NAG FORTRAN MARK 18 LIBRARY CONCISE SUMMARY N.B. This summary does not include routines which have been superseded and are scheduled for withdrawal at a future mark. A00AAF Prints details of the NAG Fortran Library implementation A02AAF Square root of a complex number A02ABF Modulus of a complex number A02ACF Quotient of two complex numbers C02AFF All zeros of complex polynomial, modified Laguerre method C02AGF All zeros of real polynomial, modified Laguerre method C02AHF All zeros of complex quadratic C02AJF All zeros of real quadratic C05ADF Zero of continuous function in given interval, Bus and Dekker algorithm C05AGF Zero of continuous function, Bus and Dekker algorithm, from given starting value, binary search for interval C05AJF Zero of continuous function, continuation method, from a given starting value C05AVF Binary search for interval containing zero of continuous function (reverse communication) C05AXF Zero of continuous function by continuation method, from given starting value (reverse communication) C05AZF Zero in given interval of continuous function by Bus and Dekker algorithm (reverse communication) C05NBF Solution of system of nonlinear equations using function values only (easy-to-use) C05NCF Solution of system of nonlinear equations using function values only (comprehensive) C05NDF Solution of systems of nonlinear equations using function values only (reverse communication) C05PBF Solution of system of nonlinear equations using 1st derivatives (easy-to-use) C05PCF Solution of system of nonlinear equations using 1st derivatives (comprehensive) C05PDF Solution of systems of nonlinear equations using 1st derivatives (reverse communication) C05ZAF Check user's routine for calculating 1st derivatives C06BAF Acceleration of convergence of sequence, Shanks' transformation and epsilon algorithm C06DBF Sum of a Chebyshev series C06EAF Single 1-D real discrete Fourier transform, no extra workspace C06EBF Single 1-D Hermitian discrete Fourier transform, no extra workspace C06ECF Single 1-D complex discrete Fourier transform, no extra workspace C06EKF Circular convolution or correlation of two real vectors, no extra workspace C06FAF Single 1-D real discrete Fourier transform, extra workspace for greater speed C06FBF Single 1-D Hermitian discrete Fourier transform, extra workspace for greater speed C06FCF Single 1-D complex discrete Fourier transform, extra workspace for greater speed C06FFF 1-D complex discrete Fourier transform of multi-dimensional data C06FJF Multi-dimensional complex discrete Fourier transform of multi-dimensional data C06FKF Circular convolution or correlation of two real vectors, extra workspace for greater speed C06FPF Multiple 1-D real discrete Fourier transforms C06FQF Multiple 1-D Hermitian discrete Fourier transforms C06FRF Multiple 1-D complex discrete Fourier transforms C06FUF 2-D complex discrete Fourier transform C06FXF 3-D complex discrete Fourier transform C06GBF Complex conjugate of Hermitian sequence C06GCF Complex conjugate of complex sequence C06GQF Complex conjugate of multiple Hermitian sequences C06GSF Convert Hermitian sequences to general complex sequences C06HAF Discrete sine transform C06HBF Discrete cosine transform C06HCF Discrete quarter-wave sine transform C06HDF Discrete quarter-wave cosine transform C06LAF Inverse Laplace transform, Crump's method C06LBF Inverse Laplace transform, modified Weeks' method C06LCF Evaluate inverse Laplace transform as computed by C06LBF D01AHF 1-D quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands D01AJF 1-D quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly-behaved integrands D01AKF 1-D quadrature, adaptive, finite interval, method suitable for oscillating functions D01ALF 1-D quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points D01AMF 1-D quadrature, adaptive, infinite or semi-infinite interval D01ANF 1-D quadrature, adaptive, finite interval, weight function cos(omega x) or sin(omega x) D01APF 1-D quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico- logarithmic type D01AQF 1-D quadrature, adaptive, finite interval, weight function 1/(x-c), Cauchy principal value (Hilbert transform) D01ARF 1-D quadrature, non-adaptive, finite interval with provision for indefinite integrals D01ASF 1-D quadrature, adaptive, semi-infinite interval, weight function cos(omega x) or sin(omega x) D01ATF 1-D quadrature, adaptive, finite interval, variant of D01AJF efficient on vector machines D01AUF 1-D quadrature, adaptive, finite interval, variant of D01AKF efficient on vector machines D01BAF 1-D Gaussian quadrature D01BBF Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule D01BCF Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule D01BDF 1-D quadrature, non-adaptive, finite interval D01DAF 2-D quadrature, finite region D01EAF Multi-dimensional adaptive quadrature over hyper-rectangle, multiple integrands D01FBF Multi-dimensional Gaussian quadrature over hyper-rectangle D01FCF Multi-dimensional adaptive quadrature over hyper-rectangle D01FDF Multi-dimensional quadrature, Sag--Szekeres method, general product region or n-sphere D01GAF 1-D quadrature, integration of function defined by data values, Gill--Miller method D01GBF Multi-dimensional quadrature over hyper-rectangle, Monte Carlo method D01GCF Multi-dimensional quadrature, general product region, number-theoretic method D01GDF Multi-dimensional quadrature, general product region, number-theoretic method, variant of D01GCF efficient on vector machines D01GYF Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is prime D01GZF Korobov optimal coefficients for use in D01GCF or D01GDF, when number of points is product of two primes D01JAF Multi-dimensional quadrature over an n-sphere, allowing for badly-behaved integrands D01PAF Multi-dimensional quadrature over an n-simplex D02AGF ODEs, boundary value problem, shooting and matching technique, allowing interior matching point, general parameters to be determined D02BGF ODEs, IVP, Runge--Kutta--Merson method, until a component attains given value (simple driver) D02BHF ODEs, IVP, Runge--Kutta--Merson method, until function of solution is zero (simple driver) D02BJF ODEs, IVP, Runge--Kutta method, until function of solution is zero, integration over range with intermediate output (simple driver) D02CJF ODEs, IVP, Adams method, until function of solution is zero, intermediate output (simple driver) D02EJF ODEs, stiff IVP, BDF method, until function of solution is zero, intermediate output (simple driver) D02GAF ODEs, boundary value problem, finite difference technique with deferred correction, simple nonlinear problem D02GBF ODEs, boundary value problem, finite difference technique with deferred correction, general linear problem D02HAF ODEs, boundary value problem, shooting and matching, boundary values to be determined D02HBF ODEs, boundary value problem, shooting and matching, general parameters to be determined D02JAF ODEs, boundary value problem, collocation and least-squares, single (n)th order linear equation D02JBF ODEs, boundary value problem, collocation and least-squares, system of 1st order linear equations D02KAF 2nd order Sturm--Liouville problem, regular system, finite range, eigenvalue only D02KDF 2nd order Sturm--Liouville problem, regular/singular system, finite/infinite range, eigenvalue only, user-specified break-points D02KEF 2nd order Sturm--Liouville problem, regular/singular system, finite/infinite range, eigenvalue and eigenfunction, user-specified break-points D02LAF 2nd order ODEs, IVP, Runge--Kutta--Nystrom method D02LXF 2nd order ODEs, IVP, set-up for D02LAF D02LYF 2nd order ODEs, IVP, diagnostics for D02LAF D02LZF 2nd order ODEs, IVP, interpolation for D02LAF D02MVF ODEs, IVP, DASSL method, set-up for D02M-N routines D02MZF ODEs, IVP, interpolation for D02M-N routines, natural interpolant D02NBF Explicit ODEs, stiff IVP, full Jacobian (comprehensive) D02NCF Explicit ODEs, stiff IVP, banded Jacobian (comprehensive) D02NDF Explicit ODEs, stiff IVP, sparse Jacobian (comprehensive) D02NGF Implicit/algebraic ODEs, stiff IVP, full Jacobian (comprehensive) D02NHF Implicit/algebraic ODEs, stiff IVP, banded Jacobian (comprehensive) D02NJF Implicit/algebraic ODEs, stiff IVP, sparse Jacobian (comprehensive) D02NMF Explicit ODEs, stiff IVP (reverse communication, comprehensive) D02NNF Implicit/algebraic ODEs, stiff IVP (reverse communication, comprehensive) D02NRF ODEs, IVP, for use with D02M-N routines, sparse Jacobian, enquiry routine D02NSF ODEs, IVP, for use with D02M-N routines, full Jacobian, linear algebra set-up D02NTF ODEs, IVP, for use with D02M-N routines, banded Jacobian, linear algebra set-up D02NUF ODEs, IVP, for use with D02M-N routines, sparse Jacobian, linear algebra set-up D02NVF ODEs, IVP, BDF method, set-up for D02M-N routines D02NWF ODEs, IVP, Blend method, set-up for D02M-N routines D02NXF ODEs, IVP, sparse Jacobian, linear algebra diagnostics, for use with D02M-N routines D02NYF ODEs, IVP, integrator diagnostics, for use with D02M-N routines D02NZF ODEs, IVP, set-up for continuation calls to integrator, for use with D02M-N routines D02PCF ODEs, IVP, Runge--Kutta method, integration over range with output D02PDF ODEs, IVP, Runge--Kutta method, integration over one step D02PVF ODEs, IVP, set-up for D02PCF and D02PDF D02PWF ODEs, IVP, resets end of range for D02PDF D02PXF ODEs, IVP, interpolation for D02PDF D02PYF ODEs, IVP, integration diagnostics for D02PCF and D02PDF D02PZF ODEs, IVP, error assessment diagnostics for D02PCF and D02PDF D02QFF ODEs, IVP, Adams method with root-finding (forward communication, comprehensive) D02QGF ODEs, IVP, Adams method with root-finding (reverse communication, comprehensive) D02QWF ODEs, IVP, set-up for D02QFF and D02QGF D02QXF ODEs, IVP, diagnostics for D02QFF and D02QGF D02QYF ODEs, IVP, root-finding diagnostics for D02QFF and D02QGF D02QZF ODEs, IVP, interpolation for D02QFF or D02QGF D02RAF ODEs, general nonlinear boundary value problem, finite difference technique with deferred correction, continuation facility D02SAF ODEs, boundary value problem, shooting and matching technique, subject to extra algebraic equations, general parameters to be determined D02TGF (n)th order linear ODEs, boundary value problem, collocation and least-squares D02TKF ODEs, general nonlinear boundary value problem, collocation technique D02TVF ODEs, general nonlinear boundary value problem, set-up for D02TKF D02TXF ODEs, general nonlinear boundary value