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kspaceFirstOrder3D-OMP
1.1
The C++ implementation of the k-wave toolbox for the time-domain simulation of acoustic wave fields in 3D
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k-Wave is an open source MATLAB toolbox designed for the time-domain simulation of propagating acoustic waves in 1D, 2D, or 3D. The toolbox has a wide range of functionality, but at its heart is an advanced numerical model that can account for both linear or nonlinear wave propagation, an arbitrary distribution of weakly heterogeneous material parameters, and power law acoustic absorption (http://www.k-wave.org).
This project is a part of the k-Wave toolbox accelerating 3D simulations using an optimized C++ implementation to run moderate to big grid sizes. Compiled binaries of the C++ code for x86 architectures are available from (http://www.k-wave.org/download). Both 64-bit Linux (Ubuntu / Debian) and 64-bit Windows versions are provided.
The source codes of kpsaceFirstOrder3D-OMP
are written using the C++ 2003 standard and the OpenMP 3.0 library. There are variety of different C++ compilers that can be used to compile the source codes. We recommend using either the GNU C++ compiler (gcc/g++) version 4.4 and higher, or the Intel C++ compiler version 11.0 and higher. The codes can be compiled on 64-bit Linux and Windows. 32-bit systems are not supported! This section describes the compilation procedure using GNU and Intel compilers on Linux. (The Windows users are encouraged to download the Visual Studio 2012 project and compile it using Intel Compiler from within Visual Studio.)
Before compiling the code, it is necessary to install a C++ compiler and several libraries. The GNU compiler is usually part of Linux distributions and distributed as open source. It can be downloaded from http://gcc.gnu.org/ if necessary. The Intel compiler can be downloaded from http://software.intel.com/en-us/intel-composer-xe/. This package also includes the Intel MKL (Math Kernel Library) library that contains FFT. The Intel compiler is only free for non-commercial use.
The code also relies on several libraries that are to be installed before compiling:
Although it is possible to use any combination of the FFT library and the compiler, the best performance is observed when using GNU compiler and FFTW, or Intel Compiler and Intel MKL.
2.1 The HDF5 library installation procedure
./configure --enable-hl --prefix=folder_to_install
make
make install
2.2 The FFTW library installation procedure
./configure --enable-single --enable-sse --enable-openmp --enable-shared --prefix=folder_to_installif you intend to use the FFTW library (and the C++ code) only on a selected machine and want to get the best possible performance, you may also add processor specific optimisations and AVX instructions set. Note, the compiled binary code is not likely to be portable on different CPUs (e.g. even from Intel Sandy Bridge to Intel Nehalem).
./configure --enable-single --enable-avx --enable-openmp --enable-shared --with-gcc-arch=native --prefix=folder_to_installMore information about the installation and customization can be found at http://www.fftw.org/fftw3_doc/Installation-and-Customization.htm. For recent CPUs based on Sandy Bridge, Ivy Bridge, Haswell and Broadwell with strongly recommend to use the AVX support.
make
make install
2.3 The Intel Compiler and MKL installation procedure
./install.sh
2.4 Compiling the C++ code on Linux
After the libraries and the compiler have been installed, you are ready to compile the kspaceFirstOrder3D-OMP
code.
kspaceFirstOrder3D-OMP
source codes.Makefile
file. The Makefile supports code compilation under GNU compiler and FFTW, or Intel compiler with MKL. Uncomment the desired compiler by removing character `#
'. #COMPILER = GNU #COMPILER = Intel
#LINKING = STATIC #LINKING = DYNAMIC
CPU_ARCH=native
. If you are about to run the same binary on different machines or you want to cross-compile the code, you are free to use any of the possible choices, where SSE 3 is the most general but slowest and AVX2 is the most recent instruction set while believed to be the fastest one. CPU_ARCH = native #CPU_ARCH = SSE3 #CPU_ARCH = SSE4 #CPU_ARCH = AVX #CPU_ARCH = AVX2
FFT_DIR=/usr/local MKL_DIR=/opt/intel/composer_xe_2013/mkl HDF5_DIR=/usr/local/hdf5-serial
makeIf you want to clean the distribution, type:
make clean
The C++ code requires two mandatory parameters and accepts a few optional parameters and flags. The mandatory parameters -i
and -o
specify the input and output file. The file names respect the path conventions for particular operating system. If any of the files is not specified, cannot be found or created, an error message is shown.
