494 lines
18 KiB
Ada
494 lines
18 KiB
Ada
------------------------------------------------------------------------------
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-- --
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-- GNAT RUN-TIME COMPONENTS --
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-- --
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-- S Y S T E M . G E N E R I C _ C O M P L E X _ L A P A C K --
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-- --
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-- B o d y --
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-- --
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-- Copyright (C) 2006-2009, Free Software Foundation, Inc. --
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-- --
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-- GNAT is free software; you can redistribute it and/or modify it under --
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-- terms of the GNU General Public License as published by the Free Soft- --
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-- ware Foundation; either version 3, or (at your option) any later ver- --
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-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
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-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
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-- or FITNESS FOR A PARTICULAR PURPOSE. --
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-- --
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-- As a special exception under Section 7 of GPL version 3, you are granted --
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-- additional permissions described in the GCC Runtime Library Exception, --
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-- version 3.1, as published by the Free Software Foundation. --
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-- --
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-- You should have received a copy of the GNU General Public License and --
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-- a copy of the GCC Runtime Library Exception along with this program; --
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-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
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-- <http://www.gnu.org/licenses/>. --
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-- --
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-- GNAT was originally developed by the GNAT team at New York University. --
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-- Extensive contributions were provided by Ada Core Technologies Inc. --
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-- --
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------------------------------------------------------------------------------
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with Ada.Unchecked_Conversion; use Ada;
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with Interfaces; use Interfaces;
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with Interfaces.Fortran; use Interfaces.Fortran;
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with Interfaces.Fortran.BLAS; use Interfaces.Fortran.BLAS;
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with Interfaces.Fortran.LAPACK; use Interfaces.Fortran.LAPACK;
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with System.Generic_Array_Operations; use System.Generic_Array_Operations;
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package body System.Generic_Complex_LAPACK is
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Is_Single : constant Boolean :=
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Real'Machine_Mantissa = Fortran.Real'Machine_Mantissa
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and then Fortran.Real (Real'First) = Fortran.Real'First
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and then Fortran.Real (Real'Last) = Fortran.Real'Last;
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Is_Double : constant Boolean :=
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Real'Machine_Mantissa = Double_Precision'Machine_Mantissa
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and then
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Double_Precision (Real'First) = Double_Precision'First
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and then
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Double_Precision (Real'Last) = Double_Precision'Last;
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subtype Complex is Complex_Types.Complex;
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-- Local subprograms
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function To_Double_Precision (X : Real) return Double_Precision;
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pragma Inline (To_Double_Precision);
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function To_Real (X : Double_Precision) return Real;
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pragma Inline (To_Real);
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function To_Double_Complex (X : Complex) return Double_Complex;
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pragma Inline (To_Double_Complex);
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function To_Complex (X : Double_Complex) return Complex;
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pragma Inline (To_Complex);
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-- Instantiations
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function To_Double_Precision is new
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Vector_Elementwise_Operation
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(X_Scalar => Real,
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Result_Scalar => Double_Precision,
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X_Vector => Real_Vector,
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Result_Vector => Double_Precision_Vector,
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Operation => To_Double_Precision);
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function To_Real is new
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Vector_Elementwise_Operation
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(X_Scalar => Double_Precision,
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Result_Scalar => Real,
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X_Vector => Double_Precision_Vector,
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Result_Vector => Real_Vector,
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Operation => To_Real);
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function To_Double_Complex is new
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Matrix_Elementwise_Operation
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(X_Scalar => Complex,
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Result_Scalar => Double_Complex,
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X_Matrix => Complex_Matrix,
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Result_Matrix => Double_Complex_Matrix,
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Operation => To_Double_Complex);
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function To_Complex is new
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Matrix_Elementwise_Operation
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(X_Scalar => Double_Complex,
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Result_Scalar => Complex,
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X_Matrix => Double_Complex_Matrix,
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Result_Matrix => Complex_Matrix,
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Operation => To_Complex);
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function To_Double_Precision (X : Real) return Double_Precision is
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begin
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return Double_Precision (X);
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end To_Double_Precision;
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function To_Real (X : Double_Precision) return Real is
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begin
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return Real (X);
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end To_Real;
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function To_Double_Complex (X : Complex) return Double_Complex is
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begin
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return (To_Double_Precision (X.Re), To_Double_Precision (X.Im));
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end To_Double_Complex;
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function To_Complex (X : Double_Complex) return Complex is
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begin
