Stable branch : update to version 3.10.0 (#6077)

* Fix: stress error with Dojo pseudopotential and LIBXC

* Fix: nspin2/4 mismatch with nspin1 with PBE

* Fix: add test case to CI

* Fix: delete useless warning of write_dmr

* Fix: DFTU output format

* Fix: error of noncolin and autoset mag

* Fix: reference of noncolin

* Revert "Fix: nspin2/4 mismatch with nspin1 with PBE"

This reverts commit ffd91ff.

* Perf: optimize the stream strategy in module_gint (#5845)

* optimize stream strategy

* limit max threads

* Fix: modify orb info manually (#5853)

* Fix: parse_expression for scientific notation (#5882)

* Fix: parse_expression for scientific notation

* modify openmp strategy (#5898)

* Fix document description for ocp and ocp_set (#5896)

* Fix: Resolve compilation issue with Libxc 7.0.0 in ABACUS (#5905)

* Fix: Resolve compilation issue with Libxc 7.0.0 in ABACUS

* Fix: Resolve compilation issue with Libxc 7.0.0 in ABACUS: fix a minor test issue (304_NO_GO_AF_atommag)

* Fix  a bug and a magic number in module_exx_symmetry (#5848)

* fix a magic number in get_euler_angle

* do not allow higher symmetry of bvk supercell than the original cell

* Docs: update docs about init_wfc (#5912)

* Fix the wrong symmetry analysis at nspin=2 (#5926)

* analyze magnetic group without time-reversal symmetry

* fix: need to calculate direct coordinates again

* fix a bug about hcontainer in exx nscf (#5927)

* fix cmake bug (#5929)

* inline function of complexarray (#5964)

* modify doc (#5965)

* Fix segmentation fault in integrate test 312_NO_GO_wfc_get_wf (#5970)

* Doc: polish Quick Start part of online doc (#6006)

* polish Quick Start in online doc

* set scf_thr 1e-6

* correct typo

* test: fix Dockerfile.intel (#5999)

Co-authored-by: root <pxlxingliang>

* fix the format (#6008)

* Fix : out_mat_dh will lead to different result with MPI-1core with MPI-4core (#6018)

* Fix: Enhance the warning message when the XC name cannot be recognized. (#6025)

* Update latest Intel oneAPI default compiler for cxx (#6035)

* Update latest Intel oneAPI default compiler for cxx

* Update elpa version to newest in demo cmake script

* Fix: Angular momentum quantum number check in reading SOC pseudopot file (#6027)

* Fix the angular momentum quantum number check in reading SOC pseudopot file

* Fix related unit test problem and add an SOC pseudopot file

* Refactor SOC check logic for improved readability

* Feature: support the `default` as the value of `dft_functional` when initialize vdw (#5949)

* Feature: support the `default` as the value of `dft_functional` when initialize vdw

* Refactor a littble bit

* Optimize: Compilation time of vdwd3_autoset_xcparam.cpp (#6042)

The compilation time of the vdwd3_autoset_xcparam.cpp file is reduced from 250 seconds to just 5 seconds in my machine.
Thanks to the suggestion from DeepSeek: replacing dynamic initialization with a static array for constructing the std::map

* directly enter exx loop when init_wfc=file (#6019)

* Perf: openmp for cal_force_stress (#5956)

* remove wrong timer

* omp for cal_force_stress

* openmp for cal_force_stress in dftu

* openmp for cal_force_stress in dspin

* little change

* fix bug

* fix a bug

* Fix: DFT+U force&stress with  of some elements are -1 (#6049)

Co-authored-by: dyzheng <[email protected]>

* Fix: add the print header for `cusolvermp` in scf info (#6038)

* fix an output for debug (#6066)

* Perf: optimize cal_DMR and folding_HR (#6068)

* modify variable name

* modify variable name

* change pointer to ptr

* modify variable name

* modify some variable names

* move functions from .cpp to .h

* optimize cal_DMR

* add schedule(dynamic)

* optimize func_folding

* add a check before calculating EXX force (#6067)

* fixing issue #5961 (#6071)

* modify warning output (#6074)