The -t
parameter sets the number of threads used, which defaults the system maximum. On CPUs with Intel Hyper-Threading (HT), the performance is sometimes better if HT is disabled in the BIOS settings. If HT is switched on, the default will be to spawn twice as many threads as there are physical processor cores, which may but again may not slow down the code execution. Therefore, if the HT is on, try specifying the number of threads manually for best performance (e.g. 4 for Intel i7). We recommend experimenting with this parameter to find the best configuration. Note, if there are other tasks being executed on the system, it might be useful to further limit the number of threads to prevent system overload.
The -r
parameter specifies how often information about the simulation progress is printed out to the command line. By default, the C++ code prints out the progress of the simulation, the elapsed time, and the estimated time of completion in intervals corresponding to 5% of the total number of times steps.
The -c
parameter specifies the compression level used by the ZIP library to reduce the size of the output file. The actual compression rate is highly dependent on the shape of the sensor mask and the range of stored quantities. In general, the output data is very hard to compress, and using higher compression levels can greatly increase the time to save data while not having a large impact on the final file size. That's why we decided to disable compression in default settings.
The
parameter enables the total length of simulation (i.e., the number of time steps) to be overridden by setting a new number of time steps to simulate. This is particularly useful for performance evaluation and benchmarking. As the code performance is relatively stable, 50-100 time steps is usually enough to predict the simulation duration. This parameter can also be used to quickly find the ideal number of CPU threads to use.–benchmark
For jobs that are expected to run for a very long time, it may be useful to checkpoint and restart the execution. One motivation is the wall clock limit per task on clusters where jobs must fit within a given time span (e.g. 24 hours). The second motivation is a level of fault-tolerance, where you can back up the state of the simulation after a predefined period. To enable checkpoint-restart, the user is asked to specify a file to store the actual state of the simulation by –checkpoint_file
and the period in seconds after which the simulation will be interrupted by –checkpoint_interval
. When running on a cluster, please allocate enough time for the checkpoint procedure that can take a non-negligible amount of time (7 matrices have to be stored in the checkpoint file and all aggregated quantities are flushed into the output file).
When controlling a multi-leg simulation by a script loop, the parameters of the code remains the same in all legs. The first leg of the simulation creates a checkpoint file while the last one deletes it. If the checkpoint file is not found the simulation starts from the beginning. In order to find out how many steps have been finished, please open the output file and read the variable t_index
.
The -h
and –help
parameters print all the parameters of the C++ code. The –version
parameter reports detail information about the code useful for debugging and bug reports. It prints out the internal version, the build date and time, the git hash allowing us to track the version of the source code, the operating system, the compiler name and version and the instruction set used.
The remaining flags specify the output quantities to be recorded during the simulation and stored on disk analogous to the sensor.record input. If the -p
or –p_raw
flags are set (these are equivalent), a time series of the acoustic pressure at the grid points specified by the sensor mask is recorded. If the –p_rms
, –p_max
, –p_min
flags are set, the root mean square and/or maximum and/or minimum values of the pressure at the grid points specified by the sensor mask are recorded. If the –p_final
flag is set, the values for the entire acoustic pressure field in the final time step of the simulation is stored (this will always include the PML, regardless of the setting for `PMLInside'
). The flags –p_max_all
and –p_min_all
allow to calculate the maximum and minimum values over the entire acoustic pressure field, regardless on the shape of the sensor mask. Flags to record the acoustic particle velocity are defined in an analogous fashion. For proper calculation of acoustic intensity, the particle velocity has to be shifted onto the same grid as the acoustic pressure. This can be done by setting –u_non_staggered_raw
flag, that first shifts the particle velocity and then samples the grid points specified by the sensor mask. Since the shift operation requires additional FFTs, the impact on the simulation time may be significant.
Any combination of p
and u
flags is admissible. If no output flag is set, a time-series for the acoustic pressure is recorded. If it is not necessary to collect the output quantities over the entire simulation, the starting time step when the collection begins can be specified using the -s parameter. Note, the index for the first time step is 1 (this follows the MATLAB indexing convention).
