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tensor_algebra_cpu.F90
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!Tensor Algebra for Multi- and Many-core CPUs (OpenMP based).
!AUTHOR: Dmitry I. Lyakh (Liakh): [email protected]
!REVISION: 2019/03/21
!Copyright (C) 2013-2019 Dmitry I. Lyakh (Liakh)
!Copyright (C) 2014-2019 Oak Ridge National Laboratory (UT-Battelle)
!This file is part of ExaTensor.
!ExaTensor is free software: you can redistribute it and/or modify
!it under the terms of the GNU Lesser General Public License as published
!by the Free Software Foundation, either version 3 of the License, or
!(at your option) any later version.
!ExaTensor is distributed in the hope that it will be useful,
!but WITHOUT ANY WARRANTY; without even the implied warranty of
!MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
!GNU Lesser General Public License for more details.
!You should have received a copy of the GNU Lesser General Public License
!along with ExaTensor. If not, see <http://www.gnu.org/licenses/>.
!GNU linking: -lblas -gfortran -lgomp
!ACRONYMS:
! - mlndx - multiindex;
! - Lm - Level-min segment size (the lowest level segment size for bricked storage);
! - dlf - dimension-led storage of tensor blocks where the 1st dimension is the most minor (Fortran like) (DEFAULT):
! Numeration within each dimension starts from 0: [0..extent-1].
! - dlc - dimension-led storage of tensor blocks where the 1st dimension is the most senior (C like);
! Numeration within each dimension starts from 0: [0..extent-1].
! - brf - bricked storage of tensor blocks where the 1st dimension is the most minor (Fortran like) (DEFAULT);
! - brc - bricked storage of tensor blocks where the 1st dimension is the most senior (C like);
! - r4 - real(4);
! - r8 - real(8);
! - c4 - complex(4);
! - c8 - complex(8);
!PREPROCESSOR:
! -D NO_OMP: Do not use OpenMP (serial);
! -D NO_BLAS: Replace BLAS calls with in-house routines (slower);
! -D USE_MKL: Use Intel MKL library interface for BLAS;
! -D NO_PHI: Ignore Intel MIC (Xeon Phi);
module tensor_algebra_cpu
! use, intrinsic:: ISO_C_BINDING
! use dil_basic
use tensor_algebra !includes ISO_C_BINDING, dil_basic
use stsubs
use combinatoric
use timers
use symm_index
#ifdef USE_MKL
!use blas95
!use lapack95
!use f95_precision
!use mkl_service
#endif
#ifndef NO_OMP
use omp_lib
implicit none
public
#else
implicit none
public
integer, external:: omp_get_max_threads,omp_set_num_threads
#endif
!PARAMETERS:
!Default output for the module procedures:
integer, private:: CONS_OUT=6 !default output device for this module (also used for INTEL MIC TAL)
logical, private:: VERBOSE=.TRUE. !verbosity (also used for INTEL MIC TAL)
integer, private:: DEBUG=0 !debugging mode
integer, private:: LOGGING=0 !logging mode
#ifndef NO_PHI
!DIR$ ATTRIBUTES OFFLOAD:mic:: CONS_OUT,VERBOSE
!DIR$ ATTRIBUTES ALIGN:128:: CONS_OUT,VERBOSE
#endif
!Global:
integer, parameter, public:: MAX_SHAPE_STR_LEN=1024 !max allowed length for a tensor shape specification string (TSSS)
integer, parameter, public:: LONGINT=INTL !long integer size in bytes
integer, parameter, private:: MAX_THREADS=1024 !max allowed number of threads in this module
integer, private:: MEM_ALLOC_POLICY=MEM_ALLOC_TMP_BUF !memory allocation policy
logical, private:: MEM_ALLOC_FALLBACK=.TRUE. !memory allocation fallback to the regular allocator
logical, private:: DATA_KIND_SYNC=.TRUE. !if .TRUE., each tensor operation will syncronize all existing data kinds
logical, private:: TRANS_SHMEM=.TRUE. !cache-efficient (true) VS scatter (false) tensor transpose algorithm
#ifndef NO_BLAS
logical, private:: DISABLE_BLAS=.FALSE. !if .TRUE. and BLAS is accessible, BLAS calls will be replaced by my own routines
#else
logical, private:: DISABLE_BLAS=.TRUE. !if .TRUE. and BLAS is accessible, BLAS calls will be replaced by my own routines
#endif
#ifndef NO_PHI
!DIR$ ATTRIBUTES OFFLOAD:mic:: MAX_SHAPE_STR_LEN,LONGINT,MAX_THREADS,MEM_ALLOC_POLICY,MEM_ALLOC_FALLBACK
!DIR$ ATTRIBUTES OFFLOAD:mic:: DATA_KIND_SYNC,TRANS_SHMEM,DISABLE_BLAS
!DIR$ ATTRIBUTES ALIGN:128:: MAX_SHAPE_STR_LEN,LONGINT,MAX_THREADS,MEM_ALLOC_POLICY,MEM_ALLOC_FALLBACK
!DIR$ ATTRIBUTES ALIGN:128:: DATA_KIND_SYNC,TRANS_SHMEM,DISABLE_BLAS
#endif
!Numerical:
real(8), parameter, private:: ABS_CMP_THRESH=1d-13 !default absolute error threshold for numerical comparisons
real(8), parameter, private:: REL_CMP_THRESH=1d-2 !default relative error threshold for numerical comparisons
#ifndef NO_PHI
!DIR$ ATTRIBUTES OFFLOAD:mic:: ABS_CMP_THRESH,REL_CMP_THRESH
!DIR$ ATTRIBUTES ALIGN:128:: ABS_CMP_THRESH,REL_CMP_THRESH
#endif
!DERIVED DATA TYPES:
!Tensor shape (storage layout specification for a tensor block):
type, public:: tensor_shape_t
integer:: num_dim=-1 !total number of dimensions (num_dim=0 defines a scalar tensor).
integer, pointer:: dim_extent(:)=>NULL() !extent of each dimension (if num_dim>0): range=[0..extent-1].
integer, pointer:: dim_divider(:)=>NULL() !divider for each dimension, i.e. the <Lm_segment_size> (ordered dimensions must have the same divider!): %dim_divider(1)=0 means that an alternative (neither dimension-led nor bricked) storage layout is used.