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return (Real (X.Re), Real (X.Im));
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end To_Complex;
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-----------
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-- getrf --
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-----------
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procedure getrf
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(M : Natural;
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N : Natural;
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A : in out Complex_Matrix;
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Ld_A : Positive;
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I_Piv : out Integer_Vector;
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Info : access Integer)
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is
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begin
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if Is_Single then
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declare
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type A_Ptr is
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access all BLAS.Complex_Matrix (A'Range (1), A'Range (2));
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function Conv_A is new Unchecked_Conversion (Address, A_Ptr);
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begin
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cgetrf (M, N, Conv_A (A'Address).all, Ld_A,
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LAPACK.Integer_Vector (I_Piv), Info);
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end;
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elsif Is_Double then
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declare
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type A_Ptr is
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access all Double_Complex_Matrix (A'Range (1), A'Range (2));
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function Conv_A is new Unchecked_Conversion (Address, A_Ptr);
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begin
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zgetrf (M, N, Conv_A (A'Address).all, Ld_A,
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LAPACK.Integer_Vector (I_Piv), Info);
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end;
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else
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declare
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DP_A : Double_Complex_Matrix (A'Range (1), A'Range (2));
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begin
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DP_A := To_Double_Complex (A);
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zgetrf (M, N, DP_A, Ld_A, LAPACK.Integer_Vector (I_Piv), Info);
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A := To_Complex (DP_A);
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end;
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end if;
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end getrf;
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-----------
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-- getri --
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-----------
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procedure getri
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(N : Natural;
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A : in out Complex_Matrix;
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Ld_A : Positive;
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I_Piv : Integer_Vector;
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Work : in out Complex_Vector;
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L_Work : Integer;
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Info : access Integer)
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is
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begin
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if Is_Single then
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declare
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type A_Ptr is
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access all BLAS.Complex_Matrix (A'Range (1), A'Range (2));
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type Work_Ptr is
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access all BLAS.Complex_Vector (Work'Range);
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function Conv_A is new Unchecked_Conversion (Address, A_Ptr);
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function Conv_Work is new Unchecked_Conversion (Address, Work_Ptr);
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begin
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cgetri (N, Conv_A (A'Address).all, Ld_A,
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LAPACK.Integer_Vector (I_Piv),
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Conv_Work (Work'Address).all, L_Work,
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Info);
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end;
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elsif Is_Double then
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declare
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type A_Ptr is
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access all Double_Complex_Matrix (A'Range (1), A'Range (2));
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type Work_Ptr is
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access all Double_Complex_Vector (Work'Range);
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function Conv_A is new Unchecked_Conversion (Address, A_Ptr);
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function Conv_Work is new Unchecked_Conversion (Address, Work_Ptr);
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begin
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zgetri (N, Conv_A (A'Address).all, Ld_A,
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LAPACK.Integer_Vector (I_Piv),
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Conv_Work (Work'Address).all, L_Work,
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Info);
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end;
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else
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declare
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DP_A : Double_Complex_Matrix (A'Range (1), A'Range (2));
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DP_Work : Double_Complex_Vector (Work'Range);
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begin
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DP_A := To_Double_Complex (A);
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zgetri (N, DP_A, Ld_A, LAPACK.Integer_Vector (I_Piv),
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DP_Work, L_Work, Info);
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A := To_Complex (DP_A);
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Work (1) := To_Complex (DP_Work (1));
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end;
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end if;
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end getri;
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-----------
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-- getrs --
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-----------
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procedure getrs
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(Trans : access constant Character;
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N : Natural;
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N_Rhs : Natural;
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A : Complex_Matrix;
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Ld_A : Positive;
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I_Piv : Integer_Vector;
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B : in out Complex_Matrix;
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Ld_B : Positive;
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Info : access Integer)
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is
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begin
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if Is_Single then
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declare
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subtype A_Type is BLAS.Complex_Matrix (A'Range (1), A'Range (2));
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type B_Ptr is
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access all BLAS.Complex_Matrix (B'Range (1), B'Range (2));
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function Conv_A is
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new Unchecked_Conversion (Complex_Matrix, A_Type);
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function Conv_B is new Unchecked_Conversion (Address, B_Ptr);
