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Topic: Sparse array

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Sparse matrix

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	Sparse matrix - Wikipedia, the free encyclopedia
		In the mathematical subfield of numerical analysis a sparse matrix is a matrix populated primarily with zeros.
		Huge sparse matrices often appear in science or engineering when solving problems for linear models.
		When storing and manipulating sparse matrices on the computer, it is often necessary to modify the standard algorithms and take advantage of the sparse structure of the matrix.
	en.wikipedia.org /wiki/Sparse_matrix (730 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		As used herein, the term"sparse array"refers to an array of active transducer elements arrange on a grid comprising a multiplicity of period- ically spaced grid points, wherein only a fraction of the grid points are occupied by active transducer elements.
		In the case where the sparse array used on transmit differs from the sparse array used on receive, separate MUX State parameters are provided for transmit and receive.
		An example of a symmetric element distribution pattern for a 2D sparse array is shown in Figure 3a of a paper by Smith et al.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=00/13038.000309&ELEMENT_SET=DECL (4101 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Sparse Array Handling Functions Sparse arrays are structures that may be used to decrease the amount of storage required to hold very large arrays when only a relatively small number of elements are used.
		All elements of the sparse array notionally have a default value (set during initialisation) but specific elements of the array may be modified.
		The array ARRAY must be of size SIZE, an overhead of 8 locations must be allowed for in calculating the size of array to use.
	www.psc.edu /general/software/packages/toolpack/tsg.txt (5599 words)

	$. Sparse (Site not responding. Last check: 2007-11-03)
		as appropriate; that is, converts a dense array to sparse and a sparse array to dense.
		We describe a sparse array extension to J using a representation that “does not store zeros”.
		Letting the sparse element be variable rather than fixed at zero makes many more functions closed on sparse arrays (e.g.
	www.jsoftware.com /books/help/dictionary/d211.htm (900 words)

	12 - C H A P T E R -
		A matrix is considered to be sparse if special techniques can be used to take advantage of the structure of the matrix (that is, the nonzero elements and their locations).
		Many different ways of storing sparse matrices have been devised to realize these advantages, which can mean better efficiency in both memory use and arithmetic operations.
		The differences among these sparse storage schemes are mostly reflections of such issues as the amount of storage required, the degree of indirect addressing necessary to perform the kernel operations (such as matrix-vector product), and the suitability for a range of different processor architectures.
	www.sun.com /products-n-solutions/hardware/docs/html/817-0086-10/prog-sparse-support.html (2873 words)

	An Implementation
		Consider the problem of displaying the contents of a sparse array by printing them on the screen.
		The obvious algorithm is to print the array in the ordinary manner, entirely ignoring the fact that the array is sparse.
		array for the index of the unused element, the index of an available element (if there are any) is always stored in the first location of the array.
	www.eecs.harvard.edu /~ellard/Q-97/HTML/root/node12.html (727 words)

	[Chapter 8] 8.5 Array Length Property (Site not responding. Last check: 2007-11-03)
		to a value smaller than its current value; the array will then be shortened to the new length--elements will be truncated from the end of the array, and their values will be lost.
		Since arrays in JavaScript are associative, sparse arrays, array elements do not have to be defined in contiguous blocks, like they do in C and related languages.
		JavaScript's arrays are implemented as sparse arrays, regardless of how you use them in any particular case.
	www.serve.com /~josh/books/web/jscript/ch08_05.htm (490 words)

	SPRSIN
		The structure consists of two linear sparse storage vectors: SA, a vector of array values, and IJA, a vector of subscripts to the SA vector.
		The length of these vectors is equal to 1 plus the number of diagonal elements of the array, plus the number of off-diagonal elements with an absolute magnitude greater that or equal to the threshold value.
		Diagonal elements of the array are always retained even if their absolute magnitude is less than the specified threshold.
	www.astro.princeton.edu /~esirko/idl_html_help/S46.html (429 words)

	Linked List Representation
		An illustration of a sparse array that represents the same array as the array in figure 3.1 is shown in figure 3.2.
		The method of accessing elements in a sparse array implemented this way is very simple: find the row list for the row of the element, and search it for the elements in the correct column.
		If most of the rows of the sparse array do not contain any elements, then the array of pointers to row lists is itself a sparse array, and can also be implemented as a linked list.
	www.eecs.harvard.edu /~ellard/Q-97/HTML/root/node11.html (720 words)

	Microsoft Office Developer Forum - VBA Algorithms: Data Structures (Site not responding. Last check: 2007-11-03)
		Sparse arrays are another data structure that a VBA program can build by using object references.
		A sparse array uses a linked list of linked lists to store only the entries that are actually needed in the array.
		Trees and sparse arrays let you model more interesting data relationships, such as hierarchical data and data that is naturally array-like.
	www.microsoft.com /products/Developer/officedeveloper/Office/Articles/movs205.htm (4962 words)

