LAPACK 3.3.1 Linear Algebra PACKage

# LIN/sget02.f

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```00001       SUBROUTINE SGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
00002      \$                   RWORK, 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          TRANS
00010       INTEGER            LDA, LDB, LDX, M, N, NRHS
00011       REAL               RESID
00012 *     ..
00013 *     .. Array Arguments ..
00014       REAL               A( LDA, * ), B( LDB, * ), RWORK( * ),
00015      \$                   X( LDX, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  SGET02 computes the residual for a solution of a system of linear
00022 *  equations  A*x = b  or  A'*x = b:
00023 *     RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
00024 *  where EPS is the machine epsilon.
00025 *
00026 *  Arguments
00027 *  =========
00028 *
00029 *  TRANS   (input) CHARACTER*1
00030 *          Specifies the form of the system of equations:
00031 *          = 'N':  A *x = b
00032 *          = 'T':  A'*x = b, where A' is the transpose of A
00033 *          = 'C':  A'*x = b, where A' is the transpose of A
00034 *
00035 *  M       (input) INTEGER
00036 *          The number of rows of the matrix A.  M >= 0.
00037 *
00038 *  N       (input) INTEGER
00039 *          The number of 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) REAL array, dimension (LDA,N)
00046 *          The original M x N matrix A.
00047 *
00048 *  LDA     (input) INTEGER
00049 *          The leading dimension of the array A.  LDA >= max(1,M).
00050 *
00051 *  X       (input) REAL array, dimension (LDX,NRHS)
00052 *          The computed solution vectors for the system of linear
00053 *          equations.
00054 *
00055 *  LDX     (input) INTEGER
00056 *          The leading dimension of the array X.  If TRANS = 'N',
00057 *          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
00058 *
00059 *  B       (input/output) REAL array, dimension (LDB,NRHS)
00060 *          On entry, the right hand side vectors for the system of
00061 *          linear equations.
00062 *          On exit, B is overwritten with the difference B - A*X.
00063 *
00064 *  LDB     (input) INTEGER
00065 *          The leading dimension of the array B.  IF TRANS = 'N',
00066 *          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
00067 *
00068 *  RWORK   (workspace) REAL array, dimension (M)
00069 *
00070 *  RESID   (output) REAL
00071 *          The maximum over the number of right hand sides of
00072 *          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
00073 *
00074 *  =====================================================================
00075 *
00076 *     .. Parameters ..
00077       REAL               ZERO, ONE
00078       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00079 *     ..
00080 *     .. Local Scalars ..
00081       INTEGER            J, N1, N2
00082       REAL               ANORM, BNORM, EPS, XNORM
00083 *     ..
00084 *     .. External Functions ..
00085       LOGICAL            LSAME
00086       REAL               SASUM, SLAMCH, SLANGE
00087       EXTERNAL           LSAME, SASUM, SLAMCH, SLANGE
00088 *     ..
00089 *     .. External Subroutines ..
00090       EXTERNAL           SGEMM
00091 *     ..
00092 *     .. Intrinsic Functions ..
00093       INTRINSIC          MAX
00094 *     ..
00095 *     .. Executable Statements ..
00096 *
00097 *     Quick exit if M = 0 or N = 0 or NRHS = 0
00098 *
00099       IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.EQ.0 ) THEN
00100          RESID = ZERO
00101          RETURN
00102       END IF
00103 *
00104       IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN
00105          N1 = N
00106          N2 = M
00107       ELSE
00108          N1 = M
00109          N2 = N
00110       END IF
00111 *
00112 *     Exit with RESID = 1/EPS if ANORM = 0.
00113 *
00114       EPS = SLAMCH( 'Epsilon' )
00115       ANORM = SLANGE( '1', N1, N2, A, LDA, RWORK )
00116       IF( ANORM.LE.ZERO ) THEN
00117          RESID = ONE / EPS
00118          RETURN
00119       END IF
00120 *
00121 *     Compute  B - A*X  (or  B - A'*X ) and store in B.
00122 *
00123       CALL SGEMM( TRANS, 'No transpose', N1, NRHS, N2, -ONE, A, LDA, X,
00124      \$            LDX, ONE, B, LDB )
00125 *
00126 *     Compute the maximum over the number of right hand sides of
00127 *        norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
00128 *
00129       RESID = ZERO
00130       DO 10 J = 1, NRHS
00131          BNORM = SASUM( N1, B( 1, J ), 1 )
00132          XNORM = SASUM( N2, X( 1, J ), 1 )
00133          IF( XNORM.LE.ZERO ) THEN
00134             RESID = ONE / EPS
00135          ELSE
00136             RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
00137          END IF
00138    10 CONTINUE
00139 *
00140       RETURN
00141 *
00142 *     End of SGET02
00143 *
00144       END
```