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begin
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cgetrs (Trans, N, N_Rhs,
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Conv_A (A), Ld_A,
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LAPACK.Integer_Vector (I_Piv),
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Conv_B (B'Address).all, Ld_B,
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Info);
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end;
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elsif Is_Double then
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declare
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subtype A_Type is
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Double_Complex_Matrix (A'Range (1), A'Range (2));
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type B_Ptr is
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access all Double_Complex_Matrix (B'Range (1), B'Range (2));
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function Conv_A is
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new Unchecked_Conversion (Complex_Matrix, A_Type);
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function Conv_B is new Unchecked_Conversion (Address, B_Ptr);
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begin
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zgetrs (Trans, N, N_Rhs,
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Conv_A (A), Ld_A,
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LAPACK.Integer_Vector (I_Piv),
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Conv_B (B'Address).all, Ld_B,
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Info);
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end;
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else
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declare
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DP_A : Double_Complex_Matrix (A'Range (1), A'Range (2));
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DP_B : Double_Complex_Matrix (B'Range (1), B'Range (2));
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begin
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DP_A := To_Double_Complex (A);
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DP_B := To_Double_Complex (B);
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zgetrs (Trans, N, N_Rhs,
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DP_A, Ld_A,
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LAPACK.Integer_Vector (I_Piv),
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DP_B, Ld_B,
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Info);
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B := To_Complex (DP_B);
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end;
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end if;
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end getrs;
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procedure heevr
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(Job_Z : access constant Character;
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Rng : access constant Character;
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Uplo : access constant Character;
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N : Natural;
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A : in out Complex_Matrix;
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Ld_A : Positive;
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Vl, Vu : Real := 0.0;
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Il, Iu : Integer := 1;
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Abs_Tol : Real := 0.0;
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M : out Integer;
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W : out Real_Vector;
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Z : out Complex_Matrix;
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Ld_Z : Positive;
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I_Supp_Z : out Integer_Vector;
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Work : out Complex_Vector;
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L_Work : Integer;
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R_Work : out Real_Vector;
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LR_Work : Integer;
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I_Work : out Integer_Vector;
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LI_Work : Integer;
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Info : access Integer)
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is
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begin
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if Is_Single then
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declare
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type A_Ptr is
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access all BLAS.Complex_Matrix (A'Range (1), A'Range (2));
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type W_Ptr is
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access all BLAS.Real_Vector (W'Range);
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type Z_Ptr is
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access all BLAS.Complex_Matrix (Z'Range (1), Z'Range (2));
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type Work_Ptr is access all BLAS.Complex_Vector (Work'Range);
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type R_Work_Ptr is access all BLAS.Real_Vector (R_Work'Range);
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function Conv_A is new Unchecked_Conversion (Address, A_Ptr);
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function Conv_W is new Unchecked_Conversion (Address, W_Ptr);
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function Conv_Z is new Unchecked_Conversion (Address, Z_Ptr);
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function Conv_Work is new Unchecked_Conversion (Address, Work_Ptr);
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function Conv_R_Work is
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new Unchecked_Conversion (Address, R_Work_Ptr);
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begin
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cheevr (Job_Z, Rng, Uplo, N,
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Conv_A (A'Address).all, Ld_A,
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Fortran.Real (Vl), Fortran.Real (Vu),
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Il, Iu, Fortran.Real (Abs_Tol), M,
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Conv_W (W'Address).all,
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Conv_Z (Z'Address).all, Ld_Z,
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LAPACK.Integer_Vector (I_Supp_Z),
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Conv_Work (Work'Address).all, L_Work,
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Conv_R_Work (R_Work'Address).all, LR_Work,
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LAPACK.Integer_Vector (I_Work), LI_Work, Info);
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end;
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elsif Is_Double then
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declare
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type A_Ptr is
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access all BLAS.Double_Complex_Matrix (A'Range (1), A'Range (2));
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type W_Ptr is
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access all BLAS.Double_Precision_Vector (W'Range);
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type Z_Ptr is
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access all BLAS.Double_Complex_Matrix (Z'Range (1), Z'Range (2));
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type Work_Ptr is
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access all BLAS.Double_Complex_Vector (Work'Range);
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type R_Work_Ptr is
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access all BLAS.Double_Precision_Vector (R_Work'Range);
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function Conv_A is new Unchecked_Conversion (Address, A_Ptr);
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function Conv_W is new Unchecked_Conversion (Address, W_Ptr);
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function Conv_Z is new Unchecked_Conversion (Address, Z_Ptr);
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function Conv_Work is new Unchecked_Conversion (Address, Work_Ptr);
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function Conv_R_Work is
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new Unchecked_Conversion (Address, R_Work_Ptr);
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begin
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zheevr (Job_Z, Rng, Uplo, N,
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Conv_A (A'Address).all, Ld_A,