The –copy_sensor_mask
will copy the sensor from the input file to the output one at the end of the simulation. This helps in post-processing and visualisation of the outputs.
---------------------------------- Usage --------------------------------- Mandatory parameters: -i <input_file_name> : HDF5 input file -o <output_file_name> : HDF5 output file Optional parameters: -t <num_threads> : Number of CPU threads (default = 4) -r <interval_in_%> : Progress print interval (default = 5%) -c <comp_level> : Output file compression level <0,9> (default = 0) --benchmark <steps> : Run a specified number of time steps --checkpoint_file <file_name> : HDF5 checkpoint file --checkpoint_interval <seconds> : Stop after a given number of seconds and store the actual state -h : Print help --help : Print help --version : Print version Output flags: -p : Store acoustic pressure (default if nothing else is on) (the same as --p_raw) --p_raw : Store raw time series of p (default) --p_rms : Store rms of p --p_max : Store max of p --p_min : Store min of p --p_max_all : Store max of p (whole domain) --p_min_all : Store min of p (whole domain) --p_final : Store final pressure field -u : Store ux, uy, uz (the same as --u_raw) --u_raw : Store raw time series of ux, uy, uz --u_non_staggered_raw : Store non-staggered raw time series of ux, uy, uz --u_rms : Store rms of ux, uy, uz --u_max : Store max of ux, uy, uz --u_min : Store min of ux, uy, uz --u_max_all : Store max of ux, uy, uz (whole domain) --u_min_all : Store min of ux, uy, uz (whole domain) --u_final : Store final acoustic velocity --copy_sensor_mask : Copy sensor mask to the output file -s <timestep> : Time step when data collection begins (default = 1) --------------------------------------------------------------------------
The C++ code has been designed as a standalone application which is not dependent on MATLAB libraries or a MEX interface. This is of particular importance when using servers and supercomputers without MATLAB support. For this reason, simulation data must be transferred between the C++ code and MATLAB using external input and output files. These files are stored using the Hierarchical Data Format HDF5 (http://www.hdfgroup.org/HDF5/). This is a data model, library, and file format for storing and managing data. It supports a variety of datatypes, and is designed for flexible and efficient I/O and for high volume and complex data. The HDF5 technology suite includes tools and applications for managing, manipulating, viewing, and analysing data in the HDF5 format.
Each HDF5 file is a container for storing a variety of scientific data and is composed of two primary types of objects: groups and datasets. A HDF5 group is a structure containing zero or more HDF5 objects, together with supporting metadata. A HDF5 group can be seen as a disk folder. A HDF5 dataset is a multidimensional array of data elements, together with supporting metadata. A HDF5 dataset can be seen as a disk file. Any HDF5 group or dataset may also have an associated attribute list. A HDF5 attribute is a user-defined HDF5 structure that provides extra information about a HDF5 object. More information can be obtained from the HDF5 documentation (http://www.hdfgroup.org/HDF5/doc/index.html).
kspaceFirstOrder3D-OMP v1.1 introduces a new version of the HDF5 input and output file format. The code is happy to work with both versions (1.0 and 1.1), however when working with an input file of version 1.0, some features are not supported, namely the cuboid sensor mask, and u_non_staggered_raw. When running from within the actual K-Wave Toolbox, the files will always be generated in version 1.1
The HDF5 input file for the C++ simulation code contains a file header with brief description of the simulation stored in string attributes, and the root group `/' which stores all the simulation properties in the form of 3D datasets (a complete list of input datasets is given bellow). The HDF5 checkpoint file contains the same file header as the input file and the root group `/' with a few datasets keeping the actual simulation state The HDF5 output file contains a file header with the simulation description as well as performance statistics, such as the simulation time and memory consumption, stored in string attributes. The results of the simulation are stored in the root group `/' in the form of 3D datasets.
