LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zla_gbrcond_c.f
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00001 *> \brief \b ZLA_GBRCOND_C
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
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00009 *> Download ZLA_GBRCOND_C + dependencies 
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00011 *> [TGZ]</a> 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       DOUBLE PRECISION FUNCTION ZLA_GBRCOND_C( TRANS, N, KL, KU, AB, 
00022 *                                                LDAB, AFB, LDAFB, IPIV,
00023 *                                                C, CAPPLY, INFO, WORK,
00024 *                                                RWORK )
00025 * 
00026 *       .. Scalar Arguments ..
00027 *       CHARACTER          TRANS
00028 *       LOGICAL            CAPPLY
00029 *       INTEGER            N, KL, KU, KD, KE, LDAB, LDAFB, INFO
00030 *       ..
00031 *       .. Array Arguments ..
00032 *       INTEGER            IPIV( * )
00033 *       COMPLEX*16         AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
00034 *       DOUBLE PRECISION   C( * ), RWORK( * )
00035 *  
00036 *  
00037 *
00038 *> \par Purpose:
00039 *  =============
00040 *>
00041 *> \verbatim
00042 *>
00043 *>    ZLA_GBRCOND_C Computes the infinity norm condition number of
00044 *>    op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
00045 *> \endverbatim
00046 *
00047 *  Arguments:
00048 *  ==========
00049 *
00050 *> \param[in] TRANS
00051 *> \verbatim
00052 *>          TRANS is CHARACTER*1
00053 *>     Specifies the form of the system of equations:
00054 *>       = 'N':  A * X = B     (No transpose)
00055 *>       = 'T':  A**T * X = B  (Transpose)
00056 *>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
00057 *> \endverbatim
00058 *>
00059 *> \param[in] N
00060 *> \verbatim
00061 *>          N is INTEGER
00062 *>     The number of linear equations, i.e., the order of the
00063 *>     matrix A.  N >= 0.
00064 *> \endverbatim
00065 *>
00066 *> \param[in] KL
00067 *> \verbatim
00068 *>          KL is INTEGER
00069 *>     The number of subdiagonals within the band of A.  KL >= 0.
00070 *> \endverbatim
00071 *>
00072 *> \param[in] KU
00073 *> \verbatim
00074 *>          KU is INTEGER
00075 *>     The number of superdiagonals within the band of A.  KU >= 0.
00076 *> \endverbatim
00077 *>
00078 *> \param[in] AB
00079 *> \verbatim
00080 *>          AB is COMPLEX*16 array, dimension (LDAB,N)
00081 *>     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
00082 *>     The j-th column of A is stored in the j-th column of the
00083 *>     array AB as follows:
00084 *>     AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
00085 *> \endverbatim
00086 *>
00087 *> \param[in] LDAB
00088 *> \verbatim
00089 *>          LDAB is INTEGER
00090 *>     The leading dimension of the array AB.  LDAB >= KL+KU+1.
00091 *> \endverbatim
00092 *>
00093 *> \param[in] AFB
00094 *> \verbatim
00095 *>          AFB is COMPLEX*16 array, dimension (LDAFB,N)
00096 *>     Details of the LU factorization of the band matrix A, as
00097 *>     computed by ZGBTRF.  U is stored as an upper triangular
00098 *>     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
00099 *>     and the multipliers used during the factorization are stored
00100 *>     in rows KL+KU+2 to 2*KL+KU+1.
00101 *> \endverbatim
00102 *>
00103 *> \param[in] LDAFB
00104 *> \verbatim
00105 *>          LDAFB is INTEGER
00106 *>     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
00107 *> \endverbatim
00108 *>
00109 *> \param[in] IPIV
00110 *> \verbatim
00111 *>          IPIV is INTEGER array, dimension (N)
00112 *>     The pivot indices from the factorization A = P*L*U
00113 *>     as computed by ZGBTRF; row i of the matrix was interchanged
00114 *>     with row IPIV(i).
