| ------------------------------------------------------------------------------ |
| -- -- |
| -- GNAT RUN-TIME COMPONENTS -- |
| -- -- |
| -- S Y S T E M . G E N E R I C _ A R R A Y _ O P E R A T I O N S -- |
| -- -- |
| -- B o d y -- |
| -- -- |
| -- Copyright (C) 2006-2021, Free Software Foundation, Inc. -- |
| -- -- |
| -- GNAT is free software; you can redistribute it and/or modify it under -- |
| -- terms of the GNU General Public License as published by the Free Soft- -- |
| -- ware Foundation; either version 3, or (at your option) any later ver- -- |
| -- sion. GNAT is distributed in the hope that it will be useful, but WITH- -- |
| -- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -- |
| -- or FITNESS FOR A PARTICULAR PURPOSE. -- |
| -- -- |
| -- As a special exception under Section 7 of GPL version 3, you are granted -- |
| -- additional permissions described in the GCC Runtime Library Exception, -- |
| -- version 3.1, as published by the Free Software Foundation. -- |
| -- -- |
| -- You should have received a copy of the GNU General Public License and -- |
| -- a copy of the GCC Runtime Library Exception along with this program; -- |
| -- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see -- |
| -- <http://www.gnu.org/licenses/>. -- |
| -- -- |
| -- GNAT was originally developed by the GNAT team at New York University. -- |
| -- Extensive contributions were provided by Ada Core Technologies Inc. -- |
| -- -- |
| ------------------------------------------------------------------------------ |
| |
| with Ada.Numerics; use Ada.Numerics; |
| package body System.Generic_Array_Operations is |
| function Check_Unit_Last |
| (Index : Integer; |
| Order : Positive; |
| First : Integer) return Integer; |
| pragma Inline_Always (Check_Unit_Last); |
| -- Compute index of last element returned by Unit_Vector or Unit_Matrix. |
| -- A separate function is needed to allow raising Constraint_Error before |
| -- declaring the function result variable. The result variable needs to be |
| -- declared first, to allow front-end inlining. |
| |
| -------------- |
| -- Diagonal -- |
| -------------- |
| |
| function Diagonal (A : Matrix) return Vector is |
| N : constant Natural := Natural'Min (A'Length (1), A'Length (2)); |
| begin |
| return R : Vector (A'First (1) .. A'First (1) + N - 1) do |
| for J in 0 .. N - 1 loop |
| R (R'First + J) := A (A'First (1) + J, A'First (2) + J); |
| end loop; |
| end return; |
| end Diagonal; |
| |
| -------------------------- |
| -- Square_Matrix_Length -- |
| -------------------------- |
| |
| function Square_Matrix_Length (A : Matrix) return Natural is |
| begin |
| if A'Length (1) /= A'Length (2) then |
| raise Constraint_Error with "matrix is not square"; |
| else |
| return A'Length (1); |
| end if; |
| end Square_Matrix_Length; |
| |
| --------------------- |
| -- Check_Unit_Last -- |
| --------------------- |
| |
| function Check_Unit_Last |
| (Index : Integer; |
| Order : Positive; |
| First : Integer) return Integer |
| is |
| begin |
| -- Order the tests carefully to avoid overflow |
| |
| if Index < First |
| or else First > Integer'Last - Order + 1 |
| or else Index > First + (Order - 1) |
| then |
| raise Constraint_Error; |
| end if; |
| |
| return First + (Order - 1); |
| end Check_Unit_Last; |
| |
| --------------------- |
| -- Back_Substitute -- |
| --------------------- |
| |
| procedure Back_Substitute (M, N : in out Matrix) is |
| pragma Assert (M'First (1) = N'First (1) |
| and then |
| M'Last (1) = N'Last (1)); |
| |
| procedure Sub_Row |
