LAPACK 3.3.1 Linear Algebra PACKage

# zgbsvx.f

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```00001       SUBROUTINE ZGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
00002      \$                   LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
00003      \$                   RCOND, FERR, BERR, WORK, RWORK, INFO )
00004 *
00005 *  -- LAPACK driver routine (version 3.2) --
00006 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00007 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00008 *     November 2006
00009 *
00010 *     .. Scalar Arguments ..
00011       CHARACTER          EQUED, FACT, TRANS
00012       INTEGER            INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
00013       DOUBLE PRECISION   RCOND
00014 *     ..
00015 *     .. Array Arguments ..
00016       INTEGER            IPIV( * )
00017       DOUBLE PRECISION   BERR( * ), C( * ), FERR( * ), R( * ),
00018      \$                   RWORK( * )
00019       COMPLEX*16         AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ),
00020      \$                   WORK( * ), X( LDX, * )
00021 *     ..
00022 *
00023 *  Purpose
00024 *  =======
00025 *
00026 *  ZGBSVX uses the LU factorization to compute the solution to a complex
00027 *  system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
00028 *  where A is a band matrix of order N with KL subdiagonals and KU
00029 *  superdiagonals, and X and B are N-by-NRHS matrices.
00030 *
00031 *  Error bounds on the solution and a condition estimate are also
00032 *  provided.
00033 *
00034 *  Description
00035 *  ===========
00036 *
00037 *  The following steps are performed by this subroutine:
00038 *
00039 *  1. If FACT = 'E', real scaling factors are computed to equilibrate
00040 *     the system:
00041 *        TRANS = 'N':  diag(R)*A*diag(C)     *inv(diag(C))*X = diag(R)*B
00042 *        TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
00043 *        TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
00044 *     Whether or not the system will be equilibrated depends on the
00045 *     scaling of the matrix A, but if equilibration is used, A is
00046 *     overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
00047 *     or diag(C)*B (if TRANS = 'T' or 'C').
00048 *
00049 *  2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
00050 *     matrix A (after equilibration if FACT = 'E') as
00051 *        A = L * U,
00052 *     where L is a product of permutation and unit lower triangular
00053 *     matrices with KL subdiagonals, and U is upper triangular with
00054 *     KL+KU superdiagonals.
00055 *
00056 *  3. If some U(i,i)=0, so that U is exactly singular, then the routine
00057 *     returns with INFO = i. Otherwise, the factored form of A is used
00058 *     to estimate the condition number of the matrix A.  If the
00059 *     reciprocal of the condition number is less than machine precision,
00060 *     INFO = N+1 is returned as a warning, but the routine still goes on
00061 *     to solve for X and compute error bounds as described below.
00062 *
00063 *  4. The system of equations is solved for X using the factored form
00064 *     of A.
00065 *
00066 *  5. Iterative refinement is applied to improve the computed solution
00067 *     matrix and calculate error bounds and backward error estimates
00068 *     for it.
00069 *
00070 *  6. If equilibration was used, the matrix X is premultiplied by
00071 *     diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
00072 *     that it solves the original system before equilibration.
00073 *
00074 *  Arguments
00075 *  =========
00076 *
00077 *  FACT    (input) CHARACTER*1
00078 *          Specifies whether or not the factored form of the matrix A is
00079 *          supplied on entry, and if not, whether the matrix A should be
00080 *          equilibrated before it is factored.
00081 *          = 'F':  On entry, AFB and IPIV contain the factored form of
00082 *                  A.  If EQUED is not 'N', the matrix A has been
00083 *                  equilibrated with scaling factors given by R and C.
00084 *                  AB, AFB, and IPIV are not modified.
00085 *          = 'N':  The matrix A will be copied to AFB and factored.
00086 *          = 'E':  The matrix A will be equilibrated if necessary, then
00087 *                  copied to AFB and factored.