problem, continuation facility for D02TKF D02TYF ODEs, general nonlinear boundary value problem, interpolation for D02TKF D02TZF ODEs, general nonlinear boundary value problem, diagnostics for D02TKF D02XJF ODEs, IVP, interpolation for D02M-N routines, natural interpolant D02XKF ODEs, IVP, interpolation for D02M-N routines, C(1) interpolant D02ZAF ODEs, IVP, weighted norm of local error estimate for D02M-N routines D03EAF Elliptic PDE, Laplace's equation, 2-D arbitrary domain D03EBF Elliptic PDE, solution of finite difference equations by SIP, five-point 2-D molecule, iterate to convergence D03ECF Elliptic PDE, solution of finite difference equations by SIP, seven-point 3-D molecule, iterate to convergence D03EDF Elliptic PDE, solution of finite difference equations by a multigrid technique D03EEF Discretize a second order elliptic PDE on a rectangle D03FAF Elliptic PDE, Helmholtz equation, 3-D Cartesian co-ordinates D03MAF Triangulation of a plane region D03PCF General system of parabolic PDEs, method of lines, finite differences, one space variable D03PDF General system of parabolic PDEs, method of lines, Chebyshev C**0 collocation, one space variable D03PEF General system of first order PDEs, method of lines, Keller box discretisation, one space variable D03PFF General system of convection-diffusion PDEs with source terms in conservative form, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable D03PHF General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, one space variable D03PJF General system of parabolic PDEs, coupled DAEs, method of lines, Chebyshev C**0 collocation, one space variable D03PKF General system of first order PDEs, coupled DAEs, method of lines, Keller box discretisation, one space variable D03PLF General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, one space variable D03PPF General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable D03PRF General system of first order PDEs, coupled DAEs, method of lines, Keller box discretisation, remeshing, one space variable D03PSF General system of convection-diffusion PDEs with source terms in conservative form, coupled DAEs, method of lines, upwind scheme using numerical flux function based on Riemann solver, remeshing, one space variable D03PUF Roe's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF D03PVF Osher's approximate Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF D03PWF Modified HLL Riemann solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF D03PXF Exact Riemann Solver for Euler equations in conservative form, for use with D03PFF, D03PLF and D03PSF D03PYF PDEs, spatial interpolation with D03PDF or D03PJF D03PZF PDEs, spatial interpolation with D03PCF, D03PEF, D03PFF, D03PHF, D03PKF, D03PLF, D03PPF, D03PRF or D03PSF D03RAF General system of second order PDEs, method of lines, finite differences, remeshing, two space variables, rectangular region D03RBF General system of second order PDEs, method of lines, finite differences, remeshing, two space variables, rectilinear region D03RYF Check initial grid data in D03RBF D03RZF Extract grid data from D03RBF D03UAF Elliptic PDE, solution of finite difference equations by SIP, five-point 2-D molecule, one iteration D03UBF Elliptic PDE, solution of finite difference equations by SIP, seven-point 3-D molecule, one iteration D04AAF Numerical differentiation, derivatives up to order 14, function of one real variable D05AAF Linear non-singular Fredholm integral equation, 2nd kind, split kernel D05ABF Linear non-singular Fredholm integral equation, 2nd kind, smooth kernel D05BAF Nonlinear Volterra convolution equation, 2nd kind D05BDF Nonlinear convolution Volterra--Abel equation, 2nd kind, weakly singular D05BEF Nonlinear convolution Volterra--Abel equation, 1st kind, weakly singular D05BWF Generate weights for use in solving Volterra equations D05BYF Generate weights for use in solving weakly singular Abel type equations E01AAF Interpolated values, Aitken's technique, unequally spaced data, one variable E01ABF Interpolated values, Everett's formula, equally spaced data, one variable E01AEF Interpolating functions, polynomial interpolant, data may include derivative values, one variable E01BAF Interpolating functions, cubic spline interpolant, one variable E01BEF Interpolating functions, monotonicity-preserving, piecewise cubic Hermite, one variable E01BFF Interpolated values, interpolant computed by E01BEF, function only, one variable, E01BGF Interpolated values, interpolant computed by E01BEF, function and 1st derivative, one variable E01BHF Interpolated values, interpolant computed by E01BEF, definite integral, one variable E01DAF Interpolating functions, fitting bicubic spline, data on rectangular grid E01RAF Interpolating functions, rational interpolant, one variable E01RBF Interpolated values, evaluate rational interpolant computed by E01RAF, one variable E01SAF Interpolating functions, method of Renka and Cline, two variables E01SBF Interpolated values, evaluate interpolant computed by E01SAF, two variables E01SEF Interpolating functions, modified Shepard's method, two variables E01SFF Interpolated values, evaluate interpolant computed by E01SEF, two variables E01SGF Interpolating functions, modified Shepard's method, two variables E01SHF Interpolated values, evaluate interpolant computed by E01SGF, function and first derivatives, two variables E01TGF Interpolating functions, modified Shepard's method, three variables E01THF Interpolated values, evaluate interpolant computed by E01TGF, function and first derivatives, three variables E02ACF 1 Minimax curve fit by polynomials E02ADF Least-squares curve fit, by polynomials, arbitrary data points E02AEF Evaluation of fitted polynomial in one variable from Chebyshev series form (simplified parameter list) E02AFF Least-squares polynomial fit, special data points (including interpolation) E02AGF Least-squares polynomial fit, values and derivatives may be constrained, arbitrary data points, E02AHF Derivative of fitted polynomial in Chebyshev series form E02AJF Integral of fitted polynomial in Chebyshev series form E02AKF Evaluation of fitted polynomial in one variable, from Chebyshev series form E02BAF Least-squares curve cubic spline fit (including interpolation) E02BBF Evaluation of fitted cubic spline, function only E02BCF Evaluation of fitted cubic spline, function and derivatives E02BDF Evaluation of fitted cubic spline, definite integral E02BEF Least-squares cubic spline curve fit, automatic knot placement E02CAF Least-squares surface fit by polynomials, data on lines E02CBF Evaluation of fitted polynomial in two variables E02DAF Least-squares surface fit, bicubic splines E02DCF Least-squares surface fit by bicubic splines with automatic knot placement, data on rectangular grid E02DDF Least-squares surface fit by bicubic splines with automatic knot placement, scattered data E02DEF Evaluation of a fitted bicubic spline at a vector of points E02DFF Evaluation of a fitted bicubic spline at a mesh of points E02GAF L(1)-approximation by general linear function E02GBF L(1)-approximation by general linear function subject to linear inequality constraints E02GCF L(infty)-approximation by general linear function E02RAF Pade-approximants E02RBF Evaluation of fitted rational function as computed by E02RAF E02ZAF Sort 2-D data into panels for fitting bicubic splines E04ABF Minimum, function of one variable using function values only E04BBF Minimum, function of one variable, using 1st derivative E04CCF 1 Unconstrained minimum, simplex algorithm, function of several variables using function values only (comprehensive) E04DGF Unconstrained minimum, pre-conditioned conjugate gradient algorithm, function of several variables using 1st derivatives (comprehensive) E04DJF Read optional parameter values for E04DGF from external file E04DKF Supply optional parameter values to E04DGF E04FCF Unconstrained minimum of a sum of squares, combined Gauss--Newton and modified Newton algorithm using function values only (comprehensive) E04FYF Unconstrained minimum of a sum of squares, combined Gauss--Newton and modified Newton algorithm using function values only (easy-to-use) E04GBF Unconstrained minimum of a sum of squares, combined Gauss--Newton and quasi-Newton algorithm using 1st derivatives (comprehensive) E04GDF Unconstrained minimum of a sum of squares, combined Gauss--Newton and modified Newton algorithm using 1st derivatives (comprehensive) E04GEF Unconstrained minimum of a sum of squares, combined Gauss--Newton and modified Newton algorithm using 1st derivatives (easy-to-use) E04GYF Unconstrained minimum of a sum of squares, combined Gauss--Newton and quasi-Newton algorithm, using 1st derivatives (easy-to-use) E04GZF Unconstrained minimum of a sum of squares, combined Gauss--Newton and modified Newton algorithm using 1st derivatives (easy-to-use) E04HCF Check user's routine for calculating 1st derivatives of function E04HDF Check user's routine for calculating 2nd derivatives of function E04HEF Unconstrained minimum of a sum of squares, combined Gauss--Newton and modified Newton algorithm, using 2nd derivatives (comprehensive) E04HFF Unconstrained minimum of a sum of squares, combined Gauss--Newton and modified Newton algorithm, using 2nd derivatives (easy-to-use) E04HYF Unconstrained minimum of a sum of squares, combined Gauss--Newton and modified Newton algorithm, using 2nd derivatives (easy-to-use) E04JYF Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using function values only (easy-to-use) E04KAF Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using 1st derivatives (easy-to-use) E04KCF Minimum, function of several variables, modified Newton algorithm, simple bounds, using 1st derivatives (easy-to-use) E04KDF Minimum, function of several variables, modified Newton algorithm, simple bounds, using 1st derivatives (comprehensive) E04KYF Minimum, function of several variables, quasi-Newton algorithm, simple bounds, using 1st derivatives (easy-to-use) E04KZF Minimum, function of several variables, modified Newton algorithm, simple bounds, using 1st derivatives (easy-to-use) E04LAF Minimum, function of several variables, modified Newton algorithm, simple bounds, using 1st and 2nd derivatives (easy-to-use) E04LBF Minimum, function of several variables, modified Newton algorithm, simple bounds, using 1st and 2nd derivatives (comprehensive) E04LYF Minimum, function of several variables, modified Newton algorithm, simple bounds, using 