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A code is presented which offers a simple clean way to get output that is very easy to read. Special support is given for the output of error messages which are a part of an application package or subprogram library. The code uses many of the features in Fortran 2003, and the "NEWUNIT=" in an open statement from Fortran 2008. The latter can easily be replaced with "UNIT=99". One goal here is to illustrate some of the nice features in recent incarnations of Fortran. [ABSTRACT FROM AUTHOR]

Software to compute angular and radial Mathieu functions is provided in the case that the parameter q is a complex variable and the independent variable x is real. After an introduction on the notation and the definitions of Mathieu functions and their related properties, Fortran 90 subroutines to compute them are described and validated with some comparisons. A sample application is also provided. [ABSTRACT FROM AUTHOR]

The SPQR_RANK package contains routines that calculate the numerical rank of large, sparse, numerically rank-deficient matrices. The routines can also calculate orthonormal bases for numerical null spaces, approximate pseudoinverse solutions to least squares problems involving rank-deficient matrices, and basic solutions to these problems. The algorithms are based on SPQR from SuiteSparseQR (ACM Transactions on Mathematical Software 38, Article 8, 2011). SPQR is a high-performance routine for forming QR factorizations of large, sparse matrices. It returns an estimate for the numerical rank that is usually, but not always, correct. The new routines improve the accuracy of the numerical rank calculated by SPQR and reliably determine the numerical rank in the sense that, based on extensive testing with matrices from applications, the numerical rank is almost always accurately determined when our methods report that the numerical rank should be correct. Reliable determination of numerical rank is critical to the other calculations in the package. The routines work well for matrices with either small or large null space dimensions. [ABSTRACT FROM AUTHOR]

Four routines called DPOTF3i, i = a,b,c,d, are presented. DPOTF3i are a novel type of level-3 BLAS for use by BPF (Slocked Packed format) Cholesky factorization and LAPACK routine DPOTRF Performance of routines DPOTF3i are still increasing when the performance of Level-2 routine DPOTF2 of LAPACK starts decreasing. This is our main result and it implies, due to the use of larger block size nb, that DGEMM, DSYRK, and DTRSM performance also increases! The four DPOTF3i routines use simple register blocking. Different platforms have different numbers of registers. Thus, our four routines have different register blocking sizes. BPF is introduced. LAPACK routines for POTRF and PPTRF using BPF instead of full and packed format are shown to be trivial modifications of LAPACK POTRF source codes. We call these codes BPTRF. There are two variants of BPF: lower and upper. Upper BPF is "identical" to Square Block Packed Format (SBPF). "LAPACK" implementations on multicore processors use SBPF Lower BPF is less efficient than upper BPF. Vector inplace transposition converts lower BPF to upper BPF very efficiently. Corroborating performance results for DPOTF3i versus DPOTF2 on a variety of common platforms are given for n & nb as well as results for large n comparing DBPTRF versus DPOTRF. [ABSTRACT FROM AUTHOR]

We present subroutines for the Cholesky factorization of a positive-definite symmetric matrix and for solving corresponding sets of linear equations. They exploit cache memory by using the block hybrid format proposed by the authors in a companion article. The matrix is packed into n(n + 1)/2 real variables, and the speed is usually better than that of the LAPACK algorithm that uses full storage (n2 variables). Included are subroutines for rearranging a matrix whose upper or lower-triangular part is packed by columns to this format and for the inverse rearrangement. Also included is a kernel subroutine that is used for the Cholesky factorization of the diagonal blocks since it is suitable for any positive-definite symmetric matrix that is small enough to be held in cache. We provide a comprehensive test program and simple example programs. [ABSTRACT FROM AUTHOR]

A translation to Fortran 90 of Gertrude Blanch's algorithm for computing the expansion coefficients of the series that represent Mathieu functions is presented. Its advantages are portability, higher precision, practicality of use, and extended documentation. In addition, numerical validations and comparisons with other existing methods are presented. [ABSTRACT FROM AUTHOR]

Proposes FORTRAN subroutines for approximately solving the feedback vertex and arc set problems on directed graphs using a Greedy Randomized Adaptive Search Procedure (GRASP). Usage of the subroutines; Property of the GRASP algorithm.

Presents information on four Fortran subroutines for nondifferentiable optimization. Description of each subroutine; Sequential quadratic programming methods for nonlinear minimax optimization; Bundle-type methods for nonsmooth optimization.

Presents a study which described subroutines for generating preconditioners for the conjugate gradient method. Use of the subroutines in linear systems; Overview of the quasi-Newton preconditioners; Results of the study.

Explains some of the changes that have been incorporated in the LAPACK subroutine for reducing a symmetric banded matrix to tridiagonal form. Banded singular value decomposition problem; Banded symmetric positive definite generalized eigenvalue problem; Accumulation of transformations for the reduction to bidiagonal form.

Presents the design, implementation and interface of a library of Basic Linear Algebra Subroutines for sparse matrices (PSBLAS) which is specifically tailored to distributed-memory computers. PSBLAS library components hierarchy; Main PSBLAS data structures; Operations in the PSBLAS library.

Discusses the modification of subroutines in EISPACK and LAPACK for finding a few of the eigenvalues of a symmetric tridiagonal matrix. Relative difference of various smallest eigenvalues of principal minors to the full matrix; Course for the smallest eigenvalue; First three modes of the fiber problem.

Deals with a study which described LAPACK-based Fortran 77 subroutines for the reduction of a Hamiltonian matrix to square-reduced form and the approximation of all its eigenvalues using the implicit version of Van Loan's method. Description of the Van Loan's square-reduced method; Implementation of the algorithm; Numerical examples of the study.

Presents information on a study which described Fortran subroutines for finding approximate solutions of the maximum planar subgraph problem (graph planarization) using a Greedy Randomized Adaptive Search Procedure (GRASP). Information on graph planarization; GRASP for graph planarization; Design and implementation of the subroutines; Usage of the subroutines; Computational results.

We show that the Fortran source code for Algorithm 815 contains an error and we propose a correction. The error may cause the algorithm to generate incorrect results. We also show that the performance of the corrected algorithm can be improved by a minor adjustment in the code. [ABSTRACT FROM AUTHOR]

Focuses on several improvements to the estimation of partial derivatives in Algorithm 761. Calculation of the probability and final weights in subroutine SDPD3P; Computation of a determinant in subroutine SDLEQN; Calculation of the condition number of a matrix in subroutine SDLEQN.