00088 *
00089 *  TRANS   (input) CHARACTER*1
00090 *          Specifies the form of the system of equations.
00091 *          = 'N':  A * X = B     (No transpose)
00092 *          = 'T':  A**T * X = B  (Transpose)
00093 *          = 'C':  A**H * X = B  (Conjugate transpose)
00094 *
00095 *  N       (input) INTEGER
00096 *          The number of linear equations, i.e., the order of the
00097 *          matrix A.  N >= 0.
00098 *
00099 *  KL      (input) INTEGER
00100 *          The number of subdiagonals within the band of A.  KL >= 0.
00101 *
00102 *  KU      (input) INTEGER
00103 *          The number of superdiagonals within the band of A.  KU >= 0.
00104 *
00105 *  NRHS    (input) INTEGER
00106 *          The number of right hand sides, i.e., the number of columns
00107 *          of the matrices B and X.  NRHS >= 0.
00108 *
00109 *  AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
00110 *          On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
00111 *          The j-th column of A is stored in the j-th column of the
00112 *          array AB as follows:
00113 *          AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
00114 *
00115 *          If FACT = 'F' and EQUED is not 'N', then A must have been
00116 *          equilibrated by the scaling factors in R and/or C.  AB is not
00117 *          modified if FACT = 'F' or 'N', or if FACT = 'E' and
00118 *          EQUED = 'N' on exit.
00119 *
00120 *          On exit, if EQUED .ne. 'N', A is scaled as follows:
00121 *          EQUED = 'R':  A := diag(R) * A
00122 *          EQUED = 'C':  A := A * diag(C)
00123 *          EQUED = 'B':  A := diag(R) * A * diag(C).
00124 *
00125 *  LDAB    (input) INTEGER
00126 *          The leading dimension of the array AB.  LDAB >= KL+KU+1.
00127 *
00128 *  AFB     (input or output) COMPLEX*16 array, dimension (LDAFB,N)
00129 *          If FACT = 'F', then AFB is an input argument and on entry
00130 *          contains details of the LU factorization of the band matrix
00131 *          A, as computed by ZGBTRF.  U is stored as an upper triangular
00132 *          band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
00133 *          and the multipliers used during the factorization are stored
00134 *          in rows KL+KU+2 to 2*KL+KU+1.  If EQUED .ne. 'N', then AFB is
00135 *          the factored form of the equilibrated matrix A.
00136 *
00137 *          If FACT = 'N', then AFB is an output argument and on exit
00138 *          returns details of the LU factorization of A.
00139 *
00140 *          If FACT = 'E', then AFB is an output argument and on exit
00141 *          returns details of the LU factorization of the equilibrated
00142 *          matrix A (see the description of AB for the form of the
00143 *          equilibrated matrix).
00144 *
00145 *  LDAFB   (input) INTEGER
00146 *          The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
00147 *
00148 *  IPIV    (input or output) INTEGER array, dimension (N)
00149 *          If FACT = 'F', then IPIV is an input argument and on entry
00150 *          contains the pivot indices from the factorization A = L*U
00151 *          as computed by ZGBTRF; row i of the matrix was interchanged
00152 *          with row IPIV(i).
00153 *
00154 *          If FACT = 'N', then IPIV is an output argument and on exit
00155 *          contains the pivot indices from the factorization A = L*U
00156 *          of the original matrix A.
00157 *
00158 *          If FACT = 'E', then IPIV is an output argument and on exit
00159 *          contains the pivot indices from the factorization A = L*U
00160 *          of the equilibrated matrix A.
00161 *
00162 *  EQUED   (input or output) CHARACTER*1
00163 *          Specifies the form of equilibration that was done.
00164 *          = 'N':  No equilibration (always true if FACT = 'N').
00165 *          = 'R':  Row equilibration, i.e., A has been premultiplied by
00166 *                  diag(R).
