In one embodiment, an apparatus comprises a memory and a memory controller. The memory comprises a plurality of memory modules, wherein each memory module comprises a plurality of storage locations. The memory controller may be configured to write data of a matrix to the memory. For example, the memory controller may be configured to write a particular row or a particular column of the matrix to the memory by: shifting a plurality of matrix elements of the particular row or the particular column; and writing the plurality of matrix elements to the plurality of memory modules.

A first control unit of a first control device executes: a synchronous copy process for writing data from a host device into a first storage medium, transmitting the data to a second control device, and replying to the host device; a storage process for storing the data written in the first storage medium into a first region, instructing the second control device on a buffer switch when a predetermined condition is satisfied, and switching a storage destination to a second region; and an asynchronous copy process for transmitting the data in the first region and the second region to a third control device at a time, respectively. A second control unit stores the data transmitted from the first control unit in a second storage medium and a third region, and when the buffer switch is instructed, stores the data in the second storage medium and a fourth region.

Disk based emulation of tape libraries is provided with features that allow easier management and administration of a backup system and also allow increased flexibility to both archive data on tape at a remote location and also have fast restore access to archived data files. Features include automatic emulation of physical libraries, and the retention and write protection of virtual tapes that correspond to exported physical tapes.

First elements of a dense vector to be multiplied with first elements of a first row of a sparse array may be determined. The determined first elements of the dense vector may be written into a memory. A dot product for the first elements of the sparse array and the first elements of the dense vector may be calculated in a plurality of increments by multiplying a subset of the first elements of the sparse array and a corresponding subset of the first elements of the dense vector. A sequence number may be updated after each increment is completed to identify a column number and/or a row number of the sparse array for which the dot product calculations have been completed.

Provided are a computer program product, system, and method for releasing space allocated to a space efficient target storage in a copy relationship with a source storage. Source and target copy relationships indicate source data in the source storage to copy to target data in the target storage. The source copy relationship indicates source data that need to be copied to the target data before being updated, and the target copy relationship indicates target data tracks updated with data copied from corresponding source data. An operation is initiated that results in terminating the source and target copy relationships. Space allocated to the target data for the source and target copy relationships is released in response to determining that the target storage comprises the space efficient storage. The source and target copy relationships are removed.

Provided are a computer program product, system, and method for using a cascade flag to process a copy relationship having a backward cascade copy relationship. Each of a plurality of copy relationships indicates to copy source data to target data and has a cascade flag. The cascade flag for a forward copy relationship of the copy relationships is set to a first value in response to determining that the source data for the forward copy relationship comprises target data for a backward copy relationship and that a background copy operation specified to copy source data to target data of the backward copy relationship has not completed. The cascade flag for the forward copy relationship is set to a second value in response to determining that the backward copy relationship does not have an uncompleted background copy operation.

Provided are a computer program product, system, and method for using a cascade flag to process a copy relationship having a backward cascade copy relationship. Each of a plurality of copy relationships indicates to copy source data to target data and has a cascade flag. The cascade flag for a forward copy relationship of the copy relationships is set to a first value in response to determining that the source data for the forward copy relationship comprises target data for a backward copy relationship and that a background copy operation specified to copy source data to target data of the backward copy relationship has not completed. The cascade flag for the forward copy relationship is set to a second value in response to determining that the backward copy relationship does not have an uncompleted background copy operation.

Fault-tolerance is improved by duplicating data and update information of that data. A storage system has a first storage apparatus that is connected to a host computer, and includes a plurality of first data volumes and a first journal volume, a second storage apparatus that is connected to the host computer and the first storage apparatus, and includes a plurality of second data volumes for storing duplicated data of each of the plurality of first data volumes, and a second journal volume for storing the duplicated data of the first journal volume, a third storage apparatus that is connected to the first storage apparatus, and includes a plurality of third data volumes that configure a remote copy pair with the plurality of first data volumes by using the journal data received from the first storage apparatus, and a fourth storage apparatus that is connected to the third storage apparatus.

A method of managing memory includes generating a page pool by aligning a plurality of pages of a memory; when a request to store first data is received, allocating a destination page corresponding to the first data using a page pool; and updating a page table using information about the allocated destination page.

A processor of a storage system calculates long-term load fluctuation prediction as a prediction of load fluctuation over time in the future of the controller nodes based on time-series data of load of the controller nodes. The processor calculates an addition/reduction completion target time to complete addition or reduction of an operating controller node out of the controller nodes based on the long-term load fluctuation prediction and a load threshold value determined from a power performance model. The processor calculates a rebalancing time for a rebalancing process based on data movement in the rebalancing process for moving data between the drive nodes in accordance with the addition or the reduction and bandwidth information of a path for the data movement. The processor calculates a start time of the rebalancing process from the addition/reduction completion target time and the rebalancing time and starts the rebalancing process at the start time.