integer, pointer:: dim_group(:)=>NULL() !dimension grouping (default group 0 means no symmetry restrictions): if %dim_divider(1)=0, then %dim_group(1) regulates the alternative storage layout kind.
end type tensor_shape_t
!Tensor block:
type, public:: tensor_block_t
integer(LONGINT):: tensor_block_size=0_LONGINT !total number of elements in the tensor block (informal, set after creation)
integer:: ptr_alloc=0 !pointer allocation status (bits set when pointers are getting allocated, not just associated)
type(tensor_shape_t):: tensor_shape !shape of the tensor block (see above)
complex(8):: scalar_value=(0d0,0d0) !scalar value if the rank is zero, otherwise can be used for storing the norm of the tensor block
real(4), pointer, contiguous:: data_real4(:)=>NULL() !tensor block data (float)
real(8), pointer, contiguous:: data_real8(:)=>NULL() !tensor block data (double)
complex(4), pointer, contiguous:: data_cmplx4(:)=>NULL() !tensor block data (float complex)
complex(8), pointer, contiguous:: data_cmplx8(:)=>NULL() !tensor block data (double complex)
end type tensor_block_t
!GENERIC INTERFACES:
interface tensor_block_shape_create
module procedure tensor_block_shape_create_sym
module procedure tensor_block_shape_create_num
end interface tensor_block_shape_create
interface array_alloc
module procedure array_alloc_r4
module procedure array_alloc_r8
module procedure array_alloc_c4
module procedure array_alloc_c8
end interface array_alloc
interface array_free
module procedure array_free_r4
module procedure array_free_r8
module procedure array_free_c4
module procedure array_free_c8
end interface array_free
interface tensor_block_slice_dlf
module procedure tensor_block_slice_dlf_r4
module procedure tensor_block_slice_dlf_r8
module procedure tensor_block_slice_dlf_c4
module procedure tensor_block_slice_dlf_c8
end interface tensor_block_slice_dlf
interface tensor_block_insert_dlf
module procedure tensor_block_insert_dlf_r4
module procedure tensor_block_insert_dlf_r8
module procedure tensor_block_insert_dlf_c4
module procedure tensor_block_insert_dlf_c8
end interface tensor_block_insert_dlf
interface tensor_block_copy_dlf
module procedure tensor_block_copy_dlf_r4
module procedure tensor_block_copy_dlf_r8
module procedure tensor_block_copy_dlf_c4
module procedure tensor_block_copy_dlf_c8
end interface tensor_block_copy_dlf
interface tensor_block_copy_scatter_dlf
module procedure tensor_block_copy_scatter_dlf_r4
module procedure tensor_block_copy_scatter_dlf_r8
module procedure tensor_block_copy_scatter_dlf_c4
module procedure tensor_block_copy_scatter_dlf_c8
end interface tensor_block_copy_scatter_dlf
interface tensor_block_fcontract_dlf
module procedure tensor_block_fcontract_dlf_r4
module procedure tensor_block_fcontract_dlf_r8
module procedure tensor_block_fcontract_dlf_c4
module procedure tensor_block_fcontract_dlf_c8
end interface tensor_block_fcontract_dlf
interface tensor_block_pcontract_dlf
module procedure tensor_block_pcontract_dlf_r4
module procedure tensor_block_pcontract_dlf_r8
module procedure tensor_block_pcontract_dlf_c4
module procedure tensor_block_pcontract_dlf_c8
end interface tensor_block_pcontract_dlf
interface tensor_block_ftrace_dlf
module procedure tensor_block_ftrace_dlf_r4
module procedure tensor_block_ftrace_dlf_r8
module procedure tensor_block_ftrace_dlf_c4
module procedure tensor_block_ftrace_dlf_c8
end interface tensor_block_ftrace_dlf
interface tensor_block_ptrace_dlf
module procedure tensor_block_ptrace_dlf_r4
module procedure tensor_block_ptrace_dlf_r8
module procedure tensor_block_ptrace_dlf_c4
module procedure tensor_block_ptrace_dlf_c8
end interface tensor_block_ptrace_dlf
!FUNCTION VISIBILITY:
public get_mem_alloc_policy !gets the current memory allocation policy for sizeable arrays
public set_mem_alloc_policy !sets the memory allocation policy for sizeable arrays
public set_data_kind_sync !turns on/off data kind synchronization (0/1)
public set_transpose_algorithm !switches between scatter (0) and shared-memory (1) tensor transpose algorithms
public set_matmult_algorithm !switches between BLAS GEMM (0) and my OpenMP matmult kernels (1)
public cmplx4_to_real4 !returns the real approximate of a complex number (algorithm by D.I.L.)
public cmplx8_to_real8 !returns the real approximate of a complex number (algorithm by D.I.L.)
