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Intel® oneAPI Math Kernel Library LAPACK Examples

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ID 766877
Date 10/31/2024
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Document Table of Contents
Document Table of Contents x
Intel® oneAPI Math Kernel Library LAPACK Examples
Intel® oneAPI Math Kernel Library LAPACK Examples x
Legal Information Intel® oneAPI Math Kernel Library LAPACK Examples LAPACK Examples LAPACK Routines: Linear Equations Least Squares and Eigenvalue Problems
Intel® oneAPI Math Kernel Library LAPACK Examples x
What's New Notational Conventions C Interface Conventions Compiling and Running Examples Compiling and Building Fortran Examples Compiling and Building C Examples Getting Help and Support
LAPACK Routines: Linear Equations x
?gesv function ?posv function ?sysv function ?hesv function
?gesv function x
CGESV Example DGESV Example SGESV Example ZGESV Example
CGESV Example x
CGESV Example Program in Fortran CGESV Example Program in C LAPACKE_cgesv Example Program in C for Row Major Data Layout LAPACKE_cgesv Example Program in C for Column Major Data Layout
DGESV Example x
DGESV Example Program in Fortran DGESV Example Program in C LAPACK_dgesv Example Program in C for Row Major Data Layout LAPACKE_dgesv Example Program in C for Column Major Data Layout
SGESV Example x
SGESV Example Program in Fortran SGESV Example Program in C LAPACK_sgesv Example Program in C for Row Major Data Layout LAPACK_sgesv Example Program in C for Column Major Data Layout
ZGESV Example x
ZGESV Example Program in Fortran ZGESV Example Program in C LAPACKE_zgesv Example Program in C for Row Major Data Layout LAPACKE_zgesv Example Program in C for Column Major Data Layout
?posv function x
CPOSV Example DPOSV Example SPOSV Example ZPOSV Example
CPOSV Example x
CPOSV Example Program in Fortran CPOSV Example Program in C LAPACKE_cposv Example Program in C for Row Major Data Layout LAPACK_cposv Example Program in C for Column Major Data Layout
DPOSV Example x
DPOSV Example Program in Fortran DPOSV Example Program in C LAPACKE_dposv Example Program in C for Row Major Data Layout LAPACK_dposv Example Program in C for Column Major Data Layout
SPOSV Example x
SPOSV Example Program in Fortran SPOSV Example Program in C LAPACK_sposv Example Program in C for Row Major Data Layout LAPACKE_sposv Example Program in C for Column Major Data Layout
ZPOSV Example x
ZPOSV Example Program in Fortran ZPOSV Example Program in C LAPACKE_zposv Example Program in C for Row Major Data Layout LAPACK_zposv Example Program in C for Column Major Data Layout
?sysv function x
CSYSV Example DSYSV Example SSYSV Example ZSYSV Example
CSYSV Example x
CSYSV Example Program in Fortran CSYSV Example Program in C LAPACKE_csysv Example Program in C for Row Major Data Layout LAPACKE_csysv Example Program in C for Column Major Data Layout
DSYSV Example x
DSYSV Example Program in Fortran DSYSV Example Program in C LAPACKE_dsysv Example Program in C for Row Major Data Layout LAPACKE_dsysv Example Program in C for Column Major Data Layout
SSYSV Example x
SSYSV Example Program in Fortran SYSV Example Program in C LAPACKE_ssysv Example Program in C for Row Major Data Layout LAPACKE_ssysv Example Program in C for Column Major Data Layout
ZSYSV Example x
ZSYSV Example Program in Fortran ZSYSV Example Program in C LAPACKE_zsysv Example Program in C for Row Major Data Layout LAPACKE_zsysv Example Program in C for Column Major Data Layout
?hesv function x
CHESV Example ZHESV Example
CHESV Example x
CHESV Example Program in Fortran CHESV Example Program in C LAPACKE_chesv Example Program in C for Row Major Data Layout LAPACKE_chesv Example Program in C for Column Major Data Layout
ZHESV Example x
ZHESV Example Program in Fortran ZHESV Example Program in C LAPACKE_zhesv Example Program in C for Row Major Data Layout LAPACKE_zhesv Example Program in C for Column Major Data Layout
Least Squares and Eigenvalue Problems x
Linear Least Squares (LLS) Problems Symmetric Eigenproblems Nonsymmetric Eigenproblems Singular Value Decomposition
Linear Least Squares (LLS) Problems x
?gels function ?gelsd function
?gels function x
CGELS Example DGELS Example SGELS Example ZGELS Example
