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Intel® oneAPI Math Kernel Library LAPACK Examples

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ID 766877
Date 3/22/2024
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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

ZHESV 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.
*  =============================================================================
*
*  ZHESV Example.
*  ==============
*
*  The program computes the solution to the system of linear equations
*  with a Hermitian matrix A and multiple right-hand sides B,
*  where A is the coefficient matrix:
*
*  ( -2.90,  0.00) (  0.31,  4.46) (  9.66, -5.66) ( -2.28,  2.14)
*  (  0.31, -4.46) ( -7.93,  0.00) (  9.55, -4.62) ( -3.51,  3.11)
*  (  9.66,  5.66) (  9.55,  4.62) (  0.30,  0.00) (  9.33, -9.66)
*  ( -2.28, -2.14) ( -3.51, -3.11) (  9.33,  9.66) (  2.40,  0.00)
*
*  and B is the right-hand side matrix:
*
*  ( -5.69, -8.21) ( -2.83,  6.46)
*  ( -3.57,  1.99) ( -7.64,  1.10)
*  (  8.42, -9.83) ( -2.33, -4.23)
*  ( -5.00,  3.85) (  6.48, -3.81)
*
*  Description.
*  ============
*
*  The routine solves for X the complex system of linear equations A*X = B,
*  where A is an n-by-n Hermitian matrix, the columns of matrix B are
*  individual right-hand sides, and the columns of X are the corresponding
*  solutions.
*
*  The diagonal pivoting method is used to factor A as A = U*D*UH or
*  A = L*D*LH, where U (or L) is a product of permutation and unit upper
*  (lower) triangular matrices, and D is Hermitian and block diagonal with
*  1-by-1 and 2-by-2 diagonal blocks.
*
*  The factored form of A is then used to solve the system of equations A*X = B.
*
*  Example Program Results.
*  ========================
*
* ZHESV Example Program Results
*
* Solution
* (  0.22, -0.95) ( -1.13,  0.18)
* ( -1.42, -1.30) (  0.70,  1.13)
* ( -0.65, -0.40) (  0.04,  0.07)
* ( -0.48,  1.35) (  1.15, -0.27)
*
* Details of factorization
* (  3.17,  0.00) (  7.32,  3.28) ( -0.36,  0.06) (  0.20, -0.82)
* (  0.00,  0.00) (  0.03,  0.00) ( -0.48,  0.03) (  0.25, -0.76)
* (  0.00,  0.00) (  0.00,  0.00) (  0.30,  0.00) (  9.33, -9.66)
* (  0.00,  0.00) (  0.00,  0.00) (  0.00,  0.00) (  2.40,  0.00)
*
* Pivot indices
*     -1     -1     -3     -3
*  =============================================================================
*
*     .. Parameters ..
      INTEGER          N, NRHS
      PARAMETER        ( N = 4, NRHS = 2 )
      INTEGER          LDA, LDB
      PARAMETER        ( LDA = N, LDB = N )
      INTEGER          LWMAX
      PARAMETER        ( LWMAX = 100 )
*
*     .. Local Scalars ..
      INTEGER          INFO, LWORK
*
*     .. Local Arrays ..
      INTEGER          IPIV( N )
      COMPLEX*16       A( LDA, N ), B( LDB, NRHS ), WORK( LWMAX )
      DATA             A/
     $ (-2.90, 0.00),( 0.00, 0.00),( 0.00, 0.00),( 0.00, 0.00),
     $ ( 0.31, 4.46),(-7.93, 0.00),( 0.00, 0.00),( 0.00, 0.00),
     $ ( 9.66,-5.66),( 9.55,-4.62),( 0.30, 0.00),( 0.00, 0.00),
     $ (-2.28, 2.14),(-3.51, 3.11),( 9.33,-9.66),( 2.40, 0.00)
     $                  /
      DATA             B/
     $ (-5.69,-8.21),(-3.57, 1.99),( 8.42,-9.83),(-5.00, 3.85),
     $ (-2.83, 6.46),(-7.64, 1.10),(-2.33,-4.23),( 6.48,-3.81)
     $                  /
*
*     .. External Subroutines ..
      EXTERNAL         ZHESV
      EXTERNAL         PRINT_MATRIX, PRINT_INT_VECTOR
*
*     .. Intrinsic Functions ..
      INTRINSIC        INT, MIN
*
*     .. Executable Statements ..
      WRITE(*,*)'ZHESV Example Program Results'
*
*     Query the optimal workspace.
*
      LWORK = -1
      CALL ZHESV( 'Upper', N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK,
     $            INFO )
      LWORK = MIN( LWMAX, INT( WORK( 1 ) ) )
*
*     Solve the equations A*X = B.
*
      CALL ZHESV( 'Upper', N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK,
     $            INFO )
*
*     Check for the exact singularity.
*
      IF( INFO.GT.0 ) THEN
         WRITE(*,*)'The element of the diagonal factor '
         WRITE(*,*)'D(',INFO,',',INFO,') is zero, so that'
         WRITE(*,*)'D is singular; the solution could not be computed.'
         STOP
      END IF
*
*     Print solution.
*
      CALL PRINT_MATRIX( 'Solution', N, NRHS, B, LDB )
*
*     Print details of factorization.
*
      CALL PRINT_MATRIX( 'Details of factorization', N, N, A, LDA )
*
*     Print pivot indices.
*
      CALL PRINT_INT_VECTOR( 'Pivot indices', N, IPIV )
      STOP
      END
*
*     End of ZHESV Example.
*
*  =============================================================================
*
*     Auxiliary routine: printing a matrix.
*
      SUBROUTINE PRINT_MATRIX( DESC, M, N, A, LDA )
      CHARACTER*(*)    DESC
      INTEGER          M, N, LDA
      COMPLEX*16       A( LDA, * )
*
      INTEGER          I, J
*
      WRITE(*,*)
      WRITE(*,*) DESC
      DO I = 1, M
         WRITE(*,9998) ( A( I, J ), J = 1, N )
      END DO
*
 9998 FORMAT( 11(:,1X,'(',F6.2,',',F6.2,')') )
      RETURN
      END
*
*     Auxiliary routine: printing a vector of integers.
*
      SUBROUTINE PRINT_INT_VECTOR( DESC, N, A )
      CHARACTER*(*)    DESC
      INTEGER          N
      INTEGER          A( N )
*
      INTEGER          I
*
      WRITE(*,*)
      WRITE(*,*) DESC
      WRITE(*,9999) ( A( I ), I = 1, N )
*
 9999 FORMAT( 11(:,1X,I6) )
      RETURN
      END
Parent topic: ZHESV Example
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