Abstract: The present invention extends to methods, systems, and computing system program products for iteratively calculating variance and/or standard deviation for Big Data. Embodiments of the invention include iteratively calculating one or more components of a variance and/or a standard deviation in a modified computation subset based on iteratively calculated one or more components of the variance and/or the standard deviation calculated for a previous computation subset and then calculating the variance and/or the standard deviation based on the iteratively calculated components. Iteratively calculating the components of variance and/or standard deviation avoids visiting all data elements in the modified computation subset and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for decrementally calculating Z-score for Big Data or streamed data. Embodiments of the invention include decrementally calculating one or more components of a Z-score for a modified computation subset based on one or more components of a Z-score calculated for a pre-modified computation subset and then calculating a Z-score for a selected data element in the modified computation subset based on one or more of the decrementally calculated components. Decrementally calculating Z-score avoids visiting all data elements in the modified computation subset and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for iteratively calculating a skewness for streamed data. Embodiments of the invention include iteratively calculating one or more components of skewness in an adjusted computation window based on the one or more components of the skewness calculated for a previous computation window and then calculating the skewness based on the iteratively calculated components. Iteratively calculating skewness avoids visiting all data elements in the computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for iteratively calculating autocorrelation function for streamed data in real time by iteratively calculating one or more components of autocorrelation function. Embodiments of the invention include iteratively calculating one or more components of autocorrelation function at a specified range of lags in an adjusted computation window based on the one or more components of the autocorrelation function at the specified range of lags calculated for a previous computation window and then calculating the autocorrelation function at the specified range of lags using the iteratively calculated components. Iteratively calculating autocorrelation function avoids visiting all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for incrementally calculating correlation for Big Data or streamed data. Embodiments of the invention include incrementally calculating one or more components of a correlation for two modified computation subsets based on one or more components calculated for two previous computation subsets and then calculating the correlation based on the incrementally calculated components. Incrementally calculating the components of a correlation avoids visiting all pairs of data elements in the two modified computation subsets and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for decrementally calculating autocorrelation for Big Data. Embodiments of the invention include decrementally calculating one or more components of autocorrelation at a specified lag for an adjusted computation window based on the one or more components of an autocorrelation at the specified lag calculated for a previous computation window and then calculating the autocorrelation at the specified lag based on one or more of the decrementally calculated components. Decrementally calculating autocorrelation avoids visiting all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for iteratively calculating covariance for Big Data. Embodiments of the invention include iteratively calculating one or more components of a covariance for two modified computation subsets based on one or more components of a covariance for two previous computation subsets and then calculate the covariance for two modified computation subsets based on the iteratively calculated components. Iteratively calculating covariance avoids visiting all data elements in the modified computation subsets and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for decrementally calculating autocorrelation for streamed data in real time. Embodiments of the invention include decrementally calculating one or more components of autocorrelation at a specified lag in an adjusted computation window based on the one or more components of an autocorrelation at a specified lag calculated for a previous computation window and then calculating the autocorrelation at the specified lag for the adjusted computation window using the components. Decrementally calculating autocorrelation avoids visiting all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing system program products for decrementally calculating autocorrelation for Big Data. Embodiments of the invention include decrementally calculating one or more components of autocorrelation at a specified lag for an adjusted computation window based on the one or more components of an autocorrelation at the specified lag calculated for a previous computation window and then calculating the autocorrelation at the specified lag based on one or more of the decrementally calculated components. Decrementally calculating autocorrelation avoids visiting all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing device program products for iteratively calculating autocorrelation function for Big Data. Embodiments of the invention include iteratively calculating one or more components of an autocorrelation function at a specified range of lags in an adjusted computation window based on one or more components of an autocorrelation function at the specified range of lags calculated for a previous computation window and then calculating the autocorrelation function at the specified range of lags for the adjusted computation window using the iteratively calculated components. Iteratively calculating autocorrelation function avoids visiting all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: Methods, systems, and computing system program products for iteratively calculating Simple Linear Regression (SLR) coefficients for Big Data, including iteratively calculating one or more components of SLR coefficients for a modified computation set based on one or more components of SLR coefficients calculated for a pre-modified computation set and then calculating the SLR coefficients for the modified computation set based on the iteratively calculated components. Iteratively calculating SLR coefficients avoids visiting all data elements in the modified computation set and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: Methods, systems, and computing system program products for iteratively calculating Simple Linear Regression (SLR) coefficients for streamed data, including iteratively calculating one or more components of SLR coefficients for an adjusted computation window based on one or more components of SLR coefficients calculated for a pre-adjusted computation window and then calculating the SLR coefficients for the adjusted computation window based on the iteratively calculated components. Iteratively calculating SLR coefficients avoids visiting all data elements in the adjusted computation window and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computing device program products for incrementally calculating simple linear regression coefficients for Big Data or streamed data. Embodiments of the invention include incrementally calculating one or more components of simple linear regression coefficients for a modified computation set based on one or more components of simple linear regression coefficients calculated for a previous computation set and then calculating the simple linear regression coefficients for the modified computation set based on the incrementally calculated components. Incrementally calculating simple linear regression coefficients avoids visiting all data elements in the modified computation set and performing redundant computations thereby increasing calculation efficiency, saving computing resources and reducing computing system's power consumption.