00115 *> \endverbatim
00116 *>
00117 *> \param[in] C
00118 *> \verbatim
00119 *>          C is DOUBLE PRECISION array, dimension (N)
00120 *>     The vector C in the formula op(A) * inv(diag(C)).
00121 *> \endverbatim
00122 *>
00123 *> \param[in] CAPPLY
00124 *> \verbatim
00125 *>          CAPPLY is LOGICAL
00126 *>     If .TRUE. then access the vector C in the formula above.
00127 *> \endverbatim
00128 *>
00129 *> \param[out] INFO
00130 *> \verbatim
00131 *>          INFO is INTEGER
00132 *>       = 0:  Successful exit.
00133 *>     i > 0:  The ith argument is invalid.
00134 *> \endverbatim
00135 *>
00136 *> \param[in] WORK
00137 *> \verbatim
00138 *>          WORK is COMPLEX*16 array, dimension (2*N).
00139 *>     Workspace.
00140 *> \endverbatim
00141 *>
00142 *> \param[in] RWORK
00143 *> \verbatim
00144 *>          RWORK is DOUBLE PRECISION array, dimension (N).
00145 *>     Workspace.
00146 *> \endverbatim
00147 *
00148 *  Authors:
00149 *  ========
00150 *
00151 *> \author Univ. of Tennessee 
00152 *> \author Univ. of California Berkeley 
00153 *> \author Univ. of Colorado Denver 
00154 *> \author NAG Ltd. 
00155 *
00156 *> \date November 2011
00157 *
00158 *> \ingroup complex16GBcomputational
00159 *
00160 *  =====================================================================
00161       DOUBLE PRECISION FUNCTION ZLA_GBRCOND_C( TRANS, N, KL, KU, AB, 
00162      $                                         LDAB, AFB, LDAFB, IPIV,
00163      $                                         C, CAPPLY, INFO, WORK,
00164      $                                         RWORK )
00165 *
00166 *  -- LAPACK computational routine (version 3.4.0) --
00167 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00168 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00169 *     November 2011
00170 *
00171 *     .. Scalar Arguments ..
00172       CHARACTER          TRANS
00173       LOGICAL            CAPPLY
00174       INTEGER            N, KL, KU, KD, KE, LDAB, LDAFB, INFO
00175 *     ..
00176 *     .. Array Arguments ..
00177       INTEGER            IPIV( * )
00178       COMPLEX*16         AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
00179       DOUBLE PRECISION   C( * ), RWORK( * )
00180 *
00181 *
00182 *  =====================================================================
00183 *
00184 *     .. Local Scalars ..
00185       LOGICAL            NOTRANS
00186       INTEGER            KASE, I, J
00187       DOUBLE PRECISION   AINVNM, ANORM, TMP
00188       COMPLEX*16         ZDUM
00189 *     ..
00190 *     .. Local Arrays ..
00191       INTEGER            ISAVE( 3 )
00192 *     ..
00193 *     .. External Functions ..
00194       LOGICAL            LSAME
00195       EXTERNAL           LSAME
00196 *     ..
00197 *     .. External Subroutines ..
00198       EXTERNAL           ZLACN2, ZGBTRS, XERBLA
00199 *     ..
00200 *     .. Intrinsic Functions ..
00201       INTRINSIC          ABS, MAX
00202 *     ..
00203 *     .. Statement Functions ..
00204       DOUBLE PRECISION   CABS1
00205 *     ..
00206 *     .. Statement Function Definitions ..
00207       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00208 *     ..
00209 *     .. Executable Statements ..