1st and 2nd derivatives (easy-to-use) E04MFF LP problem E04MGF Read optional parameter values for E04MFF from external file E04MHF Supply optional parameter values to E04MFF E04MZF Converts MPSX data file defining LP or QP problem to format required by E04NKF E04NCF Convex QP problem or linearly-constrained linear least-squares problem E04NDF Read optional parameter values for E04NCF from external file E04NEF Supply optional parameter values to E04NCF E04NFF QP problem E04NGF Read optional parameter values for E04NFF from external file E04NHF Supply optional parameter values to E04NFF E04NKF LP or QP problem E04NLF Read optional parameter values for E04NKF from external file E04NMF Supply optional parameter values to E04NKF E04UCF Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally 1st derivatives (forward communication, comprehensive) E04UDF Read optional parameter values for E04UCF or E04UFF from external file E04UEF Supply optional parameter values to E04UCF or E04UFF E04UFF Minimum, function of several variables, sequential QP method, nonlinear constraints, using function values and optionally 1st derivatives (reverse communication, comprehensive) E04UNF Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally 1st derivatives (comprehensive) E04UPF Minimum of a sum of squares, nonlinear constraints, sequential QP method, using function values and optionally 1st derivatives (comprehensive) E04UQF Read optional parameter values for E04UNF or E04UPF from external file E04URF Supply optional parameter values to E04UNF or E04UPF E04XAF Estimate (using numerical differentiation) gradient and/or Hessian of a function E04YAF Check user's routine for calculating Jacobian of 1st derivatives E04YBF Check user's routine for calculating Hessian of a sum of squares E04YCF Covariance matrix for nonlinear least-squares problem (unconstrained) E04ZCF Check user's routines for calculating 1st derivatives of function and constraints F01ABF Inverse of real symmetric positive-definite matrix using iterative refinement F01ADF Inverse of real symmetric positive-definite matrix F01BLF Pseudo-inverse and rank of a real m by n matrix (m >= n) F01BRF LU factorization of real sparse matrix F01BSF LU factorization of real sparse matrix with known sparsity pattern F01BUF ULDL**T U**T factorization of real symmetric positive-definite band matrix F01BVF Reduction to standard form, generalized real symmetric-definite banded eigenproblem F01CKF Matrix multiplication F01CRF Matrix transposition F01CTF Sum or difference of two real matrices, optional scaling and transposition F01CWF Sum or difference of two complex matrices, optional scaling and transposition F01LEF LU factorization of real tridiagonal matrix F01LHF LU factorization of real almost block diagonal matrix F01MAF LL**T factorization of real sparse symmetric positive-definite matrix F01MCF LDL**T factorization of real symmetric positive-definite variable-bandwidth matrix F01QGF RQ factorization of real m by n upper trapezoidal matrix (m <= n) F01QJF RQ factorization of real m by n matrix (m <= n) F01QKF Operations with orthogonal matrices, form rows of Q, after RQ factorization by F01QJF F01RGF RQ factorization of complex m by n upper trapezoidal matrix (m <= n) F01RJF RQ factorization of complex m by n matrix (m <= n) F01RKF Operations with unitary matrices, form rows of Q, after RQ factorization by F01RJF F01ZAF Convert real matrix between packed triangular and square storage schemes F01ZBF Convert complex matrix between packed triangular and square storage schemes F01ZCF Convert real matrix between packed banded and rectangular storage schemes F01ZDF Convert complex matrix between packed banded and rectangular storage schemes F02BBF Selected eigenvalues and eigenvectors of real symmetric matrix (Black Box) F02BCF Selected eigenvalues and eigenvectors of real matrix (Black Box) F02BDF Selected eigenvalues and eigenvectors of complex matrix (Black Box) F02BJF All eigenvalues and optionally eigenvectors of generalized eigenproblem by QZ algorithm, real matrices (Black Box) F02EAF All eigenvalues and Schur factorization of real general matrix (Black Box) F02EBF All eigenvalues and eigenvectors of real general matrix (Black Box) F02ECF Selected eigenvalues and eigenvectors of real nonsymmetric matrix (Black Box) F02FAF All eigenvalues and eigenvectors of real symmetric matrix (Black Box) F02FCF Selected eigenvalues and eigenvectors of real symmetric matrix (Black Box) F02FDF All eigenvalues and eigenvectors of real symmetric-definite generalized problem (Black Box) F02FHF All eigenvalues of generalized banded real symmetric-definite eigenproblem (Black Box) F02FJF Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box) F02GAF All eigenvalues and Schur factorization of complex general matrix (Black Box) F02GBF All eigenvalues and eigenvectors of complex general matrix (Black Box) F02GCF Selected eigenvalues and eigenvectors of complex nonsymmetric matrix (Black Box) F02GJF All eigenvalues and optionally eigenvectors of generalized complex eigenproblem by QZ algorithm (Black Box) F02HAF All eigenvalues and eigenvectors of complex Hermitian matrix (Black Box) F02HCF Selected eigenvalues and eigenvectors of complex Hermitian matrix (Black Box) F02HDF All eigenvalues and eigenvectors of complex Hermitian-definite generalized problem (Black Box) F02SDF Eigenvector of generalized real banded eigenproblem by inverse iteration F02WDF QR factorization, possibly followed by SVD F02WEF SVD of real matrix (Black Box) F02WUF SVD of a real upper triangular matrix (Black Box) F02XEF SVD of complex matrix (Black Box) F02XUF SVD of complex upper triangular matrix (Black Box) F03AAF Determinant of real matrix (Black Box) F03ABF Determinant of real symmetric positive-definite matrix (Black Box) F03ACF Determinant of real symmetric positive-definite band matrix (Black Box) F03ADF Determinant of complex matrix (Black Box) F03AEF LL**T factorization and determinant of real symmetric positive-definite matrix F03AFF LU factorization and determinant of real matrix F04AAF Solution of real simultaneous linear equations with multiple right-hand sides (Black Box) F04ABF Solution of real symmetric positive-definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box) F04ACF Solution of real symmetric positive-definite banded simultaneous linear equations with multiple right-hand sides (Black Box) F04ADF Solution of complex simultaneous linear equations with multiple right-hand sides (Black Box) F04AEF Solution of real simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box) F04AFF Solution of real symmetric positive-definite simultaneous linear equations using iterative refinement (coefficient matrix already factorized by F03AEF) F04AGF Solution of real symmetric positive-definite simultaneous linear equations (coefficient matrix already factorized by F03AEF) F04AHF Solution of real simultaneous linear equations using iterative refinement (coefficient matrix already factorized by F03AFF) F04AJF Solution of real simultaneous linear equations (coefficient matrix already factorized by F03AFF) F04AMF Least-squares solution of m real equations in n unknowns, rank = n, m >= n using iterative refinement (Black Box) F04ARF Solution of real simultaneous linear equations, one right-hand side (Black Box) F04ASF Solution of real symmetric positive-definite simultaneous linear equations, one right-hand side using iterative refinement (Black Box) F04ATF Solution of real simultaneous linear equations, one right-hand side using iterative refinement (Black Box) F04AXF Solution of real sparse simultaneous linear equations (coefficient matrix already factorized) F04EAF Solution of real tridiagonal simultaneous linear equations, one right-hand side (Black Box) F04FAF Solution of real symmetric positive-definite tridiagonal simultaneous linear equations, one right-hand side (Black Box) F04FEF Solution of the Yule--Walker equations for a real symmetric positive-definite Toeplitz matrix, one right-hand side F04FFF Solution of real symmetric positive-definite Toeplitz system, one right-hand side F04JAF Minimal least-squares solution of m real equations in n unknowns, rank <= n, m >= n F04JDF Minimal least-squares solution of m real equations in n unknowns, rank <= n, m >= n F04JGF Least-squares (if rank=n) or minimal least-squares (if rank= n F04JLF Real general Gauss--Markov linear model (including weighted least-squares) F04JMF Equality-constrained real linear least squares problem F04KLF Complex general Gauss--Markov linear model (including weighted least-squares) F04KMF Equality-constrained complex linear least-squares F04LEF Solution of real tridiagonal simultaneous linear equations (coefficient matrix already factorized by F01LEF) F04LHF Solution of real almost block diagonal simultaneous linear equations (coefficient matrix already factorized by F01LHF) F04MAF Real sparse symmetric positive-definite simultaneous linear equations (coefficient matrix already factorized by F01MAF) F04MBF Real sparse symmetric simultaneous linear equations F04MCF Solution of real symmetric positive-definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by F01MCF) F04MEF Update solution of the Yule--Walker equations for a real symmetric positive-definite Toeplitz matrix F04MFF Update solution of real symmetric positive-definite Toeplitz system F04QAF Sparse linear least-squares problem, m real equations in n unknowns F04YAF Covariance matrix for linear least-squares problems, m real equations in n unknowns F04YCF Norm estimation (for use in condition estimation), real matrix F04ZCF Norm estimation (for use in condition estimation), complex matrix F05AAF Gram--Schmidt orthogonalisation of n vectors of order m F06AAF Generate real plane rotation (SROTG/DROTG) F06BAF Generate real plane rotation, storing tangent F06BCF Recover cosine and sine from given real tangent F06BEF Generate real Jacobi plane rotation F06BHF Apply real similarity rotation to 2 by 2 symmetric matrix F06BLF Compute quotient of two real scalars, with overflow flag F06BMF Compute Euclidean norm from scaled form F06BNF Compute square root of (a**2 + b**2), real a and b F06BPF Compute eigenvalue of 2 by 2 real symmetric matrix F06CAF Generate complex plane rotation, storing tangent, real cosine F06CBF Generate complex plane rotation, storing tangent, real sine F06CCF Recover cosine and sine from given complex tangent, real cosine F06CDF Recover cosine and sine from given