### Table 3. An example of a template satisfiability matrix

"... In PAGE 12: ... Otherwise, we test the relevance of the UDI template to the query template. Table3 shows an example of a satisfiability matrix between three query templates and four UDI templates. Consider a pair of a query template QT3 and a UDI template UT4 in Table 3: QT3: SELECT I_ID, I_COST, A_FNAME, A_LNAME FROM ITEM, AUTHOR WHERE I_A_ID = A_ID AND I_ID = ? A(QT3) = {I_ID, I_COST, A_FNAME, A_LNAME, I_A_ID, A_ID} C(QT3) = {I_A_ID = A_ID AND I_ID = ?} UT4: UPDATE ITEM SET I_COST = ? WHERE I_ID = ? C(UT4) ={I_ID = ? OR I_COST = ?} A(S(UT4)) = {I_COST}.... ..."

### Table 1. MTL linear algebra operations.

1998

"... In PAGE 4: ...The MTL Generic Algorithms for Linear Algebra The Matrix Template Library provides a rich set of basic linear algebra opera- tions, roughly equivalent to the Level-1, Level-2 and Level-3 BLAS. Table1 lists the principle algorithms included in MTL. In the table, alpha and s are scalars, x,y,z are 1-D containers, A,B,C,E are row or column oriented matrices, U, L are upper and lower triangular matrices, and i is an iterator.... In PAGE 4: ... With BLAIS, the blocking sizes can be modi#0Ced at compile time through a few global constants, so that the algorithms can be customized for the memory hierarchy of a particular architecture. Note that in Table1 di#0Berent operations are not de#0Cned for each permutation of transpose, scaling, and striding. Instead, only one algorithm is provided, but it can be combined with the use of strided and scaled vector adapters, or the trans#28#29 method to create the permutations.... ..."

Cited by 7

### Table 1. MTL linear algebra operations.

1998

"... In PAGE 4: ...The MTL Generic Algorithms for Linear Algebra The Matrix Template Library provides a rich set of basic linear algebra opera- tions, roughly equivalent to the Level-1, Level-2 and Level-3 BLAS. Table1 lists the principle algorithms included in MTL. In the table, alpha and s are scalars, x,y,z are 1-D containers, A,B,C,E are row or column oriented matrices, U, L are upper and lower triangular matrices, and i is an iterator.... In PAGE 4: ... With BLAIS, the blocking sizes can be modi ed at compile time through a few global constants, so that the algorithms can be customized for the memory hierarchy of a particular architecture. Note that in Table1 di erent operations are not de ned for each permutation of transpose, scaling, and striding. Instead, only one algorithm is provided, but it can be combined with the use of strided and scaled vector adapters, or the trans() method to create the permutations.... ..."

Cited by 7

### Table 1: Matrix library MLIB 12

1994

"... In PAGE 11: ... Therefore, we present this type of matrix as just a first and modest attempt to capture some of the common characteristics of LP matrices. Table1 presents the size and the number of nonzeros of the 34 matrices from MLIB. 5 Sparse matrix-vector multiplication In this section, we present a parallel algorithm for the multiplication of a sparse matrix A and a dense vector v, u := Av;; (3) which produces a dense vector u.... In PAGE 17: ... Table 2 presents the normalised computing cost a for seven different data dis- tributions and for all sparse matrices from MLIB, cf. Table1 . Table 3 presents the normalised communication cost b for the different data distributions and the normalised synchronisation cost c for a distribution that requires all the four supersteps of the al- gorithm to be present.... ..."

Cited by 81

### Table 1: Feature templates

"... In PAGE 4: ... 6.2 Feature Construction Table1 shows the 11 feature templates that were used in our experiments to create 60, 109 features. On the around 300,000 parses for 10,000 sentences in our final training set, 10, 986 features were active, resulting in a matrix of active features times parses that has 66 million non-zero entries.... ..."

### Table 1: Matrix library MLIB 12

"... In PAGE 11: ... Therefore, we present this type of matrix as just a first and modest attempt to capture some of the common characteristics of LP matrices. Table1 presents the size and the number of nonzeros of the 34 matrices from MLIB. 5 Sparse matrix-vector multiplication In this section, we present a parallel algorithm for the multiplication of a sparse matrix A and a dense vector v, u := Av; (3) which produces a dense vector u.... In PAGE 17: ... Table 2 presents the normalised computing cost a for seven different data dis- tributions and for all sparse matrices from MLIB, cf. Table1 . Table 3 presents the normalised communication cost b for the different data distributions and the normalised synchronisation cost c for a distribution that requires all the four supersteps of the al- gorithm to be present.... ..."

### Table 3: Matrix from square meshes, 5pt. template

1990

"... In PAGE 22: ...ection 4.3. Recall that as m and n increase, the size of the scheduled computational grains decreases. In Table3 we depict the sequential time, parallel time, time required by the parallel program run on one processor, estimated communication time, and estimated commu- nication free time. on 32 nodes of an Intel iPSC/2.... ..."

Cited by 121

### Table 2: Analysis of the Livermore Loops: currently recognizable patterns. The right{hand column indicates how many loops (after applying loop distribution) can be covered by patterns from the Library. GVOP denotes a general vector operation, FOLR rst order linear recurrences, VDIF a 1D di erence star; VMINLOC nds in a vector the location with minimal absolute value. It is clearly no problem to include Fortran 90 apos;s array features and intrinsic array manipulation functions. These just occur as additional templates of their corresponding PARAMAT patterns. Furthermore it will be useful to arrange the Pattern Library as a hierarchical collection of modules which may be individually composed for special application areas. 1We have focussed in this work on algorithms operating on rectangular dense real matrices. Our approach may easily be extended to other matrix types (e.g., banded, blocked, triangular; complex).

1993

Cited by 1

### Table 1: Holistic Measurement Matrix for Library Services Topic

"... In PAGE 11: ... Therefore, bibliomining is useful in measurement but is not sufficient for evaluation. Table1 presents the matrix for holistic measurement for library services (based on Nicholson, 2004b) that summarize the different areas of measurement. The two variables in this measurement framework are the perspective of measurement and the topic of measurement.... ..."