============================================================================================================== Input File/Checkpoint File Header ============================================================================================================= created_by Short description of the tool that created this file creation_date Date when the file was created file_description Short description of the content of the file (e.g. simulation name) file_type Type of the file (input) major_version Major version of the file definition (1) minor_version Minor version of the file definition (1) ==============================================================================================================
============================================================================================================== Output File Header ============================================================================================================== created_by Short description of the tool that created this file creation_date Date when the file was created file_description Short description of the content of the file (e.g. simulation name) file_type Type of the file (output) major_version Major version of the file definition (1) minor_version Minor version of the file definition (1) ------------------------------------------------------------------------------------------------------------- host_names List of hosts (computer names) the simulation was executed on number_of_cpu_cores Number of CPU cores used for the simulation data_loading_phase_execution_time Time taken to load data from the file pre-processing_phase_execution_time Time taken to pre-process data simulation_phase_execution_time Time taken to run the simulation post-processing_phase_execution_time Time taken to complete the post-processing phase total_execution_time Total execution time peak_core_memory_in_use Peak memory required per core during the simulation total_memory_in_use Total Peak memory in use ==============================================================================================================
The input and checkpoint file stores all quantities as three dimensional datasets with dimension sizes designed by (Nx, Ny, Nz)
. In order to support scalars and 1D and 2D arrays, the unused dimensions are set to 1. For example, scalar variables are stored with a dimension size of (1,1,1)
, 1D vectors oriented in y-direction are stored with a dimension size of (1, Ny, 1)
, and so on. If the dataset stores a complex variable, the real and imaginary parts are stored in an interleaved layout and the lowest used dimension size is doubled (i.e., Nx for a 3D matrix, Ny for a 1D vector oriented in the y-direction). The datasets are physically stored in row-major order (in contrast to column-major order used by MATLAB) using either the `H5T_IEEE_F32LE'
data type for floating point datasets or `H5T_STD_U64LE'
for integer based datasets. All the datasets are store under the root group.
The output file of version 1.0 could only store recorded quantities as 3D datasets under the root group. However, with version 1.1 and the new cuboid corner sensor mask, the sampled quantities may be laid out as 4D quantities stored under specific groups. The dimensions are always (Nx, Ny, Nz, Nt)
, every sampled cuboid is stored as a distinct dataset and the datasets are grouped under a group named by the quantity stored. This makes the file clearly readable and easy to parse.
In order to enable compression and more efficient data processing, big datasets are not stored as monolithic blocks but broken into chunks that may be compressed by the ZIP library and stored separately. The chunk size is defined as follows:
(1M elements, 1, 1)
in the case of 1D variables - index sensor mask (8MB blocks). (Nx, Ny, 1)
in the case of 3D variables (one 2D slab). (Nx, Ny, Nz, 1)
in the case of 4D variables (one time step). (N_sensor_points, 1, 1)
in the case of the output time series (one time step of the simulation).All datasets have two attributes that specify the content of the dataset. The `data_type'
attribute specifies the data type of the dataset. The admissible values are either `float'
or `long'
. The `domain_type'
attribute specifies the domain of the dataset. The admissible values are either `real'
for the real domain or `complex'
for the complex domain. The C++ code reads these attributes and checks their values.