complex tangent, real sine F06CHF Apply complex similarity rotation to 2 by 2 Hermitian matrix F06CLF Compute quotient of two complex scalars, with overflow flag F06DBF Broadcast scalar into integer vector F06DFF Copy integer vector F06EAF Dot product of two real vectors (SDOT/DDOT) F06ECF Add scalar times real vector to real vector (SAXPY/DAXPY) F06EDF Multiply real vector by scalar (SSCAL/DSCAL) F06EFF Copy real vector (SCOPY/DCOPY) F06EGF Swap two real vectors (SSWAP/DSWAP) F06EJF Compute Euclidean norm of real vector (SNRM2/DNRM2) F06EKF Sum the absolute values of real vector elements (SASUM/DASUM) F06EPF Apply real plane rotation (SROT/DROT) F06ERF Dot product of two real sparse vectors (SDOTI/DDOTI) F06ETF Add a scalar times a real sparse vector to another real sparse vector (SAXPYI/DAXPYI) F06EUF Gather a real sparse vector (SGTHR/DGTHR) F06EVF Gather and set to zero a real sparse vector (SGTHRZ/DGTHRZ) F06EWF Scatter a real sparse vector (SSCTR/DSCTR) F06EXF Apply plane rotation to two real sparse vectors (SROTI/DROTI) F06FAF Compute cosine of angle between two real vectors F06FBF Broadcast scalar into real vector F06FCF Multiply real vector by diagonal matrix F06FDF Multiply real vector by scalar, preserving input vector F06FGF Negate real vector F06FJF Update Euclidean norm of real vector in scaled form F06FKF Compute weighted Euclidean norm of real vector F06FLF Elements of real vector with largest and smallest absolute value F06FPF Apply real symmetric plane rotation to two vectors F06FQF Generate sequence of real plane rotations F06FRF Generate real elementary reflection, NAG style F06FSF Generate real elementary reflection, LINPACK style F06FTF Apply real elementary reflection, NAG style F06FUF Apply real elementary reflection, LINPACK style F06GAF Dot product of two complex vectors, unconjugated (CDOTU/ZDOTU) F06GBF Dot product of two complex vectors, conjugated (CDOTC/ZDOTC) F06GCF Add scalar times complex vector to complex vector (CAXPY/ZAXPY) F06GDF Multiply complex vector by complex scalar (CSCAL/ZSCAL) F06GFF Copy complex vector (CCOPY/ZCOPY) F06GGF Swap two complex vectors (CSWAP/ZSWAP) F06GRF Dot product of two complex sparse vector, unconjugated (CDOTUI/ZDOTUI) F06GSF Dot product of two complex sparse vector, conjugated (CDOTCI/ZDOTCI) F06GTF Add a scalar times a complex sparse vector to another complex sparse vector (CAXPYI/ZAXPYI) F06GUF Gather a complex sparse vector (CGTHR/ZGTHR) F06GVF Gather and set to zero a complex sparse vector (CGTHRZ/ZGTHRZ) F06GWF Scatter a complex sparse vector (CSCTR/ZSCTR) F06HBF Broadcast scalar into complex vector F06HCF Multiply complex vector by complex diagonal matrix F06HDF Multiply complex vector by complex scalar, preserving input vector F06HGF Negate complex vector F06HPF Apply complex plane rotation F06HQF Generate sequence of complex plane rotations F06HRF Generate complex elementary reflection F06HTF Apply complex elementary reflection F06JDF Multiply complex vector by real scalar (CSSCAL/ZDSCAL) F06JJF Compute Euclidean norm of complex vector (SCNRM2/DZNRM2) F06JKF Sum the absolute values of complex vector elements (SCASUM/DZASUM) F06JLF Index, real vector element with largest absolute value (ISAMAX/IDAMAX) F06JMF Index, complex vector element with largest absolute value (ICAMAX/IZAMAX) F06KCF Multiply complex vector by real diagonal matrix F06KDF Multiply complex vector by real scalar, preserving input vector F06KFF Copy real vector to complex vector F06KJF Update Euclidean norm of complex vector in scaled form F06KLF Last non-negligible element of real vector F06KPF Apply real plane rotation to two complex vectors F06PAF Matrix-vector product, real rectangular matrix (SGEMV/DGEMV) F06PBF Matrix-vector product, real rectangular band matrix (SGBMV/DGBMV) F06PCF Matrix-vector product, real symmetric matrix (SSYMV/DSYMV) F06PDF Matrix-vector product, real symmetric band matrix (SSBMV/DSBMV) F06PEF Matrix-vector product, real symmetric packed matrix (SSPMV/DSPMV) F06PFF Matrix-vector product, real triangular matrix (STRMV/DTRMV) F06PGF Matrix-vector product, real triangular band matrix (STBMV/DTBMV) F06PHF Matrix-vector product, real triangular packed matrix (STPMV/DTPMV) F06PJF System of equations, real triangular matrix (STRSV/DTRSV) F06PKF System of equations, real triangular band matrix (STBSV/DTBSV) F06PLF System of equations, real triangular packed matrix (STPSV/DTPSV) F06PMF Rank-1 update, real rectangular matrix (SGER/DGER) F06PPF Rank-1 update, real symmetric matrix (SSYR/DSYR) F06PQF Rank-1 update, real symmetric packed matrix (SSPR/DSPR) F06PRF Rank-2 update, real symmetric matrix (SSYR2/DSYR2) F06PSF Rank-2 update, real symmetric packed matrix (SSPR2/DSPR2) F06QFF Matrix copy, real rectangular or trapezoidal matrix F06QHF Matrix initialisation, real rectangular matrix F06QJF Permute rows or columns, real rectangular matrix, permutations represented by an integer array F06QKF Permute rows or columns, real rectangular matrix, permutations represented by a real array F06QMF Orthogonal similarity transformation of a real symmetric matrix as a sequence of plane rotations F06QPF QR factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix F06QQF QR factorization by sequence of plane rotations, real upper triangular matrix augmented by a full row F06QRF QR or RQ factorization by sequence of plane rotations, real upper Hessenberg matrix F06QSF QR or RQ factorization by sequence of plane rotations, real upper spiked matrix F06QTF QR factorization of UZ or RQ factorization of ZU, U real upper triangular, Z a sequence of plane rotations F06QVF Compute upper Hessenberg matrix by sequence of plane rotations, real upper triangular matrix F06QWF Compute upper spiked matrix by sequence of plane rotations, real upper triangular matrix F06QXF Apply sequence of plane rotations, real rectangular matrix F06RAF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real general matrix F06RBF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real band matrix F06RCF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real symmetric matrix F06RDF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage F06REF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real symmetric band matrix F06RJF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real trapezoidal/triangular matrix F06RKF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real triangular matrix, packed storage F06RLF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real triangular band matrix F06RMF 1-norm, infinity-norm, Frobenius norm, largest absolute element, real Hessenberg matrix F06SAF Matrix-vector product, complex rectangular matrix (CGEMV/ZGEMV) F06SBF Matrix-vector product, complex rectangular band matrix (CGBMV/ZGBMV) F06SCF Matrix-vector product, complex Hermitian matrix (CHEMV/ZHEMV) F06SDF Matrix-vector product, complex Hermitian band matrix (CHBMV/ZHBMV) F06SEF Matrix-vector product, complex Hermitian packed matrix (CHPMV/ZHPMV) F06SFF Matrix-vector product, complex triangular matrix (CTRMV/ZTRMV) F06SGF Matrix-vector product, complex triangular band matrix (CTBMV/ZTBMV) F06SHF Matrix-vector product, complex triangular packed matrix (CTPMV/ZTPMV) F06SJF System of equations, complex triangular matrix (CTRSV/ZTRSV) F06SKF System of equations, complex triangular band matrix (CTBSV/ZTBSV) F06SLF System of equations, complex triangular packed matrix (CTPSV/ZTPSV) F06SMF Rank-1 update, complex rectangular matrix, unconjugated vector (CGERU/ZGERU) F06SNF Rank-1 update, complex rectangular matrix, conjugated vector (CGERC/ZGERC) F06SPF Rank-1 update, complex Hermitian matrix (CHER/ZHER) F06SQF Rank-1 update, complex Hermitian packed matrix (CHPR/ZHPR) F06SRF Rank-2 update, complex Hermitian matrix (CHER2/ZHER2) F06SSF Rank-2 update, complex Hermitian packed matrix (CHPR2/ZHPR2) F06TFF Matrix copy, complex rectangular or trapezoidal matrix F06THF Matrix initialisation, complex rectangular matrix F06TMF Unitary similarity transformation of a Hermitian matrix as a sequence of plane rotations F06TPF QR factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix F06TQF QR*k factorization by sequence of plane rotations, complex upper triangular matrix augmented by a full row F06TRF QR or RQ factorization by sequence of plane rotations, complex upper Hessenberg matrix F06TSF QR or RQ factorization by sequence of plane rotations, complex upper spiked matrix F06TTF QR factorization of UZ or RQ factorization of ZU, U complex upper triangular, Z a sequence of plane rotations F06TVF Compute upper Hessenberg matrix by sequence of plane rotations, complex upper triangular matrix F06TWF Compute upper spiked matrix by sequence of plane rotations, complex upper triangular matrix F06TXF Apply sequence of plane rotations, complex rectangular matrix, real cosine and complex sine F06TYF Apply sequence of plane rotations, complex rectangular matrix, complex cosine and real sine F06UAF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex general matrix F06UBF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex band matrix F06UCF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex Hermitian matrix F06UDF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex Hermitian matrix, packed storage F06UEF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex Hermitian band matrix F06UFF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex symmetric matrix F06UGF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage F06UHF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex symmetric band matrix F06UJF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex trapezoidal/triangular matrix F06UKF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex triangular matrix, packed storage F06ULF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex triangular band matrix F06UMF 1-norm, infinity-norm, Frobenius norm, largest absolute element, complex Hessenberg matrix F06VJF Permute rows or columns, complex rectangular matrix, permutations represented by an integer array F06VKF Permute rows or columns, complex rectangular matrix, permutations represented by a real array F06VXF Apply sequence of plane rotations, complex rectangular matrix, real cosine and sine F06YAF Matrix-matrix product, two real rectangular matrices (SGEMM/DGEMM) F06YCF Matrix-matrix product, one real symmetric matrix, one real rectangular matrix (SSYMM/DSYMM) F06YFF Matrix-matrix product, one real triangular matrix, one real rectangular matrix (STRMM/DTRMM) F06YJF Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix (STRSM/DTRSM) F06YPF Rank-k update of a real symmetric matrix (SSYRK/DSYRK) F06YRF Rank-2k update of a real symmetric matrix (SSYR2K/DSYR2K) F06ZAF Matrix-matrix product, two complex rectangular matrices (CGEMM/ZGEMM) F06ZCF Matrix-matrix product, one complex Hermitian matrix, one complex rectangular matrix (CHEMM/ZHEMM) F06ZFF Matrix-matrix product, one complex triangular matrix, one complex rectangular matrix (CTRMM/ZTRMM) F06ZJF Solves system of equations with multiple right-hand sides, complex triangular coefficient matrix (CTRSM/ZTRSM) F06ZPF Rank-k update of a complex Hermitian matrix (CHERK/ZHERK) F06ZRF Rank-2k update of a complex Hermitian matrix (CHER2K/ZHER2K) F06ZTF Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix (CSYMM/ZSYMM) F06ZUF Rank-k update of a complex symmetric matrix (CSYRK/ZSYRK) F06ZWF Rank-2k update of a complex symmetric matrix (CSYR2K/ZHER2K) F07ADF LU factorization of real m by n matrix (SGETRF/DGETRF) F07AEF Solution of real system of linear equations, multiple right-hand sides, matrix already factorized by F07ADF (SGETRS/DGETRS) F07AGF Estimate condition number of real matrix, matrix already factorized by F07ADF (SGECON/DGECON) F07AHF Refined solution with error bounds of real system of linear equations, multiple right-hand sides (SGERFS/DGERFS) F07AJF Inverse of a real matrix, matrix already factorized by F07ADF (SGETRI/DGETRI) F07ARF LU factorization of complex m by n matrix (CGETRF/ZGETRF) F07ASF Solution of complex system of linear equations, multiple right-hand sides, matrix already factorized by F07ARF (CGETRS/ZGETRS) F07AUF Estimate condition number of complex matrix, matrix already factorized by F07ARF (CGECON/ZGECON) F07AVF Refined solution with error bounds of complex system of linear equations, multiple right-hand sides (CGERFS/ZGERFS) F07AWF Inverse of a complex matrix, matrix already factorized by F07ARF (CGETRI/ZGETRI) F07BDF LU factorization of real m by n band matrix (SGBTRF/DGBTRF) F07BEF Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by F07BDF (SGBTRS/DGBTRS) F07BGF Estimate condition number of real band matrix, matrix already factorized by F07BDF (SGBCON/DGBCON) F07BHF Refined solution with error bounds of real band system of linear equations, multiple right-hand sides (SGBRFS/DGBRFS) F07BRF LU factorization of complex m by n band matrix (CGBTRF/ZGBTRF) F07BSF Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by F07BRF (CGBTRS/ZGBTRS) F07BUF Estimate condition number of complex band matrix, matrix already factorized by F07BRF (CGBCON/ZGBCON) F07BVF Refined solution with error bounds of complex band system of linear equations, multiple right-hand sides (CGBRFS/ZGBRFS) F07FDF Cholesky factorization of real symmetric positive-definite matrix (SPOTRF/DPOTRF) F07FEF Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF (SPOTRS/DPOTRS) F07FGF Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07FDF (SPOCON/DPOCON) F07FHF Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides (SPORFS/DPORFS) F07FJF Inverse of a real symmetric positive-definite matrix, matrix already factorized by F07FDF (SPOTRI/DPOTRI) F07FRF Cholesky factorization of complex Hermitian positive-definite matrix (CPOTRF/ZPOTRF) F07FSF Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FRF (CPOTRS/ZPOTRS) F07FUF Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07FRF (CPOCON/ZPOCON) F07FVF Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides (CPORFS/ZPORFS) F07FWF Inverse of a complex Hermitian positive-definite matrix, matrix already factorized by F07FRF (CPOTRI/ZPOTRI) F07GDF Cholesky factorization of a real symmetric positive-definite matrix, packed storage (SPPTRF/DPPTRF) F07GEF Solution of real symmetric positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF, packed storage (SPPTRS/DPPTRS) F07GGF Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by F07GDF, packed storage (SPPCON/DPPCON) F07GHF Refined solution with error bounds of real symmetric positive-definite system of linear equations, multiple right-hand sides, packed storage (SPPRFS/DPPRFS) F07GJF Inverse of a real symmetric positive-definite matrix, matrix already factorized by F07GDF, packed storage (SPPTRI/DPPTRI) F07GRF Cholesky factorization of complex Hermitian positive-definite matrix, packed storage (CPPTRF/ZPPTRF) F07GSF Solution of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GRF, packed storage (CPPTRS/ZPPTRS) F07GUF Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by F07GRF, packed storage (CPPCON/ZPPCON) F07GVF Refined solution with error bounds of complex Hermitian positive-definite system of linear equations, multiple right-hand sides, packed storage (CPPRFS/ZPPRFS) F07GWF Inverse of a complex Hermitian positive-definite matrix, matrix already factorized by F07GRF, packed storage (CPPTRI/ZPPTRI) F07HDF Cholesky factorization of real symmetric positive-definite band matrix (SPBTRF/DPBTRF) F07HEF Solution of real symmetric positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF (SPBTRS/DPBTRS) F07HGF Estimate condition number of real symmetric positive-definite band matrix, matrix already factorized by F07HDF (SPBCON/DPBCON) F07HHF Refined solution with error bounds of real symmetric positive-definite band system of linear equations, multiple right-hand sides (SPBRFS/DPBRFS) F07HRF Cholesky factorization of complex Hermitian positive-definite band matrix (CPBTRF/ZPBTRF) F07HSF Solution of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HRF (CPBTRS/ZPBTRS) F07HUF Estimate condition number of complex Hermitian positive-definite band matrix, matrix already factorized by F07HRF (CPBCON/ZPBCON) F07HVF Refined solution with error bounds of complex Hermitian positive-definite band system of linear equations, multiple right-hand sides (CPBRFS/ZPBRFS) F07MDF Bunch--Kaufman factorization of real symmetric indefinite matrix (SSYTRF/DSYTRF) F07MEF Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF (SSYTRS/DSYTRS) F07MGF Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF (SSYCON/DSYCON) F07MHF Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides (SSYRFS/DSYRFS) F07MJF Inverse of a real symmetric indefinite matrix, matrix already factorized by F07MDF (SSYTRI/DSYTRI) F07MRF Bunch--Kaufman factorization of complex Hermitian indefinite matrix (CHETRF/ZHETRF) F07MSF Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MRF (CHETRS/ZHETRS) F07MUF Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07MRF (CHECON/ZHECON) F07MVF Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides (CHERFS/ZHERFS) F07MWF Inverse of a complex Hermitian indefinite matrix, matrix already factorized by F07MRF (CHETRI/ZHETRI) F07NRF Bunch--Kaufman factorization of complex symmetric matrix (CSYTRF/ZSYTRF) F07NSF Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF (CSYTRS/ZSYTRS) F07NUF Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF (CSYCON/ZSYCON) F07NVF Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides (CSYRFS/ZSYRFS) F07NWF Inverse of a complex symmetric matrix, matrix already factorized by F07NRF (CSYTRI/ZSYTRI) F07PDF Bunch--Kaufman factorization of real symmetric indefinite matrix, packed storage (SSPTRF/DSPTRF) F07PEF Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF, packed storage (SSPTRS/DSPTRS) F07PGF Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage (SSPCON/DSPCON) F07PHF Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage (SSPRFS/DSPRFS) F07PJF Inverse of a real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage (SSPTRI/DSPTRI) F07PRF Bunch--Kaufman factorization of complex Hermitian indefinite matrix, packed storage (CHPTRF/ZHPTRF) F07PSF Solution of complex Hermitian indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PRF, packed storage (CHPTRS/ZHPTRS) F07PUF Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage (CHPCON/ZHPCON) F07PVF Refined solution with error bounds of complex Hermitian indefinite system of linear equations, multiple right-hand sides, packed storage (CHPRFS/ZHPRFS) F07PWF Inverse of a complex Hermitian indefinite matrix, matrix already factorized by F07PRF, packed storage (CHPTRI/ZHPTRI) F07QRF Bunch--Kaufman factorization of complex symmetric matrix, packed storage (CSPTRF/ZSPTRF) F07QSF Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF, packed storage (CSPTRS/ZSPTRS) F07QUF Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF, packed storage (CSPCON/ZSPCON) F07QVF Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage (CSPRFS/ZSPRFS) F07QWF Inverse of a complex symmetric matrix, matrix already factorized by F07QRF, packed storage (CSPTRI/ZSPTRI) F07TEF Solution of real triangular system of linear equations, multiple right-hand sides (STRTRS/DTRTRS) F07TGF Estimate condition number of real triangular matrix (STRCON/DTRCON) F07THF Error bounds for solution of real triangular system of linear equations, multiple right-hand sides (STRRFS/DTRRFS) F07TJF Inverse of a real triangular matrix (STRTRI/DTRTRI) F07TSF Solution of complex triangular system of linear equations, multiple right-hand sides (CTRTRS/ZTRTRS) F07TUF Estimate condition number of complex triangular matrix (CTRCON/ZTRCON) F07TVF Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides (CTRRFS/ZTRRFS) F07TWF Inverse of a complex triangular matrix (CTRTRI/ZTRTRI) F07UEF Solution of real triangular system of linear equations, multiple right-hand sides, packed storage (STPTRS/DTPTRS) F07UGF Estimate condition number of real triangular matrix, packed storage (STPCON/DTPCON) F07UHF Error bounds for solution of real triangular system of linear equations, multiple right-hand sides, packed storage (STPRFS/DTPRFS) F07UJF Inverse of a real triangular matrix, packed storage (STPTRI/DTPTRI) F07USF Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage (CTPTRS/ZTPTRS) F07UUF Estimate condition number of complex triangular matrix, packed storage (CTPCON/ZTPCON) F07UVF Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides, packed storage (CTPRFS/ZTPRFS) F07UWF Inverse of a complex triangular matrix, packed storage (CTPTRI/ZTPTRI) F07VEF Solution of real band triangular system of linear equations, multiple right-hand sides (STBTRS/DTBTRS) F07VGF Estimate condition number of real band triangular matrix (STBCON/DTBCON) F07VHF Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides (STBRFS/DTBRFS) F07VSF Solution of complex band triangular system of linear equations, multiple right-hand sides (CTBTRS/ZTBTRS) F07VUF