(* Copyright 2013 Ivan Raikov. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. *) fun putStr out str = TextIO.output (out, str) fun putStrLn out str = (TextIO.output (out, str); TextIO.output (out, "\n")) signature SPARSE_INDEX = sig type t type array = IntArray.array type nonzero = { indptr: array, indices: array } type indexer = t -> int option datatype storage = CSR | CSC exception Index exception Shape val order : storage val toInt : t -> nonzero -> t -> int option val inBounds : t -> t -> bool val eq : t * t -> bool val app : t -> nonzero -> (t -> unit) -> unit val iteri : t -> nonzero -> (t * int -> unit) -> unit end (* MONO_SPARSE - Signature - Monomorphic sparse matrices. structure Number : NUMBER Structure that describe type type of the elements of the matrix and their operations (+,*,etc) type elem = Number.t The type of the elements of the matrix structure Tensor : MONO_TENSOR Tensors of 'elem' type. fromTensor [[number,number,...]*] fromTensor' [[number,number,...]*] Builds a sparse matrix up from a tensor. fromTensor converts the tensor to sparse format; fromTensor' uses it as-is fromTensorList [[number,number,...]*] Builds a sparse matrix up from a list of tensors. sub (matrix,row,column) update (matrix,row,column,value) Retrieves or sets an element from/to a sparse matrix map op matrix mapi op matrix app op matrix appi op matrix Maps or applies 'op' to the elements of a matrix. 'mapi' and 'appi' have the pecularity that 'op' receives the row and the column indices plust the value. matrix + matrix matrix - matrix matrix * matrix matrix / matrix *> n matrix Elementwise operations. *) signature MONO_SPARSE_MATRIX = sig structure Tensor : MONO_TENSOR structure TensorSlice : MONO_TENSOR_SLICE structure Number : NUMBER structure Index : SPARSE_INDEX type index = Index.t type elem = Number.t type matrix exception Data and Shape val zero : Number.t val fromList : index -> ((int * (int * elem) list) list * index * (index option)) -> matrix val fromTensor : index -> (Tensor.tensor * (index option)) -> matrix val fromTensorList : index -> {tensor: Tensor.tensor, offset: index, sparse: bool} list -> matrix val fromGenerator : index -> ((index -> elem) * index * (index option)) -> matrix val fromGeneratorList : index -> ({f: (index -> elem), fshape: index, offset: index} list) -> matrix val insert : matrix * matrix -> matrix val shape : matrix -> index val sub : matrix * index -> elem val update : matrix * index * elem -> unit val map : (elem -> elem) -> matrix -> matrix val app : (elem -> unit) -> matrix -> unit val appi : (index * elem -> unit) -> matrix -> unit val *> : elem -> matrix -> matrix datatype slice = SLSPARSE of {offset: index, indices: Index.array, data: Tensor.tensor} | SLDENSE of {offset: index, data: TensorSlice.slice} val slice : (matrix * int * int) -> slice list val sliceAppi: ((int * elem) -> unit) -> slice list -> unit val sliceFoldi: ((int * elem * 'a) -> 'a) -> 'a -> slice list -> 'a end structure SparseIndex = struct type t = int list type array = IntArray.array type nonzero = { indptr: array, indices: array } type indexer = t -> int option datatype storage = CSR | CSC exception Index exception Shape val order = CSC fun validShape shape = List.all (fn