LAPACK95 ‐ high performance linear algebra package

LAPACK95 is a set of FORTRAN95 subroutines which interfaces FORTRAN95 with LAPACK. All LAPACK driver subroutines (including expert drivers) and some LAPACK computationals have both generic LAPACK95 interfaces and generic LAPACK77 interfaces. The remaining computationals have only generic LAPACK77 interfaces. In both types of interfaces no distinction is made between single and double precision or between real and complex data types. LAPACK95 - didelio našumo tiesinės algebros algoritmų paketas Santrauka Šiame darbe aprašytas LAPACK 95 paketas, kuri sudaro FORTRAN95 paprogramiu rinkinys. Jos skirtos realizuoti FORTRAN 95 interfeisa su standartine LAPACK biblioteka. Pateikiama būtiniausia informacija apie LAPACK, ScaLAPACK, FORTRAN 95 ir HPF bibliotekas. Po to trumpai suformuluojami bendri interfeiso sudarymo principai. LAPACK 95 nera nauja tiesines algebros algoritmu biblioteka, o tik konverteris, leidžiantis ir FORTRAN 95 programose naudoti LAPACK algoritmus. Parodyta, kaip galima išnaudoti platesnes FORTRAN 95 galimybes lyginant su standartiniu FORTRAN 77. Pateikti interfeisu pavyzdžiai. First Published Online: 14 Oct 201

Rectangular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion

We describe a new data format for storing triangular, symmetric, and Hermitian matrices called RFPF (Rectangular Full Packed Format). The standard two dimensional arrays of Fortran and C (also known as full format) that are used to represent triangular and symmetric matrices waste nearly half of the storage space but provide high performance via the use of Level 3 BLAS. Standard packed format arrays fully utilize storage (array space) but provide low performance as there is no Level 3 packed BLAS. We combine the good features of packed and full storage using RFPF to obtain high performance via using Level 3 BLAS as RFPF is a standard full format representation. Also, RFPF requires exactly the same minimal storage as packed format. Each LAPACK full and/or packed triangular, symmetric, and Hermitian routine becomes a single new RFPF routine based on eight possible data layouts of RFPF. This new RFPF routine usually consists of two calls to the corresponding LAPACK full format routine and two calls to Level 3 BLAS routines. This means {\it no} new software is required. As examples, we present LAPACK routines for Cholesky factorization, Cholesky solution and Cholesky inverse computation in RFPF to illustrate this new work and to describe its performance on several commonly used computer platforms. Performance of LAPACK full routines using RFPF versus LAPACK full routines using standard format for both serial and SMP parallel processing is about the same while using half the storage. Performance gains are roughly one to a factor of 43 for serial and one to a factor of 97 for SMP parallel times faster using vendor LAPACK full routines with RFPF than with using vendor and/or reference packed routines

Ilościowa analiza kompozytów poliuretanowych z nieorganicznym napełniaczem do zastosowań na implanty krążka międzykręgowego

The aim of this research was to develop a composite material to be used as an elastomeric core of the artificial intervertebral disc. Two types of polyurethane composites with non-modified SiO2 and SiO2 modified NH2 group were obtained. The composites made of these materials have different filler content. The effect of modifying fillers for the structure and properties of these materials were investigated.Celem pracy było opracowanie kompozytu do zastosowań na elastomerowy rdzeń sztucznego krążka międzykręgowego. Wytworzono dwa rodzaje kompozytów poliuretanowych zawierających niemodyfikowany SiO2 jak również SiO2 modyfikowany grupami NH2. W ramach pracy przeanalizowano wpływ modyfikacji napełniacza na strukturę i właściwości wytworzonych materiałów

Effect of the content of rigid segments on the properties of polycarbonate urethanes for use in intervertebral disc implants

Otrzymano serię poli(węglanouretanów), o zawartości 30, 34 i 45 % mas. segmentów sztywnych, z diizocyjanianu 4,4'-dicykloheksylometanu (HMDI) ioligowęglanodiolu. Scharakteryzowano właściwości oraz strukturę wytworzonych poli(węglanouretanów) za pomocą spektroskopii w podczerwieni FT-IR, różnicowej kalorymetrii skaningowej (DSC), analizy dynamicznych właściwości mechanicznych (DMA), analizy termograwimetrycznej (TGA) oraz skaningowej mikroskopii elektronowej (SEM). Oceniono również właściwości wytrzymałościowe, odporność na zużycie ścierne, a także wykonano testy tribologiczne, oznaczono twardość, elastyczność przy odbiciu, gęstość i kąt zwilżania oraz obliczono swobodną energię powierzchniową. Przeprowadzono wstępne badania biologiczne, określające toksyczność opracowanych materiałów. Wybrane próbki otrzymanych materiałów testowano na symulatorze segmentu ruchowego kręgosłupa. Wytworzony implant krążka międzykręgowego po 3 mln cykli nie wykazywał śladów niszczenia spowodowanego użyciem ściernym i nie zmienił swojej charakterystyki wytrzymałościowej.A series of polycarbonate urethanes (PUR) containing 30, 34 and 45 wt % hard segments was synthesized from oligocarbonate diol (OCD) and dicyclohexylmethane 4,4'-diisocyanate (HMDI). The structure and properties of the obtained polymers were characterized using infrared spectroscopy with Fourier transformation (FT-IR), differential scanning calorimetry (DSC), dynamic mechanical thermal analysis (DMA), thermogravimetric analysis (TGA) and scanning electron microscopy (SEM). The tensile strength properties, hardness, resilience and density of PUR were determined and abrasive wear resistance was evaluated in a tribological test. The surface properties were examined using contact angle measurements and free surface energy was calculated. The preliminary cytotoxicity tests were performed. The selected samples of the obtained materials were tested using the simulator of spine motion segment. The intervertebral disc implant produced from polycarbonate urethane with 34 wt % hard segments showed no signs of decay caused by abrasion wear and did not change its mechanical characteristics after 3 million cycles

A Fully Portable High Performance Minimal Storage Hybrid Format Cholesky Algorithm

We consider the efficient implementation of the Cholesky solution of symmetric positive-definite dense linear systems of equations using packed storage. We take the same starting point as that of LINPACK and LAPACK, with the upper (or lower) triangular part of the matrix being stored by columns. Following LINPACK and LAPACK, we overwrite the given matrix by its Cholesky factor. We consider the use of a hybrid format in which blocks of the matrices are held contiguously and compare this to the present LAPACK code. Code based on this format has the storage advantages of the present code, but substantially outperforms it. Furthermore, it compares favourably to using conventional full format (LAPACK) and using the recursive format of Andersen, Gustavson, and Wa´sniewski