public tensor_shape_assoc !constructs a tensor shape object by pointer associating with external data
public tensor_block_layout !returns the type of the storage layout for a given tensor block
public tensor_block_shape_size !determines the tensor block size induced by its shape
public tensor_master_data_kind !determines the master data kind present in a tensor block
public tensor_common_data_kind !determines the common data kind present in two compatible tensor blocks
public tensor_block_compatible !determines whether two tensor blocks are compatible (under an optional index permutation)
public tensor_block_mimic !mimics the internal structure of a tensor block without copying the actual data
public tensor_block_create !creates a tensor block based on the shape specification string (SSS)
public tensor_block_init !initializes a tensor block with either a predefined value or random numbers
public tensor_block_is_empty !returns TRUE if the tensor block is empty, FALSE otherwise
public tensor_block_assoc !associates an empty <tensor_block_t> object with externally provided data
public tensor_block_destroy !destroys a tensor block
public tensor_block_sync !allocates and/or synchronizes different data kinds in a tensor block
public tensor_block_scale !multiplies all elements of a tensor block by some factor
public tensor_block_conjg !complex conjugates all elements of a tensor block
public tensor_block_norm1 !determines the 1-norm of a tensor block (the sum of moduli of all elements)
public tensor_block_norm2 !determines the squared Euclidean (Frobenius) 2-norm of a tensor block
public tensor_block_max !determines the maximal (by modulus) tensor block element
public tensor_block_min !determines the minimal (by modulus) tensor block element
public tensor_block_slice !extracts a slice from a tensor block
public tensor_block_insert !inserts a slice into a tensor block
public tensor_block_print !prints a tensor block
public tensor_block_trace !intra-tensor index contraction (accumulative trace)
public tensor_block_cmp !compares two tensor blocks
public tensor_block_copy !makes a copy of a tensor block (with an optional index permutation)
public tensor_block_add !adds one tensor block to another
public tensor_block_contract !inter-tensor index contraction (accumulative contraction)
public tensor_block_scalar_value !returns the scalar value component of <tensor_block_t>
public get_mlndx_addr !generates an array of addressing increments for the linearization map for symmetric multi-indices
public mlndx_value !returns the address associated with a (symmetric) multi-index, based on the array generated by <get_mlndx_addr>
public tensor_shape_rnd !returns a random tensor-shape-specification-string (TSSS)
public tensor_shape_rank !returns the number of dimensions in a tensor-shape-specification-string (TSSS)
public tensor_shape_str_create !creates a tensor shape specification string
public get_contr_pattern_dig !converts a symbolic tensor contraction pattern into the digital form (used by tensor_block_contract)
public get_contr_pattern_sym !converts a digital tensor contraction pattern into a symbolic form
public get_contr_permutations !given a digital contraction pattern, returns all tensor permutations necessary for the subsequent matrix multiplication
public contr_pattern_rnd !returns a random digital tensor contraction pattern
public coherence_control_var !returns a coherence control variable based on a mnemonic input
public tensor_block_shape_create !generates the tensor shape based on either the tensor shape specification string (TSSS) or numeric arguments
public tensor_block_shape_create_sym !generates the tensor shape based on the tensor shape specification string (TSSS)
public tensor_block_shape_create_num !generates the tensor shape based on the numeric arguments
public tensor_block_shape_ok !checks the correctness of a tensor shape generated from a tensor shape specification string (TSSS)
public tensor_block_alloc !sets/queries the allocation status of data pointers in a tensor block
private array_alloc !allocates an array pointer {R4,R8,C4,C8}
private array_alloc_r4 !allocates an array pointer R4
private array_alloc_r8 !allocates an array pointer R8
private array_alloc_c4 !allocates an array pointer C4
private array_alloc_c8 !allocates an array pointer C8
private array_free !frees an array pointer {R4,R8,C4,C8}
private array_free_r4 !frees an array pointer R4
private array_free_r8 !frees an array pointer R8
private array_free_c4 !frees an array pointer C4
private array_free_c8 !frees an array pointer C8
private tensor_block_slice_dlf !extracts a slice from a tensor block (Fortran-like dimension-led storage layout)
private tensor_block_insert_dlf !inserts a slice into a tensor block (Fortran-like dimension-led storage layout)
private tensor_block_copy_dlf !tensor transpose for dimension-led (Fortran-like-stored) dense tensor blocks
private tensor_block_copy_scatter_dlf !tensor transpose for dimension-led (Fortran-like-stored) dense tensor blocks (scattering variant)
private tensor_block_fcontract_dlf !multiplies two matrices derived from tensors to produce a scalar (left is transposed, right is normal)
private tensor_block_pcontract_dlf !multiplies two matrices derived from tensors to produce a third matrix (left is transposed, right is normal)
private tensor_block_ftrace_dlf !takes a full trace of a tensor block
private tensor_block_ptrace_dlf !takes a partial trace of a tensor block
contains
!-----------------
!PUBLIC FUNCTIONS:
!----------------------------------------------------------------------
#ifndef NO_PHI
!DIR$ ATTRIBUTES OFFLOAD:mic:: get_mem_alloc_policy
#endif
function get_mem_alloc_policy(ierr,fallback) result(mem_policy) !SERIAL
!Gets the current memory allocation policy.
implicit none
integer:: mem_policy !out: memory allocation policy
integer, intent(out), optional:: ierr !out: error code
logical, intent(out), optional:: fallback !out: fallback status
mem_policy=MEM_ALLOC_POLICY
if(present(fallback)) fallback=MEM_ALLOC_FALLBACK
if(present(ierr)) ierr=0
return
end function get_mem_alloc_policy
!----------------------------------------------------------------
#ifndef NO_PHI
!DIR$ ATTRIBUTES OFFLOAD:mic:: set_mem_alloc_policy
#endif
subroutine set_mem_alloc_policy(mem_policy,ierr,fallback) !SERIAL
!Sets the memory allocation policy.
implicit none
integer, intent(in):: mem_policy !in: memory allocation policy
integer, intent(out), optional:: ierr !out: error code
logical, intent(in), optional:: fallback !in: memory allocation fallback to regular
select case(mem_policy)
case(MEM_ALLOC_REGULAR,MEM_ALLOC_TMP_BUF,MEM_ALLOC_ALL_BUF)
!!!$OMP ATOMIC WRITE SEQ_CST
!$OMP ATOMIC WRITE
MEM_ALLOC_POLICY=mem_policy
case default
if(present(ierr)) ierr=1 !invalid policy
return
end select
if(present(fallback)) then
!!!$OMP ATOMIC WRITE SEQ_CST
!$OMP ATOMIC WRITE
MEM_ALLOC_FALLBACK=fallback
endif
if(present(ierr)) ierr=0
return
end subroutine set_mem_alloc_policy
!-----------------------------------------
#ifndef NO_PHI
!DIR$ ATTRIBUTES OFFLOAD:mic:: set_data_kind_sync
#endif
subroutine set_data_kind_sync(alg) !SERIAL
implicit none
integer, intent(in):: alg
if(alg.eq.0) then
!!!$OMP ATOMIC WRITE SEQ_CST
!$OMP ATOMIC WRITE
DATA_KIND_SYNC=.FALSE.
else
!!!$OMP ATOMIC WRITE SEQ_CST
!$OMP ATOMIC WRITE
DATA_KIND_SYNC=.TRUE.
endif
return
end subroutine set_data_kind_sync
!----------------------------------------------
#ifndef NO_PHI
!DIR$ ATTRIBUTES OFFLOAD:mic:: set_transpose_algorithm
#endif
subroutine set_transpose_algorithm(alg) !SERIAL
implicit none
integer, intent(in):: alg
if(alg.eq.0) then
!!!$OMP ATOMIC WRITE SEQ_CST
!$OMP ATOMIC WRITE
TRANS_SHMEM=.FALSE.
else
!!!$OMP ATOMIC WRITE SEQ_CST
!$OMP ATOMIC WRITE
TRANS_SHMEM=.TRUE.