x => x > 0) shape fun validIndex index = List.all (fn x => x >= 0) index fun compare ([],[]) = EQUAL | compare (_, []) = raise Index | compare ([],_) = raise Index | compare (a::ra, b::rb) = case Int.compare (a,b) of EQUAL => compare (ra,rb) | LESS => LESS | GREATER => GREATER fun eq (a, b) = compare(a,b) = EQUAL val sub = IntArray.sub fun findFromTo (i,v,s,e) = let fun loop (j) = if ((j >= s) andalso (j < e)) then (if (sub (v,j) = i) then SOME j else loop (j+1)) else NONE in loop s end fun inBounds shape index = ListPair.all (fn (x,y) => (x >= 0) andalso (x < y)) (index, shape) fun toInt shape {indptr, indices} index = let val nptr = IntArray.length indptr val nind = IntArray.length indices in case order of CSR => (case (index, shape) of ([i,j],[s,rs]) => let val s = sub (indptr, j) val e = if (j < (nptr-1)) then sub (indptr,j+1) else nind in findFromTo (i, indices, s, e) end | ([],[]) => SOME 0 | (_,_) => raise Index) | CSC => (case (index, shape) of ([i,j],[s,rs]) => if (i >= 0) andalso (i < s) then (let val s = sub (indptr,i) val e = if (i < (nptr-1)) then sub (indptr,i+1) else nind in findFromTo (j, indices, s, e) end) else raise Index | ([],[]) => SOME 0 | (_,_) => raise Index) end fun iteri shape {indptr, indices} f = (case order of CSC => (let val ni = IntArray.length indices val nj = IntArray.length indptr in Loop.app (0, nj, fn (j) => (let val jj = sub (indptr, j) val jj' = if (j < (nj-1)) then sub (indptr, j+1) else ni in List.app f (List.tabulate (jj'-jj, fn (jk) => let val n = jj+jk in ([sub(indices,n),j],n) end)) end)) end) | CSR => (let val nj = IntArray.length indices val ni = IntArray.length indptr in Loop.app (0, ni, fn (i) => (let val ii = sub (indptr, i) val ii' = if (i < (ni-1)) then sub (indptr, i+1) else nj in List.app f (List.tabulate (ii'-ii, fn (ik) => let val n = ii+ik in ([i,sub(indices,n)],n) end)) end)) end) ) fun app shape nz f = iteri shape nz (fn (index,i) => f index) end structure SparseMatrix : MONO_SPARSE_MATRIX = struct structure Tensor : MONO_TENSOR = RTensor structure TensorSlice : MONO_TENSOR_SLICE = RTensorSlice structure Number = RTensor.Number structure Index = SparseIndex type index = Index.t type nonzero = Index.nonzero type elem = Number.t val zero = Number.zero datatype block = SPARSE of {offset: index, shape: index, nz: nonzero, data: Tensor.Array.array} | DENSE of {offset: index, data: Tensor.tensor} type matrix = {shape: index, blocks: block list} datatype slice = SLSPARSE of {offset: index, indices: Index.array, data: Tensor.tensor} | SLDENSE of {offset: index, data: TensorSlice.slice} exception Data exception Shape exception Index exception Overlap (* --- LOCALS --- *) fun dimVals [m,n] = (m,n) | dimVals _ = raise Shape fun array_map f a = let fun apply index = f(Tensor.Array.sub(a,index)) in Tensor.Array.tabulate(Tensor.Array.length a, apply) end fun findBlock (i,j,blocks) = let val block = List.find (fn (SPARSE {offset=offset, shape=shape, nz, data}) => (let val (u,v) = dimVals offset val (t,s) = dimVals shape in ((j>=v) andalso (j-v=u) andalso (i-u (let val (u,v) = dimVals offset val (t,s) = dimVals (Tensor.shape data) in ((j>=v) andalso (j-v=u) andalso (i-u let val data: (((int * elem) DynArray.array) option) Array.array = Array.array(cols,NONE) val nzcount = ref 0 val _ = List.app (fn (icol,lst) => case lst of [(irow,v)] => if not (Number.