00167 *          = 'C':  Column equilibration, i.e., A has been postmultiplied
00168 *                  by diag(C).
00169 *          = 'B':  Both row and column equilibration, i.e., A has been
00170 *                  replaced by diag(R) * A * diag(C).
00171 *          EQUED is an input argument if FACT = 'F'; otherwise, it is an
00172 *          output argument.
00173 *
00174 *  R       (input or output) DOUBLE PRECISION array, dimension (N)
00175 *          The row scale factors for A.  If EQUED = 'R' or 'B', A is
00176 *          multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
00177 *          is not accessed.  R is an input argument if FACT = 'F';
00178 *          otherwise, R is an output argument.  If FACT = 'F' and
00179 *          EQUED = 'R' or 'B', each element of R must be positive.
00180 *
00181 *  C       (input or output) DOUBLE PRECISION array, dimension (N)
00182 *          The column scale factors for A.  If EQUED = 'C' or 'B', A is
00183 *          multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
00184 *          is not accessed.  C is an input argument if FACT = 'F';
00185 *          otherwise, C is an output argument.  If FACT = 'F' and
00186 *          EQUED = 'C' or 'B', each element of C must be positive.
00187 *
00188 *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
00189 *          On entry, the right hand side matrix B.
00190 *          On exit,
00191 *          if EQUED = 'N', B is not modified;
00192 *          if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by
00193 *          diag(R)*B;
00194 *          if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is
00195 *          overwritten by diag(C)*B.
00196 *
00197 *  LDB     (input) INTEGER
00198 *          The leading dimension of the array B.  LDB >= max(1,N).
00199 *
00200 *  X       (output) COMPLEX*16 array, dimension (LDX,NRHS)
00201 *          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X
00202 *          to the original system of equations.  Note that A and B are
00203 *          modified on exit if EQUED .ne. 'N', and the solution to the
00204 *          equilibrated system is inv(diag(C))*X if TRANS = 'N' and
00205 *          EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C'
00206 *          and EQUED = 'R' or 'B'.
00207 *
00208 *  LDX     (input) INTEGER
00209 *          The leading dimension of the array X.  LDX >= max(1,N).
00210 *
00211 *  RCOND   (output) DOUBLE PRECISION
00212 *          The estimate of the reciprocal condition number of the matrix
00213 *          A after equilibration (if done).  If RCOND is less than the
00214 *          machine precision (in particular, if RCOND = 0), the matrix
00215 *          is singular to working precision.  This condition is
00216 *          indicated by a return code of INFO > 0.
00217 *
00218 *  FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
00219 *          The estimated forward error bound for each solution vector
00220 *          X(j) (the j-th column of the solution matrix X).
00221 *          If XTRUE is the true solution corresponding to X(j), FERR(j)
00222 *          is an estimated upper bound for the magnitude of the largest
00223 *          element in (X(j) - XTRUE) divided by the magnitude of the
00224 *          largest element in X(j).  The estimate is as reliable as
00225 *          the estimate for RCOND, and is almost always a slight
00226 *          overestimate of the true error.
00227 *
00228 *  BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
00229 *          The componentwise relative backward error of each solution
00230 *          vector X(j) (i.e., the smallest relative change in
00231 *          any element of A or B that makes X(j) an exact solution).
00232 *
00233 *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)
00234 *
00235 *  RWORK   (workspace/output) DOUBLE PRECISION array, dimension (N)
00236 *          On exit, RWORK(1) contains the reciprocal pivot growth
00237 *          factor norm(A)/norm(U). The "max absolute element" norm is
00238 *          used. If RWORK(1) is much less than 1, then the stability
00239 *          of the LU factorization of the (equilibrated) matrix A
00240 *          could be poor. This also means that the solution X, condition
00241 *          estimator RCOND, and forward error bound FERR could be
00242 *          unreliable. If factorization fails with 0<INFO<=N, then
00243 *          RWORK(1) contains the reciprocal pivot growth factor for the
00244 *          leading INFO columns of A.