* Version: 3.10.0

---------

Co-authored-by: dzzz2001 <[email protected]>
Co-authored-by: Yu Liu <[email protected]>
Co-authored-by: jiyuyang <[email protected]>
Co-authored-by: Taoni Bao <[email protected]>
Co-authored-by: Qianrui Liu <[email protected]>
Co-authored-by: LUNASEA <[email protected]>
Co-authored-by: wqzhou <[email protected]>
Co-authored-by: Peng Xingliang <[email protected]>
Co-authored-by: Xinyuan Liang <[email protected]>
Co-authored-by: Liang Sun <[email protected]>
Co-authored-by: Chen Nuo <[email protected]>
Co-authored-by: kirk0830 <[email protected]>
Co-authored-by: dyzheng <[email protected]>
Co-authored-by: Jie Bao <[email protected]>

Author: 15 people

Dockerfile.intel

@@ -44,6 +44,9 @@ RUN source /opt/intel/oneapi/setvars.sh && \
     ln -s /usr/local/include/elpa_openmp-$ELPA_VER/elpa /usr/local/include/ && \
     cd /tmp && rm -rf elpa-$ELPA_VER
 
+RUN cd /tmp && git clone https://github.com/Tencent/rapidjson.git && cp -r rapidjson/include/rapidjson /usr/include/ \
+    && rm -rf rapidjson
+
 RUN wget https://download.pytorch.org/libtorch/cpu/libtorch-cxx11-abi-shared-with-deps-2.0.0%2Bcpu.zip \
         --no-check-certificate --quiet -O libtorch.zip && \
     unzip -q libtorch.zip -d /opt  && rm libtorch.zip

README.md

@@ -12,7 +12,7 @@
 
 # About ABACUS
 
-ABACUS (Atomic-orbital Based Ab-initio Computation at UStc) is an open-source package based on density functional theory (DFT). The package utilizes both plane wave and numerical atomic basis sets with the usage of norm-conserving pseudopotentials to describe the interactions between nuclear ions and valence electrons. ABACUS supports LDA, GGA, meta-GGA, and hybrid functionals. Apart from single-point calculations, the package allows geometry optimizations and ab-initio molecular dynamics with various ensembles. The package also provides a variety of advanced functionalities for simulating materials, including the DFT+U, VdW corrections, and implicit solvation model, etc. In addition, ABACUS strives to provide a general infrastructure to facilitate the developments and applications of novel machine-learning-assisted DFT methods (DeePKS, DP-GEN, DeepH, DeePTB etc.) in molecular and material simulations.
+ABACUS (**A**tomic-orbital **B**ased **A**b-initio **C**omputation at **US**tc) is an open-source package based on density functional theory (DFT). The package utilizes both plane wave and numerical atomic basis sets with the usage of pseudopotentials to describe the interactions between nuclear ions and valence electrons. ABACUS supports LDA, GGA, meta-GGA, and hybrid functionals. Apart from single-point calculations, the package allows geometry optimizations and ab-initio molecular dynamics with various ensembles. The package also provides a variety of advanced functionalities for simulating materials, including the DFT+U, VdW corrections, and implicit solvation model, etc. In addition, ABACUS strives to provide a general infrastructure to facilitate the developments and applications of novel machine-learning-assisted DFT methods (DeePKS, DP-GEN, DeepH, DeePTB etc.) in molecular and material simulations.
 
 # Online Documentation
 For detailed documentation, please refer to [our documentation website](https://abacus.deepmodeling.com/).

cmake/FindMKL.cmake

@@ -83,7 +83,7 @@ endif()
 endif() # MKL::MKL
 
 # For compatibility with legacy libpaw_interface CMakeLists.txt
-if(TARGET MKL::MKL)
+if(TARGET MKL::MKL AND NOT TARGET IntelMKL::MKL)
   add_library(IntelMKL::MKL ALIAS MKL::MKL)
 endif()
 

docs/CITATIONS.md

@@ -4,10 +4,18 @@ The following references are required to be cited when using ABACUS. Specificall
 
 - **For general purpose:**
 
+    *For LCAO basis:*
+
     Mohan Chen, G. C. Guo, and Lixin He. "Systematically improvable optimized atomic basis sets for ab initio calculations." Journal of Physics: Condensed Matter 22.44 (2010): 445501.
 
     Pengfei Li, et al. "Large-scale ab initio simulations based on systematically improvable atomic basis." Computational Materials Science 112 (2016): 503-517.
 