endif
return
end subroutine set_transpose_algorithm
!--------------------------------------------
#ifndef NO_PHI
!DIR$ ATTRIBUTES OFFLOAD:mic:: set_matmult_algorithm
#endif
subroutine set_matmult_algorithm(alg) !SERIAL
implicit none
integer, intent(in):: alg
#ifndef NO_BLAS
if(alg.eq.0) then
!!!$OMP ATOMIC WRITE SEQ_CST
!$OMP ATOMIC WRITE
DISABLE_BLAS=.FALSE.
else
!!!$OMP ATOMIC WRITE SEQ_CST
!$OMP ATOMIC WRITE
DISABLE_BLAS=.TRUE.
endif
#endif
return
end subroutine set_matmult_algorithm
!---------------------------------------------
#ifndef NO_PHI
!DIR$ ATTRIBUTES OFFLOAD:mic:: cmplx4_to_real4
#endif
real(4) function cmplx4_to_real4(cmplx_num) !SERIAL
!This function returns a real approximant for a complex number with the following properties:
! 1) The Euclidean (Frobenius) norm (modulus) is preserved;
! 2) The sign inversion symmetry is preserved.
implicit none
complex(4), intent(in):: cmplx_num
real(4):: real_part
real_part=real(cmplx_num)
if(real_part.ne.0.0) then
cmplx4_to_real4=abs(cmplx_num)*sign(1.0,real_part)
else
cmplx4_to_real4=aimag(cmplx_num)
endif
return
end function cmplx4_to_real4
!---------------------------------------------
#ifndef NO_PHI
!DIR$ ATTRIBUTES OFFLOAD:mic:: cmplx8_to_real8
#endif
real(8) function cmplx8_to_real8(cmplx_num) !SERIAL
!This function returns a real approximant for a complex number with the following properties:
! 1) The Euclidean (Frobenius) norm (modulus) is preserved;
! 2) The sign inversion symmetry is preserved.
implicit none
complex(8), intent(in):: cmplx_num
real(8):: real_part
real_part=real(cmplx_num,8)
if(real_part.ne.0d0) then
cmplx8_to_real8=abs(cmplx_num)*sign(1d0,real_part)
else
cmplx8_to_real8=aimag(cmplx_num)
endif
return
end function cmplx8_to_real8
!--------------------------------------------------------------------
subroutine tensor_shape_assoc(tens_shape,ierr,dims,divs,grps)
!Constructs a tensor shape object <tensor_shape_t) by pointer associating it
!with external data. Incoming <tens_shape> must be empty on entrance.
implicit none
type(tensor_shape_t), intent(inout):: tens_shape !inout: tensor shape
integer, intent(out):: ierr !out: error code (0:success)
integer, intent(in), pointer, contiguous, optional:: dims(:) !in: dimension extents (length = tensor rank)
integer, intent(in), pointer, contiguous, optional:: divs(:) !in: dimension dividers
integer, intent(in), pointer, contiguous, optional:: grps(:) !in: dimension groups
integer:: n
ierr=0
if(tens_shape%num_dim.lt.0.and.&
&(.not.(associated(tens_shape%dim_extent).or.&
&associated(tens_shape%dim_divider).or.&
&associated(tens_shape%dim_group)))) then
if(present(dims)) then
if(associated(dims)) then
n=size(dims)
if(n.ge.0.and.n.le.MAX_TENSOR_RANK) then
tens_shape%num_dim=n
if(n.gt.0) then
tens_shape%dim_extent(1:n)=>dims(1:n)
if(present(divs)) then
if(associated(divs)) then
if(size(divs).eq.n) then
tens_shape%dim_divider(1:n)=>divs(1:n)
else
ierr=1; return
endif
endif
endif
if(present(grps)) then
if(associated(grps)) then
if(size(grps).eq.n) then
tens_shape%dim_group(1:n)=>grps(1:n)
else
ierr=2; return
endif
endif
endif
endif
else
ierr=3
endif
else
tens_shape%num_dim=0
endif
else
tens_shape%num_dim=0
endif
else
ierr=4 !tensor shape is not empty
endif
return
end subroutine tensor_shape_assoc
!------------------------------------------------------------------
integer function tensor_block_layout(tens,ierr,check_shape) !SERIAL
!Returns the type of the storage layout for a given tensor block <tens>.
!INPUT:
! - tens - tensor block;
! - check_shape - (optional) if .TRUE., the tensor shape will be checked;
!OUTPUT:
! - tensor_block_layout - tensor block storage layout;
! - ierr - error code (0:sucess).
!NOTES:
! - %dim_divider(1)=0 means that an alternative (neither dimension-led nor bricked) storage layout is used,
! whose kind is regulated by the %dim_group(1) then.
! - For dimension_led, bricked_dense and bricked_ordered tensor blocks,
! index group 0 does not imply any index ordering restrictions.
! The presence of group 1,2,etc...(up to the tensor rank) assumes
! that the bricked_ordered storage layout is in use. It is illegal
! to assign non-zero group numbers to indices for dimension_led
! and bricked_dense tensor blocks.
implicit none
type(tensor_block_t), intent(inout):: tens !(out) because of <tensor_block_shape_ok>
logical, intent(in), optional:: check_shape
integer, intent(inout):: ierr
integer i,j,k,l,m,n,ibus(0:max_tensor_rank)
ierr=0; tensor_block_layout=not_allocated
if(present(check_shape)) then
if(check_shape) then; ierr=tensor_block_shape_ok(tens); if(ierr.ne.0) return; endif
endif
if(tens%tensor_shape%num_dim.gt.0.and.associated(tens%tensor_shape%dim_extent).and.&
&associated(tens%tensor_shape%dim_divider).and.associated(tens%tensor_shape%dim_group)) then !true tensor
if(tens%tensor_shape%dim_divider(1).gt.0) then !dimension-led or bricked
tensor_block_layout=dimension_led
do i=1,tens%tensor_shape%num_dim
if(tens%tensor_shape%dim_extent(i).ne.tens%tensor_shape%dim_divider(i)) then
tensor_block_layout=bricked_dense; exit
endif
enddo
if(tensor_block_layout.eq.bricked_dense) then
ibus(0:tens%tensor_shape%num_dim)=0
do i=1,tens%tensor_shape%num_dim
j=tens%tensor_shape%dim_group(i); if(j.lt.0.or.j.gt.tens%tensor_shape%num_dim) then; ierr=1000; return; endif
if(j.gt.0.and.ibus(j).gt.0) then; tensor_block_layout=bricked_ordered; exit; endif
ibus(j)=ibus(j)+1
enddo
endif
else !alternative storage layout
!`Future
endif
elseif(tens%tensor_shape%num_dim.eq.0) then !scalar tensor
tensor_block_layout=scalar_tensor
endif
return
end function tensor_block_layout
!-------------------------------------------------------------------------
integer(LONGINT) function tensor_block_shape_size(tens_block,ierr) !SERIAL
!This function determines the size of a tensor block (number of elements) by its shape.