CGELS Example x
CGELS Example Program in Fortran CGELS Example Program in C LAPACKE_cgels Example Program in C for Row Major Data Layout LAPACKE_cgels Example Program in C for Column Major Data Layout
DGELS Example x
DGELS Example Program in Fortran DGELS Example Program in C LAPACKE_dgels Example Program in C for Row Major Data Layout LAPACKE_dgels Example Program in C for Column Major Data Layout
SGELS Example x
SGELS Example Program in Fortran SGELS Example Program in C LAPACKE_sgels Example Program in C for Row Major Data Layout LAPACKE_sgels Example Program in C for Column Major Data Layout
ZGELS Example x
ZGELS Example Program in Fortran ZGELS Example Program in C LAPACKE_zgels Example Program in C for Row Major Data Layout LAPACKE_zgels Example Program in C for Column Major Data Layout
?gelsd function x
CGELSD Example DGELSD Example SGELSD Example ZGELSD Example
CGELSD Example x
CGELSD Example Program in Fortran CGELSD Example Program in C LAPACKE_cgelsd Example Program in C for Row Major Data Layout LAPACKE_cgelsd Example Program in C for Column Major Data Layout
DGELSD Example x
DGELSD Example Program in Fortran DGELSD Example Program in C LAPACKE_dgelsd Example Program in C for Row Major Data Layout LAPACKE_dgelsd Example Program in C for Column Major Data Layout
SGELSD Example x
SGELSD Example Program in Fortran SGELSD Example Program in C LAPACKE_sgelsd Example Program in C for Row Major Data Layout LAPACKE_sgelsd Example Program in C for Column Major Data Layout
ZGELSD Example x
ZGELSD Example Program in Fortran ZGELSD Example Program in C LAPACKE_zgelsd Example Program in C for Row Major Data Layout LAPACKE_zgelsd Example Program in C for Column Major Data Layout
Symmetric Eigenproblems x
?syev function ?heev function ?syevd function ?heevd function ?syevx function ?heevx function ?syevr function ?heevr function
?syev function x
DSYEV Example SSYEV Example
DSYEV Example x
DSYEV Example Program in Fortran DSYEV Example Program in C LAPACKE_dsyev Example Program in C for Row Major Data Layout LAPACKE_dsyev Example Program in C for Column Major Data Layout
SSYEV Example x
SSYEV Example Program in Fortran SSYEV Example Program in C LAPACKE_ssyev Example Program in C for Row Major Data Layout LAPACKE_ssyev Example Program in C for Column Major Data Layout
?heev function x
CHEEV Example ZHEEV Example
CHEEV Example x
CHEEV Example Program in Fortran CHEEV Example Program in C LAPACKE_cheev Example Program in C for Row Major Data Layout LAPACKE_cheev Example Program in C for Column Major Data Layout
ZHEEV Example x
ZHEEV Example Program in Fortran ZHEEV Example Program in C LAPACKE_zheev Example Program in C for Row Major Data Layout LAPACKE_zheev Example Program in C for Column Major Data Layout
?syevd function x
DSYEVD Example SSYEVD Example
DSYEVD Example x
DSYEVD Example Program in Fortran DSYEVD Example Program in C LAPACKE_dsyevd Example Program in C for Row Major Data Layout LAPACKE_dsyevd Example Program in C for Column Major Data Layout
SSYEVD Example x
SSYEVD Example Program in Fortran SSYEVD Example Program in C LAPACKE_ssyevd Example Program in C for Row Major Data Layout LAPACKE_ssyevd Example Program in C for Column Major Data Layout
?heevd function x
CHEEVD Example ZHEEVD Example
CHEEVD Example x
CHEEVD Example Program in Fortran CHEEVD Example Program in C LAPACKE_cheevd Example Program in C for Row Major Data Layout LAPACKE_cheevd Example Program in C for Column Major Data Layout
ZHEEVD Example x
ZHEEVD Example Program in Fortran ZHEEVD Example Program in C LAPACKE_zheevd Example Program in C for Row Major Data Layout LAPACKE_zheevd Example Program in C for Column Major Data Layout
?syevx function x
DSYEVX Example SSYEVX Example
DSYEVX Example x
DSYEVX Example Program in Fortran DSYEVX Example Program in C LAPACKE_dsyevx Example Program in C for Row Major Data Layout LAPACKE_dsyevx Example Program in C for Column Major Data Layout
SSYEVX Example x
SSYEVX Example Program in Fortran SSYEVX Example Program in C LAPACKE_ssyevx Example Program in C for Row Major Data Layout LAPACKE_ssyevx Example Program in C for Column Major Data Layout
?heevx function x
CHEEVX Example ZHEEVX Example
CHEEVX Example x