	Spase Array Asst. CSC 172 (Summer 1999)
		The usual sequential storage of arrays provided by JAVA or any usual programming language lends itself to quick lookup: a simple formula tells what offset an element occupies from the start of the block of continuous array storage.
		In a 2-D (rows X cols) array stored so the last index varies fastest (you move across rows and then down columns) and indices start at 0, an element (i,j) is found at offset i*cols +j.
		The array header has the number of rows and cols and the row and col headers have the number of the row or column they represent in the appropriate field.
	www.cs.rochester.edu /u/pawlicki/CSC172SUM99/sparse/sparse.html (880 words)

	SPRSIN
		The SPRSIN function converts an array into a row-index sparse storage mode, retaining only elements with an absolute magnitude greater than or equal to the specified threshold.
		The result is a row-indexed sparse array contained in structure form.
		The length of these vectors is equal to the number of diagonal elements of the array, plus the number of off-diagonal elements with an absolute magnitude greater that or equal to the threshold value.
	www.astro.virginia.edu /class/oconnell/astr511/idl_5.1_html/idl1b2.htm (262 words)

	Guide and Reference
		Specifying Sparse Matrices for the Fortran 90 and Fortran 77 Sparse Linear Algebraic Equations
		For the Fortran 90 and Fortran 77 sparse linear algebraic equation subroutines, you must use the sparse utility subroutines provided with Parallel ESSL to build the sparse matrices on each process in the process grid.
		The actual length of the array descriptor depends on the sparse matrix structure and therefore is known after a call to PDSPASB.
	www.umiacs.umd.edu /~jhu/DOCS/SP/docs/pessl/pessl071.html (1306 words)

	CIS353 Sparse Matrix Module
		A sparse matrix behaves like a two dimensional array, with the characteristic that most of the elements are zero.
		In the described laboratory assignment, the mechanism of the sparse matrix is an array (row index) of linked lists storing only the nonzero values within a row, together with the column index of the saved element.
		You are to implement an abstract data type for a sparse (2 dimensional) array, using the class mechanism of C++ to provide appropriate data abstraction and encapsulation.
	www.cstc.org /data/resources/52/Sparse.htm (1727 words)

	Holly Tajlil - Implementing a Hierarchical Data Structure in Java (Site not responding. Last check: 2007-11-03)
		The data structure being investigated is the sparse array, similar to the sparse array provided by M language, one of the very few languages accepted by ANSI.
		M's sparse array has had many successful applications in the area of data base management.
		The operations include inserting and deleting an element in the sparse array with multiple subscripts, removing partial or entire sparse array, searching or changing the value of a given element in the array, and searching and determining the order or sequence of available subscripts in the sparse array.
	www.ecs.csus.edu /csc/grad/tajlil.html (188 words)

	READ_SPR (Site not responding. Last check: 2007-11-03)
		The READ_SPR function reads a row-indexed sparse array from a specified file and returns the array as the result.
		Row-indexed sparse arrays are created using the SPRSIN function and written to a file using the WRITE_SPR function.
		A scalar string specifying the name of the file containing a row-indexed sparse array.
	www.astro.virginia.edu /class/oconnell/astr511/IDLresources/idl_5.1_html/idl169.htm (105 words)

	Creating a sparse matrix
		The most common type of sparse matrix is a banded matrix, that is, a matrix with a few nonzero diagonals.
		In Matlab's indexing scheme, the nonzero diagonals of A are numbers -3, -1, 0, 1, and 3 (the main diagonal is number 0, the first subdiagonal is number -1, the first superdiagonal is number 1, and so forth).
		Perhaps the most common sparse matrix is the identity.
	www.math.mtu.edu /~msgocken/intro/node18.html (396 words)

	Array Reduction Recognition. (Site not responding. Last check: 2007-11-03)
		Reductions on array variables are also common in scientific codes and are a potential source of significant improvements in parallelization results.
		Sparse computations pose what is usually considered an insurmountable problem for parallelizing compilers.
		When arrays are part of subscript expressions, a compiler cannot determine the locations of the array being read or written.
	suif.stanford.edu /papers/mhall95a/node8.html (190 words)

	3 - C H A P T E R -
		Sun S3L distributes arrays on an axis-by-axis basis across multiple processes, enabling operations to be performed in parallel on different sections of the array.
		Sets up a sparse matrix and populates it with random nonzero values in a sparsity pattern that is specified by arguments in the function argument list.
		When no part of a Sun S3L array is distributed--that is, when all axes are local--all elements of the array are on a single process.
	www.sun.com /products-n-solutions/hardware/docs/html/817-0086-10/prog-arrays.html (2109 words)

