 
F16JPF  22  BLAS_DMIN_VAL Minimum value and location, real vector 
F16JQF  22  BLAS_DAMAX_VAL Maximum absolute value and location, real vector 
F16JRF  22  BLAS_DAMIN_VAL Minimum absolute value and location, real vector 
F16JSF  22  BLAS_ZAMAX_VAL Maximum absolute value and location, complex vector 
F16JTF  22  BLAS_ZAMIN_VAL Minimum absolute value and location, complex vector 
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  Twoway 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 fivepoint summary (median, hinges and extremes) 
G01AMF  22  Find quantiles of an unordered vector, real numbers 
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 variancecovariance 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 tdistribution 
G01ECF  14  Computes probabilities for χ^{2} distribution 
G01EDF  14  Computes probabilities for Fdistribution 
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 onesample Kolmogorov–Smirnov distribution 
G01EZF  14  Computes probabilities for the twosample Kolmogorov–Smirnov distribution 
G01FAF  15  Computes deviates for the standard Normal distribution 
G01FBF  14  Computes deviates for Student's tdistribution 
G01FCF  14  Computes deviates for the χ^{2} distribution 
G01FDF  14  Computes deviates for the Fdistribution 
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 noncentral Student's tdistribution 
G01GCF  14  Computes probabilities for the noncentral χ^{2} distribution 
G01GDF  14  Computes probabilities for the noncentral Fdistribution 
G01GEF  14  Computes probabilities for the noncentral 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 
G02AAF  22  Computes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun 
G02BAF  4  Pearson productmoment correlation coefficients, all variables, no missing values 
G02BBF  4  Pearson productmoment correlation coefficients, all variables, casewise treatment of missing values 
G02BCF  4  Pearson productmoment correlation coefficients, all variables, pairwise treatment of missing values 
G02BDF  4  Correlationlike coefficients (about zero), all variables, no missing values 
G02BEF  4  Correlationlike coefficients (about zero), all variables, casewise treatment of missing values 
G02BFF  4  Correlationlike coefficients (about zero), all variables, pairwise treatment of missing values 
G02BGF  4  Pearson productmoment correlation coefficients, subset of variables, no missing values 
G02BHF  4  Pearson productmoment correlation coefficients, subset of variables, casewise treatment of missing values 
G02BJF  4  Pearson productmoment correlation coefficients, subset of variables, pairwise treatment of missing values 
G02BKF  4  Correlationlike coefficients (about zero), subset of variables, no missing values 
G02BLF  4  Correlationlike coefficients (about zero), subset of variables, casewise treatment of missing values 
G02BMF  4  Correlationlike coefficients (about zero), subset of variables, pairwise treatment of missing values 
G02BNF  4  Kendall/Spearman nonparametric rank correlation coefficients, no missing values, overwriting input data 
G02BPF  4  Kendall/Spearman nonparametric rank correlation coefficients, casewise treatment of missing values, overwriting input data 
G02BQF  4  Kendall/Spearman nonparametric rank correlation coefficients, no missing values, preserving input data 
G02BRF  4  Kendall/Spearman nonparametric rank correlation coefficients, casewise treatment of missing values, preserving input data 
G02BSF  4  Kendall/Spearman nonparametric 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/variancecovariance matrix from correlation/variancecovariance 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, reorder elements of vectors and matrices 
G02CGF  4  Multiple linear regression, from correlation coefficients, with constant term 
G02CHF  4  Multiple linear regression, from correlationlike 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 
G02GPF  22  Computes a predicted value and its associated standard error based on a previously fitted generalized linear model. 