CHEEVX Example Program in Fortran CHEEVX Example Program in C LAPACKE_cheevx Example Program in C for Row Major Data Layout LAPACKE_cheevx Example Program in C for Column Major Data Layout
ZHEEVX Example x
ZHEEVX Example Program in Fortran ZHEEVX Example Program in C LAPACKE_zheevx Example Program in C for Row Major Data Layout LAPACKE_zheevx Example Program in C for Column Major Data Layout
?syevr function x
DSYEVR Example SSYEVR Example
DSYEVR Example x
DSYEVR Example Program in Fortran DSYEVR Example Program in C LAPACKE_dsyevr Example Program in C for Row Major Data Layout LAPACKE_dsyevr Example Program in C for Column Major Data Layout
SSYEVR Example x
SSYEVR Example Program in Fortran SSYEVR Example Program in C LAPACKE_ssyevr Example Program in C for Row Major Data Layout LAPACKE_ssyevr Example Program in C for Column Major Data Layout
?heevr function x
CHEEVR Example ZHEEVR Example
CHEEVR Example x
CHEEVR Example Program in Fortran CHEEVR Example Program in C LAPACKE_cheevr Example Program in C for Row Major Data Layout LAPACKE_cheevr Example Program in C for Column Major Data Layout
ZHEEVR Example x
ZHEEVR Example Program in Fortran ZHEEVR Example Program in C LAPACKE_zheevr Example Program in C for Row Major Data Layout LAPACKE_zheevr Example Program in C for Column Major Data Layout
Nonsymmetric Eigenproblems x
?geev function
?geev function x
CGEEV Example DGEEV Example SGEEV Example ZGEEV Example
CGEEV Example x
CGEEV Example Program in Fortran CGEEV Example Program in C LAPACKE_cgeev Example Program in C for Row Major Data Layout LAPACKE_cgeev Example Program in C for Column Major Data Layout
DGEEV Example x
DGEEV Example Program in Fortran DGEEV Example Program in C LAPACKE_dgeev Example Program in C for Row Major Data Layout LAPACKE_dgeev Example Program in C for Column Major Data Layout
SGEEV Example x
SGEEV Example Program in Fortran SGEEV Example Program in C LAPACKE_sgeev Example Program in C for Row Major Data Layout LAPACKE_sgeev Example Program in C for Column Major Data Layout
ZGEEV Example x
ZGEEV Example Program in Fortran ZGEEV Example Program in C LAPACKE_zgeev Example Program in C for Row Major Data Layout LAPACKE_zgeev Example Program in C for Column Major Data Layout
Singular Value Decomposition x
?gesvd function ?gesdd function
?gesvd function x
CGESVD Example DGESVD Example SGESVD Example ZGESVD Example
CGESVD Example x
CGESVD Example Program in Fortran CGESVD Example Program in C LAPACKE_cgesvd Example Program in C for Row Major Data Layout LAPACKE_cgesvd Example Program in C for Column Major Data Layout
DGESVD Example x
DGESVD Example Program in Fortran DGESVD Example Program in C LAPACKE_dgesvd Example Program in C for Row Major Data Layout LAPACKE_dgesvd Example Program in C for Column Major Data Layout
SGESVD Example x
SGESVD Example Program in Fortran SGESVD Example Program in C LAPACKE_sgesvd Example Program in C for Row Major Data Layout LAPACKE_sgesvd Example Program in C for Column Major Data Layout
ZGESVD Example x
ZGESVD Example Program in Fortran ZGESVD Example Program in C LAPACKE_zgesvd Example Program in C for Row Major Data Layout LAPACKE_zgesvd Example Program in C for Column Major Data Layout
?gesdd function x
CGESDD Example DGESDD Example SGESDD Example ZGESDD Example
CGESDD Example x
CGESDD Example Program in Fortran CGESDD Example Program in C LAPACKE_cgesdd Example Program in C for Row Major Data Layout LAPACKE_cgesdd Example Program in C for Column Major Data Layout
DGESDD Example x
DGESDD Example Program in Fortran DGESDD Example Program in C LAPACKE_dgesdd Example Program in C for Row Major Data Layout LAPACKE_dgesdd Example Program in C for Column Major Data Layout
SGESDD Example x
SGESDD Example Program in Fortran SGESDD Example Program in C LAPACKE_sgesdd Example Program in C for Row Major Data Layout LAPACKE_sgesdd Example Program in C for Column Major Data Layout
ZGESDD Example x
ZGESDD Example Program in Fortran ZGESDD Example Program in C LAPACKE_zgesdd Example Program in C for Row Major Data Layout LAPACKE_zgesdd Example Program in C for Column Major Data Layout
Intel® oneAPI Math Kernel Library LAPACK Examples

DGEEV Example Program in Fortran

*  Copyright (C) 2009-2015 Intel Corporation. All Rights Reserved.