============================================================================================================== Input File Datasets ============================================================================================================== Name Size Data type Domain Type Condition of Presence ============================================================================================================== 1. Simulation Flags -------------------------------------------------------------------------------------------------------------- ux_source_flag (1, 1, 1) long real uy_source_flag (1, 1, 1) long real uz_source_flag (1, 1, 1) long real p_source_flag (1, 1, 1) long real p0_source_flag (1, 1, 1) long real transducer_source_flag (1, 1, 1) long real nonuniform_grid_flag (1, 1, 1) long real must be set to 0 nonlinear_flag (1, 1, 1) long real absorbing_flag (1, 1, 1) long real -------------------------------------------------------------------------------------------------------------- 2. Grid Properties -------------------------------------------------------------------------------------------------------------- Nx (1, 1, 1) long real Ny (1, 1, 1) long real Nz (1, 1, 1) long real Nt (1, 1, 1) long real dt (1, 1, 1) float real dx (1, 1, 1) float real dy (1, 1, 1) float real dz (1, 1, 1) float real x_shift_neg_r (Nx/2+1, 1, 1) float complex File version 1.1 y_shift_neg_r (1, Ny/2+1, 1) float complex File version 1.1 z_shift_neg_r (1, 1, Nz/2+1) float complex File version 1.1 -------------------------------------------------------------------------------------------------------------- 3 Medium Properties -------------------------------------------------------------------------------------------------------------- 3.1 Regular Medium Properties rho0 (Nx, Ny, Nz) float real heterogenous (1, 1, 1) float real homogenous rho0_sgx (Nx, Ny, Nz) float real heterogenous (1, 1, 1) float real homogenous rho0_sgy (Nx, Ny, Nz) float real heterogenous (1, 1, 1) float real homogenous rho0_sgz (Nx, Ny, Nz) float real heterogenous (1, 1, 1) float real homogenous c0 (Nx, Ny, Nz) float real heterogenous (1, 1, 1) float real homogenous c_ref (1, 1, 1) float real 3.2 Nonlinear Medium Properties (defined if (nonlinear_flag == 1)) BonA (Nx, Ny, Nz) float real heterogenous (1, 1, 1) float real homogenous 3.3 Absorbing Medium Properties (defined if (absorbing_flag == 1)) alpha_coef (Nx, Ny, Nz) float real heterogenous (1, 1, 1) float real homogenous alpha_power (1, 1, 1) float real -------------------------------------------------------------------------------------------------------------- 4. Sensor Variables -------------------------------------------------------------------------------------------------------------- sensor_mask_type (1, 1, 1) long real File version 1.1 (0 = index, 1 = corners) sensor_mask_index (Nsens, 1, 1) long real File version 1.0 always, File version 1.1 if sensor_mask_type == 0 sensor_mask_corners (Ncubes, 6, 1) long real File version 1.1, if sensor_mask_type == 1 -------------------------------------------------------------------------------------------------------------- 5 Source Properties -------------------------------------------------------------------------------------------------------------- 5.1 Velocity Source Terms (defined if (ux_source_flag == 1 || uy_source_flag == 1 || uz_source_flag == 1)) u_source_mode (1, 1, 1) long real u_source_many (1, 1, 1) long real u_source_index (Nsrc, 1, 1) long real ux_source_input (1, Nt_src, 1) float real u_source_many == 0 (Nsrc, Nt_src, 1) float real u_source_many == 1 uy_source_input (1, Nt_src, 1) float real u_source_many == 0 (Nsrc, Nt_src, 1) float real u_source_many == 1 uz_source_input (1, Nt_src, 1) float real u_source_many == 0 (Nt_src, Nsrc, 1) float real u_source_many == 1 5.2 Pressure Source Terms (defined if p_source_flag == 1)) p_source_mode (1, 1, 1) long real p_source_many (1, 1, 1) long real p_source_index (Nsrc, 1, 1) long real p_source_input (Nsrc, Nt_src, 1) float real p_source_many == 1 (1, Nt_src, 1) float real p_source_many == 0 5.3 Transducer Source Terms (defined if (transducer_source_flag == 1)) u_source_index (Nsrc, 1, 1) long real transducer_source_input (Nt_src, 1, 1) float real delay_mask (Nsrc, 1, 1) float real 5.4 IVP Source Terms (defined if ( p0_source_flag ==1)) p0_source_input (Nx, Ny, Nz) float real -------------------------------------------------------------------------------------------------------------- 6. K-space and Shift Variables -------------------------------------------------------------------------------------------------------------- ddx_k_shift_pos_r (Nx/2 + 1, 1, 1) float complex ddx_k_shift_neg_r (Nx/2 + 1, 1, 1) float complex ddy_k_shift_pos (1, Ny, 1) float complex ddy_k_shift_neg (1, Ny, 1) float complex ddz_k_shift_pos (1, 