!Note that a scalar (0-dimensional tensor) and a 1-dimensional tensor with extent 1 are not the same!
implicit none
type(tensor_block_t), intent(inout):: tens_block !(out) because of <tensor_block_layout> because of <tensor_block_shape_ok>
integer, intent(inout):: ierr
integer i,j,k,l,m,n,k0,k1,k2,k3,ks,kf,tst
ierr=0; tensor_block_shape_size=0_LONGINT
tst=tensor_block_layout(tens_block,ierr); if(ierr.ne.0) return
select case(tst)
case(not_allocated)
tensor_block_shape_size=0_LONGINT; ierr=-1
case(scalar_tensor)
tensor_block_shape_size=1_LONGINT
case(dimension_led,bricked_dense)
tensor_block_shape_size=1_LONGINT
do i=1,tens_block%tensor_shape%num_dim
if(tens_block%tensor_shape%dim_extent(i).gt.0.and.&
&tens_block%tensor_shape%dim_divider(i).gt.0.and.&
&tens_block%tensor_shape%dim_divider(i).le.tens_block%tensor_shape%dim_extent(i)) then
tensor_block_shape_size=tensor_block_shape_size*int(tens_block%tensor_shape%dim_extent(i),LONGINT)
else
ierr=100+i; return !invalid dimension specificator in tens_block%tensor_shape%
endif
enddo
case(bricked_ordered)
!`Future: Compute volumes of all ordered multi-indices and multiply them.
case(sparse_list)
!`Future
case(compressed)
!`Future
case default
ierr=-2
end select
return
end function tensor_block_shape_size
!---------------------------------------------------------------
character(2) function tensor_master_data_kind(tens,ierr) !SERIAL
!This function determines the master data kind present in a tensor block.
!INPUT:
! - tens - tensor block;
!OUTPUT:
! - tensor_master_data_kind - one of {'r4','r8','c4','c8','--'}, where the latter means "not allocated";
! - ierr - error code (0:success).
implicit none
type(tensor_block_t), intent(in):: tens
integer, intent(inout):: ierr
ierr=0; tensor_master_data_kind='--'
if(tens%tensor_shape%num_dim.eq.0) then
tensor_master_data_kind='c8'
elseif(tens%tensor_shape%num_dim.gt.0) then
if(associated(tens%data_real4)) tensor_master_data_kind='r4'
if(associated(tens%data_real8)) tensor_master_data_kind='r8'
if(associated(tens%data_cmplx4)) tensor_master_data_kind='c4'
if(associated(tens%data_cmplx8)) tensor_master_data_kind='c8'
endif
return
end function tensor_master_data_kind
!----------------------------------------------------------------------
character(2) function tensor_common_data_kind(tens1,tens2,ierr) !SERIAL
!This function determines the common data kind present in two commpatible tensor blocks.
!INPUT:
! - tens1, tens2 - compatible tensor blocks;
!OUTPUT:
! - tensor_common_data_kind - one of {'r4','r8','c4','c8','--'}, where the latter means "not applicable";
! - ierr - error code (0:success).
implicit none
type(tensor_block_t), intent(in):: tens1,tens2
integer, intent(inout):: ierr
ierr=0; tensor_common_data_kind='--'
if(tens1%tensor_shape%num_dim.eq.0.and.tens2%tensor_shape%num_dim.eq.0) then
tensor_common_data_kind='c8'
elseif(tens1%tensor_shape%num_dim.gt.0.and.tens2%tensor_shape%num_dim.gt.0) then
if(associated(tens1%data_real4).and.associated(tens2%data_real4)) tensor_common_data_kind='r4'
if(associated(tens1%data_real8).and.associated(tens2%data_real8)) tensor_common_data_kind='r8'
if(associated(tens1%data_cmplx4).and.associated(tens2%data_cmplx4)) tensor_common_data_kind='c4'
if(associated(tens1%data_cmplx8).and.associated(tens2%data_cmplx8)) tensor_common_data_kind='c8'
endif
return
end function tensor_common_data_kind
!-------------------------------------------------------------------------------------------------
logical function tensor_block_compatible(tens_in,tens_out,ierr,transp,no_check_data_kinds) !SERIAL
!This function decides whether two tensor blocks are compatible
!under some index permutation (the latter is optional).
!INPUT:
! - tens_in - input tensor;
! - tens_out - output tensor;
! - transp(0:*) - (optional) O2N index permutation;
! - no_check_data_kinds - (optional) if .TRUE., the two tensor blocks do not have to have the same data kinds allocated;
!OUTPUT:
! - tensor_block_compatible - .TRUE./.FALSE.;
! - ierr - error code (0:success).
!NOTES:
! - Non-allocated tensor blocks are all compatible.
! - Tensor block storage layouts are ignored.
implicit none
type(tensor_block_t), intent(in):: tens_in,tens_out
integer, intent(in), optional:: transp(0:*)
logical, intent(in), optional:: no_check_data_kinds
integer, intent(inout):: ierr
integer i,j,k,l,m,n,k0,k1,k2,k3,ks,kf
integer trn(0:max_tensor_rank)
integer(LONGINT) ls
logical chdtk
ierr=0; tensor_block_compatible=.TRUE.