+    Peize Lin, Xinguo Ren, Xiaohui Liu, Lixin He. Ab initio electronic structure calculations based on numerical atomic orbitals: Basic fomalisms and recent progresses. Wiley Interdisciplinary Reviews: Computational Molecular Science, 2024, 14(1): e1687.
+
+    *For LCAO and PW basis:*
+
+    Weiqing Zhou, Deye Zheng, Qianrui Liu, et al. ABACUS: An Electronic Structure Analysis Package for the AI Era. arXiv preprint arXiv:2501.08697, 2025.
+
 - **If Stochastic DFT is used:**
 
     Qianrui Liu, and Mohan Chen. "Plane-Wave-Based Stochastic-Deterministic Density Functional Theory for Extended Systems." <https://arxiv.org/abs/2204.05662>.

docs/DevelopingTeam.md

@@ -4,5 +4,5 @@ The current development team consists the following research groups/affiliations
 - University of Science and Technology of China (Dr. Lixin He)
 - Peking University (Dr. Mohan Chen)
 - Institute of Physics, Chinese Academy of Sciences (Dr. Xinguo Ren)
-- Beijing AI for Science Institute
-- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center. 
+- Beijing AI for Science Institute (Dr. Daye Zheng)
+- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center (Dr. Lixin He). 

docs/advanced/input_files/input-main.md

@@ -564,7 +564,7 @@ These variables are used to control general system parameters.
 ### init_wfc
 
 - **Type**: String
-- **Description**: Only useful for plane wave basis only now. It is the name of the starting wave functions. In the future. we should also make this variable available for localized orbitals set.
+- **Description**: The type of the starting wave functions.
 
   Available options are:
 
@@ -576,6 +576,8 @@ These variables are used to control general system parameters.
   with `psi_initializer 1`, two more options are supported:
   - nao: from numerical atomic orbitals. If they are not enough, other wave functions are initialized with random numbers.
   - nao+random: add small random numbers on numerical atomic orbitals
+  
+  > Only the `file` option is useful for the lcao basis set, which is mostly used when [calculation](#calculation) is set to `set_wf` and `get_pchg`. See more details in [out_wfc_lcao](#out_wfc_lcao).
 - **Default**: atomic
 
 ### init_chg
@@ -3518,19 +3520,24 @@ These variables are used to control berry phase and wannier90 interface paramete
 
 - **Type**: Boolean
 - **Availability**:
-  - For PW and LCAO codes. if set to 1, occupations of bands will be setting of "ocp_set".
-  - For TDDFT in LCAO codes. if set to 1, occupations will be constrained since second ionic step.
-  - For OFDFT, this feature can't be used.
+  - For PW and LCAO codes: If set to 1, the band occupations will be determined by `ocp_set`.
+  - For RT-TDDFT in LCAO codes: If set to 1, same as above, but the occupations will be constrained starting from the second ionic step.
+  - For OFDFT: This feature is not available.
 - **Description**:
-- True: fix the occupations of bands.
-- False: do not fix the occupations of bands.
+- True: Fixes the band occupations based on the values specified in `ocp_set`.
+- False: Does not fix the band occupations.
 - **Default**: False
 
 ### ocp_set
 
 - **Type**: String
-- **Description**: If ocp is True, the ocp_set is a string to set the number of occupancy, like '1 10 * 1 0 1' representing the 13 band occupancy, 12th band occupancy 0 and the rest 1, the code is parsing this string into an array through a regular expression.
-- **Default**: none
+- **Description**:
+  - If `ocp` is set to 1, `ocp_set` must be provided as a string specifying the occupation numbers for each band across all k-points. The format follows a space-separated pattern, where occupations are assigned sequentially to bands for each k-point. A shorthand notation `N*x` can be used to repeat a value `x` for `N` bands.
+  - Example:
+    - `1 10*1 0 1` represents occupations for 13 bands, where the 12th band is fully unoccupied (`0`), and all others are occupied (`1`).
+    - For a system with multiple k-points, the occupations must be specified for all k-points, following their order in the output file kpoints (may lead to fractional occupations).
+  - Incorrect specification of `ocp_set` could lead to inconsistencies in electron counting, causing the calculation to terminate with an error.
+- **Default**: None
 
 [back to top](#full-list-of-input-keywords)
 

docs/community/faq.md

@@ -109,7 +109,7 @@ write(cs_stru, cs_atoms, format='abacus', pp=pp, basis=basis)
 
 ABACUS applies the density difference between two SCF steps (labeled as `DRHO` in the screen output) as the convergence criterion, which is considered as a more robust choice compared with the energy difference. `DRHO` is calculated via `DRHO = |rho(G)-rho_previous(G)|^2`. Note that the energy difference between two SCF steps (labed as `EDIFF`) is also printed out in the screen output.
 
