CERN Accelerating science

NAG Fortran Library - New Features coming with Mark 16

Mark 16 represents a further considerable expansion of the NAG Fortran Library. It contains a total of 1134 documented routines, of which 126 are new at this Mark. Two new chapters have been introduced:

• F08 - Least-squares and Eigenvalue Problems
  (LAPACK)
• G10 - Smoothing

Out of 126 new routines, 72 are in the new chapter F08. This new chapter includes routines to compute the solution of linear least-squares, symmetric eigenvalue, unsymmetric eigenvalue, singular value and generalized symmetric-definite eigenvalue problems. In addition there are routines to perform various matrix factorizations associated with the above problems, estimate condition numbers of eigenvalues and eigenvectors, estimate the rank of a matrix, and solve the Sylvester matrix equation. 22 of the new routines are in the Statistics chapters. They include facilities (in the stated chapters) for:

• further statistical distribution functions (G01)
• cluster analysis (G03)
• improved analysis of variance routines (G04)
• further random number generators, including matrices (G05)
• computation of robust confidence intervals (G07)
• smoothing techniques (G10)
• two way contigency table analysis (G11)
• computation of partial autoregressive matrices (G13)

Coverage in the differential and integral equations chapters has been improved and extended with (in the stated chapters):

• new Runge-Kutta methods for the initial value problem in ordinary differential equations (D02)

• a Keller box discretization technique for first order partial differential equations (with coupled differential algebraic systems) in one spatial dimension and remeshing facilities (D03)

• routines to solve weakly singular nonlinear convolution Volterra-Abel equations (D05)

New more robust techniques have been incorporated in the optimization Chapter (E04) for the solution of linear programming and quadratic programming problems.

New black-box eigenvalue problem routines which exploit software in the new F08 Chapter have been included in the eigenvalues and eigenvectors Chapter (F02).