if(tens_in%tensor_shape%num_dim.eq.tens_out%tensor_shape%num_dim) then
n=tens_in%tensor_shape%num_dim
if(n.gt.0) then
!Check tensor shapes:
if(associated(tens_in%tensor_shape%dim_extent).and.associated(tens_in%tensor_shape%dim_divider).and.&
&associated(tens_in%tensor_shape%dim_group).and.associated(tens_out%tensor_shape%dim_extent).and.&
&associated(tens_out%tensor_shape%dim_divider).and.associated(tens_out%tensor_shape%dim_group)) then
if(present(transp)) then; trn(0:n)=transp(0:n); else; trn(0:n)=(/+1,(j,j=1,n)/); endif
do i=1,n
if(tens_out%tensor_shape%dim_extent(trn(i)).ne.tens_in%tensor_shape%dim_extent(i).or.&
&tens_out%tensor_shape%dim_divider(trn(i)).ne.tens_in%tensor_shape%dim_divider(i).or.&
&tens_out%tensor_shape%dim_group(trn(i)).ne.tens_in%tensor_shape%dim_group(i)) then
tensor_block_compatible=.FALSE.
exit
endif
enddo
!Check data kinds:
if(tensor_block_compatible) then
if(tens_in%tensor_block_size.ne.tens_out%tensor_block_size) then
tensor_block_compatible=.FALSE.; ierr=1 !the same shape tensor blocks have different total sizes
else
if(present(no_check_data_kinds)) then; chdtk=no_check_data_kinds; else; chdtk=.FALSE.; endif
if(.not.chdtk) then
if((associated(tens_in%data_real4).and.(.not.associated(tens_out%data_real4))).or.&
&((.not.associated(tens_in%data_real4)).and.associated(tens_out%data_real4))) then
tensor_block_compatible=.FALSE.; return
else
if(associated(tens_in%data_real4)) then
ls=size(tens_in%data_real4)
if(size(tens_out%data_real4).ne.ls.or.tens_out%tensor_block_size.ne.ls) then
tensor_block_compatible=.FALSE.; ierr=2; return
endif
endif
endif
if((associated(tens_in%data_real8).and.(.not.associated(tens_out%data_real8))).or.&
&((.not.associated(tens_in%data_real8)).and.associated(tens_out%data_real8))) then
tensor_block_compatible=.FALSE.; return
else
if(associated(tens_in%data_real8)) then
ls=size(tens_in%data_real8)
if(size(tens_out%data_real8).ne.ls.or.tens_out%tensor_block_size.ne.ls) then
tensor_block_compatible=.FALSE.; ierr=3; return
endif
endif
endif
if((associated(tens_in%data_cmplx4).and.(.not.associated(tens_out%data_cmplx4))).or.&
&((.not.associated(tens_in%data_cmplx4)).and.associated(tens_out%data_cmplx4))) then
tensor_block_compatible=.FALSE.; return
else
if(associated(tens_in%data_cmplx4)) then
ls=size(tens_in%data_cmplx4)
if(size(tens_out%data_cmplx4).ne.ls.or.tens_out%tensor_block_size.ne.ls) then
tensor_block_compatible=.FALSE.; ierr=4; return
endif
endif
endif
if((associated(tens_in%data_cmplx8).and.(.not.associated(tens_out%data_cmplx8))).or.&
&((.not.associated(tens_in%data_cmplx8)).and.associated(tens_out%data_cmplx8))) then
tensor_block_compatible=.FALSE.; return
else
if(associated(tens_in%data_cmplx8)) then
ls=size(tens_in%data_cmplx8)
if(size(tens_out%data_cmplx8).ne.ls.or.tens_out%tensor_block_size.ne.ls) then
tensor_block_compatible=.FALSE.; ierr=5; return
endif
endif
endif
endif
endif
endif
else
tensor_block_compatible=.FALSE.; ierr=6 !some of the %tensor_shape arrays were not allocated
endif
endif
else
tensor_block_compatible=.FALSE.
endif
return
end function tensor_block_compatible
!------------------------------------------------------------------
subroutine tensor_block_mimic(tens_in,tens_out,ierr,transp) !SERIAL
!This subroutine copies the internal structure of a tensor block without copying the actual data.
!Optionally, it can also initialize the tensor shape according to a given permutation (O2N).
!INPUT:
! - tens_in - tensor block being mimicked;
! - transp(0:) - (optional) if present, the tensor shape will also be initialized according to this permutation (O2N);
!OUTPUT:
! - tens_out - output tensor block;
! - ierr - error code (0:success).
!NOTES:
! - Tensor block storage layouts are ignored.
implicit none
type(tensor_block_t), intent(in):: tens_in
type(tensor_block_t), intent(inout):: tens_out
integer, intent(in), optional:: transp(0:*)
integer, intent(inout):: ierr
integer i,j,k,l,m,n,k0,k1,k2,k3,ks,kf
logical res
ierr=0
n=tens_in%tensor_shape%num_dim
if(tens_out%tensor_shape%num_dim.ne.n.or.tens_out%tensor_block_size.ne.tens_in%tensor_block_size) then
call tensor_block_destroy(tens_out,ierr); if(ierr.ne.0) then; ierr=1; return; endif
!Allocate tensor shape:
if(n.gt.0) then
allocate(tens_out%tensor_shape%dim_extent(1:n),STAT=ierr); if(ierr.ne.0) then; ierr=2; return; endif
allocate(tens_out%tensor_shape%dim_divider(1:n),STAT=ierr); if(ierr.ne.0) then; ierr=3; return; endif
allocate(tens_out%tensor_shape%dim_group(1:n),STAT=ierr); if(ierr.ne.0) then; ierr=4; return; endif
res=tensor_block_alloc(tens_out,'sp',ierr,.TRUE.); if(ierr.ne.0) then; ierr=5; return; endif
endif
tens_out%tensor_shape%num_dim=n; tens_out%tensor_block_size=tens_in%tensor_block_size
endif
if(n.gt.0) then
if(present(transp)) then !adopt the tensor shape in full according to the given permutation (O2N)
tens_out%tensor_shape%dim_extent(transp(1:n))=tens_in%tensor_shape%dim_extent(1:n)
tens_out%tensor_shape%dim_divider(transp(1:n))=tens_in%tensor_shape%dim_divider(1:n)
tens_out%tensor_shape%dim_group(transp(1:n))=tens_in%tensor_shape%dim_group(1:n)
endif
!Allocate data arrays, if needed:
!REAL4:
if(associated(tens_in%data_real4)) then
if(size(tens_in%data_real4).eq.tens_in%tensor_block_size) then
if(.not.associated(tens_out%data_real4)) then