Estimate condition number of complex band triangular matrix (CTBCON/ZTBCON) F07VVF Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides (CTBRFS/ZTBRFS) F08AEF QR factorization of real general rectangular matrix (SGEQRF/DGEQRF) F08AFF Form all or part of orthogonal Q from QR factorization determined by F08AEF or F08BEF (SORGQR/DORGQR) F08AGF Apply orthogonal transformation determined by F08AEF or F08BEF (SORMQR/DORMQR) F08AHF LQ factorization of real general rectangular matrix (SGELQF/DGELQF) F08AJF Form all or part of orthogonal Q from LQ factorization determined by F08AHF (SORGLQ/DORGLQ) F08AKF Apply orthogonal transformation determined by F08AHF (SORMLQ/DORMLQ) F08ASF QR factorization of complex general rectangular matrix (CGEQRF/ZGEQRF) F08ATF Form all or part of unitary Q from QR factorization determined by F08ASF or F08BSF (CUNGQR/ZUNGQR) F08AUF Apply unitary transformation determined by F08ASF or F08BSF (CUNMQR/ZUNMQR) F08AVF LQ factorization of complex general rectangular matrix (CGELQF/ZGELQF) F08AWF Form all or part of unitary Q from LQ factorization determined by F08AVF (CUNGLQ/ZUNGLQ) F08AXF Apply unitary transformation determined by F08AVF (CUNMLQ/ZUNMLQ) F08BEF Form all or part of orthogonal Q from QR factorization determined by F08AEF or F08BEF (SORGQR/DORGQR) F08BSF Form all or part of unitary Q from QR factorization determined by F08ASF or F08BSF (CUNGQR/ZUNGQR) F08FEF Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form (SSYTRD/DSYTRD) F08FFF Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (SORGTR/DORGTR) F08FGF Apply orthogonal transformation determined by F08FEF (SORMTR/DORMTR) F08FSF Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form (CHETRD/ZHETRD) F08FTF Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (CUNGTR/ZUNGTR) F08FUF Apply unitary transformation matrix determined by F08FSF (CUNMTR/ZUNMTR) F08GEF Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage (SSPTRD/DSPTRD) F08GFF Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (SOPGTR/DOPGTR) F08GGF Apply orthogonal transformation determined by F08GEF (SOPMTR/DOPMTR) F08GSF Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage (CHPTRD/ZHPTRD) F08GTF Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (CUPGTR/ZUPGTR) F08GUF Apply unitary transformation matrix determined by F08GSF (CUPMTR/ZUPMTR) F08HEF Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form (SSBTRD/DBSTRD) F08HSF Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form (CHBTRD/ZHBTRD) F08JEF All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR (SSTEQR/DSTEQR) F08JFF All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR (SSTERF/DSTERF) F08JGF All eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix (SPTEQR/DPTEQR) F08JJF Selected eigenvalues of real symmetric tridiagonal matrix by bisection (SSTEBZ/DSTEBZ) F08JKF Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array (SSTEIN/DSTEIN) F08JSF All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR (CSTEQR/ZSTEQR) F08JUF All eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix (CPTEQR/ZPTEQR) F08JXF Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array (CSTEIN/ZSTEIN) F08KEF Orthogonal reduction of real general rectangular matrix to bidiagonal form (SGEBRD/DGEBRD) F08KFF Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (SORGBR/DORGBR) F08KGF Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (SORMBR/DORMBR) F08KSF Unitary reduction of complex general rectangular matrix to bidiagonal form (CGEBRD/ZGEBRD) F08KTF Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (CUNGBR/ZUNGBR) F08KUF Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (CUNMBR/ZUNMBR) F08MEF SVD of real bidiagonal matrix reduced from real general matrix (SBDSQR/DBDSQR) F08MSF SVD of real bidiagonal matrix reduced from complex general matrix (CBDSQR/ZBDSQR) F08NEF Orthogonal reduction of real general matrix to upper Hessenberg form (SGEHRD/DGEHRD) F08NFF Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (SORGHR/DORGHR) F08NGF Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (SORMHR/DORMHR) F08NHF Balance real general matrix (SGEBAL/DGEBAL) F08NJF Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (SGEBAK/DGEBAK) F08NSF Unitary reduction of complex general matrix to upper Hessenberg form (CGEHRD/ZGEHRD) F08NTF Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (CUNGHR/ZUNGHR) F08NUF Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (CUNMHR/ZUNMHR) F08NVF Balance complex general matrix (CGEBAL/ZGEBAL) F08NWF Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (CGEBAK/ZGEBAK) F08PEF Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix (SHSEQR/DHSEQR) F08PKF Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration (SHSEIN/DHSEIN) F08PSF Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix (CHSEQR/ZHSEQR) F08PXF Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration (CHSEIN/ZHSEIN) F08QFF Reorder Schur factorization of real matrix using orthogonal similarity transformation (STREXC/DTREXC) F08QGF Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities (STRSEN/DTRSEN) F08QHF Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes (STRSYL/DTRSYL) F08QKF Left and right eigenvectors of a real upper quasi-triangular matrix (STREVC/DTREVC) F08QLF Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix (STRSNA/DTRSNA) F08QTF Reorder Schur factorization of complex matrix using unitary similarity transformation (CTREXC/ZTREXC) F08QUF Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities (CTRSEN/ZTRSEN) F08QVF Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes (CTRSYL/ZTRSYL) F08QXF Left and right eigenvectors of a complex upper triangular matrix (CTREVC/ZTREVC) F08QYF Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix (CTRSNA/ZTRSNA) F08SEF Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = lambda Bx, ABx = lambda x or BAx = lambda x, B factorized by F07FDF (SSYGST/DSYGST) F08SSF Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = lambda Bx, ABx = lambda x or BAx = lambda x, B factorized by F07FRF (CHEGST/ZHEGST) F08TEF Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = lambda Bx, ABx = lambda x or BAx = lambda x, packed storage, B factorized by F07GDF (SSPGST/DSPGST) F08TSF Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = lambda Bx, ABx = lambda x or BAx = lambda x, packed storage, B factorized by F07GRF (CHPGST/ZHPGST) F11BAF Real sparse nonsymmetric linear systems, set-up for F11BBF F11BBF Real sparse nonsymmetric linear systems, preconditioned RGMRES, CGS or Bi-CGSTAB F11BCF Real sparse nonsymmetric linear systems, diagnostic for F11BBF F11DAF Real sparse nonsymmetric linear systems, incomplete LU factorization F11DBF Solution of linear system involving incomplete LU preconditioning matrix generated by F11DAF F11DCF Solution of real sparse nonsymmetric linear system, RGMRES, CGS or Bi-CGSTAB method, preconditioner computed by F11DAF (Black Box) F11DDF Solution of linear system involving pre-conditioning matrix gnerated by applying SSOR to real sparse nonsymmetric matrix F11DEF Solution of real sparse nonsymmetric linear system, RGMRES, CGS, or Bi-CGSTAB method, Jacobi or SSOR preconditioner (Black Box) F11GAF Real sparse symmetric linear systems, set-up for F11GBF F11GBF Real sparse symmetric linear systems, pre-conditioned conjugate gradient or Lanczos F11GCF Real sparse symmetric linear systems, diagnostic for F11GBF F11JAF Real sparse symmetric matrix, incomplete Cholesky factorization F11JBF Solution of linear system involving incomplete Cholseky preconditioning matrix generated by F11JAF F11JCF Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box) F11JDF Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix F11JEF Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box) F11XAF Real sparse nonsymmetric matrix vector multiply F11XEF Real sparse symmetric matrix vector multiply F11ZAF Real sparse nonsymmetric matrix reorder routine F11ZBF Real sparse symmetric matrix reorder routine G01AAF Mean, variance, skewness, kurtosis etc, one variable, from raw data G01ABF Mean, variance, skewness, kurtosis etc, two variables, from raw data G01ADF Mean, variance, skewness, kurtosis etc, one variable, from frequency table G01AEF Frequency table from raw data G01AFF Two-way contingency table analysis, with chi**2/Fisher's exact test G01AGF Lineprinter scatterplot of two variables G01AHF Lineprinter scatterplot of one variable against Normal scores G01AJF Lineprinter histogram of one variable G01ALF Computes a five-point summary (median, hinges and extremes) G01ARF Constructs a stem and leaf plot G01ASF Constructs a box and whisker plot G01BJF Binomial distribution function G01BKF Poisson distribution function G01BLF Hypergeometric distribution function G01DAF Normal scores, accurate values G01DBF Normal scores, approximate values G01DCF Normal scores, approximate variance--covariance matrix G01DDF Shapiro and Wilk's W test for Normality G01DHF Ranks, Normal scores, approximate Normal scores or exponential (Savage) scores G01EAF Computes probabilities for the standard Normal distribution G01EBF Computes probabilities for Student's t-distribution G01ECF Computes probabilities for chi**2 distribution G01EDF Computes probabilities for F-distribution G01EEF Computes upper and lower tail probabilities and probability density function for the beta distribution G01EFF Computes probabilities for the gamma distribution G01EMF Computes probability for the Studentized range statistic G01EPF Computes bounds for the significance of a Durbin--Watson statistic G01ERF Computes probability for Von Mises distribution G01EYF Computes probabilities for the one-sample Kolmogorov--Smirnov distribution G01EZF Computes probabilities for the two-sample Kolmogorov--Smirnov distribution G01FAF Computes deviates for the standard Normal distribution G01FBF Computes deviates for Student's t-distribution G01FCF Computes deviates for the chi**2 distribution G01FDF Computes deviates for the F-distribution G01FEF Computes deviates for the beta distribution G01FFF Computes deviates for the gamma distribution G01FMF Computes deviates for the Studentized range statistic G01GBF Computes probabilities for the non-central Student's t-distribution G01GCF Computes probabilities for the non-central chi**2 distribution G01GDF Computes probabilities for the non-central F-distribution G01GEF Computes probabilities for the non-central beta distribution G01HAF Computes probability for the bivariate Normal distribution G01HBF Computes