G02HAF  13  Robust regression, standard Mestimates 
G02HBF  13  Robust regression, compute weights for use with G02HDF 
G02HDF  13  Robust regression, compute regression with usersupplied functions and weights 
G02HFF  13  Robust regression, variancecovariance 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, usersupplied weight function plus derivatives 
G02HMF  14  Calculates a robust estimation of a correlation matrix, usersupplied weight function 
G02JAF  21  Linear mixed effects regression using Restricted Maximum Likelihood (REML) 
G02JBF  21  Linear mixed effects regression using Maximum Likelihood (ML) 
G02KAF  22  Ridge regression, optimizing a ridge regression parameter 
G02KBF  22  Ridge regression using a number of supplied ridge regression parameters 
G02LAF  22  Partial leastsquares (PLS) regression using singular value decomposition 
G02LBF  22  Partial leastsquares (PLS) regression using Wold's iterative method 
G02LCF  22  PLS parameter estimates following partial leastsquares regression by G02LAF or G02LBF 
G02LDF  22  PLS predictions based on parameter estimates from G02LCF 
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 
G03BDF  22  ProMax 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 withingroup covariance matrices and matrices for discriminant analysis 
G03DBF  15  Computes Mahalanobis squared distances for group or pooled variancecovariance 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  Kmeans cluster analysis 
G03EHF  16  Constructs dendrogram (for use after G03ECF) 
G03EJF  16  Computes cluster indicator variable (for use after G03ECF) 
G03FAF  17  Performs principal coordinate analysis, classical metric scaling 
G03FCF  17  Performs nonmetric (ordinal) multidimensional scaling 
G03ZAF  15  Produces standardized values (zscores) for a data matrix 
Routine Name 
Mark of Introduction 
Purpose 
G04AGF  8  Twoway 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} Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05HLF  20  Univariate time series, generate n terms of a GARCH process with asymmetry of the form (ε_{t  1} + γε_{t  1})^{2} Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05HMF  20  Univariate time series, generate n terms of an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05HNF  20  Univariate time series, generate n terms of an exponential GARCH (EGARCH) process Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05KAF  20  Pseudorandom real numbers, uniform distribution over (0,1), seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05KBF  20  Initialize seeds of a given generator for random number generating routines (that pass seeds explicitly) to give a repeatable
sequence Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05KCF  20  Initialize seeds of a given generator for random number generating routines (that pass seeds expicitly) to give nonrepeatable
sequence Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05KEF  20  Pseudorandom logical (boolean) value, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05KFF  22  Initializes a pseudorandom number generator to give a repeatable sequence 
G05KGF  22  Initializes a pseudorandom number generator to give a nonrepeatable sequence 
G05KHF  22  Primes a pseudorandom number generator for generating multiple streams using leapfrog 
G05KJF  22  Primes a pseudorandom number generator for generating multiple streams using skipahead 
G05LAF  20  Generates a vector of random numbers from a Normal distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LBF  20  Generates a vector of random numbers from a Student's tdistribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LCF  20  Generates a vector of random numbers from a χ^{2} distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LDF  20  Generates a vector of random numbers from an Fdistribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LEF  20  Generates a vector of random numbers from a β distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LFF  20  Generates a vector of random numbers from a γ distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LGF  20  Generates a vector of random numbers from a uniform distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LHF  20  Generates a vector of random numbers from a triangular distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LJF  20  Generates a vector of random numbers from an exponential distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LKF  20  Generates a vector of random numbers from a lognormal distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LLF  20  Generates a vector of random numbers from a Cauchy distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LMF  20  Generates a vector of random numbers from a Weibull distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LNF  20  Generates a vector of random numbers from a logistic distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LPF  20  Generates a vector of random