== (v,zero)) then (Array.update (data, icol, SOME (DynArray.fromList [(irow,v)])); nzcount := (!nzcount) + 1) else () | (_ :: _) => (Array.update (data, icol, SOME (DynArray.fromList lst)); nzcount := (!nzcount) + (List.length lst)) | [] => ()) a val data' = Tensor.Array.array (!nzcount, zero) val indices = IntArray.array (!nzcount, 0) val indptr = IntArray.array (cols, 0) val update = IntArray.update val fi = Array.foldli (fn (n,SOME cols,i) => let val i' = DynArray.foldr (fn ((rowind,v),i) => (Tensor.Array.update (data',i,v); update (indices,i,rowind); i+1)) i cols in (update (indptr,n,i); i') end | (n,NONE,i) => (update (indptr,n,i); i)) 0 data in {shape=shape, blocks=[SPARSE {offset=case offset of NONE => [0, 0] | SOME i => i, shape=shape_a, nz={ indptr= indptr, indices=indices }, data=data'}]} end | Index.CSR => let val data: (((int * elem) DynArray.array) option) Array.array = Array.array(rows,NONE) val nzcount = ref 0 val _ = List.app (fn (irow,lst) => case lst of [(icol,v)] => if not (Number.== (v,zero)) then (Array.update (data, irow, SOME (DynArray.fromList [(icol,v)])); nzcount := (!nzcount) + 1) else () | (_ :: _) => (Array.update (data, irow, SOME (DynArray.fromList lst)); nzcount := (!nzcount) + (List.length lst)) | [] => ()) a val data' = Tensor.Array.array (!nzcount, zero) val indices = IntArray.array (!nzcount, 0) val indptr = IntArray.array (rows, 0) val update = IntArray.update val fi = Array.foldli (fn (n,SOME rows,i) => let val i' = DynArray.foldr (fn ((colind,v),i) => (Tensor.Array.update (data',i,v); update (indices,i,colind); i+1)) i rows in (update (indptr,n,i); i') end | (n,NONE,i) => (update (indptr,n,i); i)) 0 data in {shape=shape, blocks=[SPARSE {offset = case offset of NONE => [0,0] | SOME i => i, shape=shape_a, nz={ indptr= indptr, indices=indices }, data=data'}]} end end) fun fromTensor shape (a: Tensor.tensor, offset) = (let val shape_a = Tensor.shape a val (rows,cols) = dimVals shape_a in case Index.order of Index.CSC => let val data: (((int * elem) DynArray.array) option) Array.array = Array.array(cols,NONE) val nzcount = ref 0 val _ = Tensor.Index.app (List.rev shape_a) (fn (i) => let val v = Tensor.sub (a, i) in if not (Number.== (v, zero)) then let val (irow,icol) = dimVals i val colv = Array.sub (data, icol) (*val col' = (irow,v) :: col*) in (case colv of SOME col => (DynArray.update(col,DynArray.length col,(irow,v))) | NONE => Array.update (data, icol, SOME (DynArray.fromList [(irow,v)])); nzcount := (!nzcount) + 1) end else () end) val data' = Tensor.Array.array (!nzcount, zero) val indices = IntArray.array (!nzcount, 0) val indptr = IntArray.array (cols, 0) val update = IntArray.update val fi = Array.foldli (fn (n,SOME cols,i) => let val i' = DynArray.foldr (fn ((rowind,v),i) => (Tensor.Array.update (data',i,v); update (indices,i,rowind); i+1)) i cols in (update (indptr,n,i); i') end | (n,NONE,i) => (update (indptr,n,i); i)) 0 data in {shape=shape, blocks=[SPARSE {offset=case offset of NONE => [0, 0] | SOME i => i, shape=shape_a, nz={ indptr= indptr, indices=indices }, data=data'}]} end | Index.CSR => let val data: (((int * elem) DynArray.array) option) Array.array = Array.array(rows,NONE) val nzcount = ref 0 val _ = Tensor.Index.app shape_a (fn (i) => let val v = Tensor.sub (a, i) in if not (Number.