*  The information and material ("Material") provided below is owned by Intel
*  Corporation or its suppliers or licensors, and title to such Material remains
*  with Intel Corporation or its suppliers or licensors. The Material contains
*  proprietary information of Intel or its suppliers and licensors. The Material
*  is protected by worldwide copyright laws and treaty provisions. No part of
*  the Material may be copied, reproduced, published, uploaded, posted,
*  transmitted, or distributed in any way without Intel's prior express written
*  permission. No license under any patent, copyright or other intellectual
*  property rights in the Material is granted to or conferred upon you, either
*  expressly, by implication, inducement, estoppel or otherwise. Any license
*  under such intellectual property rights must be express and approved by Intel
*  in writing.
*  =============================================================================
*
*  DGEEV Example.
*  ==============
*
*  Program computes the eigenvalues and left and right eigenvectors of a general
*  rectangular matrix A:
*
*   -1.01   0.86  -4.60   3.31  -4.81
*    3.98   0.53  -7.04   5.29   3.55
*    3.30   8.26  -3.89   8.20  -1.51
*    4.43   4.96  -7.66  -7.33   6.18
*    7.31  -6.43  -6.16   2.47   5.58
*
*  Description.
*  ============
*
*  The routine computes for an n-by-n real nonsymmetric matrix A, the
*  eigenvalues and, optionally, the left and/or right eigenvectors. The right
*  eigenvector v(j) of A satisfies
*
*  A*v(j)= lambda(j)*v(j)
*
*  where lambda(j) is its eigenvalue. The left eigenvector u(j) of A satisfies
*
*  u(j)H*A = lambda(j)*u(j)H
*
*  where u(j)H denotes the conjugate transpose of u(j). The computed
*  eigenvectors are normalized to have Euclidean norm equal to 1 and
*  largest component real.
*
*  Example Program Results.
*  ========================
*
* DGEEV Example Program Results
*
* Eigenvalues
* (  2.86, 10.76) (  2.86,-10.76) ( -0.69,  4.70) ( -0.69, -4.70) -10.46
*
* Left eigenvectors
* (  0.04,  0.29) (  0.04, -0.29) ( -0.13, -0.33) ( -0.13,  0.33)   0.04
* (  0.62,  0.00) (  0.62,  0.00) (  0.69,  0.00) (  0.69,  0.00)   0.56
* ( -0.04, -0.58) ( -0.04,  0.58) ( -0.39, -0.07) ( -0.39,  0.07)  -0.13
* (  0.28,  0.01) (  0.28, -0.01) ( -0.02, -0.19) ( -0.02,  0.19)  -0.80
* ( -0.04,  0.34) ( -0.04, -0.34) ( -0.40,  0.22) ( -0.40, -0.22)   0.18
*
* Right eigenvectors
* (  0.11,  0.17) (  0.11, -0.17) (  0.73,  0.00) (  0.73,  0.00)   0.46
* (  0.41, -0.26) (  0.41,  0.26) ( -0.03, -0.02) ( -0.03,  0.02)   0.34
* (  0.10, -0.51) (  0.10,  0.51) (  0.19, -0.29) (  0.19,  0.29)   0.31
* (  0.40, -0.09) (  0.40,  0.09) ( -0.08, -0.08) ( -0.08,  0.08)  -0.74
* (  0.54,  0.00) (  0.54,  0.00) ( -0.29, -0.49) ( -0.29,  0.49)   0.16
*  =============================================================================
*
*     .. Parameters ..
      INTEGER          N
      PARAMETER        ( N = 5 )
      INTEGER          LDA, LDVL, LDVR
      PARAMETER        ( LDA = N, LDVL = N, LDVR = N )
      INTEGER          LWMAX
      PARAMETER        ( LWMAX = 1000 )
*
*     .. Local Scalars ..
