LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cla_gbrcond_c.f
Go to the documentation of this file.
00001 *> \brief \b CLA_GBRCOND_C
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLA_GBRCOND_C + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_gbrcond_c.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cla_gbrcond_c.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_gbrcond_c.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL FUNCTION CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB,
00022 *                                    LDAFB, IPIV, C, CAPPLY, INFO, WORK,
00023 *                                    RWORK )
00024 * 
00025 *       .. Scalar Arguments ..
00026 *       CHARACTER          TRANS
00027 *       LOGICAL            CAPPLY
00028 *       INTEGER            N, KL, KU, KD, KE, LDAB, LDAFB, INFO
00029 *       ..
00030 *       .. Array Arguments ..
00031 *       INTEGER            IPIV( * )
00032 *       COMPLEX            AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
00033 *       REAL               C( * ), RWORK( * )
00034 *       ..
00035 *  
00036 *
00037 *> \par Purpose:
00038 *  =============
00039 *>
00040 *> \verbatim
00041 *>
00042 *>    CLA_GBRCOND_C Computes the infinity norm condition number of
00043 *>    op(A) * inv(diag(C)) where C is a REAL vector.
00044 *> \endverbatim
00045 *
00046 *  Arguments:
00047 *  ==========
00048 *
00049 *> \param[in] TRANS
00050 *> \verbatim
00051 *>          TRANS is CHARACTER*1
00052 *>     Specifies the form of the system of equations:
00053 *>       = 'N':  A * X = B     (No transpose)
00054 *>       = 'T':  A**T * X = B  (Transpose)
00055 *>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
00056 *> \endverbatim
00057 *>
00058 *> \param[in] N
00059 *> \verbatim
00060 *>          N is INTEGER
00061 *>     The number of linear equations, i.e., the order of the
00062 *>     matrix A.  N >= 0.
00063 *> \endverbatim
00064 *>
00065 *> \param[in] KL
00066 *> \verbatim
00067 *>          KL is INTEGER
00068 *>     The number of subdiagonals within the band of A.  KL >= 0.
00069 *> \endverbatim
00070 *>
00071 *> \param[in] KU
00072 *> \verbatim
00073 *>          KU is INTEGER
00074 *>     The number of superdiagonals within the band of A.  KU >= 0.
00075 *> \endverbatim
00076 *>
00077 *> \param[in] AB
00078 *> \verbatim
00079 *>          AB is COMPLEX array, dimension (LDAB,N)
00080 *>     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
00081 *>     The j-th column of A is stored in the j-th column of the
00082 *>     array AB as follows:
00083 *>     AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
00084 *> \endverbatim
00085 *>
00086 *> \param[in] LDAB
00087 *> \verbatim
00088 *>          LDAB is INTEGER
00089 *>     The leading dimension of the array AB.  LDAB >= KL+KU+1.
00090 *> \endverbatim
00091 *>
00092 *> \param[in] AFB
00093 *> \verbatim
00094 *>          AFB is COMPLEX array, dimension (LDAFB,N)
00095 *>     Details of the LU factorization of the band matrix A, as
00096 *>     computed by CGBTRF.  U is stored as an upper triangular
00097 *>     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
00098 *>     and the multipliers used during the factorization are stored
00099 *>     in rows KL+KU+2 to 2*KL+KU+1.
00100 *> \endverbatim
00101 *>
00102 *> \param[in] LDAFB
00103 *> \verbatim
00104 *>          LDAFB is INTEGER
00105 *>     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
00106 *> \endverbatim
00107 *>
00108 *> \param[in] IPIV
00109 *> \verbatim
00110 *>          IPIV is INTEGER array, dimension (N)
00111 *>     The pivot indices from the factorization A = P*L*U
00112 *>     as computed by CGBTRF; row i of the matrix was interchanged
00113 *>     with row IPIV(i).
00114 *> \endverbatim
00115 *>
00116 *> \param[in] C
00117 *> \verbatim
00118 *>          C is REAL array, dimension (N)
00119 *>     The vector C in the formula op(A) * inv(diag(C)).
00120 *> \endverbatim
00121 *>
00122 *> \param[in] CAPPLY
00123 *> \verbatim
00124 *>          CAPPLY is LOGICAL
00125 *>     If .TRUE. then access the vector C in the formula above.
00126 *> \endverbatim
00127 *>
00128 *> \param[out] INFO
00129 *> \verbatim
00130 *>          INFO is INTEGER
00131 *>       = 0:  Successful exit.
00132 *>     i > 0:  The ith argument is invalid.
00133 *> \endverbatim
00134 *>
00135 *> \param[in] WORK
00136 *> \verbatim
00137 *>          WORK is COMPLEX array, dimension (2*N).
00138 *>     Workspace.
00139 *> \endverbatim
00140 *>
00141 *> \param[in] RWORK
00142 *> \verbatim
00143 *>          RWORK is REAL array, dimension (N).
00144 *>     Workspace.
00145 *> \endverbatim
00146 *
00147 *  Authors:
00148 *  ========
00149 *
00150 *> \author Univ. of Tennessee 
00151 *> \author Univ. of California Berkeley 
00152 *> \author Univ. of Colorado Denver 
00153 *> \author NAG Ltd. 
00154 *
00155 *> \date November 2011
00156 *
00157 *> \ingroup complexGBcomputational
00158 *
00159 *  =====================================================================
00160       REAL FUNCTION CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB,
00161      $                             LDAFB, IPIV, C, CAPPLY, INFO, WORK,
00162      $                             RWORK )
00163 *
00164 *  -- LAPACK computational routine (version 3.4.0) --
00165 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00166 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00167 *     November 2011
00168 *
00169 *     .. Scalar Arguments ..