| (M : in out Matrix; |
| Target : Integer; |
| Source : Integer; |
| Factor : Scalar); |
| -- Elementary row operation that subtracts Factor * M (Source, <>) from |
| -- M (Target, <>) |
| |
| ------------- |
| -- Sub_Row -- |
| ------------- |
| |
| procedure Sub_Row |
| (M : in out Matrix; |
| Target : Integer; |
| Source : Integer; |
| Factor : Scalar) |
| is |
| begin |
| for J in M'Range (2) loop |
| M (Target, J) := M (Target, J) - Factor * M (Source, J); |
| end loop; |
| end Sub_Row; |
| |
| -- Local declarations |
| |
| Max_Col : Integer := M'Last (2); |
| |
| -- Start of processing for Back_Substitute |
| |
| begin |
| Do_Rows : for Row in reverse M'Range (1) loop |
| Find_Non_Zero : for Col in reverse M'First (2) .. Max_Col loop |
| if Is_Non_Zero (M (Row, Col)) then |
| |
| -- Found first non-zero element, so subtract a multiple of this |
| -- element from all higher rows, to reduce all other elements |
| -- in this column to zero. |
| |
| declare |
| -- We can't use a for loop, as we'd need to iterate to |
| -- Row - 1, but that expression will overflow if M'First |
| -- equals Integer'First, which is true for aggregates |
| -- without explicit bounds.. |
| |
| J : Integer := M'First (1); |
| |
| begin |
| while J < Row loop |
| Sub_Row (N, J, Row, (M (J, Col) / M (Row, Col))); |
| Sub_Row (M, J, Row, (M (J, Col) / M (Row, Col))); |
| J := J + 1; |
| end loop; |
| end; |
| |
| -- Avoid potential overflow in the subtraction below |
| |
| exit Do_Rows when Col = M'First (2); |
| |
| Max_Col := Col - 1; |
| |
| exit Find_Non_Zero; |
| end if; |
| end loop Find_Non_Zero; |
| end loop Do_Rows; |
| end Back_Substitute; |
| |
| ----------------------- |
| -- Forward_Eliminate -- |
| ----------------------- |
| |
| procedure Forward_Eliminate |
| (M : in out Matrix; |
| N : in out Matrix; |
| Det : out Scalar) |
| is |
| pragma Assert (M'First (1) = N'First (1) |
| and then |
| M'Last (1) = N'Last (1)); |
| |
| -- The following are variations of the elementary matrix row operations: |
| -- row switching, row multiplication and row addition. Because in this |
| -- algorithm the addition factor is always a negated value, we chose to |
| -- use row subtraction instead. Similarly, instead of multiplying by |
| -- a reciprocal, we divide. |
| |
| procedure Sub_Row |
| (M : in out Matrix; |
| Target : Integer; |
| Source : Integer; |
| Factor : Scalar); |
| -- Subtrace Factor * M (Source, <>) from M (Target, <>) |
| |
| procedure Divide_Row |
| (M, N : in out Matrix; |
| Row : Integer; |
| Scale : Scalar); |
| -- Divide M (Row) and N (Row) by Scale, and update Det |
| |
| procedure Switch_Row |
| (M, N : in out Matrix; |
| Row_1 : Integer; |
| Row_2 : Integer); |
| -- Exchange M (Row_1) and N (Row_1) with M (Row_2) and N (Row_2), |
| -- negating Det in the process. |
| |
| ------------- |
| -- Sub_Row -- |
| ------------- |
| |
| procedure Sub_Row |
| (M : in out Matrix; |
| Target : Integer; |
| Source : Integer; |
| Factor : Scalar) |
| is |
| begin |
| for J in M'Range (2) loop |
| M (Target, J) := M (Target, J) - Factor * M (Source, J); |
| end loop; |
| end Sub_Row; |
| |
| ---------------- |
| -- Divide_Row -- |
| ---------------- |
| |
| procedure Divide_Row |
| (M, N : in out Matrix; |
| Row : Integer; |
| Scale : Scalar) |
| is |
| begin |
| Det := Det * Scale; |
| |
| for J in M'Range (2) loop |
| M (Row, J) := M (Row, J) / Scale; |
| end loop; |
| |
| for J in N'Range (2) loop |
| N (Row - M'First (1) + N'First (1), J) := |
| N (Row - M'First (1) + N'First (1), J) / Scale; |