Abstract: The present invention extends to methods, systems, and computer program products for iteratively calculating standard deviation for streamed data. Embodiments of the invention include iteratively calculating standard deviation in a current computation window based on the standard deviation calculation for a previous computation window. Iteratively calculating standard deviation avoids visiting all previous input and performing redundant computations thereby increasing calculation efficiency. In general, streaming data is added to a buffer of size n until the buffer is filled up. Once the buffer is filled, a sum and standard deviation are calculated for the first n data points. As new data elements are received, a new sum is calculated by reusing the prior sum and a new standard deviation is calculated by reusing the prior standard deviation.

Abstract: The present invention extends to methods, systems, and computer program products for iteratively calculating standard deviation for streamed data. Embodiments of the invention include iteratively calculating standard deviation in a current computation window based on the standard deviation calculation for a previous computation window. Iteratively calculating standard deviation avoids visiting all previous input and performing redundant computations thereby increasing calculation efficiency. In general, streaming data is added to a buffer of size n until the buffer is filled up. Once the buffer is filled, a sum and standard deviation are calculated for the first n data points. As new data elements are received, a new sum is calculated by reusing the prior sum and a new standard deviation is calculated by reusing the prior standard deviation.

Abstract: The present invention extends to methods, systems, and computer program products for iteratively calculating standard deviation for streamed data. Embodiments of the invention include iteratively calculating standard deviation in a current computation window based on the standard deviation calculation for a previous computation window. Iteratively calculating standard deviation avoids visiting all previous input and performing redundant computations thereby increasing calculation efficiency. In general, streaming data is added to a buffer of size n until the buffer is filled up. Once the buffer is filled, a sum and standard deviation are calculated for the first n data points. As new data elements are received, a new sum is calculated by reusing the prior sum and a new standard deviation is calculated by reusing the prior standard deviation.

Abstract: The present invention extends to methods, systems, and computer program products for iteratively calculating standard deviation for streamed data. Embodiments of the invention include iteratively calculating standard deviation in a current computation window based on the standard deviation calculation for a previous computation window. Iteratively calculating standard deviation avoids visiting all previous input and performing redundant computations thereby increasing calculation efficiency. In general, streaming data is added to a buffer of size n until the buffer is filled up. Once the buffer is filled, a sum and standard deviation are calculated for the first n data points. As new data elements are received, a new sum is calculated by reusing the prior sum and a new standard deviation is calculated by reusing the prior standard deviation.

Abstract: A mechanism is provided for improving the efficiency of multiple smaller direct memory access transfers. The mechanism uses one input buffer and a small result buffer, or some temporary variables, to temporarily store computation results. The mechanism performs a computation on a segment of data in the input buffer and stores the result in the temporary result buffer. The mechanism then copies the result back into the input buffer. As such, the mechanism uses the input buffer as both an input buffer and a results buffer. The mechanism then performs a direct memory access transfer on the segment of the input buffer that contains the computation result and then performs a computation on the next segment of the input buffer. The mechanism then repeats this process until the entire input buffer has been processed.

Abstract: Zero elements are added to respective lines (e.g., rows/columns) of a sparse matrix. The added zero elements increase the number of elements in the respective lines to be a multiple of a predetermined even number “n” (e.g., 2, 4, 8, etc.), based upon an n-fold unrolling loop, where n=2, 4, 8, etc. By forming a sparse matrix having lines (e.g., rows or columns) that are multiples of the predetermined number “n”, the n-fold unrolling loop thereby acts upon a predetermined number of elements in respective iterations, avoiding unnecessarily costly operations (e.g., additional loop unrolling code) on remainder non-zero elements (e.g. remainder row/column elements not within an n-fold unrolling loop) left in a row or column after unrolling. This improves the efficiency of sparse matrix linear algebra solvers and key sparse linear algebra kernels (e.g., SPMV) thereby improving the overall performance of a computer (e.g., running an application).

Abstract: A mechanism is provided for improving the efficiency of multiple smaller direct memory access transfers. The mechanism uses one input buffer and a small result buffer, or some temporary variables, to temporarily store computation results. The mechanism performs a computation on a segment of data in the input buffer and stores the result in the temporary result buffer. The mechanism then copies the result back into the input buffer. As such, the mechanism uses the input buffer as both an input buffer and a results buffer. The mechanism then performs a direct memory access transfer on the segment of the input buffer that contains the computation result and then performs a computation on the next segment of the input buffer. The mechanism then repeats this process until the entire input buffer has been processed.