1, Nz) float complex ddz_k_shift_neg (1, 1, Nz) float complex -------------------------------------------------------------------------------------------------------------- 7. PML Variables -------------------------------------------------------------------------------------------------------------- pml_x_size (1, 1, 1) long real pml_y_size (1, 1, 1) long real pml_z_size (1, 1, 1) long real pml_x_alpha (1, 1, 1) float real pml_y_alpha (1, 1, 1) float real pml_z_alpha (1, 1, 1) float real pml_x (Nx, 1, 1) float real pml_x_sgx (Nx, 1, 1) float real pml_y (1, Ny, 1) float real pml_y_sgy (1, Ny, 1) float real pml_z (1, 1, Nz) float real pml_z_sgz (1, 1, Nz) float real ==============================================================================================================
============================================================================================================== Checkpoint File Datasets ============================================================================================================== Name Size Data type Domain Type Condition of Presence ============================================================================================================== 1. Grid Properties -------------------------------------------------------------------------------------------------------------- Nx (1, 1, 1) long real Ny (1, 1, 1) long real Nz (1, 1, 1) long real Nt (1, 1, 1) long real t_index (1, 1, 1) long real -------------------------------------------------------------------------------------------------------------- 2. Simulation state -------------------------------------------------------------------------------------------------------------- p (Nx, Ny, Nz) float real ux_sgx (Nx, Ny, Nz) float real uy_sgy (Nx, Ny, Nz) float real uz_sgz (Nx, Ny, Nz) float real rhox (Nx, Ny, Nz) float real rhoy (Nx, Ny, Nz) float real rhoz (Nx, Ny, Nz) float real --------------------------------------------------------------------------------------------------------------
============================================================================================================== Output File Datasets ============================================================================================================== Name Size Data type Domain Type Condition of Presence ============================================================================================================== 1. Simulation Flags -------------------------------------------------------------------------------------------------------------- ux_source_flag (1, 1, 1) long real uy_source_flag (1, 1, 1) long real uz_source_flag (1, 1, 1) long real p_source_flag (1, 1, 1) long real p0_source_flag (1, 1, 1) long real transducer_source_flag (1, 1, 1) long real nonuniform_grid_flag (1, 1, 1) long real nonlinear_flag (1, 1, 1) long real absorbing_flag (1, 1, 1) long real u_source_mode (1, 1, 1) long real if u_source u_source_many (1, 1, 1) long real if u_source p_source_mode (1, 1, 1) long real if p_source p_source_many (1, 1, 1) long real if p_source -------------------------------------------------------------------------------------------------------------- 2. Grid Properties -------------------------------------------------------------------------------------------------------------- Nx (1, 1, 1) long real Ny (1, 1, 1) long real Nz (1, 1, 1) long real Nt (1, 1, 1) long real dt (1, 1, 1) float real dx (1, 1, 1) float real dy (1, 1, 1) float real dz (1, 1, 1) float real ------------------------------------------------------------------------------------------------------------- 3. PML Variables -------------------------------------------------------------------------------------------------------------- pml_x_size (1, 1, 1) long real pml_y_size (1, 1, 1) long real pml_z_size (1, 1, 1) long real pml_x_alpha (1, 1, 1) float real pml_y_alpha (1, 1, 1) float real pml_z_alpha (1, 1, 1) float real pml_x (Nx, 1, 1) float real pml_x_sgx (Nx, 1, 1) float real pml_y (1, Ny, 1) float real pml_y_sgy (1, Ny, 1) float real pml_z (1, 1, Nz) float real pml_z_sgz (1, 1, Nz) float real -------------------------------------------------------------------------------------------------------------- 4. Sensor Variables (present if --copy_sensor_mask) -------------------------------------------------------------------------------------------------------------- sensor_mask_type (1, 1, 1) long real File version 1.1 and --copy_sensor_mask sensor_mask_index (Nsens, 1, 1) long real File version 1.1 and if sensor_mask_type == 0 sensor_mask_corners (Ncubes, 6, 1) long real File version 1.1 and if sensor_mask_type == 1 -------------------------------------------------------------------------------------------------------------- 5a. Simulation Results: if sensor_mask_type == 0 (index), or File version == 