| pragma Annotate |
| (CodePeer, False_Positive, "divide by zero", "Scale /= 0"); |
| end loop; |
| end Divide_Row; |
| |
| ---------------- |
| -- Switch_Row -- |
| ---------------- |
| |
| procedure Switch_Row |
| (M, N : in out Matrix; |
| Row_1 : Integer; |
| Row_2 : Integer) |
| is |
| procedure Swap (X, Y : in out Scalar); |
| -- Exchange the values of X and Y |
| |
| ---------- |
| -- Swap -- |
| ---------- |
| |
| procedure Swap (X, Y : in out Scalar) is |
| T : constant Scalar := X; |
| begin |
| X := Y; |
| Y := T; |
| end Swap; |
| |
| -- Start of processing for Switch_Row |
| |
| begin |
| if Row_1 /= Row_2 then |
| Det := Zero - Det; |
| |
| for J in M'Range (2) loop |
| Swap (M (Row_1, J), M (Row_2, J)); |
| end loop; |
| |
| for J in N'Range (2) loop |
| Swap (N (Row_1 - M'First (1) + N'First (1), J), |
| N (Row_2 - M'First (1) + N'First (1), J)); |
| end loop; |
| end if; |
| end Switch_Row; |
| |
| -- Local declarations |
| |
| Row : Integer := M'First (1); |
| |
| -- Start of processing for Forward_Eliminate |
| |
| begin |
| Det := One; |
| |
| for J in M'Range (2) loop |
| declare |
| Max_Row : Integer := Row; |
| Max_Abs : Real'Base := 0.0; |
| |
| begin |
| -- Find best pivot in column J, starting in row Row |
| |
| for K in Row .. M'Last (1) loop |
| declare |
| New_Abs : constant Real'Base := abs M (K, J); |
| begin |
| if Max_Abs < New_Abs then |
| Max_Abs := New_Abs; |
| Max_Row := K; |
| end if; |
| end; |
| end loop; |
| |
| if Max_Abs > 0.0 then |
| Switch_Row (M, N, Row, Max_Row); |
| |
| -- The temporaries below are necessary to force a copy of the |
| -- value and avoid improper aliasing. |
| |
| declare |
| Scale : constant Scalar := M (Row, J); |
| begin |
| Divide_Row (M, N, Row, Scale); |
| end; |
| |
| for U in Row + 1 .. M'Last (1) loop |
| declare |
| Factor : constant Scalar := M (U, J); |
| begin |
| Sub_Row (N, U, Row, Factor); |
| Sub_Row (M, U, Row, Factor); |
| end; |
| end loop; |
| |
| exit when Row >= M'Last (1); |
| |
| Row := Row + 1; |
| |
| else |
| -- Set zero (note that we do not have literals) |
| |
| Det := Zero; |
| end if; |
| end; |
| end loop; |
| end Forward_Eliminate; |
| |
| ------------------- |
| -- Inner_Product -- |
| ------------------- |
| |
| function Inner_Product |
| (Left : Left_Vector; |
| Right : Right_Vector) return Result_Scalar |
| is |
| R : Result_Scalar := Zero; |
| |
| begin |
| if Left'Length /= Right'Length then |
| raise Constraint_Error with |
| "vectors are of different length in inner product"; |
| end if; |
| |
| for J in Left'Range loop |
| R := R + Left (J) * Right (J - Left'First + Right'First); |
| end loop; |
| |
| return R; |
| end Inner_Product; |
| |
| ------------- |
| -- L2_Norm -- |
| ------------- |
| |
| function L2_Norm (X : X_Vector) return Result_Real'Base is |
| Sum : Result_Real'Base := 0.0; |
| |
| begin |
| for J in X'Range loop |
| Sum := Sum + Result_Real'Base (abs X (J))**2; |
| end loop; |
| |
| return Sqrt (Sum); |
| end L2_Norm; |
| |
| ---------------------------------- |
| -- Matrix_Elementwise_Operation -- |
| ---------------------------------- |
| |
| function Matrix_Elementwise_Operation (X : X_Matrix) return Result_Matrix is |
| begin |
| return R : Result_Matrix (X'Range (1), X'Range (2)) do |
| for J in R'Range (1) loop |
| for K in R'Range (2) loop |
| R (J, K) := Operation (X (J, K)); |
| end loop; |
| end loop; |
| end return; |
| end Matrix_Elementwise_Operation; |
| |
| ---------------------------------- |
| -- Vector_Elementwise_Operation -- |
| ---------------------------------- |