-**4. Why EDIFF is much slower than DRHO?
+**4. Why EDIFF is much slower than DRHO?**
 
 For metaGGA calculations, it is normal because in addition to charge density, kinetic density also needs to be considered in metaGGA calculations. In this case, you can try set `mixing_tau = true`. If you find EDIFF is much slower than DRHO for non-metaGGA calculations, please start a new issue to us.
 

docs/index.rst

@@ -10,7 +10,7 @@ ABACUS Documentation
 ABACUS (Atomic-orbital Based Ab-initio Computation at UStc) is
 an open-source computer code package based on density functional
 theory (DFT). The package utilizes both plane wave and numerical
-atomic basis sets with the usage of norm-conserving pseudopotentials
+atomic basis sets with the usage of pseudopotentials
 to describe the interactions between nuclear ions and valence electrons.
 ABACUS supports LDA, GGA, meta-GGA, and hybrid functionals. Apart from
 single-point calculations, the package allows geometry optimizations

docs/quick_start/easy_install.md

@@ -1,6 +1,6 @@
 # Easy Installation
 
-This guide helps you install ABACUS with basic features. **For DeePKS, DeePMD and Libxc support, or building with `make`, please refer to [the advanced installation guide](../advanced/install.md)** after going through this page. We recommend building ABACUS with `cmake` to avoid dependency issues. We recommend compiling ABACUS(and possibly its requirements) from the source code using the latest compiler for the best performace. You can try [toolchain](#install-requirements-by-toolchain) to install ABACUS and dependencies in a source-code compilation way with convience. You can also deploy ABACUS **without building** by [Docker](#container-deployment) or [conda](#install-by-conda). Please note that ABACUS only supports Linux; for Windows users, please consider using [WSL](https://learn.microsoft.com/en-us/windows/wsl/) or docker.
+This guide helps you install ABACUS with basic features. **For DeePKS, DeePMD and Libxc support, or building with `make`, please refer to [the advanced installation guide](../advanced/install.md)** after going through this page. We recommend building ABACUS with `cmake` to avoid dependency issues. We recommend compiling ABACUS (and possibly its requirements) from the source code using the latest compiler for the best performace. You can try [toolchain](#install-requirements-by-toolchain) to install ABACUS and dependencies in a source-code compilation way with convience. You can also deploy ABACUS **without building** by [Docker](#container-deployment) or [conda](#install-by-conda). Please note that ABACUS only supports Linux; for Windows users, please consider using [WSL](https://learn.microsoft.com/en-us/windows/wsl/) or docker.
 
 ## Get ABACUS source code
 
@@ -79,7 +79,7 @@ git remote -v
 
 # Replace "origin" with "upstream" or the remote name corresponding to deepmodeling/abacus-develop if necessary
 git fetch origin
-git checkout v3.8.4 # Replace the tag with the latest version
+git checkout v3.x.x # Replace the tag with the latest version, like v3.10.0
 git describe --tags # Verify if the tag has been successfully checked out
 ```
 
@@ -106,7 +106,7 @@ Here, 'build' is the path for building ABACUS; and '-D' is used for setting up s
 - `CMAKE_INSTALL_PREFIX`: the path of ABACUS binary to install; `/usr/local/bin/abacus` by default
 - Compilers
   - `CMAKE_CXX_COMPILER`: C++ compiler; usually `g++`(GNU C++ compiler) or `icpx`(Intel C++ compiler). Can also set from environment variable `CXX`. It is OK to use MPI compiler here.
-  - `MPI_CXX_COMPILER`: MPI wrapper for C++ compiler; usually `mpicxx` or `mpiicpc`(for Intel MPI).
+  - `MPI_CXX_COMPILER`: MPI wrapper for C++ compiler; usually `mpicxx` or `mpiicpx`(for Intel toolkits) or `mpiicpc`(for classic Intel Compiler Classic MPI before 2024.0).
 - Requirements: Unless indicated, CMake will try to find under default paths.
   - `MKLROOT`: If environment variable `MKLROOT` exists, `cmake` will take MKL as a preference, i.e. not using `LAPACK`, `ScaLAPACK` and `FFTW`. To disable MKL, unset environment variable `MKLROOT`, or pass `-DMKLROOT=OFF` to `cmake`.
   - `LAPACK_DIR`: Path to OpenBLAS library `libopenblas.so`(including BLAS and LAPACK)
@@ -136,7 +136,7 @@ Here, 'build' is the path for building ABACUS; and '-D' is used for setting up s
 Here is an example:
 