! allocate(tens_out%data_real4(0:tens_in%tensor_block_size-1),STAT=ierr)
ierr=array_alloc(tens_out%data_real4,tens_in%tensor_block_size,base=0_LONGINT)
if(ierr.ne.0) then; ierr=6; return; endif
res=tensor_block_alloc(tens_out,'r4',ierr,.TRUE.); if(ierr.ne.0) then; ierr=7; return; endif
endif
else
ierr=8; return
endif
endif
!REAL8:
if(associated(tens_in%data_real8)) then
if(size(tens_in%data_real8).eq.tens_in%tensor_block_size) then
if(.not.associated(tens_out%data_real8)) then
! allocate(tens_out%data_real8(0:tens_in%tensor_block_size-1),STAT=ierr)
ierr=array_alloc(tens_out%data_real8,tens_in%tensor_block_size,base=0_LONGINT)
if(ierr.ne.0) then; ierr=9; return; endif
res=tensor_block_alloc(tens_out,'r8',ierr,.TRUE.); if(ierr.ne.0) then; ierr=10; return; endif
endif
else
ierr=11; return
endif
endif
!CMPLX4:
if(associated(tens_in%data_cmplx4)) then
if(size(tens_in%data_cmplx4).eq.tens_in%tensor_block_size) then
if(.not.associated(tens_out%data_cmplx4)) then
! allocate(tens_out%data_cmplx4(0:tens_in%tensor_block_size-1),STAT=ierr)
ierr=array_alloc(tens_out%data_cmplx4,tens_in%tensor_block_size,base=0_LONGINT)
if(ierr.ne.0) then; ierr=12; return; endif
res=tensor_block_alloc(tens_out,'c4',ierr,.TRUE.); if(ierr.ne.0) then; ierr=13; return; endif
endif
else
ierr=14; return
endif
endif
!CMPLX8:
if(associated(tens_in%data_cmplx8)) then
if(size(tens_in%data_cmplx8).eq.tens_in%tensor_block_size) then
if(.not.associated(tens_out%data_cmplx8)) then
! allocate(tens_out%data_cmplx8(0:tens_in%tensor_block_size-1),STAT=ierr)
ierr=array_alloc(tens_out%data_cmplx8,tens_in%tensor_block_size,base=0_LONGINT)
if(ierr.ne.0) then; ierr=15; return; endif
res=tensor_block_alloc(tens_out,'c8',ierr,.TRUE.); if(ierr.ne.0) then; ierr=16; return; endif
endif
else
ierr=17; return
endif
endif
endif
return
end subroutine tensor_block_mimic
!------------------------------------------------------------------------------------------------------
subroutine tensor_block_create(shape_str,data_kind,tens_block,ierr,val_r4,val_r8,val_c4,val_c8) !PARALLEL
!This subroutine creates a tensor block <tens_block> based on the tensor shape specification string (TSSS) <shape_str>.
!FORMAT of <shape_str>:
!"(E1/D1{G1},E2/D2{G2},...)":
! Ex is the extent of the dimension x (segment);
! /Dx specifies an optional segment divider for the dimension x (lm_segment_size), 1<=Dx<=Ex (DEFAULT = Ex);
! Ex MUST be a multiple of Dx.
! {Gx} optionally specifies the symmetric group the dimension belongs to, Gx>=0 (default group 0 has no symmetry ordering).
! Dimensions grouped together (group#>0) will obey a non-descending ordering from left to right.
!By default, the 1st dimension is the most minor one while the last is the most senior (Fortran-like).
!If the number of dimensions equals to zero, the %scalar_value field will be initialized.
!INPUT:
! - shape_str - tensor shape specification string (SSS);
! - data_kind - requested data kind, one of {"r4","r8","c4","c8"};
! - tens_block - tensor block;
! - val_r4/val_r8/val_c4/val_c8 - (optional) initialization value for different data kinds (otherwise a random fill will be invoked);
!OUTPUT:
! - tens_block - filled tensor_block;
! - ierr - error code (0: success);
!NOTES:
! - If the tensor block has already been allocated before, it will be reshaped and reinitialized.
! - If ordered dimensions are present, the data feed may not reflect a proper symmetry (antisymmetry)!
implicit none
character(*), intent(in):: shape_str
character(2), intent(in):: data_kind
type(tensor_block_t), intent(inout):: tens_block
real(4), intent(in), optional:: val_r4
real(8), intent(in), optional:: val_r8
complex(4), intent(in), optional:: val_c4
complex(8), intent(in), optional:: val_c8
integer, intent(inout):: ierr
ierr=0
call tensor_block_shape_create(tens_block,shape_str,ierr); if(ierr.ne.0) then; ierr=1; return; endif
ierr=tensor_block_shape_ok(tens_block); if(ierr.ne.0) then; ierr=2; return; endif
select case(data_kind)
case('r4','R4')
if(present(val_r4)) then
call tensor_block_init(data_kind,tens_block,ierr,val_r4=val_r4); if(ierr.ne.0) then; ierr=3; return; endif
else
if(present(val_r8)) then
call tensor_block_init(data_kind,tens_block,ierr,val_r8=val_r8); if(ierr.ne.0) then; ierr=4; return; endif
else
if(present(val_c4)) then
call tensor_block_init(data_kind,tens_block,ierr,val_c4=val_c4); if(ierr.ne.0) then; ierr=5; return; endif
else
if(present(val_c8)) then
call tensor_block_init(data_kind,tens_block,ierr,val_c8=val_c8); if(ierr.ne.0) then; ierr=6; return; endif
else
call tensor_block_init(data_kind,tens_block,ierr); if(ierr.ne.0) then; ierr=7; return; endif
endif
endif
endif
endif
case('r8','R8')
if(present(val_r8)) then
call tensor_block_init(data_kind,tens_block,ierr,val_r8=val_r8); if(ierr.ne.0) then; ierr=8; return; endif
else
if(present(val_r4)) then
call tensor_block_init(data_kind,tens_block,ierr,val_r4=val_r4); if(ierr.ne.0) then; ierr=9; return; endif
else
if(present(val_c4)) then
call tensor_block_init(data_kind,tens_block,ierr,val_c4=val_c4); if(ierr.ne.0) then; ierr=10; return; endif
else
if(present(val_c8)) then
call tensor_block_init(data_kind,tens_block,ierr,val_c8=val_c8); if(ierr.ne.0) then; ierr=11; return; endif
else