| |
| function Vector_Elementwise_Operation (X : X_Vector) return Result_Vector is |
| begin |
| return R : Result_Vector (X'Range) do |
| for J in R'Range loop |
| R (J) := Operation (X (J)); |
| end loop; |
| end return; |
| end Vector_Elementwise_Operation; |
| |
| ----------------------------------------- |
| -- Matrix_Matrix_Elementwise_Operation -- |
| ----------------------------------------- |
| |
| function Matrix_Matrix_Elementwise_Operation |
| (Left : Left_Matrix; |
| Right : Right_Matrix) return Result_Matrix |
| is |
| begin |
| return R : Result_Matrix (Left'Range (1), Left'Range (2)) do |
| if Left'Length (1) /= Right'Length (1) |
| or else |
| Left'Length (2) /= Right'Length (2) |
| then |
| raise Constraint_Error with |
| "matrices are of different dimension in elementwise operation"; |
| end if; |
| |
| for J in R'Range (1) loop |
| for K in R'Range (2) loop |
| R (J, K) := |
| Operation |
| (Left (J, K), |
| Right |
| (J - R'First (1) + Right'First (1), |
| K - R'First (2) + Right'First (2))); |
| end loop; |
| end loop; |
| end return; |
| end Matrix_Matrix_Elementwise_Operation; |
| |
| ------------------------------------------------ |
| -- Matrix_Matrix_Scalar_Elementwise_Operation -- |
| ------------------------------------------------ |
| |
| function Matrix_Matrix_Scalar_Elementwise_Operation |
| (X : X_Matrix; |
| Y : Y_Matrix; |
| Z : Z_Scalar) return Result_Matrix |
| is |
| begin |
| return R : Result_Matrix (X'Range (1), X'Range (2)) do |
| if X'Length (1) /= Y'Length (1) |
| or else |
| X'Length (2) /= Y'Length (2) |
| then |
| raise Constraint_Error with |
| "matrices are of different dimension in elementwise operation"; |
| end if; |
| |
| for J in R'Range (1) loop |
| for K in R'Range (2) loop |
| R (J, K) := |
| Operation |
| (X (J, K), |
| Y (J - R'First (1) + Y'First (1), |
| K - R'First (2) + Y'First (2)), |
| Z); |
| end loop; |
| end loop; |
| end return; |
| end Matrix_Matrix_Scalar_Elementwise_Operation; |
| |
| ----------------------------------------- |
| -- Vector_Vector_Elementwise_Operation -- |
| ----------------------------------------- |
| |
| function Vector_Vector_Elementwise_Operation |
| (Left : Left_Vector; |
| Right : Right_Vector) return Result_Vector |
| is |
| begin |
| return R : Result_Vector (Left'Range) do |
| if Left'Length /= Right'Length then |
| raise Constraint_Error with |
| "vectors are of different length in elementwise operation"; |
| end if; |
| |
| for J in R'Range loop |
| R (J) := Operation (Left (J), Right (J - R'First + Right'First)); |
| end loop; |
| end return; |
| end Vector_Vector_Elementwise_Operation; |
| |
| ------------------------------------------------ |
| -- Vector_Vector_Scalar_Elementwise_Operation -- |
| ------------------------------------------------ |
| |
| function Vector_Vector_Scalar_Elementwise_Operation |
| (X : X_Vector; |
| Y : Y_Vector; |
| Z : Z_Scalar) return Result_Vector is |
| begin |
| return R : Result_Vector (X'Range) do |
| if X'Length /= Y'Length then |
| raise Constraint_Error with |
| "vectors are of different length in elementwise operation"; |
| end if; |
| |
| for J in R'Range loop |
| R (J) := Operation (X (J), Y (J - X'First + Y'First), Z); |
| end loop; |
| end return; |
| end Vector_Vector_Scalar_Elementwise_Operation; |
| |
| ----------------------------------------- |
| -- Matrix_Scalar_Elementwise_Operation -- |
| ----------------------------------------- |
| |
| function Matrix_Scalar_Elementwise_Operation |
| (Left : Left_Matrix; |