	MATLAB 6.5 Release Notes (MATLAB Release Notes)
		functions have been modified to handle cell arrays of strings having one of more trailing spaces in a manner that is consistent with its handling of other array types.
		Empty arrays in concatenation operations can now affect the data type of the output.
		When you use an empty array in an equal or not equal comparison statement, MATLAB now returns an empty array as the result.
	www-rohan.sdsu.edu /doc/matlab/base/relnotes/matlab/matlab1315.html (2753 words)

	Matrix Operations (Site not responding. Last check: 2007-11-03)
		The value array component of the sparse array.
		The index array component of the sparse array.
		The dense array produced by converting the sparse array represented by value-array and index-array.
	www.cs.fsu.edu /g2/g2doc/g2sprm/matrix26.htm (216 words)

	Matrix Operations
		The index array of the second sparse array.
		A dense array corresponding to the sparse array represented by value-array-2 and index-array-2.
		In the resulting array, the sum has the same index value as the two elements that were added.
	www.cs.fsu.edu /g2/g2doc/g2sprm/matrix22.htm (612 words)

	Master's Projects (Site not responding. Last check: 2007-11-03)
		The data structure being investigated is sparse array, similar to the sparse array provided by the M language, one of the few languages accepted by ANSI.
		A sparse array is an array in which many of the possible values that could be used to fill in an array are empty, and no storage has been allocated for the empty values.
		From this definition we can see that there is no requirement that sparse arrays be dense, only elements that have been assigned values occupy space, and it is not necessary to specify storage space ahead of time.
	gaia.ecs.csus.edu /~zhangc/projects.html (10355 words)

	Visual Basic Sparse Array (Site not responding. Last check: 2007-11-03)
		(A one-dimensional array is known as a Vector within Entisoft Tools.) Set the Value of an element when using the SparseArray as a one-dimensional array.
		(A two-dimensional array is known as a Matrix within Entisoft Tools.) Set the Value of an element when using the SparseArray as a two-dimensional array.
		(A three-dimensional array is known as a Cube within Entisoft Tools.) Set the Value of an element when using the SparseArray as a three-dimensional array.
	www.entisoft.com /ESTools/SparseArray.HTML (288 words)

	The transmit_as Attribute (Site not responding. Last check: 2007-11-03)
		This is primarily useful as a way to deal with data structures that the stubs cannot marshall efficiently, such as sparse arrays.
		The client code to exercise the sparse array transmitted type is as follows:
		You could also add code to show the format of the transmitted array before it is reconstructed by the from_xmit routine.
	support.entegrity.com /private/doclib/docs/osfhtm/develop/apgstyle/Apgst193.htm (487 words)

	FULSTR (Site not responding. Last check: 2007-11-03)
		The FULSTR restores a row-indexed sparse array to full storage mode.
		If the sparse array was created with the SPRSIN function using the THRESH keyword, any values in the original array that were below the specified threshold are replaced with zeros.
		The variable SPARSE now contains a representation of the array A in structure form.
	idlastro.gsfc.nasa.gov /idl_html_help/F36.html (178 words)

	Drizzling and Chunking in IDL
		I use sparse arrays to solve the chunk decimation problem, with the chunk fill method generating the row numbers of non-zero (unity actually) entries, and the original reverse indices generating the column numbers.
		Unfortunately, RSI's Numerical Recipes-based sparse array routines demand square arrays (which seems unnecessary to me), so you either have to pad the data or truncate the result, depending on whether you have more repeated indices than skipped indices.
		Fortunately, "sparse" arrays were invented for just this problem: you specify only the non-zero elements, and, when multiplying using sprsax, they alone are computed.
	www.dfanning.com /code_tips/drizzling.html (3806 words)

	[No title]
		For that reason, we sometimes refer to the child trees as * vectors or arrays.
		Traversal within an array is handled by the binary tree functions.
		If RootPtr * is NULL, then the array is the 'empty' array and NULL will be * returned.
	ubiqx.org /~crh/ubiqx/src/ubi_SparseArray.c (1084 words)

	Guide and Reference
		SSCTR, DSCTR, CSCTR, ZSCTR--Scatter the Elements of a Sparse Vector X in Compressed-Vector Storage Mode into Specified Elements of a Sparse Vector Y in Full-Vector Storage Mode
		These subprograms scatter the elements of sparse vector x, stored in compressed-vector storage mode, into specified elements of sparse vector y, stored in full-vector storage mode.
		For a description of how sparse vectors are stored, see "Sparse Vector".
	www.umiacs.umd.edu /~jhu/DOCS/SP/docs/essl/essl262.html (467 words)

	[No title]
		* * -------------------------------------------------------------------------- ** * This is a simple implementation of a sparse array based on binary trees.
		* * Output: A pointer to the top-most root in the sparse array.
		* * Input: NewRootPtr - Pointer to the root of the vector (tree) that * is to be added as a child array at the node * indicated by ParentNodePtr.
	ubiqx.org /~crh/ubiqx/src/ubi_SparseArray.h (1087 words)

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