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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

ZGESDD 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.
*  =============================================================================
*
*  ZGESDD Example.
*  ==============
*
*  Program computes the singular value decomposition of a general
*  rectangular complex matrix A using a divide and conquer method, where A is:
*
*  ( -5.40,  7.40) (  6.00,  6.38) (  9.91,  0.16) ( -5.28, -4.16)
*  (  1.09,  1.55) (  2.60,  0.07) (  3.98, -5.26) (  2.03,  1.11)
*  (  9.88,  1.91) (  4.92,  6.31) ( -2.11,  7.39) ( -9.81, -8.98)
*
*  Description.
*  ============
*
*  The routine computes the singular value decomposition (SVD) of a complex
*  m-by-n matrix A, optionally computing the left and/or right singular
*  vectors. If singular vectors are desired, it uses a divide and conquer
*  algorithm. The SVD is written as
*
*  A = U*SIGMA*VH
*
*  where SIGMA is an m-by-n matrix which is zero except for its min(m,n)
*  diagonal elements, U is an m-by-m unitary matrix and VH (V conjugate
*  transposed) is an n-by-n unitary matrix. The diagonal elements of SIGMA
*  are the singular values of A; they are real and non-negative, and are
*  returned in descending order. The first min(m, n) columns of U and V are
*  the left and right singular vectors of A.
*
*  Note that the routine returns VH, not V.
*
*  Example Program Results.
*  ========================
*
* ZGESDD Example Program Results
*
* Singular values
*  21.76  16.60   3.97
*
* Left singular vectors (stored columnwise)
* (  0.55,  0.00) (  0.76,  0.00) ( -0.34,  0.00)
* ( -0.04, -0.15) (  0.27, -0.23) (  0.55, -0.74)
* (  0.81,  0.12) ( -0.52, -0.14) (  0.13, -0.11)
*
* Right singular vectors (stored rowwise)
* (  0.23,  0.21) (  0.37,  0.39) (  0.24,  0.33) ( -0.56, -0.37)
* ( -0.58,  0.40) (  0.11,  0.17) (  0.60, -0.27) (  0.16,  0.06)
* (  0.60,  0.12) ( -0.19,  0.30) (  0.39,  0.20) (  0.45,  0.31)
*  =============================================================================
*
*     .. Parameters ..
      INTEGER          M, N
      PARAMETER        ( M = 3, N = 4 )
      INTEGER          LDA, LDU, LDVT
      PARAMETER        ( LDA = M, LDU = M, LDVT = N )
      INTEGER          LWMAX
      PARAMETER        ( LWMAX = 1000 )
*
*     .. Local Scalars ..
      INTEGER          INFO, LWORK
*
*     .. Local Arrays ..
*     IWORK dimension should be at least 8*MIN(M,N)
      INTEGER          IWORK( 8*M )
*     RWORK dimension should be at least 5*(MIN(M,N))**2 + 7*MIN(M,N))
      DOUBLE PRECISION S( M ), RWORK( 5*M*M + 7*M )
      COMPLEX*16       A( LDA, N ), U( LDU, M ), VT( LDVT, N ),
     $                 WORK( LWMAX )
      DATA             A/
     $ (-5.40, 7.40),( 1.09, 1.55),( 9.88, 1.91),
     $ ( 6.00, 6.38),( 2.60, 0.07),( 4.92, 6.31),
     $ ( 9.91, 0.16),( 3.98,-5.26),(-2.11, 7.39),
     $ (-5.28,-4.16),( 2.03, 1.11),(-9.81,-8.98)
     $                  /
*
*     .. External Subroutines ..
      EXTERNAL         ZGESDD
      EXTERNAL         PRINT_MATRIX, PRINT_RMATRIX
*
*     .. Intrinsic Functions ..
      INTRINSIC        INT, MIN
*
*     .. Executable Statements ..
      WRITE(*,*)'ZGESDD Example Program Results'
*
*     Query the optimal workspace.
*
      LWORK = -1
      CALL ZGESDD( 'Singular vectors', M, N, A, LDA, S, U, LDU, VT,
     $             LDVT, WORK, LWORK, RWORK, IWORK, INFO )
      LWORK = MIN( LWMAX, INT( WORK( 1 ) ) )
*
*     Compute SVD.
*
      CALL ZGESDD( 'Singular vectors', M, N, A, LDA, S, U, LDU, VT,
     $             LDVT, WORK, LWORK, RWORK, IWORK, INFO )
*
*     Check for convergence.
*
      IF( INFO.GT.0 ) THEN
         WRITE(*,*)'The algorithm computing SVD failed to converge.'
         STOP
      END IF
*
*     Print singular values.
*
      CALL PRINT_RMATRIX( 'Singular values', 1, M, S, 1 )
*
*     Print left singular vectors.
*
      CALL PRINT_MATRIX( 'Left singular vectors (stored columnwise)',
     $                   M, M, U, LDU )
*
*     Print right singular vectors.
*
      CALL PRINT_MATRIX( 'Right singular vectors (stored rowwise)',
     $                   M, N, VT, LDVT )
      STOP
      END
*
*     End of ZGESDD 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 real matrix.
*
      SUBROUTINE PRINT_RMATRIX( DESC, M, N, A, LDA )
      CHARACTER*(*)    DESC
      INTEGER          M, N, LDA
      DOUBLE PRECISION 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) )
      RETURN
      END
Parent topic: ZGESDD Example
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