call tensor_block_init(data_kind,tens_block,ierr); if(ierr.ne.0) then; ierr=12; return; endif
endif
endif
endif
endif
case('c4','C4')
if(present(val_c4)) then
call tensor_block_init(data_kind,tens_block,ierr,val_c4=val_c4); if(ierr.ne.0) then; ierr=13; return; endif
else
if(present(val_c8)) then
call tensor_block_init(data_kind,tens_block,ierr,val_c8=val_c8); if(ierr.ne.0) then; ierr=14; return; endif
else
if(present(val_r8)) then
call tensor_block_init(data_kind,tens_block,ierr,val_r8=val_r8); if(ierr.ne.0) then; ierr=15; return; endif
else
if(present(val_r4)) then
call tensor_block_init(data_kind,tens_block,ierr,val_r4=val_r4); if(ierr.ne.0) then; ierr=16; return; endif
else
call tensor_block_init(data_kind,tens_block,ierr); if(ierr.ne.0) then; ierr=17; return; endif
endif
endif
endif
endif
case('c8','C8')
if(present(val_c8)) then
call tensor_block_init(data_kind,tens_block,ierr,val_c8=val_c8); if(ierr.ne.0) then; ierr=18; return; endif
else
if(present(val_c4)) then
call tensor_block_init(data_kind,tens_block,ierr,val_c4=val_c4); if(ierr.ne.0) then; ierr=19; return; endif
else
if(present(val_r8)) then
call tensor_block_init(data_kind,tens_block,ierr,val_r8=val_r8); if(ierr.ne.0) then; ierr=20; return; endif
else
if(present(val_r4)) then
call tensor_block_init(data_kind,tens_block,ierr,val_r4=val_r4); if(ierr.ne.0) then; ierr=21; return; endif
else
call tensor_block_init(data_kind,tens_block,ierr); if(ierr.ne.0) then; ierr=22; return; endif
endif
endif
endif
endif
case default
ierr=23
end select
return
end subroutine tensor_block_create
!------------------------------------------------------------------------------------------
subroutine tensor_block_init(data_kind,tens_block,ierr,val_r4,val_r8,val_c4,val_c8) !PARALLEL
!This subroutine initializes a tensor block <tens_block> with either some value or random numbers.
!INPUT:
! - data_kind - requested data kind, one of {"r4","r8","c4","c8"};
! - tens_block - tensor block;
! - val_r4/val_r8/val_c4/val_c8 - (optional) if present, the tensor block is assigned the value <val> (otherwise, a random fill);
!OUTPUT:
! - tens_block - filled tensor block;
! - ierr - error code (0: success):
! -1: invalid (negative) tensor rank;
! -2: negative tensor size returned;
! x>0: invalid <tensor_shape> (zero/negative xth dimension extent);
! 666: invalid <data_kind>;
! 667: memory allocation failed;
!NOTES:
! - For tensors with a non-zero rank, the %scalar_value field will be set to the Euclidean norm of the tensor block.
! - Scalar tensors will be initialized with the <val_XX> value (if present), regardless of the <data_kind>.
! - In general, a tensor block may have dimension ordering (symmetry) restrictions.
! In this case, the number fill done here might not reflect the proper symmetry (e.g., antisymmetry)!
implicit none
!-----------------------------------------------------
integer(LONGINT), parameter:: chunk_size=2**10
integer(LONGINT), parameter:: vec_size=2**8
!--------------------------------------------------
character(2), intent(in):: data_kind
type(tensor_block_t), intent(inout):: tens_block
real(4), intent(in), optional:: val_r4
real(8), intent(in), optional:: val_r8
complex(4), intent(in), optional:: val_c4
complex(8), intent(in), optional:: val_c8
integer, intent(inout):: ierr
integer i,j,k,l,m,n,k0,k1,k2,k3,k4,ks,kf
integer(LONGINT) tens_size,l0,l1
real(8) vec_r8(0:vec_size-1),valr8,val,rnd_buf(2)
real(4) vec_r4(0:vec_size-1),valr4
complex(4) vec_c4(0:vec_size-1),valc4
complex(8) vec_c8(0:vec_size-1),valc8
logical res
ierr=0; tens_block%tensor_block_size=tensor_block_shape_size(tens_block,ierr)
if(ierr.ne.0) then; ierr=1; return; endif
if(tens_block%tensor_block_size.le.0_LONGINT) then; ierr=2; return; endif
if(tens_block%tensor_shape%num_dim.eq.0) then !scalar tensor
if(associated(tens_block%data_real4)) then
if(tensor_block_alloc(tens_block,'r4',ierr)) then
if(ierr.ne.0) then; ierr=3; return; endif
! deallocate(tens_block%data_real4,STAT=ierr)
call array_free(tens_block%data_real4,ierr)
if(ierr.ne.0) then; ierr=4; return; endif
res=tensor_block_alloc(tens_block,'r4',ierr,.FALSE.); if(ierr.ne.0) then; ierr=5; return; endif
else
if(ierr.ne.0) then; ierr=6; return; endif
nullify(tens_block%data_real4)
endif
endif
if(associated(tens_block%data_real8)) then
if(tensor_block_alloc(tens_block,'r8',ierr)) then
if(ierr.ne.0) then; ierr=7; return; endif
! deallocate(tens_block%data_real8,STAT=ierr)
call array_free(tens_block%data_real8,ierr)
if(ierr.ne.0) then; ierr=8; return; endif
res=tensor_block_alloc(tens_block,'r8',ierr,.FALSE.); if(ierr.ne.0) then; ierr=9; return; endif
else
if(ierr.ne.0) then; ierr=10; return; endif
nullify(tens_block%data_real8)
endif
endif
if(associated(tens_block%data_cmplx4)) then
if(tensor_block_alloc(tens_block,'c4',ierr)) then
if(ierr.ne.0) then; ierr=11; return; endif
! deallocate(tens_block%data_cmplx4,STAT=ierr)
call array_free(tens_block%data_cmplx4,ierr)
if(ierr.ne.0) then; ierr=12; return; endif
res=tensor_block_alloc(tens_block,'c4',ierr,.FALSE.); if(ierr.ne.0) then; ierr=13; return; endif
else
if(ierr.ne.0) then; ierr=14; return; endif
nullify(tens_block%data_cmplx4)
endif
endif
if(associated(tens_block%data_cmplx8)) then
if(tensor_block_alloc(tens_block,'c8',ierr)) then
if(ierr.ne.0) then; ierr=15; return; endif