probabilities for the multivariate Normal distribution G01JCF Computes probability for a positive linear combination of chi**2 variables G01JDF Computes lower tail probability for a linear combination of (central) chi**2 variables G01MBF Computes reciprocal of Mills' Ratio G01NAF Cumulants and moments of quadratic forms in Normal variables G01NBF Moments of ratios of quadratic forms in Normal variables, and related statistics G02BAF Pearson product-moment correlation coefficients, all variables, no missing values G02BBF Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values G02BCF Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values G02BDF Correlation-like coefficients (about zero), all variables, no missing values G02BEF Correlation-like coefficients (about zero), all variables, casewise treatment of missing values G02BFF Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values G02BGF Pearson product-moment correlation coefficients, subset of variables, no missing values G02BHF Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values G02BJF Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values G02BKF Correlation-like coefficients (about zero), subset of variables, no missing values G02BLF Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values G02BMF Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values G02BNF Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data G02BPF Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data G02BQF Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data G02BRF Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data G02BSF Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values G02BTF Update a weighted sum of squares matrix with a new observation G02BUF Computes a weighted sum of squares matrix G02BWF Computes a correlation matrix from a sum of squares matrix G02BXF Computes (optionally weighted) correlation and covariance matrices G02BYF Computes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by G02BXF G02CAF Simple linear regression with constant term, no missing values G02CBF Simple linear regression without constant term, no missing values G02CCF Simple linear regression with constant term, missing values G02CDF Simple linear regression without constant term, missing values G02CEF Service routines for multiple linear regression, select elements from vectors and matrices G02CFF Service routines for multiple linear regression, re-order elements of vectors and matrices G02CGF Multiple linear regression, from correlation coefficients, with constant term G02CHF Multiple linear regression, from correlation-like coefficients, without constant term G02DAF Fits a general (multiple) linear regression model G02DCF Add/delete an observation to/from a general linear regression model G02DDF Estimates of linear parameters and general linear regression model from updated model G02DEF Add a new variable to a general linear regression model G02DFF Delete a variable from a general linear regression model G02DGF Fits a general linear regression model for new dependent variable G02DKF Estimates and standard errors of parameters of a general linear regression model for given constraints G02DNF Computes estimable function of a general linear regression model and its standard error G02EAF Computes residual sums of squares for all possible linear regressions for a set of independent variables G02ECF Calculates R**2 and C(P values from residual sums of squares G02EEF Fits a linear regression model by forward selection G02FAF Calculates standardized residuals and influence statistics G02FCF Computes Durbin--Watson test statistic G02GAF Fits a generalized linear model with Normal errors G02GBF Fits a generalized linear model with binomial errors G02GCF Fits a generalized linear model with Poisson errors G02GDF Fits a generalized linear model with gamma errors G02GKF Estimates and standard errors of parameters of a general linear model for given constraints G02GNF Computes estimable function of a generalized linear model and its standard error G02HAF Robust regression, standard M-estimates G02HBF Robust regression, compute weights for use with G02HDF G02HDF Robust regression, compute regression with user-supplied functions and weights G02HFF Robust regression, variance-covariance matrix following G02HDF G02HKF Calculates a robust estimation of a correlation matrix, Huber's weight function G02HLF Calculates a robust estimation of a correlation matrix, user-supplied weight function plus derivatives G02HMF Calculates a robust estimation of a correlation matrix, user-supplied weight function G03AAF Performs principal component analysis G03ACF Performs canonical variate analysis G03ADF Performs canonical correlation analysis G03BAF Computes orthogonal rotations for loading matrix, generalized orthomax criterion G03BCF Computes Procrustes rotations G03CAF Computes the maximum likelihood estimates of the parameters of a factor analysis model, factor loadings, communalities and residual correlations G03CCF Computes factor score coefficients (for use after G03CAF) G03DAF Computes test statistic for equality of within-group covariance matrices and matrices for discriminant analysis G03DBF Computes Mahalanobis squared distances for group or pooled variance-covariance matrices (for use after G03DAF) G03DCF Allocates observations to groups according to selected rules (for use after G03DAF) G03EAF Computes distance matrix G03ECF Hierarchical cluster analysis G03EFF K-means cluster analysis G03EHF Constructs dendrogram (for use after G03ECF) G03EJF Computes cluster indicator variable (for use after G03ECF) G03FAF Performs principal co-ordinate analysis, classical metric scaling G03FCF Performs non-metric (ordinal) multidimensional scaling G03ZAF Produces standardized values (z-scores) for a data matrix G04AGF Two-way analysis of variance, hierarchical classification, subgroups of unequal size G04BBF Analysis of variance, randomized block or completely randomized design, treatment means and standard errors G04BCF Analysis of variance, general row and column design, treatment means and standard errors G04CAF Analysis of variance, complete factorial design, treatment means and standard errors G04DAF Computes sum of squares for contrast between means G04DBF Computes confidence intervals for differences between means computed by G04BBF or G04BCF G04EAF Computes orthogonal polynomials or dummy variables for factor/classification variable G05CAF Pseudo-random real numbers, uniform distribution over (0,1) G05CBF Initialise random number generating routines to give repeatable sequence G05CCF Initialise random number generating routines to give non-repeatable sequence G05CFF Save state of random number generating routines G05CGF Restore state of random number generating routines G05DAF Pseudo-random real numbers, uniform distribution over (a,b) G05DBF Pseudo-random real numbers, (negative) exponential distribution G05DCF Pseudo-random real numbers, logistic distribution G05DDF Pseudo-random real numbers, Normal distribution G05DEF Pseudo-random real numbers, lognormal distribution G05DFF Pseudo-random real numbers, Cauchy distribution G05DHF Pseudo-random real numbers, chi**2 distribution G05DJF Pseudo-random real numbers, Student's t-distribution G05DKF Pseudo-random real numbers, F-distribution G05DPF Pseudo-random real numbers, Weibull distribution G05DRF Pseudo-random integer, Poisson distribution G05DYF Pseudo-random integer from uniform distribution G05DZF Pseudo-random logical (boolean) value G05EAF Set up reference vector for multivariate Normal distribution G05EBF Set up reference vector for generating pseudo-random integers, uniform distribution G05ECF Set up reference vector for generating pseudo-random integers, Poisson distribution G05EDF Set up reference vector for generating pseudo-random integers, binomial distribution G05EEF Set up reference vector for generating pseudo-random integers, negative binomial distribution G05EFF Set up reference vector for generating pseudo-random integers, hypergeometric distribution G05EGF Set up reference vector for univariate ARMA time series model G05EHF Pseudo-random permutation of an integer vector G05EJF Pseudo-random sample from an integer vector G05EWF Generate next term from reference vector for ARMA time series model G05EXF Set up reference vector from supplied cumulative distribution function or probability distribution function G05EYF Pseudo-random integer from reference vector G05EZF Pseudo-random multivariate Normal vector from reference vector G05FAF Generates a vector of random numbers from a uniform distribution G05FBF Generates a vector of random numbers from an (negative) exponential distribution G05FDF Generates a vector of random numbers from a Normal distribution G05FEF Generates a vector of pseudo-random numbers from a beta distribution G05FFF Generates a vector of pseudo-random numbers from a gamma distribution G05FSF Generates vector of pseudo-random variates from Von Mises distribution G05GAF Computes random orthogonal matrix G05GBF Computes random correlation matrix G05HDF Generates a realisation of a multivariate time series from a VARMA model G07AAF Computes confidence interval for the parameter of a binomial distribution G07ABF Computes confidence interval for the parameter of a Poisson distribution G07BBF Computes maximum likelihood estimates for parameters of the Normal distribution from grouped and/or censored data G07BEF Computes maximum likelihood estimates for parameters of the Weibull distribution G07CAF Computes t-test statistic for a difference in means between two Normal populations, confidence interval G07DAF Robust estimation, median, median absolute deviation, robust standard deviation G07DBF Robust estimation, M-estimates for location and scale parameters, standard weight functions G07DCF Robust estimation, M-estimates for location and scale parameters, user-defined weight functions G07DDF Computes a trimmed and winsorized mean of a single sample with estimates of their variance G07EAF Robust confidence intervals, 1 sample G07EBF Robust confidence intervals, 2 sample G08AAF Sign test on two paired samples G08ACF Median test on two samples of unequal size G08AEF Friedman two-way analysis of variance on k matched samples G08AFF Kruskal--Wallis one-way analysis of variance on k samples of unequal size G08AGF Performs the Wilcoxon one-sample (matched pairs) signed rank test G08AHF Performs the