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Double_Precision (Vl), Double_Precision (Vu),
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Il, Iu, Double_Precision (Abs_Tol), M,
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Conv_W (W'Address).all,
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Conv_Z (Z'Address).all, Ld_Z,
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LAPACK.Integer_Vector (I_Supp_Z),
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Conv_Work (Work'Address).all, L_Work,
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Conv_R_Work (R_Work'Address).all, LR_Work,
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LAPACK.Integer_Vector (I_Work), LI_Work, Info);
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end;
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else
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declare
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DP_A : Double_Complex_Matrix (A'Range (1), A'Range (2));
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DP_W : Double_Precision_Vector (W'Range);
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DP_Z : Double_Complex_Matrix (Z'Range (1), Z'Range (2));
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DP_Work : Double_Complex_Vector (Work'Range);
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DP_R_Work : Double_Precision_Vector (R_Work'Range);
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begin
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DP_A := To_Double_Complex (A);
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zheevr (Job_Z, Rng, Uplo, N,
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DP_A, Ld_A,
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Double_Precision (Vl), Double_Precision (Vu),
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Il, Iu, Double_Precision (Abs_Tol), M,
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DP_W, DP_Z, Ld_Z,
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LAPACK.Integer_Vector (I_Supp_Z),
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DP_Work, L_Work,
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DP_R_Work, LR_Work,
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LAPACK.Integer_Vector (I_Work), LI_Work, Info);
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A := To_Complex (DP_A);
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W := To_Real (DP_W);
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Z := To_Complex (DP_Z);
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Work (1) := To_Complex (DP_Work (1));
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R_Work (1) := To_Real (DP_R_Work (1));
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end;
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end if;
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end heevr;
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-----------
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-- steqr --
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-----------
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procedure steqr
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(Comp_Z : access constant Character;
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N : Natural;
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D : in out Real_Vector;
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E : in out Real_Vector;
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Z : in out Complex_Matrix;
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Ld_Z : Positive;
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Work : out Real_Vector;
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Info : access Integer)
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is
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begin
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if Is_Single then
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declare
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type D_Ptr is access all BLAS.Real_Vector (D'Range);
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type E_Ptr is access all BLAS.Real_Vector (E'Range);
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type Z_Ptr is
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access all BLAS.Complex_Matrix (Z'Range (1), Z'Range (2));
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type Work_Ptr is
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access all BLAS.Real_Vector (Work'Range);
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function Conv_D is new Unchecked_Conversion (Address, D_Ptr);
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function Conv_E is new Unchecked_Conversion (Address, E_Ptr);
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function Conv_Z is new Unchecked_Conversion (Address, Z_Ptr);
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function Conv_Work is new Unchecked_Conversion (Address, Work_Ptr);
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begin
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csteqr (Comp_Z, N,
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Conv_D (D'Address).all,
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Conv_E (E'Address).all,
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Conv_Z (Z'Address).all,
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Ld_Z,
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Conv_Work (Work'Address).all,
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Info);
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end;
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elsif Is_Double then
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declare
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type D_Ptr is access all Double_Precision_Vector (D'Range);
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type E_Ptr is access all Double_Precision_Vector (E'Range);
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type Z_Ptr is
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access all Double_Complex_Matrix (Z'Range (1), Z'Range (2));
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type Work_Ptr is
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access all Double_Precision_Vector (Work'Range);
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function Conv_D is new Unchecked_Conversion (Address, D_Ptr);
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function Conv_E is new Unchecked_Conversion (Address, E_Ptr);
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function Conv_Z is new Unchecked_Conversion (Address, Z_Ptr);
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function Conv_Work is new Unchecked_Conversion (Address, Work_Ptr);
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begin
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zsteqr (Comp_Z, N,
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Conv_D (D'Address).all,
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Conv_E (E'Address).all,
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Conv_Z (Z'Address).all,
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Ld_Z,
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Conv_Work (Work'Address).all,
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Info);
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end;
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else
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declare
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DP_D : Double_Precision_Vector (D'Range);
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DP_E : Double_Precision_Vector (E'Range);
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DP_Z : Double_Complex_Matrix (Z'Range (1), Z'Range (2));
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DP_Work : Double_Precision_Vector (Work'Range);
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begin
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DP_D := To_Double_Precision (D);
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DP_E := To_Double_Precision (E);
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if Comp_Z.all = 'V' then
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DP_Z := To_Double_Complex (Z);
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end if;
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zsteqr (Comp_Z, N, DP_D, DP_E, DP_Z, Ld_Z, DP_Work, Info);
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D := To_Real (DP_D);
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E := To_Real (DP_E);
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if Comp_Z.all /= 'N' then
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Z := To_Complex (DP_Z);
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end if;
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end;
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end if;
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end steqr;
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end System.Generic_Complex_LAPACK;
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