00210       ZLA_GBRCOND_C = 0.0D+0
00211 *
00212       INFO = 0
00213       NOTRANS = LSAME( TRANS, 'N' )
00214       IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
00215      $     LSAME( TRANS, 'C' ) ) THEN
00216          INFO = -1
00217       ELSE IF( N.LT.0 ) THEN
00218          INFO = -2
00219       ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN
00220          INFO = -3
00221       ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
00222          INFO = -4
00223       ELSE IF( LDAB.LT.KL+KU+1 ) THEN
00224          INFO = -6
00225       ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
00226          INFO = -8
00227       END IF
00228       IF( INFO.NE.0 ) THEN
00229          CALL XERBLA( 'ZLA_GBRCOND_C', -INFO )
00230          RETURN
00231       END IF
00232 *
00233 *     Compute norm of op(A)*op2(C).
00234 *
00235       ANORM = 0.0D+0
00236       KD = KU + 1
00237       KE = KL + 1
00238       IF ( NOTRANS ) THEN
00239          DO I = 1, N
00240             TMP = 0.0D+0
00241             IF ( CAPPLY ) THEN
00242                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00243                   TMP = TMP + CABS1( AB( KD+I-J, J ) ) / C( J )
00244                END DO
00245             ELSE
00246                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00247                   TMP = TMP + CABS1( AB( KD+I-J, J ) )
00248                END DO
00249             END IF
00250             RWORK( I ) = TMP
00251             ANORM = MAX( ANORM, TMP )
00252          END DO
00253       ELSE
00254          DO I = 1, N
00255             TMP = 0.0D+0
00256             IF ( CAPPLY ) THEN
00257                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00258                   TMP = TMP + CABS1( AB( KE-I+J, I ) ) / C( J )
00259                END DO
00260             ELSE
00261                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00262                   TMP = TMP + CABS1( AB( KE-I+J, I ) )
00263                END DO
00264             END IF
00265             RWORK( I ) = TMP
00266             ANORM = MAX( ANORM, TMP )
00267          END DO
00268       END IF
00269 *
00270 *     Quick return if possible.
00271 *
00272       IF( N.EQ.0 ) THEN
00273          ZLA_GBRCOND_C = 1.0D+0
00274          RETURN
00275       ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
00276          RETURN
00277       END IF
00278 *
00279 *     Estimate the norm of inv(op(A)).
00280 *
00281       AINVNM = 0.0D+0
00282 *
00283       KASE = 0
00284    10 CONTINUE
00285       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00286       IF( KASE.NE.0 ) THEN
00287          IF( KASE.EQ.2 ) THEN
00288 *
00289 *           Multiply by R.
00290 *
00291             DO I = 1, N
00292                WORK( I ) = WORK( I ) * RWORK( I )
00293             END DO
00294 *
00295             IF ( NOTRANS ) THEN
00296                CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
00297      $              IPIV, WORK, N, INFO )
00298             ELSE
00299                CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
00300      $              LDAFB, IPIV, WORK, N, INFO )
00301             ENDIF
00302 *
00303 *           Multiply by inv(C).
00304 *
00305             IF ( CAPPLY ) THEN
00306                DO I = 1, N
00307                   WORK( I ) = WORK( I ) * C( I )
00308                END DO
00309             END IF
00310          ELSE
00311 *
00312 *           Multiply by inv(C**H).
00313 *
00314             IF ( CAPPLY ) THEN
00315                DO I = 1, N
00316                   WORK( I ) = WORK( I ) * C( I )
00317                END DO
00318             END IF
00319 *
00320             IF ( NOTRANS ) THEN
00321                CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
00322      $              LDAFB, IPIV,  WORK, N, INFO )
00323             ELSE
00324                CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
00325      $              IPIV, WORK, N, INFO )
00326             END IF
00327 *
00328 *           Multiply by R.
00329 *
00330             DO I = 1, N
00331                WORK( I ) = WORK( I ) * RWORK( I )
00332             END DO
00333          END IF
00334          GO TO 10
00335       END IF
00336 *
00337 *     Compute the estimate of the reciprocal condition number.
00338 *
00339       IF( AINVNM .NE. 0.0D+0 )
00340      $   ZLA_GBRCOND_C = 1.0D+0 / AINVNM
00341 *
00342       RETURN
00343 *
00344       END
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