== (v, zero)) then let val (irow,icol) = dimVals i val rowv = Array.sub (data, irow) (*val row' = (icol,v) :: row*) in (case rowv of (*Array.update(data,irow,row');*) SOME row => DynArray.update (row,DynArray.length row,(icol,v)) | NONE => Array.update (data, irow, SOME (DynArray.fromList [(icol,v)])); nzcount := (!nzcount) + 1) end else () end) val data' = Tensor.Array.array (!nzcount, zero) val indices = IntArray.array (!nzcount, 0) val indptr = IntArray.array (rows, 0) val update = IntArray.update val fi = Array.foldli (fn (n,SOME rows,i) => let val i' = DynArray.foldr (fn ((colind,v),i) => (Tensor.Array.update (data',i,v); update (indices,i,colind); i+1)) i rows in (update (indptr,n,i); i') end | (n,NONE,i) => (update (indptr,n,i); i)) 0 data in {shape=shape, blocks=[SPARSE {offset = case offset of NONE => [0,0] | SOME i => i, shape=shape_a, nz={ indptr= indptr, indices=indices }, data=data'}]} end end) fun fromTensor' shape (a: Tensor.tensor, offset) = let val shape_a = Tensor.shape a val (rows,cols) = dimVals shape_a in {shape=shape, blocks=[DENSE {offset=(case offset of NONE => [0, 0] | SOME i => i), data=a}]} end fun fromGenerator shape (f: index -> elem, fshape, offset) = (let val (rows,cols) = dimVals fshape in case Index.order of Index.CSC => let val data: (((int * elem) DynArray.array) option) Array.array = Array.array(cols,NONE) val nzcount = ref 0 val _ = Tensor.Index.app (List.rev fshape) (fn (i) => let val v = f (i) in if not (Number.== (v, zero)) then let val (irow,icol) = dimVals i val colv = Array.sub (data, icol) (*val col' = (irow,v) :: col*) in (case colv of SOME col => (DynArray.update(col,DynArray.length col,(irow,v))) | NONE => Array.update (data, icol, SOME (DynArray.fromList [(irow,v)])); nzcount := (!nzcount) + 1) end else () end) val data' = Tensor.Array.array (!nzcount, zero) val indices = IntArray.array (!nzcount, 0) val indptr = IntArray.array (cols, 0) val update = IntArray.update val fi = Array.foldli (fn (n,SOME cols,i) => let val i' = DynArray.foldr (fn ((rowind,v),i) => (Tensor.Array.update (data',i,v); update (indices,i,rowind); i+1)) i cols in (update (indptr,n,i); i') end | (n,NONE,i) => (update (indptr,n,i); i)) 0 data in {shape=shape, blocks=[SPARSE {offset=case offset of NONE => [0, 0] | SOME i => i, shape=fshape, nz={ indptr= indptr, indices=indices }, data=data'}]} end | Index.CSR => let val data: (((int * elem) DynArray.array) option) Array.array = Array.array(rows,NONE) val nzcount = ref 0 val _ = Tensor.Index.app fshape (fn (i) => let val v = f (i) in if not (Number.== (v, zero)) then let val (irow,icol) = dimVals i val rowv = Array.sub (data, irow) in (case rowv of SOME row => DynArray.update (row,DynArray.length row,(icol,v)) | NONE => Array.update (data, irow, SOME (DynArray.fromList [(icol,v)])); nzcount := (!nzcount) + 1) end else () end) val data' = Tensor.Array.array (!nzcount, zero) val indices = IntArray.array (!nzcount, 0) val indptr = IntArray.array (rows, 0) val update = IntArray.update val fi = Array.foldli (fn (n,SOME rows,i) => let val i' = DynArray.foldr (fn ((colind,v),i) => (Tensor.Array.update (data',i,v); update (indices,i,colind); i+1)) i rows in (update (indptr,n,i); i') end | (n,NONE,i) => (update (indptr,n,i); i)) 0 data in {shape=shape, blocks=[SPARSE {offset = case offset of NONE => [0,0] | SOME i => i, shape=fshape, nz={ indptr= indptr, indices=indices }, data=data'}]} end end) fun insertBlock ({shape, blocks},b',boffset) = let val (i,j) = dimVals boffset val (m,n) = dimVals (case b' of SPARSE {offset, shape, nz, data} => shape | DENSE {offset, data} => Tensor.shape data) val blocks' = let fun merge ([], []) = [b'] | merge (b::rst, ax) = let val (bm,bn) = dimVals (case b of SPARSE {offset,shape=shape,nz,data} => shape | DENSE {offset,data} => Tensor.shape data) val (bi,bj) = dimVals (case b of SPARSE {offset=offset,shape,nz,data} => offset | DENSE {offset=offset,data} => offset) in if (j < bj) then List.rev (rst@(b::b'::ax)) else (if (i >= bi) andalso (j >= bj) andalso (i+m <= bi+bm) andalso (j+n <= bj+bn) then raise Overlap else merge (rst, b::ax)) end | merge ([], ax) = List.rev (b'::ax) in merge (blocks, []) end in {shape=shape, blocks=blocks'} end fun insertTensor (S as {shape, blocks},t,offset) = let val (i,j) = dimVals offset val {shape=_, blocks=bs} = fromTensor shape (t,SOME [i,j]) val b': block = case bs of [b] => b | _ => raise Match in insertBlock (S,b',offset) end fun insertTensor' (S as {shape, blocks},t,offset) = let val (i,j) = dimVals offset val {shape=_, blocks=bs} = fromTensor' shape (t,SOME [i,j]) val b': block = case bs of [b] => b | _ => raise Match in insertBlock (S,b',offset) end (* Builds a sparse matrix from a list of the form: {tensor,offset=[xoffset,yoffset],sparse) ... where xoffset and yoffset are the positions where to insert the given tensor. The tensors to be inserted must be non-overlapping. sparse is a boolean flag that indicates whether the tensor should be converted to sparse form. *) fun fromTensorList shape (al: ({tensor: Tensor.tensor, offset: index, sparse: bool}) list) = (case al of {tensor,offset,sparse}::rst => (List.foldl (fn ({tensor,offset,sparse},ax) => if sparse then insertTensor (ax,tensor,offset) else insertTensor' (ax,tensor,offset)) (if sparse then fromTensor shape (tensor, SOME offset) else fromTensor' shape (tensor, SOME offset) ) rst) | _ => raise Match) fun fromGeneratorList shape (gg: ({f: index -> elem, fshape: index, offset: index}) list) = case gg of ({f,fshape,offset}::rst) => (List.foldl (fn ({f,fshape,offset},S) => let val {shape=_, blocks=bs} = fromGenerator shape (f,fshape,SOME offset) val b': block = case bs of [b] => b | _ => raise Match in insertBlock (S,b',offset) end) (fromGenerator shape (f,fshape,SOME offset)) rst) | _ => raise Match fun insert (x: matrix, y: matrix) = let val {shape=_, blocks=bs} = x in foldl (fn (b,S) => let val offset = (case b of SPARSE {offset, shape, nz, data} => offset | DENSE {offset, data} => offset) in insertBlock (S,b,offset) end) y bs end (* --- ACCESSORS --- *) fun shape {shape, blocks} = shape fun sub ({shape, blocks},index) = let val (i,j) = dimVals index val block = findBlock (i,j,blocks) in case block of SOME (b) => (case b of SPARSE {offset, shape, nz, data} => (let val (m,n) = dimVals offset val p = Index.toInt shape