numbers from a von Mises distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LQF  20  Generates a vector of random numbers from an exponential mixture distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LXF  21  Generates a matrix of random numbers from a multivariate Student's tdistribution, seeds and generator passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LYF  21  Generates a matrix of random numbers from a multivariate Normal distribution, seeds and generator passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05LZF  20  Generates a vector of random numbers from a multivariate Normal distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05MAF  20  Generates a vector of random integers from a uniform distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05MBF  20  Generates a vector of random integers from a geometric distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05MCF  20  Generates a vector of random integers from a negative binomial distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05MDF  20  Generates a vector of random integers from a logarithmic distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05MEF  20  Generates a vector of random integers from a Poisson distribution with varying mean, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05MJF  20  Generates a vector of random integers from a binomial distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05MKF  20  Generates a vector of random integers from a Poisson distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05MLF  20  Generates a vector of random integers from a hypergeometric distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05MRF  20  Generates a vector of random integers from a multinomial distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05MZF  20  Generates a vector of random integers from a general discrete distribution, seeds and generator number passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05NAF  20  Pseudorandom permutation of an integer vector Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05NBF  20  Pseudorandom sample from an integer vector Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05NCF  22  Pseudorandom permutation of an integer vector 
G05NDF  22  Pseudorandom sample from an integer vector 
G05PAF  20  Generates a realization of a time series from an ARMA model Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05PCF  20  Generates a realization of a multivariate time series from a VARMA model Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05PDF  22  Generates a realization of a time series from a GARCH process with asymmetry of the form (ε_{t  1} + γ)^{2} 
G05PEF  22  Generates a realization of a time series from a GARCH process with asymmetry of the form (ε_{t  1} + γε_{t  1})^{2} 
G05PFF  22  Generates a realization of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process 
G05PGF  22  Generates a realization of a time series from an exponential GARCH (EGARCH) process 
G05PHF  22  Generates a realization of a time series from an ARMA model 
G05PJF  22  Generates a realization of a multivariate time series from a VARMA model 
G05PMF  22  Generates a realization of a time series from an exponential smoothing model 
G05PXF  22  Generates a random orthogonal matrix 
G05PYF  22  Generates a random correlation matrix 
G05PZF  22  Generates a random twoway table 
G05QAF  20  Computes a random orthogonal matrix Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05QBF  20  Computes a random correlation matrix Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05QDF  20  Generates a random table matrix Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05RAF  21  Generates a matrix of random numbers from a Gaussian copula, seeds and generator passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05RBF  21  Generates a matrix of random numbers from a Student's tcopula, seeds and generator passed explicitly Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05RCF  22  Generates a matrix of pseudorandom numbers from a Student's tcopula 
G05RDF  22  Generates a matrix of pseudorandom numbers from a Gaussian copula 
G05RYF  22  Generates a matrix of pseudorandom numbers from a multivariate Student's tdistribution 
G05RZF  22  Generates a matrix of pseudorandom numbers from a multivariate Normal distribution 
G05SAF  22  Generates a vector of pseudorandom numbers from a uniform distribution over (0,1] 
G05SBF  22  Generates a vector of pseudorandom numbers from a beta distribution 
G05SCF  22  Generates a vector of pseudorandom numbers from a Cauchy distribution 
G05SDF  22  Generates a vector of pseudorandom numbers from a χ^{2} distribution 
G05SEF  22  Generates a vector of pseudorandom numbers from a Dirichlet distribution 
G05SFF  22  Generates a vector of pseudorandom numbers from an exponential distribution 
G05SGF  22  Generates a vector of pseudorandom numbers from an exponential mix distribution 