00245 *
00246 *  INFO    (output) INTEGER
00247 *          = 0:  successful exit
00248 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00249 *          > 0:  if INFO = i, and i is
00250 *                <= N:  U(i,i) is exactly zero.  The factorization
00251 *                       has been completed, but the factor U is exactly
00252 *                       singular, so the solution and error bounds
00253 *                       could not be computed. RCOND = 0 is returned.
00254 *                = N+1: U is nonsingular, but RCOND is less than machine
00255 *                       precision, meaning that the matrix is singular
00256 *                       to working precision.  Nevertheless, the
00257 *                       solution and error bounds are computed because
00258 *                       there are a number of situations where the
00259 *                       computed solution can be more accurate than the
00260 *                       value of RCOND would suggest.
00261 *
00262 *  =====================================================================
00263 *  Moved setting of INFO = N+1 so INFO does not subsequently get
00264 *  overwritten.  Sven, 17 Mar 05.
00265 *  =====================================================================
00266 *
00267 *     .. Parameters ..
00268       DOUBLE PRECISION   ZERO, ONE
00269       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00270 *     ..
00271 *     .. Local Scalars ..
00272       LOGICAL            COLEQU, EQUIL, NOFACT, NOTRAN, ROWEQU
00273       CHARACTER          NORM
00274       INTEGER            I, INFEQU, J, J1, J2
00275       DOUBLE PRECISION   AMAX, ANORM, BIGNUM, COLCND, RCMAX, RCMIN,
00276      \$                   ROWCND, RPVGRW, SMLNUM
00277 *     ..
00278 *     .. External Functions ..
00279       LOGICAL            LSAME
00280       DOUBLE PRECISION   DLAMCH, ZLANGB, ZLANTB
00281       EXTERNAL           LSAME, DLAMCH, ZLANGB, ZLANTB
00282 *     ..
00283 *     .. External Subroutines ..
00284       EXTERNAL           XERBLA, ZCOPY, ZGBCON, ZGBEQU, ZGBRFS, ZGBTRF,
00285      \$                   ZGBTRS, ZLACPY, ZLAQGB
00286 *     ..
00287 *     .. Intrinsic Functions ..
00288       INTRINSIC          ABS, MAX, MIN
00289 *     ..
00290 *     .. Executable Statements ..
00291 *
00292       INFO = 0
00293       NOFACT = LSAME( FACT, 'N' )
00294       EQUIL = LSAME( FACT, 'E' )
00295       NOTRAN = LSAME( TRANS, 'N' )
00296       IF( NOFACT .OR. EQUIL ) THEN
00297          EQUED = 'N'
00298          ROWEQU = .FALSE.
00299          COLEQU = .FALSE.
00300       ELSE
00301          ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' )
00302          COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' )
00303          SMLNUM = DLAMCH( 'Safe minimum' )
00304          BIGNUM = ONE / SMLNUM
00305       END IF
00306 *
00307 *     Test the input parameters.