1.0 -------------------------------------------------------------------------------------------------------------- p (Nsens, Nt - s, 1) float real -p or --p_raw p_rms (Nsens, 1, 1) float real --p_rms p_max (Nsens, 1, 1) float real --p_max p_min (Nsens, 1, 1) float real --p_min p_max_all (Nx, Ny, Nz) float real --p_max_all p_min_all (Nx, Ny, Nz) float real --p_min_all p_final (Nx, Ny, Nz) float real --p_final ux (Nsens, Nt - s, 1) float real -u or --u_raw uy (Nsens, Nt - s, 1) float real -u or --u_raw uz (Nsens, Nt - s, 1) float real -u or --u_raw ux_non_staggered (Nsens, Nt - s, 1) float real --u_non_staggered_raw (File version ==1.1) uy_non_staggered (Nsens, Nt - s, 1) float real --u_non_staggered_raw (File version ==1.1) uz_non_staggered (Nsens, Nt - s, 1) float real --u_non_staggered_raw (File version ==1.1) ux_rms (Nsens, 1, 1) float real --u_rms uy_rms (Nsens, 1, 1) float real --u_rms uz_rms (Nsens, 1, 1) float real --u_rms ux_max (Nsens, 1, 1) float real --u_max uy_max (Nsens, 1, 1) float real --u_max uz_max (Nsens, 1, 1) float real --u_max ux_min (Nsens, 1, 1) float real --u_min uy_min (Nsens, 1, 1) float real --u_min uz_min (Nsens, 1, 1) float real --u_min ux_max_all (Nx, Ny, Nz) float real --u_max_all uy_max_all (Nx, Ny, Nz) float real --u_max_all uz_max_all (Nx, Ny, Nz) float real --u_max_all ux_min_all (Nx, Ny, Nz) float real --u_min_all uy_min_all (Nx, Ny, Nz) float real --u_min_all uz_min_all (Nx, Ny, Nz) float real --u_min_all ux_final (Nx, Ny, Nz) float real --u_final uy_final (Nx, Ny, Nz) float real --u_final uz_final (Nx, Ny, Nz) float real --u_final -------------------------------------------------------------------------------------------------------------- 5b. Simulation Results: if sensor_mask_type == 1 (corners) and File version == 1.1 -------------------------------------------------------------------------------------------------------------- /p group of datasets, one per cuboid -p or --p_raw /p/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /p/2 (Cx, Cy, Cz, Nt-s) float real 2nd sampled cuboid, etc. /p_rms group of datasets, one per cuboid --p_rms /p_rms/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /p_max group of datasets, one per cuboid --p_max /p_max/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /p_min group of datasets, one per cuboid --p_min /p_min/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid p_max_all (Nx, Ny, Nz) float real --p_max_all p_min_all (Nx, Ny, Nz) float real --p_min_all p_final (Nx, Ny, Nz) float real --p_final /ux group of datasets, one per cuboid -u or --u_raw /ux/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /uy group of datasets, one per cuboid -u or --u_raw /uy/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /uz group of datasets, one per cuboid -u or --u_raw /uz/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /ux_non_staggered group of datasets, one per cuboid --u_non_staggered_raw /ux_non_staggered/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /uy_non_staggered group of datasets, one per cuboid --u_non_staggered_raw /uy_non_staggered/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /uz_non_staggered group of datasets, one per cuboid --u_non_staggered_raw /uz_non_staggered/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /ux_rms group of datasets, one per cuboid --u_rms /ux_rms/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /uy_rms group of datasets, one per cuboid --u_rms /uy_rms/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /uz_rms group of datasets, one per cuboid --u_rms /uy_rms/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /ux_max group of datasets, one per cuboid --u_max /ux_max/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /uy_max group of datasets, one per cuboid --u_max /ux_max/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /uz_max group of datasets, one per cuboid --u_max /ux_max/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /ux_min group of datasets, one per cuboid --u_min /ux_min/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /uy_min group of datasets, one per cuboid --u_min /ux_min/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid /uz_min group of datasets, one per cuboid --u_min /ux_min/1 (Cx, Cy, Cz, Nt-s) float real 1st sampled cuboid ux_max_all (Nx, Ny, Nz) float real --u_max_all uy_max_all (Nx, Ny, Nz) float real --u_max_all uz_max_all (Nx, Ny, Nz) float real --u_max_all ux_min_all (Nx, Ny, Nz) float real --u_min_all uy_min_all (Nx, Ny, Nz) float real --u_min_all uz_min_all (Nx, Ny, Nz) float real --u_min_all ux_final (Nx, Ny, Nz) float real --u_final uy_final (Nx, Ny, Nz) float real --u_final uz_final (Nx, Ny, Nz) float real --u_final ==============================================================================================================