 ```bash
-CXX=mpiicpc cmake -B build -DCMAKE_INSTALL_PREFIX=~/abacus -DELPA_DIR=~/elpa-2016.05.004/build -DCEREAL_INCLUDE_DIR=~/cereal/include
+CXX=mpiicpx cmake -B build -DCMAKE_INSTALL_PREFIX=~/abacus -DELPA_DIR=~/elpa-2025.01.001/build -DCEREAL_INCLUDE_DIR=~/cereal/include
 ```
 
 ## Build and Install
@@ -192,6 +192,8 @@ OMP_NUM_THREADS=4 mpirun -n 4 abacus
 
 In this case, the total thread count is 16.
 
+> Notice: If the MPI library you are using is OpenMPI, which is commonly the case, when you set the number of processes to 1 or 2, OpenMPI will default to `--bind-to core`. This means that no matter how many threads you set, these threads will be restricted to run on 1 or 2 CPU cores. Therefore, setting a higher number of OpenMP threads might result in slower program execution. Hence, when using `mpirun -n` set to 1 or 2, it is recommended to set `--bind-to none` to avoid performance degradation. For example:`OMP_NUM_THREADS=6 mpirun --bind-to none -n 1 abacus`. The detailed binding strategy of OpenMPI can be referred to at https://docs.open-mpi.org/en/v5.0.x/man-openmpi/man1/mpirun.1.html#quick-summary.
+
 ABACUS will try to determine the number of threads used by each process if `OMP_NUM_THREADS` is not set. However, it is **required** to set `OMP_NUM_THREADS` before running `mpirun` to avoid potential performance issues.
 
 Please refer to [hands-on guide](./hands_on.md) for more instructions.

docs/quick_start/hands_on.md

@@ -4,7 +4,7 @@
 
 ### A quick LCAO example
 
-ABACUS is well known for its support of LCAO (Linear Combination of Atomic Orbital) basis set in calculating periodic condensed matter systems, so it's a good choice to start from a LCAO example of self-consistent field (SCF) calculation. Here, FCC MgO has been chosen as a quick start example. The default name of a structure file in ABACUS is `STRU`. The `STRU` file for FCC MgO in a LCAO calculation is shown below:
+ABACUS is well known for its support of LCAO (Linear Combination of Atomic Orbital) basis set in calculating periodic condensed matter systems. It's a good choice to start from a LCAO example of self-consistent field (SCF) calculation. Here, FCC MgO has been chosen as a quick start example. The default name of a structure file in ABACUS is `STRU`. The `STRU` file for FCC MgO in a LCAO calculation is shown below:
 
 ```
 #This is the atom file containing all the information
@@ -48,11 +48,10 @@ Next, the `INPUT` file is required, which sets all key parameters to direct ABAC
 ```
 INPUT_PARAMETERS
 suffix                  MgO
-ntype                   2
 pseudo_dir              ./
 orbital_dir		./
 ecutwfc                 100             # Rydberg
-scf_thr                 1e-4		# Rydberg
+scf_thr                 1e-6		    # SCF criterion
 basis_type              lcao            
 calculation             scf		# this is the key parameter telling abacus to do a scf calculation
 ```
@@ -71,7 +70,7 @@ Gamma
 After all the above input files have been set, one should be able to run the first quick example. The simplest way is to use the command line, e.g.:
 
 ```
-mpirun -np 2 abacus
+OMP_NUM_THREADS=1 mpirun -np 2 abacus
 ```
 
