Abstract: A method and structure for an in-place transformation of matrix data. For a matrix A stored in one of a standard full format or a packed format and a transformation T having a compact representation, blocking parameters MB and NB are chosen, based on a cache size. A sub-matrix A1 of A, A1 having size M1=m*MB by N1=n*NB, is worked on, and any of a residual remainder of A is saved in a buffer B. Sub-matrix A1 is worked on by contiguously moving and contiguously transforming A1 in-place into a New Data Structure (NDS), applying the transformation T in units of MB*NB contiguous double words to the NDS format of A1, thereby replacing A1 with the contents of T(A1), and moving and transforming NDS T(A1) to standard data format T(A1) with holes for the remainder of A in buffer B. The contents of buffer B is contiguously copied into the holes of A2, thereby providing in-place transformed matrix T(A).

Abstract: A method and structure for transposing a rectangular matrix A in a computer includes subdividing the rectangular matrix A into one or more square submatrices and executing an in-place transposition for each of the square submatrices Aij.

Abstract: A method (and structure) for performing a matrix subroutine, includes storing data for a matrix subroutine call in a computer memory in an increment block size that is based on a cache size.

Abstract: A structure (and method) including a plurality of coprocessing units and a controller that selectively loads data for processing on the plurality of coprocessing units, using a compound loading instruction. The compound loading instruction includes a plurality of low-level software instructions that preliminarily processes input data in a manner predetermined to simulate an effect of a single hardware loading instruction that would provide optimal loading of complex matrix data by loading input data in accordance with the effect of multiplying i·i=?1.

Abstract: A method (and structure) of executing a matrix operation, includes, for a matrix A, separating the matrix A into blocks, each block having a size p-by-q. The blocks of size p-by-q are then stored in a cache or memory in at least one of the two following ways. The elements in at least one of the blocks is stored in a format in which elements of the block occupy a location different from an original location in the block, and/or the blocks of size p-by-q are stored in a format in which at least one block occupies a position different relative to its original position in the matrix A.

Abstract: A signal-bearing medium tangibly embodying a program of machine-readable instructions executable by a digital processing apparatus to perform a method to at least one of reduce a memory space requirement and to increase a processing efficiency in a computerized method of linear algebra processing. A hybrid full-packed data structure is generated for processing data of a triangular matrix by one or more dense linear algebra (DLA) matrix subroutines designed to process matrix data in a full format, as modified to process matrix data using said hybrid full-packed data structure into a hybrid full-packed data structure, as follows. A portion of the triangular matrix data is determined that would comprise a square portion having a dimension approximately one half a dimension of the triangular matrix data.

Abstract: A method (and structure) for executing a linear algebra subroutine on a computer having a cache, includes streaming data for matrices involved in processing the linear algebra subroutine such that data is processed using data for a first matrix stored in the cache as a matrix format and data from a second matrix and a third matrix is stored in a memory device at a higher level than the cache, the streaming providing data from the higher level as the streaming data is required for the processing.

Abstract: A structure (and method) including a plurality of coprocessing units and a controller that selectively loads data for processing on the plurality of coprocessing units, using a compound loading instruction. The compound loading instruction includes a plurality of low-level software instructions that preliminarily processes input data in a manner predetermined to simulate an effect of a single hardware loading instruction that would provide optimal loading of complex matrix data by loading input data in accordance with the effect of multiplying i·i=?1.

Abstract: A method (and system) for detecting at least one faulty object in a system including a plurality of objects in communication with each other in an n-dimensional architecture, includes probing a first plane of objects in the n-dimensional architecture and probing at least one other plane of objects in the n-dimensional architecture which would result in identifying a faulty object in the system.

Abstract: A computerized method provides for an in-place transformation of matrix A data including a New Data Structure (NDS) format and a transformation T having a compact representation. The NDS represents data of the matrix A in a format other than a row major format or a column major format, such that the data for the matrix A is stored as contiguous sub matrices of size MB by NB in an order predetermined to provide the data for a matrix processing. The transformation T is applied to the MB by NB blocks, using an in-place transformation processing, thereby replacing data of the block A1 with the contents of T(A1).

Abstract: A method (and structure) for executing linear algebra subroutines, includes, for an execution code controlling operation of a floating point unit (FPU) performing the linear algebra subroutine execution, unrolling instructions to preload data into a floating point register (FReg) of the FPU. The unrolling generates an instruction to load data into the FReg and the instruction is inserted into a sequence of instructions that execute the linear algebra subroutine on the FPU.

Abstract: A method (and structure) of managing memory in which a low-level mechanism is executed to signal, in a sequence of instructions generated at a higher level, that at least a portion of a contiguous area of memory is permitted to be overwritten.

Abstract: A method (and structure) for executing a linear algebra subroutine on a computer having a cache, includes streaming data for matrices involved in processing the linear algebra subroutine such that data is processed using data for a first matrix stored in the cache as a matrix format and data from a second matrix and a third matrix is stored in a memory device at a higher level than the cache, the streaming providing data from the higher level as the streaming data is required for the processing.

Abstract: A method (and structure) for performing a matrix subroutine, includes storing data for a matrix subroutine call in a computer memory in an increment block size that is based on a cache size.

Abstract: A method (and system) for detecting at least one faulty object in a system including a plurality of objects in communication with each other in an n-dimensional architecture, includes probing a first plane of objects in the n-dimensional architecture and probing at least one other plane of objects in the n-dimensional architecture which would result in identifying a faulty object in the system.

Abstract: A computerized method provides for an in-place transformation of matrix A data including a New Data Structure (NDS) format and a transformation T having a compact representation. The NDS represents data of the matrix A in a format other than a row major format or a column major format, such that the data for the matrix A is stored as contiguous sub matrices of size MB by NB in an order predetermined to provide the data for a matrix processing. The transformation T is applied to the MB by NB blocks, using an in-place transformation processing, thereby replacing data of the block A1 with the contents of T(A1).

Abstract: A method and structure for an in-place transformation of matrix data. For a matrix A stored in one of a standard full format or a packed format and a transformation T having a compact representation, blocking parameters MB and NB are chosen, based on a cache size. A sub-matrix A1 of A, A1 having size M1=m*MB by N1=n*NB, is worked on, and any of a residual remainder of A is saved in a buffer B. Sub-matrix A1 is worked on by contiguously moving and contiguously transforming A1 in-place into a New Data Structure (NDS), applying the transformation T in units of MB*NB contiguous double words to the NDS format of A1, thereby replacing A1 with the contents of T(A1), and moving and transforming NDS T(A1) to standard data format T(A1) with holes for the remainder of A in buffer B. The contents of buffer B is contiguously copied into the holes of A2, thereby providing in-place transformed matrix T(A).

Abstract: A method (and system) for detecting at least one faulty object in a system including a plurality of objects in communication with each other in an n-dimensional architecture, includes probing a first plane of objects in the n-dimensional architecture and probing at least one other plane of objects in the n-dimensional architecture which would result in identifying a faulty object in the system.

Abstract: A method (and structure) for improving at least one of speed and efficiency when executing level 3 dense linear algebra subroutines on a computer. An optimal matrix subroutine is selected from among a plurality of matrix subroutines stored in a memory that could alternatively perform a level 3 matrix multiplication or factorization processing.

Abstract: A method (and structure) for performing a matrix subroutine, includes storing data for a matrix subroutine call in a computer memory in an increment block size that is based on a cache size.