G05SHF  22  Generates a vector of pseudorandom numbers from an Fdistribution 
G05SJF  22  Generates a vector of pseudorandom numbers from a gamma distribution 
G05SKF  22  Generates a vector of pseudorandom numbers from a Normal distribution 
G05SLF  22  Generates a vector of pseudorandom numbers from a logistic distribution 
G05SMF  22  Generates a vector of pseudorandom numbers from a lognormal distribution 
G05SNF  22  Generates a vector of pseudorandom numbers from a Student's tdistribution 
G05SPF  22  Generates a vector of pseudorandom numbers from a triangular distribution 
G05SQF  22  Generates a vector of pseudorandom numbers from a uniform distribution over [a,b] 
G05SRF  22  Generates a vector of pseudorandom numbers from a von Mises distribution 
G05SSF  22  Generates a vector of pseudorandom numbers from a Weibull distribution 
G05TAF  22  Generates a vector of pseudorandom integers from a binomial distribution 
G05TBF  22  Generates a vector of pseudorandom logical values 
G05TCF  22  Generates a vector of pseudorandom integers from a geometric distribution 
G05TDF  22  Generates a vector of pseudorandom integers from a general discrete distribution 
G05TEF  22  Generates a vector of pseudorandom integers from a hypergeometric distribution 
G05TFF  22  Generates a vector of pseudorandom integers from a logarithmic distribution 
G05TGF  22  Generates a vector of pseudorandom integers from a multinomial distribution 
G05THF  22  Generates a vector of pseudorandom integers from a negative binomial distribution 
G05TJF  22  Generates a vector of pseudorandom integers from a Poisson distribution 
G05TKF  22  Generates a vector of pseudorandom integers from a Poisson distribution with varying mean 
G05TLF  22  Generates a vector of pseudorandom integers from a uniform distribution 
G05YAF  20  Multidimensional quasirandom number generator with a uniform probability distribution Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05YBF  20  Multidimensional quasirandom number generator with a Gaussian or lognormal probability distribution Note: this routine is scheduled for withdrawal at Mark 23, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05YCF  21  Initializes the Faure generator (G05YDF/G05YJF/G05YKF) Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05YDF  21  Generates a sequence of quasirandom numbers using Faure's method Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05YEF  21  Initializes the Sobol generator (G05YFF/G05YJF/G05YKF) Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05YFF  21  Generates a sequence of quasirandom numbers using Sobol's method Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05YGF  21  Initializes the Niederreiter generator (G05YHF/G05YJF/G05YKF) Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05YHF  21  Generates a sequence of quasirandom numbers using Niederreiter's method Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G05YJF  21  Generates a Normal quasirandom number sequence 
G05YKF  21  Generates a lognormal quasirandom number sequence 
G05YLF  22  Initializes a quasirandom number generator 
G05YMF  22  Generates a uniform quasirandom number sequence 
G05YNF  22  Initializes a scrambled quasirandom number generator 
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 ttest 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, Mestimates for location and scale parameters, standard weight functions 
G07DCF  13  Robust estimation, Mestimates for location and scale parameters, userdefined weight functions 
G07DDF  14  Computes a trimmed and winsorized mean of a single sample with estimates of their variance 
G07EAF  16  Robust confidence intervals, onesample 
G07EBF  16  Robust confidence intervals, twosample 
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 twoway analysis of variance on k matched samples 
G08AFF  8  Kruskal–Wallis oneway analysis of variance on k samples of unequal size 
G08AGF  14  Performs the Wilcoxon onesample (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 crossclassified binary data 
G08BAF  8  Mood's and David's tests on two samples of unequal size 
G08CBF  14  Performs the onesample Kolmogorov–Smirnov test for standard distributions 
G08CCF  14  Performs the onesample Kolmogorov–Smirnov test for a usersupplied distribution 
G08CDF  14  Performs the twosample 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, rightcensored 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 twoway 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 (productlimit) 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 nonseasonal 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 (easytouse) 
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 
G13AMF  22  Univariate time series, exponential smoothing 
G13ASF  13  Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF 
G13AUF  14  Computes quantities needed for rangemean or standard deviationmean plot 
G13BAF  10  Multivariate time series, filtering (prewhitening) by an ARIMA model 