| Right : Right_Scalar) return Result_Matrix |
| is |
| begin |
| return R : Result_Matrix (Left'Range (1), Left'Range (2)) do |
| for J in R'Range (1) loop |
| for K in R'Range (2) loop |
| R (J, K) := Operation (Left (J, K), Right); |
| end loop; |
| end loop; |
| end return; |
| end Matrix_Scalar_Elementwise_Operation; |
| |
| ----------------------------------------- |
| -- Vector_Scalar_Elementwise_Operation -- |
| ----------------------------------------- |
| |
| function Vector_Scalar_Elementwise_Operation |
| (Left : Left_Vector; |
| Right : Right_Scalar) return Result_Vector |
| is |
| begin |
| return R : Result_Vector (Left'Range) do |
| for J in R'Range loop |
| R (J) := Operation (Left (J), Right); |
| end loop; |
| end return; |
| end Vector_Scalar_Elementwise_Operation; |
| |
| ----------------------------------------- |
| -- Scalar_Matrix_Elementwise_Operation -- |
| ----------------------------------------- |
| |
| function Scalar_Matrix_Elementwise_Operation |
| (Left : Left_Scalar; |
| Right : Right_Matrix) return Result_Matrix |
| is |
| begin |
| return R : Result_Matrix (Right'Range (1), Right'Range (2)) do |
| for J in R'Range (1) loop |
| for K in R'Range (2) loop |
| R (J, K) := Operation (Left, Right (J, K)); |
| end loop; |
| end loop; |
| end return; |
| end Scalar_Matrix_Elementwise_Operation; |
| |
| ----------------------------------------- |
| -- Scalar_Vector_Elementwise_Operation -- |
| ----------------------------------------- |
| |
| function Scalar_Vector_Elementwise_Operation |
| (Left : Left_Scalar; |
| Right : Right_Vector) return Result_Vector |
| is |
| begin |
| return R : Result_Vector (Right'Range) do |
| for J in R'Range loop |
| R (J) := Operation (Left, Right (J)); |
| end loop; |
| end return; |
| end Scalar_Vector_Elementwise_Operation; |
| |
| ---------- |
| -- Sqrt -- |
| ---------- |
| |
| function Sqrt (X : Real'Base) return Real'Base is |
| Root, Next : Real'Base; |
| |
| begin |
| -- Be defensive: any comparisons with NaN values will yield False. |
| |
| if not (X > 0.0) then |
| if X = 0.0 then |
| return X; |
| else |
| raise Argument_Error; |
| end if; |
| |
| elsif X > Real'Base'Last then |
| pragma Annotate |
| (CodePeer, Intentional, |
| "test always false", "test for infinity"); |
| |
| -- X is infinity, which is its own square root |
| |
| return X; |
| end if; |
| |
| -- Compute an initial estimate based on: |
| |
| -- X = M * R**E and Sqrt (X) = Sqrt (M) * R**(E / 2.0), |
| |
| -- where M is the mantissa, R is the radix and E the exponent. |
| |
| -- By ignoring the mantissa and ignoring the case of an odd |
| -- exponent, we get a final error that is at most R. In other words, |
| -- the result has about a single bit precision. |
| |
| Root := Real'Base (Real'Machine_Radix) ** (Real'Exponent (X) / 2); |
| |
| -- Because of the poor initial estimate, use the Babylonian method of |
| -- computing the square root, as it is stable for all inputs. Every step |
| -- will roughly double the precision of the result. Just a few steps |
| -- suffice in most cases. Eight iterations should give about 2**8 bits |
| -- of precision. |
| |
| for J in 1 .. 8 loop |
| pragma Assert (Root /= 0.0); |
| |
| Next := (Root + X / Root) / 2.0; |
| exit when Root = Next; |
| Root := Next; |
| end loop; |
| |
| return Root; |
| end Sqrt; |
| |
| --------------------------- |
| -- Matrix_Matrix_Product -- |
| --------------------------- |
| |
| function Matrix_Matrix_Product |
| (Left : Left_Matrix; |
| Right : Right_Matrix) return Result_Matrix |
| is |
| begin |
