LAPACK 3.3.1 Linear Algebra PACKage

# zppt02.f

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```00001       SUBROUTINE ZPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
00002      \$                   RESID )
00003 *
00004 *  -- LAPACK test routine (version 3.1) --
00005 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          UPLO
00010       INTEGER            LDB, LDX, N, NRHS
00011       DOUBLE PRECISION   RESID
00012 *     ..
00013 *     .. Array Arguments ..
00014       DOUBLE PRECISION   RWORK( * )
00015       COMPLEX*16         A( * ), B( LDB, * ), X( LDX, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  ZPPT02 computes the residual in the solution of a Hermitian system
00022 *  of linear equations  A*x = b  when packed storage is used for the
00023 *  coefficient matrix.  The ratio computed is
00024 *
00025 *     RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
00026 *
00027 *  where EPS is the machine precision.
00028 *
00029 *  Arguments
00030 *  =========
00031 *
00032 *  UPLO    (input) CHARACTER*1
00033 *          Specifies whether the upper or lower triangular part of the
00034 *          Hermitian matrix A is stored:
00035 *          = 'U':  Upper triangular
00036 *          = 'L':  Lower triangular
00037 *
00038 *  N       (input) INTEGER
00039 *          The number of rows and columns of the matrix A.  N >= 0.
00040 *
00041 *  NRHS    (input) INTEGER
00042 *          The number of columns of B, the matrix of right hand sides.
00043 *          NRHS >= 0.
00044 *
00045 *  A       (input) COMPLEX*16 array, dimension (N*(N+1)/2)
00046 *          The original Hermitian matrix A, stored as a packed
00047 *          triangular matrix.
00048 *
00049 *  X       (input) COMPLEX*16 array, dimension (LDX,NRHS)
00050 *          The computed solution vectors for the system of linear
00051 *          equations.
00052 *
00053 *  LDX     (input) INTEGER
00054 *          The leading dimension of the array X.   LDX >= max(1,N).
00055 *
00056 *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
00057 *          On entry, the right hand side vectors for the system of
00058 *          linear equations.
00059 *          On exit, B is overwritten with the difference B - A*X.
00060 *
00061 *  LDB     (input) INTEGER
00062 *          The leading dimension of the array B.  LDB >= max(1,N).
00063 *
00064 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
00065 *
00066 *  RESID   (output) DOUBLE PRECISION
00067 *          The maximum over the number of right hand sides of
00068 *          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
00069 *
00070 *  =====================================================================
00071 *
00072 *     .. Parameters ..
00073       DOUBLE PRECISION   ZERO, ONE
00074       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00075       COMPLEX*16         CONE
00076       PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ) )
00077 *     ..
00078 *     .. Local Scalars ..
00079       INTEGER            J
00080       DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
00081 *     ..
00082 *     .. External Functions ..
00083       DOUBLE PRECISION   DLAMCH, DZASUM, ZLANHP
00084       EXTERNAL           DLAMCH, DZASUM, ZLANHP
00085 *     ..
00086 *     .. External Subroutines ..
00087       EXTERNAL           ZHPMV
00088 *     ..
00089 *     .. Intrinsic Functions ..
00090       INTRINSIC          MAX
00091 *     ..
00092 *     .. Executable Statements ..
00093 *
00094 *     Quick exit if N = 0 or NRHS = 0.
00095 *
00096       IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
00097          RESID = ZERO
00098          RETURN
00099       END IF
00100 *
00101 *     Exit with RESID = 1/EPS if ANORM = 0.
00102 *
00103       EPS = DLAMCH( 'Epsilon' )
00104       ANORM = ZLANHP( '1', UPLO, N, A, RWORK )
00105       IF( ANORM.LE.ZERO ) THEN
00106          RESID = ONE / EPS
00107          RETURN
00108       END IF
00109 *
00110 *     Compute  B - A*X  for the matrix of right hand sides B.
00111 *
00112       DO 10 J = 1, NRHS
00113          CALL ZHPMV( UPLO, N, -CONE, A, X( 1, J ), 1, CONE, B( 1, J ),
00114      \$               1 )
00115    10 CONTINUE
00116 *
00117 *     Compute the maximum over the number of right hand sides of
00118 *        norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
00119 *
00120       RESID = ZERO
00121       DO 20 J = 1, NRHS
00122          BNORM = DZASUM( N, B( 1, J ), 1 )
00123          XNORM = DZASUM( N, X( 1, J ), 1 )
00124          IF( XNORM.LE.ZERO ) THEN
00125             RESID = ONE / EPS
00126          ELSE
00127             RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
00128          END IF
00129    20 CONTINUE
00130 *
00131       RETURN
00132 *
00133 *     End of ZPPT02
00134 *
00135       END
```