00170       CHARACTER          TRANS
00171       LOGICAL            CAPPLY
00172       INTEGER            N, KL, KU, KD, KE, LDAB, LDAFB, INFO
00173 *     ..
00174 *     .. Array Arguments ..
00175       INTEGER            IPIV( * )
00176       COMPLEX            AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
00177       REAL               C( * ), RWORK( * )
00178 *     ..
00179 *
00180 *  =====================================================================
00181 *
00182 *     .. Local Scalars ..
00183       LOGICAL            NOTRANS
00184       INTEGER            KASE, I, J
00185       REAL               AINVNM, ANORM, TMP
00186       COMPLEX            ZDUM
00187 *     ..
00188 *     .. Local Arrays ..
00189       INTEGER            ISAVE( 3 )
00190 *     ..
00191 *     .. External Functions ..
00192       LOGICAL            LSAME
00193       EXTERNAL           LSAME
00194 *     ..
00195 *     .. External Subroutines ..
00196       EXTERNAL           CLACN2, CGBTRS, XERBLA
00197 *     ..
00198 *     .. Intrinsic Functions ..
00199       INTRINSIC          ABS, MAX
00200 *     ..
00201 *     .. Statement Functions ..
00202       REAL               CABS1
00203 *     ..
00204 *     .. Statement Function Definitions ..
00205       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00206 *     ..
00207 *     .. Executable Statements ..
00208       CLA_GBRCOND_C = 0.0E+0
00209 *
00210       INFO = 0
00211       NOTRANS = LSAME( TRANS, 'N' )
00212       IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
00213      $     LSAME( TRANS, 'C' ) ) THEN
00214          INFO = -1
00215       ELSE IF( N.LT.0 ) THEN
00216          INFO = -2
00217       ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN
00218          INFO = -3
00219       ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
00220          INFO = -4
00221       ELSE IF( LDAB.LT.KL+KU+1 ) THEN
00222          INFO = -6
00223       ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
00224          INFO = -8
00225       END IF
00226       IF( INFO.NE.0 ) THEN
00227          CALL XERBLA( 'CLA_GBRCOND_C', -INFO )
00228          RETURN
00229       END IF
00230 *
00231 *     Compute norm of op(A)*op2(C).
00232 *
00233       ANORM = 0.0E+0
00234       KD = KU + 1
00235       KE = KL + 1
00236       IF ( NOTRANS ) THEN
00237          DO I = 1, N
00238             TMP = 0.0E+0
00239             IF ( CAPPLY ) THEN
00240                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00241                   TMP = TMP + CABS1( AB( KD+I-J, J ) ) / C( J )
00242                END DO
00243             ELSE
00244                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00245                   TMP = TMP + CABS1( AB( KD+I-J, J ) )
00246                END DO
00247             END IF
00248             RWORK( I ) = TMP
00249             ANORM = MAX( ANORM, TMP )
00250          END DO
00251       ELSE
00252          DO I = 1, N
00253             TMP = 0.0E+0
00254             IF ( CAPPLY ) THEN
00255                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00256                   TMP = TMP + CABS1( AB( KE-I+J, I ) ) / C( J )
00257                END DO
00258             ELSE
00259                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00260                   TMP = TMP + CABS1( AB( KE-I+J, I ) )
00261                END DO
00262             END IF
00263             RWORK( I ) = TMP
00264             ANORM = MAX( ANORM, TMP )
00265          END DO
00266       END IF
00267 *
00268 *     Quick return if possible.
00269 *
00270       IF( N.EQ.0 ) THEN
00271          CLA_GBRCOND_C = 1.0E+0
00272          RETURN
00273       ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
00274          RETURN
00275       END IF
00276 *
00277 *     Estimate the norm of inv(op(A)).
00278 *
00279       AINVNM = 0.0E+0
00280 *
00281       KASE = 0
00282    10 CONTINUE
00283       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00284       IF( KASE.NE.0 ) THEN
00285          IF( KASE.EQ.2 ) THEN
00286 *
00287 *           Multiply by R.
00288 *
00289             DO I = 1, N
00290                WORK( I ) = WORK( I ) * RWORK( I )
00291             END DO
00292 *
00293             IF ( NOTRANS ) THEN
00294                CALL CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
00295      $              IPIV, WORK, N, INFO )
00296             ELSE
00297                CALL CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
00298      $              LDAFB, IPIV, WORK, N, INFO )
00299             ENDIF
00300 *
00301 *           Multiply by inv(C).
00302 *
00303             IF ( CAPPLY ) THEN
00304                DO I = 1, N
00305                   WORK( I ) = WORK( I ) * C( I )
00306                END DO
00307             END IF
00308          ELSE
00309 *
00310 *           Multiply by inv(C**H).
00311 *
00312             IF ( CAPPLY ) THEN
00313                DO I = 1, N
00314                   WORK( I ) = WORK( I ) * C( I )
00315                END DO
00316             END IF
00317 *
00318             IF ( NOTRANS ) THEN
00319                CALL CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
00320      $              LDAFB, IPIV,  WORK, N, INFO )
00321             ELSE
00322                CALL CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
00323      $              IPIV, WORK, N, INFO )
00324             END IF
00325 *
00326 *           Multiply by R.
00327 *
00328             DO I = 1, N
00329                WORK( I ) = WORK( I ) * RWORK( I )
00330             END DO
00331          END IF
00332          GO TO 10
00333       END IF
00334 *
00335 *     Compute the estimate of the reciprocal condition number.
00336 *
00337       IF( AINVNM .NE. 0.0E+0 )
00338      $   CLA_GBRCOND_C = 1.0E+0 / AINVNM
00339 *
00340       RETURN
00341 *
00342       END
 All Files Functions