G13BBF  11  Multivariate time series, filtering by a transfer function model 
G13BCF  10  Multivariate time series, crosscorrelations 
G13BDF  11  Multivariate time series, preliminary estimation of transfer function model 
G13BEF  11  Multivariate time series, estimation of multiinput model 
G13BGF  11  Multivariate time series, update state set for forecasting from multiinput model 
G13BHF  11  Multivariate time series, forecasting from state set of multiinput model 
G13BJF  11  Multivariate time series, state set and forecasts from fully specified multiinput 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 Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
G13DDF  22  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 crosscorrelation or crosscovariance 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 G13DDF 
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, timevarying, square root covariance filter 
G13EBF  17  Combined measurement and time update, one iteration of Kalman filter, timeinvariant, 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), using E04NKF/E04NKA 
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 
M01NAF  22  Binary search in set of real numbers 
M01NBF  22  Binary search in set of integer numbers 
M01NCF  22  Binary search in set of character data 
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 Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
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 realx 
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 
S15AGF  22  Scaled complement of error function, erfcx(x) 
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), reala ≥ 0, complex z, ν = 0,1,2, … 
S17DEF  13  Bessel functions J_{ν + a}(z), reala ≥ 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, reala ≥ 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), reala ≥ 0, complex z, ν = 0,1,2, … 
S18DEF  13  Modified Bessel functions I_{ν + a}(z), reala ≥ 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) 
S21BEF  22  Elliptic integral of 1st kind, Legendre form, F(φm) 
S21BFF  22  Elliptic integral of 2nd kind, Legendre form, E(φm) 
S21BGF  22  Elliptic integral of 3rd kind, Legendre form, Π(n ; φm) 
S21BHF  22  Complete elliptic integral of 1st kind, Legendre form, K(m) 
S21BJF  22  Complete elliptic integral of 2nd kind, Legendre form, E(m) 
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) 
S30AAF  22  Black–Scholes–Merton option pricing formula 
S30ABF  22  Black–Scholes–Merton option pricing formula with Greeks 
S30BAF  22  Floatingstrike lookback option pricing formula 
S30BBF  22  Floatingstrike lookback option pricing formula with Greeks 
S30CAF  22  Binary option: cashornothing pricing formula 
S30CBF  22  Binary option: cashornothing pricing formula with Greeks 
S30CCF  22  Binary option: assetornothing pricing formula 
S30CDF  22  Binary option: assetornothing pricing formula with Greeks 
S30FAF  22  Standard barrier option pricing formula 
S30JAF  22  Jumpdiffusion, Merton's model, option pricing formula 
S30JBF  22  Jumpdiffusion, Merton's model, option pricing formula with Greeks 
S30NAF  22  Heston's model option pricing formula 
S30QCF  22  American option: Bjerksund and Stensland pricing formula 
S30SAF  22  Asian option: geometric continuous average rate pricing formula 
S30SBF  22  Asian option: geometric continuous average rate pricing formula with Greeks 
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 floatingpoint arithmetic 
X02BBF  5  The largest representable integer 
X02BEF  5  The maximum number of decimal digits that can be represented 
X02BHF  12  The floatingpoint model parameter, b 
X02BJF  12  The floatingpoint model parameter, p 
X02BKF  12  The floatingpoint model parameter e_{min} 
X02BLF  12  The floatingpoint model parameter e_{max} 
X02DAF  8  Switch for taking precautions to avoid underflow Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
X02DJF  12  The floatingpoint model parameter ROUNDS Note: this routine is scheduled for withdrawal at Mark 24, see Advice on Replacement Calls for Withdrawn/Superseded Routines for further information. 
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 (easytouse) 
X04CBF  14  Print real general matrix (comprehensive) 
X04CCF  14  Print real packed triangular matrix (easytouse) 
X04CDF  14  Print real packed triangular matrix (comprehensive) 
X04CEF  14  Print real packed banded matrix (easytouse) 
X04CFF  14  Print real packed banded matrix (comprehensive) 
X04DAF  14  Print complex general matrix (easytouse) 
X04DBF  14  Print complex general matrix (comprehensive) 
X04DCF  14  Print complex packed triangular matrix (easytouse) 
X04DDF  14  Print complex packed triangular matrix (comprehensive) 
X04DEF  14  Print complex packed banded matrix (easytouse) 
X04DFF  14  Print complex packed banded matrix (comprehensive) 
X04EAF  14  Print integer matrix (easytouse) 
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 