Mann--Whitney U test on two independent samples G08AJF Computes the exact probabilities for the Mann--Whitney U statistic, no ties in pooled sample G08AKF Computes the exact probabilities for the Mann--Whitney U statistic, ties in pooled sample G08ALF Performs the Cochran Q test on cross-classified binary data G08BAF Mood's and David's tests on two samples of unequal size G08CBF Performs the one-sample Kolmogorov--Smirnov test for standard distributions G08CCF Performs the one-sample Kolmogorov--Smirnov test for a user-supplied distribution G08CDF Performs the two-sample Kolmogorov--Smirnov test G08CGF Performs the chi**2 goodness of fit test, for standard continuous distributions G08DAF Kendall's coefficient of concordance G08EAF Performs the runs up or runs down test for randomness G08EBF Performs the pairs (serial) test for randomness G08ECF Performs the triplets test for randomness G08EDF Performs the gaps test for randomness G08RAF Regression using ranks, uncensored data G08RBF Regression using ranks, right-censored data G10ABF Fit cubic smoothing spline, smoothing parameter given G10ACF Fit cubic smoothing spline, smoothing parameter estimated G10BAF Kernel density estimate using Gaussian kernel G10CAF Compute smoothed data sequence using running median smoothers G10ZAF Reorder data to give ordered distinct observations G11AAF chi**2 statistics for two-way contingency table G11BAF Computes multiway table from set of classification factors using selected statistic G11BBF Computes multiway table from set of classification factors using given percentile/quantile G11BCF Computes marginal tables for multiway table computed by G11BAF or G11BBF G11SAF Contingency table, latent variable model for binary data G11SBF Frequency count for G11SAF G12AAF Computes Kaplan--Meier (product-limit) estimates of survival probabilities G12BAF Fits Cox's proportional hazard model G13AAF Univariate time series, seasonal and non-seasonal differencing G13ABF Univariate time series, sample autocorrelation function G13ACF Univariate time series, partial autocorrelations from autocorrelations G13ADF Univariate time series, preliminary estimation, seasonal ARIMA model G13AEF Univariate time series, estimation, seasonal ARIMA model (comprehensive) G13AFF Univariate time series, estimation, seasonal ARIMA model (easy-to-use) G13AGF Univariate time series, update state set for forecasting G13AHF Univariate time series, forecasting from state set G13AJF Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model G13ASF Univariate time series, diagnostic checking of residuals, following G13AEF or G13AFF G13AUF Computes quantities needed for range-mean or standard deviation-mean plot G13BAF Multivariate time series, filtering (pre-whitening) by an ARIMA model G13BBF Multivariate time series, filtering by a transfer function model G13BCF Multivariate time series, cross-correlations G13BDF Multivariate time series, preliminary estimation of transfer function model G13BEF Multivariate time series, estimation of multi-input model G13BGF Multivariate time series, update state set for forecasting from multi-input model G13BHF Multivariate time series, forecasting from state set of multi-input model G13BJF Multivariate time series, state set and forecasts from fully specified multi-input model G13CAF Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window G13CBF Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window G13CCF Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window G13CDF Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window G13CEF Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra G13CFF Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra G13CGF Multivariate time series, noise spectrum, bounds, impulse response function and its standard error G13DBF Multivariate time series, multiple squared partial autocorrelations G13DCF Multivariate time series, estimation of VARMA model G13DJF Multivariate time series, forecasts and their standard errors G13DKF Multivariate time series, updates forecasts and their standard errors G13DLF Multivariate time series, differences and/or transforms (for use before G13DCF) G13DMF Multivariate time series, sample cross-correlation or cross-covariance matrices G13DNF Multivariate time series, sample partial lag correlation matrices, chi**2 statistics and significance levels G13DPF Multivariate time series, partial autoregression matrices G13DSF Multivariate time series, diagnostic checking of residuals, following G13DCF G13DXF Calculates the zeros of a vector autoregressive (or moving average) operator G13EAF Combined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter G13EBF Combined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter H02BBF Integer programming problem, branch and bound method H02BFF Interpret MPSX data file defining IP or LP problem, optimize and print solution H02BUF Converts MPSX data file defining IP or LP problem to format required by H02BBF or E04MFF H02BVF Prints IP or LP solutions with user specified names for rows and columns H02BZF Integer programming solution, supplies further information on solution obtained by H02BBF H03ABF Transportation problem, modified `stepping stone' method H03ADF Shortest path problem, Dijkstra's algorithm M01CAF Sort a vector, real numbers M01CBF Sort a vector, integer numbers M01CCF Sort a vector, character data M01DAF Rank a vector, real numbers M01DBF Rank a vector, integer numbers M01DCF Rank a vector, character data M01DEF Rank rows of a matrix, real numbers M01DFF Rank rows of a matrix, integer numbers M01DJF Rank columns of a matrix, real numbers M01DKF Rank columns of a matrix, integer numbers M01DZF Rank arbitrary data M01EAF Rearrange a vector according to given ranks, real numbers M01EBF Rearrange a vector according to given ranks, integer numbers M01ECF Rearrange a vector according to given ranks, character data M01ZAF Invert a permutation M01ZBF Check validity of a permutation M01ZCF Decompose a permutation into cycles P01ABF Return value of error indicator/terminate with error message S01BAF ln(1+x) S01EAF Complex exponential, e**z S07AAF tan x S09AAF arcsin x S09ABF arccos x S10AAF tanh x S10ABF sinh x S10ACF cosh x S11AAF arctanh x S11ABF arcsinh x S11ACF arccosh x S13AAF Exponential integral E(1(x)) S13ACF Cosine integral Ci(x) S13ADF Sine integral Si(x) S14AAF Gamma function S14ABF Log Gamma function S14ACF psi(x) - ln x S14ADF Scaled derivatives of psi(x) S14BAF Incomplete gamma functions P(a,x) and Q(a,x) S15ABF Cumulative normal distribution function P(x) S15ACF Complement of cumulative normal distribution function Q(x) S15ADF Complement of error function erfc(x) S15AEF Error function erf(x) S15AFF Dawson's integral S15DDF Scaled complex complement of error function, exp(-z**2)erfc(-iz) S17ACF Bessel function Y(0(x)) S17ADF Bessel function Y(1(x)) S17AEF Bessel function J(0(x)) S17AFF Bessel function J(1(x)) S17AGF Airy function Ai(x) S17AHF Airy function Bi(x) S17AJF Airy function Ai'(x) S17AKF Airy function Bi'(x) S17DCF Bessel functions Y(nu+a(z)) real a >= 0, complex z, nu = 0,1, 2,... S17DEF Bessel functions J(nu+a(z)), real a >= 0, complex z, nu = 0,1, 2,... S17DGF Airy functions Ai(z) and Ai'(z), complex z S17DHF Airy functions Bi(z) and Bi'(z), complex z S17DLF Hankel functions H(nu+a**(j))(z), j = 1,2, real a >= 0, complex z, nu = 0,1,2,... S18ACF Modified Bessel function K(0 (x) S18ADF Modified Bessel function K(1 (x) S18AEF Modified Bessel function I(0 (x) S18AFF Modified Bessel function I(1(x) S18CCF Modified Bessel function e**xK(0(x) S18CDF Modified Bessel function e**xK(1(x) S18CEF Modified Bessel function e**(-|x|I(0(x)) S18CFF Modified Bessel function e**(-|x|I**1(x)) S18DCF Modified Bessel functions K(nu+a(z)), real a >= 0, complex z, nu = 0,1,2,... S18DEF Modified Bessel functions I(nu+a(z)), real a >= 0, complex z, nu = 0,1,2,... S19AAF Kelvin function ber x S19ABF Kelvin function bei x S19ACF Kelvin function ker x S19ADF Kelvin function kei x S20ACF Fresnel integral S(x) S20ADF Fresnel integral C(x) S21BAF Degenerate symmetrised elliptic integral of 1st kind R(C(x,y) S21BBF Symmetrised elliptic integral of 1st kind R(F(x,y,z) S21BCF Symmetrised elliptic integral of 2nd kind R(D(x,y,z) S21BDF Symmetrised elliptic integral of 3rd kind R(J(x,y,z,r) S21CAF Jacobian elliptic functions sn, cn and dn X01AAF Provides the mathematical constant pi X01ABF Provides the mathematical constant gamma (Euler's Constant), X02AHF The largest permissable argument for sin and cos X02AJF The machine precision X02AKF The smallest positive model number X02ALF The largest positive model number X02AMF The safe range parameter X02ANF The safe range parameter for complex floating-point arithmetic X02BBF The largest representable integer X02BEF The maximum number of decimal digits that can be represented X02BHF The floating-point model parameter, b X02BJF The floating-point model parameter, p X02BKF The floating-point model parameter e(min) X02BLF The floating-point model parameter e(max) X02DAF Switch for taking precautions to avoid underflow X02DJF The floating-point model parameter ROUNDS X03AAF Real inner product added to initial value, basic/additional precision X03ABF Complex inner product added to initial value, basic/additional precision X04AAF Return or set unit number for error messages X04ABF Return or set unit number for advisory messages X04BAF Write formatted record to external file X04BBF Read formatted record from external file X04CAF Print a real general matrix (easy-to-use) X04CBF Print a real general matrix (comprehensive) X04CCF Print a real packed triangular matrix (easy-to-use) X04CDF Print a real packed triangular matrix (comprehensive) X04CEF Print a real packed banded matrix (easy-to-use) X04CFF Print a real packed banded matrix (comprehensive) X04DAF Print a complex general matrix (easy-to-use) X04DBF Print a complex general matrix (comprehensive) X04DCF Print a complex packed triangular matrix (easy-to-use) X04DDF Print a complex packed triangular matrix (comprehensive) X04DEF Print a complex packed banded matrix (easy-to-use) X04DFF Print a complex packed banded matrix (comprehensive) X04EAF Print an integer matrix (easy-to-use) X04EBF Print an integer matrix (comprehensive) X05AAF Return date and time as an array of integers X05ABF Convert array of integers representing date and time to character string X05ACF Compare two character strings representing date and time X05BAF Return the CPU time