00308 *
00309       IF( .NOT.NOFACT .AND. .NOT.EQUIL .AND. .NOT.LSAME( FACT, 'F' ) )
00310      \$     THEN
00311          INFO = -1
00312       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
00313      \$         LSAME( TRANS, 'C' ) ) THEN
00314          INFO = -2
00315       ELSE IF( N.LT.0 ) THEN
00316          INFO = -3
00317       ELSE IF( KL.LT.0 ) THEN
00318          INFO = -4
00319       ELSE IF( KU.LT.0 ) THEN
00320          INFO = -5
00321       ELSE IF( NRHS.LT.0 ) THEN
00322          INFO = -6
00323       ELSE IF( LDAB.LT.KL+KU+1 ) THEN
00324          INFO = -8
00325       ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
00326          INFO = -10
00327       ELSE IF( LSAME( FACT, 'F' ) .AND. .NOT.
00328      \$         ( ROWEQU .OR. COLEQU .OR. LSAME( EQUED, 'N' ) ) ) THEN
00329          INFO = -12
00330       ELSE
00331          IF( ROWEQU ) THEN
00332             RCMIN = BIGNUM
00333             RCMAX = ZERO
00334             DO 10 J = 1, N
00335                RCMIN = MIN( RCMIN, R( J ) )
00336                RCMAX = MAX( RCMAX, R( J ) )
00337    10       CONTINUE
00338             IF( RCMIN.LE.ZERO ) THEN
00339                INFO = -13
00340             ELSE IF( N.GT.0 ) THEN
00341                ROWCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
00342             ELSE
00343                ROWCND = ONE
00344             END IF
00345          END IF
00346          IF( COLEQU .AND. INFO.EQ.0 ) THEN
00347             RCMIN = BIGNUM
00348             RCMAX = ZERO
00349             DO 20 J = 1, N
00350                RCMIN = MIN( RCMIN, C( J ) )
00351                RCMAX = MAX( RCMAX, C( J ) )
00352    20       CONTINUE
00353             IF( RCMIN.LE.ZERO ) THEN
00354                INFO = -14
00355             ELSE IF( N.GT.0 ) THEN
00356                COLCND = MAX( RCMIN, SMLNUM ) / MIN( RCMAX, BIGNUM )
00357             ELSE
00358                COLCND = ONE
00359             END IF
00360          END IF
00361          IF( INFO.EQ.0 ) THEN
00362             IF( LDB.LT.MAX( 1, N ) ) THEN
00363                INFO = -16
00364             ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
00365                INFO = -18
00366             END IF
00367          END IF
00368       END IF
00369 *
00370       IF( INFO.NE.0 ) THEN
00371          CALL XERBLA( 'ZGBSVX', -INFO )
00372          RETURN
00373       END IF
00374 *
00375       IF( EQUIL ) THEN
00376 *
00377 *        Compute row and column scalings to equilibrate the matrix A.
00378 *
00379          CALL ZGBEQU( N, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
00380      \$                AMAX, INFEQU )
00381          IF( INFEQU.EQ.0 ) THEN
00382 *
00383 *           Equilibrate the matrix.
00384 *
00385             CALL ZLAQGB( N, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
00386      \$                   AMAX, EQUED )
00387             ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' )
00388             COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' )
00389          END IF
00390       END IF
00391 *
00392 *     Scale the right hand side.
00393 *
00394       IF( NOTRAN ) THEN
00395          IF( ROWEQU ) THEN
00396             DO 40 J = 1, NRHS
00397                DO 30 I = 1, N
00398                   B( I, J ) = R( I )*B( I, J )
00399    30          CONTINUE
00400    40       CONTINUE
00401          END IF
00402       ELSE IF( COLEQU ) THEN
00403          DO 60 J = 1, NRHS
00404             DO 50 I = 1, N
00405                B( I, J ) = C( I )*B( I, J )
00406    50       CONTINUE
00407    60    CONTINUE
00408       END IF
00409 *
00410       IF( NOFACT .OR. EQUIL ) THEN
00411 *
00412 *        Compute the LU factorization of the band matrix A.
00413 *
00414          DO 70 J = 1, N
00415             J1 = MAX( J-KU, 1 )
00416             J2 = MIN( J+KL, N )
00417             CALL ZCOPY( J2-J1+1, AB( KU+1-J+J1, J ), 1,
00418      \$                  AFB( KL+KU+1-J+J1, J ), 1 )
00419    70    CONTINUE
00420 *
00421          CALL ZGBTRF( N, N, KL, KU, AFB, LDAFB, IPIV, INFO )
00422 *
00423 *        Return if INFO is non-zero.
00424 *
00425          IF( INFO.GT.0 ) THEN
00426 *
00427 *           Compute the reciprocal pivot growth factor of the
00428 *           leading rank-deficient INFO columns of A.