      INTEGER          INFO, LWORK
*
*     .. Local Arrays ..
      DOUBLE PRECISION A( LDA, N ), VL( LDVL, N ), VR( LDVR, N ),
     $                 WR( N ), WI( N ), WORK( LWMAX )
      DATA             A/
     $ -1.01, 3.98, 3.30, 4.43, 7.31,
     $  0.86, 0.53, 8.26, 4.96,-6.43,
     $ -4.60,-7.04,-3.89,-7.66,-6.16,
     $  3.31, 5.29, 8.20,-7.33, 2.47,
     $ -4.81, 3.55,-1.51, 6.18, 5.58
     $                  /
*
*     .. External Subroutines ..
      EXTERNAL         DGEEV
      EXTERNAL         PRINT_EIGENVALUES, PRINT_EIGENVECTORS
*
*     .. Intrinsic Functions ..
      INTRINSIC        INT, MIN
*
*     .. Executable Statements ..
      WRITE(*,*)'DGEEV Example Program Results'
*
*     Query the optimal workspace.
*
      LWORK = -1
      CALL DGEEV( 'Vectors', 'Vectors', N, A, LDA, WR, WI, VL, LDVL,
     $            VR, LDVR, WORK, LWORK, INFO )
      LWORK = MIN( LWMAX, INT( WORK( 1 ) ) )
*
*     Solve eigenproblem.
*
      CALL DGEEV( 'Vectors', 'Vectors', N, A, LDA, WR, WI, VL, LDVL,
     $            VR, LDVR, WORK, LWORK, INFO )
*
*     Check for convergence.
*
      IF( INFO.GT.0 ) THEN
         WRITE(*,*)'The algorithm failed to compute eigenvalues.'
         STOP
      END IF
*
*     Print eigenvalues.
*
      CALL PRINT_EIGENVALUES( 'Eigenvalues', N, WR, WI )
*
*     Print left eigenvectors.
*
      CALL PRINT_EIGENVECTORS( 'Left eigenvectors', N, WI, VL, LDVL )
*
*     Print right eigenvectors.
*
      CALL PRINT_EIGENVECTORS( 'Right eigenvectors', N, WI, VR, LDVR )
      STOP
      END
*
*     End of DGEEV Example.
*
*  =============================================================================
*
*     Auxiliary routine: printing eigenvalues.
*
      SUBROUTINE PRINT_EIGENVALUES( DESC, N, WR, WI )
      CHARACTER*(*)    DESC
      INTEGER          N
      DOUBLE PRECISION WR( * ), WI( * )
*
      DOUBLE PRECISION ZERO
      PARAMETER        ( ZERO = 0.0 )
      INTEGER          J
*
      WRITE(*,*)
      WRITE(*,*) DESC
      DO J = 1, N
         IF( WI( J ).EQ.ZERO ) THEN
            WRITE(*,9998,ADVANCE='NO') WR( J )
         ELSE
            WRITE(*,9999,ADVANCE='NO') WR( J ), WI( J )
         END IF
      END DO
      WRITE(*,*)
*
 9998 FORMAT( 11(:,1X,F6.2) )
 9999 FORMAT( 11(:,1X,'(',F6.2,',',F6.2,')') )
      RETURN
      END
*
*     Auxiliary routine: printing eigenvectors.
*
      SUBROUTINE PRINT_EIGENVECTORS( DESC, N, WI, V, LDV )
      CHARACTER*(*)    DESC
      INTEGER          N, LDV
      DOUBLE PRECISION WI( * ), V( LDV, * )
*
      DOUBLE PRECISION ZERO
      PARAMETER        ( ZERO = 0.0 )
      INTEGER          I, J
*
      WRITE(*,*)
      WRITE(*,*) DESC
      DO I = 1, N
         J = 1
         DO WHILE( J.LE.N )
            IF( WI( J ).EQ.ZERO ) THEN
               WRITE(*,9998,ADVANCE='NO') V( I, J )
               J = J + 1
            ELSE
               WRITE(*,9999,ADVANCE='NO') V( I, J ), V( I, J+1 )
               WRITE(*,9999,ADVANCE='NO') V( I, J ), -V( I, J+1 )
               J = J + 2
            END IF
         END DO
         WRITE(*,*)
      END DO
*
 9998 FORMAT( 11(:,1X,F6.2) )
 9999 FORMAT( 11(:,1X,'(',F6.2,',',F6.2,')') )
      RETURN
      END
Parent topic: DGEEV Example
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