| return R : Result_Matrix (Left'Range (1), Right'Range (2)) do |
| if Left'Length (2) /= Right'Length (1) then |
| raise Constraint_Error with |
| "incompatible dimensions in matrix multiplication"; |
| end if; |
| |
| for J in R'Range (1) loop |
| for K in R'Range (2) loop |
| declare |
| S : Result_Scalar := Zero; |
| |
| begin |
| for M in Left'Range (2) loop |
| S := S + Left (J, M) * |
| Right |
| (M - Left'First (2) + Right'First (1), K); |
| end loop; |
| |
| R (J, K) := S; |
| end; |
| end loop; |
| end loop; |
| end return; |
| end Matrix_Matrix_Product; |
| |
| ---------------------------- |
| -- Matrix_Vector_Solution -- |
| ---------------------------- |
| |
| function Matrix_Vector_Solution (A : Matrix; X : Vector) return Vector is |
| N : constant Natural := A'Length (1); |
| MA : Matrix := A; |
| MX : Matrix (A'Range (1), 1 .. 1); |
| R : Vector (A'Range (2)); |
| Det : Scalar; |
| |
| begin |
| if A'Length (2) /= N then |
| raise Constraint_Error with "matrix is not square"; |
| end if; |
| |
| if X'Length /= N then |
| raise Constraint_Error with "incompatible vector length"; |
| end if; |
| |
| for J in 0 .. MX'Length (1) - 1 loop |
| MX (MX'First (1) + J, 1) := X (X'First + J); |
| end loop; |
| |
| Forward_Eliminate (MA, MX, Det); |
| |
| if Det = Zero then |
| raise Constraint_Error with "matrix is singular"; |
| end if; |
| |
| Back_Substitute (MA, MX); |
| |
| for J in 0 .. R'Length - 1 loop |
| R (R'First + J) := MX (MX'First (1) + J, 1); |
| end loop; |
| |
| return R; |
| end Matrix_Vector_Solution; |
| |
| ---------------------------- |
| -- Matrix_Matrix_Solution -- |
| ---------------------------- |
| |
| function Matrix_Matrix_Solution (A, X : Matrix) return Matrix is |
| N : constant Natural := A'Length (1); |
| MA : Matrix (A'Range (2), A'Range (2)); |
| MB : Matrix (A'Range (2), X'Range (2)); |
| Det : Scalar; |
| |
| begin |
| if A'Length (2) /= N then |
| raise Constraint_Error with "matrix is not square"; |
| end if; |
| |
| if X'Length (1) /= N then |
| raise Constraint_Error with "matrices have unequal number of rows"; |
| end if; |
| |
| for J in 0 .. A'Length (1) - 1 loop |
| for K in MA'Range (2) loop |
| MA (MA'First (1) + J, K) := A (A'First (1) + J, K); |
| end loop; |
| |
| for K in MB'Range (2) loop |
| MB (MB'First (1) + J, K) := X (X'First (1) + J, K); |
| end loop; |
| end loop; |
| |
| Forward_Eliminate (MA, MB, Det); |
| |
| if Det = Zero then |
| raise Constraint_Error with "matrix is singular"; |
| end if; |
| |
| Back_Substitute (MA, MB); |
| |
| return MB; |
| end Matrix_Matrix_Solution; |
| |
| --------------------------- |
| -- Matrix_Vector_Product -- |
| --------------------------- |
| |
| function Matrix_Vector_Product |
| (Left : Matrix; |
| Right : Right_Vector) return Result_Vector |
| is |
| begin |
| return R : Result_Vector (Left'Range (1)) do |
| if Left'Length (2) /= Right'Length then |
| raise Constraint_Error with |
| "incompatible dimensions in matrix-vector multiplication"; |
| end if; |
| |
| for J in Left'Range (1) loop |
| declare |
| S : Result_Scalar := Zero; |
| |
| begin |
| for K in Left'Range (2) loop |
| S := S + Left (J, K) |
| * Right (K - Left'First (2) + Right'First); |
| end loop; |
| |
| R (J) := S; |
| end; |
| end loop; |
| end return; |
| end Matrix_Vector_Product; |
| |
| ------------------- |
| -- Outer_Product -- |
| ------------------- |
| |
| function Outer_Product |
| (Left : Left_Vector; |
| Right : Right_Vector) return Matrix |
| is |
| begin |
| return R : Matrix (Left'Range, Right'Range) do |