00429 *
00430             ANORM = ZERO
00431             DO 90 J = 1, INFO
00432                DO 80 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
00433                   ANORM = MAX( ANORM, ABS( AB( I, J ) ) )
00434    80          CONTINUE
00435    90       CONTINUE
00436             RPVGRW = ZLANTB( 'M', 'U', 'N', INFO, MIN( INFO-1, KL+KU ),
00437      \$                       AFB( MAX( 1, KL+KU+2-INFO ), 1 ), LDAFB,
00438      \$                       RWORK )
00439             IF( RPVGRW.EQ.ZERO ) THEN
00440                RPVGRW = ONE
00441             ELSE
00442                RPVGRW = ANORM / RPVGRW
00443             END IF
00444             RWORK( 1 ) = RPVGRW
00445             RCOND = ZERO
00446             RETURN
00447          END IF
00448       END IF
00449 *
00450 *     Compute the norm of the matrix A and the
00451 *     reciprocal pivot growth factor RPVGRW.
00452 *
00453       IF( NOTRAN ) THEN
00454          NORM = '1'
00455       ELSE
00456          NORM = 'I'
00457       END IF
00458       ANORM = ZLANGB( NORM, N, KL, KU, AB, LDAB, RWORK )
00459       RPVGRW = ZLANTB( 'M', 'U', 'N', N, KL+KU, AFB, LDAFB, RWORK )
00460       IF( RPVGRW.EQ.ZERO ) THEN
00461          RPVGRW = ONE
00462       ELSE
00463          RPVGRW = ZLANGB( 'M', N, KL, KU, AB, LDAB, RWORK ) / RPVGRW
00464       END IF
00465 *
00466 *     Compute the reciprocal of the condition number of A.
00467 *
00468       CALL ZGBCON( NORM, N, KL, KU, AFB, LDAFB, IPIV, ANORM, RCOND,
00469      \$             WORK, RWORK, INFO )
00470 *
00471 *     Compute the solution matrix X.
00472 *
00473       CALL ZLACPY( 'Full', N, NRHS, B, LDB, X, LDX )
00474       CALL ZGBTRS( TRANS, N, KL, KU, NRHS, AFB, LDAFB, IPIV, X, LDX,
00475      \$             INFO )
00476 *
00477 *     Use iterative refinement to improve the computed solution and
00478 *     compute error bounds and backward error estimates for it.
00479 *
00480       CALL ZGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV,
00481      \$             B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
00482 *
00483 *     Transform the solution matrix X to a solution of the original
00484 *     system.
00485 *
00486       IF( NOTRAN ) THEN
00487          IF( COLEQU ) THEN
00488             DO 110 J = 1, NRHS
00489                DO 100 I = 1, N
00490                   X( I, J ) = C( I )*X( I, J )
00491   100          CONTINUE
00492   110       CONTINUE
00493             DO 120 J = 1, NRHS
00494                FERR( J ) = FERR( J ) / COLCND
00495   120       CONTINUE
00496          END IF
00497       ELSE IF( ROWEQU ) THEN
00498          DO 140 J = 1, NRHS
00499             DO 130 I = 1, N
00500                X( I, J ) = R( I )*X( I, J )
00501   130       CONTINUE
00502   140    CONTINUE
00503          DO 150 J = 1, NRHS
00504             FERR( J ) = FERR( J ) / ROWCND
00505   150    CONTINUE
00506       END IF
00507 *
00508 *     Set INFO = N+1 if the matrix is singular to working precision.
00509 *
00510       IF( RCOND.LT.DLAMCH( 'Epsilon' ) )
00511      \$   INFO = N + 1
00512 *
00513       RWORK( 1 ) = RPVGRW
00514       RETURN
00515 *
00516 *     End of ZGBSVX
00517 *
00518       END
```