nz [i-m,j-n] in case p of SOME p' => Tensor.Array.sub (data, p') | NONE => zero end) | DENSE {offset, data} => (let val (m,n) = dimVals offset in Tensor.sub (data,[i+m,j+n]) end) ) | NONE => zero end fun update ({shape,blocks},index,new) = let val (i,j) = dimVals index val block = findBlock (i,j,blocks) in case block of SOME (b) => (case b of SPARSE {offset, shape, nz, data} => (let val (m,n) = dimVals shape val p = Index.toInt shape nz [i-m,j-n] in case p of SOME p' => Tensor.Array.update (data, p', new) | NONE => () end) | DENSE {offset, data} => (let val (m,n) = dimVals offset in Tensor.update (data,[i+m,j+n],new) end) ) | NONE => () end fun findBlocks (i,axis,blocks) = let val blocks' = List.mapPartial (fn (b ) => let val (u,v) = case b of SPARSE {offset=offset, shape=shape, nz, data} => dimVals offset | DENSE {offset, data} => dimVals offset val (t,s) = case b of SPARSE {offset=offset, shape=shape, nz, data} => dimVals shape | DENSE {offset, data} => dimVals (Tensor.shape data) in (case axis of 1 => if ((i>=v) andalso (i-v if ((i>=u) andalso (i-u raise Match) end) blocks in blocks' end fun slice ({shape,blocks},axis,i) = let val (m,n) = dimVals shape val _ = case axis of 0 => if (i > m) then raise Index else () | 1 => if (i > n) then raise Index else () | _ => raise Data in List.mapPartial (fn (SPARSE {offset=offset, shape=shape, nz={indptr, indices}, data}) => let val (u,v) = dimVals offset val (m,n) = dimVals shape val i' = case axis of 1 => i-v | 0 => i-u | _ => raise Match in (case (Index.order,axis) of (Index.CSC,1) => (let val s = IntArray.sub (indptr, i') val e = (if i' < (n-1) then IntArray.sub (indptr, i'+1) else Tensor.Array.length data) val len = e-s val res = Tensor.Array.array (len, zero) val rsi = IntArray.array (len, 0) fun loop (i,n) = if i < e then (Tensor.Array.update (res,n,Tensor.Array.sub (data,i)); IntArray.update (rsi,i-s,Index.sub (indices,i)); loop (i+1,n+1)) else () in loop (s,0); if len > 0 then SOME (SLSPARSE {data=Tensor.fromArray ([1,len],res), indices=rsi, offset=offset}) else NONE end) | (Index.CSR,0) => (let val s = IntArray.sub (indptr, i') val e = (if i' < (m-1) then IntArray.sub (indptr, i'+1) else Tensor.Array.length data) val len = e-s val res = Tensor.Array.array (len, zero) val rsi = IntArray.array (len, 0) fun loop (i,n) = if i < e then (Tensor.Array.update (res,n,Tensor.Array.sub (data,i)); IntArray.update (rsi,i-s,Index.sub (indices,i)); loop (i+1,n+1)) else () in loop (s,0); if len > 0 then SOME (SLSPARSE {data=Tensor.fromArray ([1,len],res), indices=rsi, offset=offset}) else NONE end) | (Index.CSC,0) => (let fun findcol (n) = case IntArray.findi (fn (_,x) => n < x) indptr of SOME (m,_) => (m-1) | NONE => m-1 val vs = IntArray.foldri (fn (n,ii,ax) => if i'=ii then (Tensor.Array.sub(data,n),findcol n)::ax else ax) [] indices val len = List.length vs in if len > 0 then SOME (SLSPARSE {data=Tensor.fromList ([1,len],map #1 vs), indices=IntArray.fromList (map #2 vs), offset=offset}) else NONE end) | (Index.CSR,1) => (let fun findrow (n) = case IntArray.findi (fn (_,x) => n < x) indptr of SOME (n,_) => (n-1) | NONE => n-1 val vs = IntArray.foldri (fn (n,ii,ax) => if i'=ii then (Tensor.Array.sub(data,n),findrow n)::ax else ax) [] indices val