| for J in R'Range (1) loop |
| for K in R'Range (2) loop |
| R (J, K) := Left (J) * Right (K); |
| end loop; |
| end loop; |
| end return; |
| end Outer_Product; |
| |
| ----------------- |
| -- Swap_Column -- |
| ----------------- |
| |
| procedure Swap_Column (A : in out Matrix; Left, Right : Integer) is |
| Temp : Scalar; |
| begin |
| for J in A'Range (1) loop |
| Temp := A (J, Left); |
| A (J, Left) := A (J, Right); |
| A (J, Right) := Temp; |
| end loop; |
| end Swap_Column; |
| |
| --------------- |
| -- Transpose -- |
| --------------- |
| |
| procedure Transpose (A : Matrix; R : out Matrix) is |
| begin |
| for J in R'Range (1) loop |
| for K in R'Range (2) loop |
| R (J, K) := A (K - R'First (2) + A'First (1), |
| J - R'First (1) + A'First (2)); |
| end loop; |
| end loop; |
| end Transpose; |
| |
| ------------------------------- |
| -- Update_Matrix_With_Matrix -- |
| ------------------------------- |
| |
| procedure Update_Matrix_With_Matrix (X : in out X_Matrix; Y : Y_Matrix) is |
| begin |
| if X'Length (1) /= Y'Length (1) |
| or else |
| X'Length (2) /= Y'Length (2) |
| then |
| raise Constraint_Error with |
| "matrices are of different dimension in update operation"; |
| end if; |
| |
| for J in X'Range (1) loop |
| for K in X'Range (2) loop |
| Update (X (J, K), Y (J - X'First (1) + Y'First (1), |
| K - X'First (2) + Y'First (2))); |
| end loop; |
| end loop; |
| end Update_Matrix_With_Matrix; |
| |
| ------------------------------- |
| -- Update_Vector_With_Vector -- |
| ------------------------------- |
| |
| procedure Update_Vector_With_Vector (X : in out X_Vector; Y : Y_Vector) is |
| begin |
| if X'Length /= Y'Length then |
| raise Constraint_Error with |
| "vectors are of different length in update operation"; |
| end if; |
| |
| for J in X'Range loop |
| Update (X (J), Y (J - X'First + Y'First)); |
| end loop; |
| end Update_Vector_With_Vector; |
| |
| ----------------- |
| -- Unit_Matrix -- |
| ----------------- |
| |
| function Unit_Matrix |
| (Order : Positive; |
| First_1 : Integer := 1; |
| First_2 : Integer := 1) return Matrix |
| is |
| begin |
| return R : Matrix (First_1 .. Check_Unit_Last (First_1, Order, First_1), |
| First_2 .. Check_Unit_Last (First_2, Order, First_2)) |
| do |
| R := (others => (others => Zero)); |
| |
| for J in 0 .. Order - 1 loop |
| R (First_1 + J, First_2 + J) := One; |
| end loop; |
| end return; |
| end Unit_Matrix; |
| |
| ----------------- |
| -- Unit_Vector -- |
| ----------------- |
| |
| function Unit_Vector |
| (Index : Integer; |
| Order : Positive; |
| First : Integer := 1) return Vector |
| is |
| begin |
| return R : Vector (First .. Check_Unit_Last (Index, Order, First)) do |
| R := (others => Zero); |
| R (Index) := One; |
| end return; |
| end Unit_Vector; |
| |
| --------------------------- |
| -- Vector_Matrix_Product -- |
| --------------------------- |
| |
| function Vector_Matrix_Product |
| (Left : Left_Vector; |
| Right : Matrix) return Result_Vector |
| is |
| begin |
| return R : Result_Vector (Right'Range (2)) do |
| if Left'Length /= Right'Length (1) then |
| raise Constraint_Error with |
| "incompatible dimensions in vector-matrix multiplication"; |
| end if; |
| |
| for J in Right'Range (2) loop |
| declare |
| S : Result_Scalar := Zero; |
| |
| begin |
| for K in Right'Range (1) loop |
| S := S + Left (K - Right'First (1) |
| + Left'First) * Right (K, J); |
| end loop; |
| |
| R (J) := S; |
| end; |
| end loop; |
| end return; |
| end Vector_Matrix_Product; |
| |
| end System.Generic_Array_Operations; |