 The main output information is stored in the file `OUT.MgO/running_scf.log`, which starts with
@@ -138,10 +137,9 @@ The `INPUT` file follows as:
 ```
 INPUT_PARAMETERS
 suffix                  MgO
-ntype                   2
 pseudo_dir              ./
 ecutwfc                 100             # Rydberg
-scf_thr                 1e-4		# Rydberg
+scf_thr                 1e-6		    # SCF criterion
 basis_type              pw              # changes the type of basis set
 calculation             scf		# this is the key parameter telling abacus to do a scf calculation
 ```
@@ -201,12 +199,11 @@ The `INPUT` is provided as follows:
 ```
 INPUT_PARAMETERS
 suffix                  MgO
-ntype                   2
 nelec                   0.0
 pseudo_dir              ./
 orbital_dir             ./
 ecutwfc                 100             # Rydberg
-scf_thr                 1e-4		# Rydberg
+scf_thr                 1e-6		# SCF criterion
 basis_type              lcao 
 calculation             cell-relax	# this is the key parameter telling abacus to do a optimization calculation
 force_thr_ev		0.01		# the threshold of the force convergence, in unit of eV/Angstrom
@@ -223,11 +220,10 @@ The `INPUT` is provided as follows:
 ```
 INPUT_PARAMETERS
 suffix                  MgO
-ntype                   2
 nelec                   0.0
 pseudo_dir              ./
 ecutwfc                 100             # Rydberg
-scf_thr                 1e-4		# Rydberg
+scf_thr                 1e-6		# SCF criterion
 basis_type              pw
 calculation             cell-relax	# this is the key parameter telling abacus to do a optimization calculation
 force_thr_ev		0.01		# the threshold of the force convergence, in unit of eV/Angstrom
@@ -236,4 +232,4 @@ relax_nmax		100		# the maximal number of ionic iteration steps
 out_stru		1
 ```
 
-Use the same `KPT`, `STRU`, and pseudopotential files as in the above SCF-PW examples. The final optimized structure can be found in `STRU_NOW.cif` and `OUT.MgO/running_cell-relax.log`.
+Use the same `KPT`, `STRU`, and pseudopotential files as in the above SCF-PW examples. The final optimized structure can be found in `STRU_NOW.cif` and `STRU_ION_D` with different format.

docs/quick_start/output.md

@@ -6,7 +6,7 @@ The following files are the central output files for ABACUS. After executing the
 
 Different from `INPUT` given by the users, `OUT.suffix/INPUT` contains all parameters in ABACUS.
 
-> **Note:** `OUT.suffix/INPUT` contain the initial default of ABACUS instead of the real parameters used in calculations. If you want to figure out the real parameters used in calculations, you can open `OUT.suffix/runing_scf.log` and research corresponding parameter you are interested.
+> **Note:** `OUT.suffix/INPUT` contain the initial default of ABACUS instead of the real parameters used in calculations. This file is stored for reproduction in case the default value is changed during development. If you want to figure out the real parameters used in calculations, you can open `OUT.suffix/runing_scf.log` and research corresponding parameter you are interested.
 
 For a complete list of input parameters, please consult this [instruction](../advanced/input_files/input-main.md).
 
@@ -33,9 +33,9 @@ BAND               Energy(ev)               Occupation                Kpoint = 1
       5                  9.41058                        0
 ```
 
-## *STRU_SIMPLE.cif*
+## *STRU.cif*
 
-ABACUS generates a `.cif` format structure file based on the input file `STRU`, facilitating users to visualize with commonly used software. `STRU_READIN_ADJUST.cif` is the structure after considering symmetry.
+ABACUS generates a `.cif` format structure file based on the input file `STRU`, facilitating users to visualize with commonly used software.
 
 ## *warning.log*
 

source/module_base/complexarray.cpp

@@ -262,18 +262,4 @@ void point_mult(ComplexArray &in1, ComplexArray &in2, ComplexArray &out){
 		              in1.ptr[i].real() * in2.ptr[i].imag() +
 		              in1.ptr[i].imag() * in2.ptr[i].real());}
 }
-const std::complex <double> &ComplexArray::operator()(const int ind1, const int ind2, const int ind3, const int ind4) const{
-	assert(ind1>=0);	assert(ind1<bound1);
-	assert(ind2>=0);	assert(ind2<bound2);
-	assert(ind3>=0);	assert(ind3<bound3);
-	assert(ind4>=0);	assert(ind4<bound4);
-	const int ind = ((ind1 * bound2 + ind2) * bound3 + ind3) * bound4 + ind4;
-	return ptr[ind];}
-std::complex<double>& ComplexArray::operator()(const int ind1,const int ind2,const int ind3,const int ind4){
-	assert(ind1>=0);	assert(ind1<bound1);
-	assert(ind2>=0);	assert(ind2<bound2);
-	assert(ind3>=0);	assert(ind3<bound3);
-	assert(ind4>=0);	assert(ind4<bound4);
-	const int ind = ((ind1 * bound2 + ind2) * bound3 + ind3) * bound4 + ind4;
-	return ptr[ind];}
 }