len = List.length vs in if len > 0 then SOME (SLSPARSE {data=Tensor.fromList ([1,len],map #1 vs), indices=IntArray.fromList (map #2 vs), offset=offset}) else NONE end) | (_,_) => raise Index) end | (DENSE {offset=offset, data}) => let val (u,v) = dimVals offset val (m,n) = dimVals (Tensor.shape data) val i' = case axis of 1 => i-v | 0 => i-u | _ => raise Match val sl = case axis of 1 => TensorSlice.fromto ([0,i'],[m-1,i'],data) | 0 => TensorSlice.fromto ([i',0],[i',n-1],data) | _ => raise Match in SOME (SLDENSE {data=sl, offset=offset}) end ) (findBlocks (i,axis,blocks) ) end (* --- MAPPING --- *) fun map f {shape, blocks} = {shape=shape, blocks=(List.map (fn (SPARSE {offset, shape, nz, data}) => (SPARSE {offset=offset, shape=shape, nz=nz, data=array_map f data}) | (DENSE {offset, data}) => (DENSE {data=(Tensor.map f data), offset=offset})) blocks)} fun app f {shape, blocks} = List.app (fn (SPARSE {offset, shape, nz, data}) => Tensor.Array.app f data | (DENSE {offset, data}) => Tensor.app f data) blocks fun appi f {shape, blocks} = List.app (fn (SPARSE {offset, shape, nz, data}) => Index.iteri shape nz (fn (idx,i) => f (ListPair.map (op +) (offset, idx), Tensor.Array.sub (data,i))) | (DENSE {offset, data}) => Tensor.appi (fn (i,v) => f (ListPair.map (op +) (offset, i),v)) data) blocks fun *> n a = map (fn x => Number.*(n,x)) a (* --- BINOPS --- *) fun map2 f ({shape', blocks'}) ({shape'', blocks''}) = if Index.eq(shape',shape') then {shape=shape', blocks=(ListPair.map (fn (SPARSE {offset=offset', shape=shape', nz=nz', data=data'}, SPARSE {offset=offset'', shape=shape'', nz=nz'', data=data''}) => (if Index.eq (offset',offset'') andalso Index.eq (shape',shape'') then (let val t = Tensor.new (shape', zero) val _ = Index.iteri shape' nz' (fn (idx,i) => Tensor.update (t,idx,Tensor.Array.sub (data',i))) val _ = Index.iteri shape' nz'' (fn (idx,i) => let val v' = Tensor.sub (t,idx) val v'' = f(v',Tensor.Array.sub(data'',i)) in Tensor.update (t,idx,v'') end) in hd (#blocks (fromTensor shape' (t, SOME offset'))) end) else raise Match) | (DENSE {offset=offset', data=data'}, DENSE {offset=offset'', data=data''}) => (if Index.eq (offset',offset'') then DENSE {offset=offset',data=Tensor.map2 f data' data''} else raise Match) | (_, _) => raise Match) (blocks',blocks''))} else raise Index (* --- SLICE OPERATIONS --- *) fun sliceAppi f sl = List.app (fn (SLSPARSE {data=sl,indices=si,offset}) => let val (m,n) = dimVals offset in (RTensor.foldl (fn (x,i) => let val i' = Index.sub (si,i)+m in (f (i',x); i+1) end) 0 sl; ()) end | (SLDENSE {data=sl,offset}) => let val (m,n) = dimVals offset in (RTensorSlice.foldl (fn (x,i) => let val i' = i+m in (f (i',x); i+1) end) 0 sl; ()) end) sl fun sliceFoldi f init sl = List.foldl (fn (SLSPARSE {data=sl,indices=si,offset},ax) => let val (m,n) = dimVals offset in #2 (RTensor.foldl (fn (x,(i,ax)) => let val i' = Index.sub (si,i)+m in (i+1, f (i',x,ax)) end) (0,ax) sl) end | (SLDENSE {data=sl,offset},ax) => let val (m,n) = dimVals offset in #2 (RTensorSlice.foldl (fn (x,(i,ax)) => let val i' = i+m in (i+1, f (i',x,ax)) end) (0,ax) sl) end) init sl fun a + b = map2 Number.+ a b fun a * b = map2 Number.* a b fun a - b = map2 Number.- a b fun a / b = map2 Number./ a b end