LAPACK: SRC/cla_gbrcond_c.f Source File

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00001       REAL FUNCTION CLA_GBRCOND_C( TRANS, N, KL, KU, AB, LDAB, AFB,
00002      $                             LDAFB, IPIV, C, CAPPLY, INFO, WORK,
00003      $                             RWORK )
00004 *
00005 *     -- LAPACK routine (version 3.2.1)                               --
00006 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
00007 *     -- Jason Riedy of Univ. of California Berkeley.                 --
00008 *     -- April 2009                                                   --
00009 *
00010 *     -- LAPACK is a software package provided by Univ. of Tennessee, --
00011 *     -- Univ. of California Berkeley and NAG Ltd.                    --
00012 *
00013       IMPLICIT NONE
00014 *     ..
00015 *     .. Scalar Arguments ..
00016       CHARACTER          TRANS
00017       LOGICAL            CAPPLY
00018       INTEGER            N, KL, KU, KD, KE, LDAB, LDAFB, INFO
00019 *     ..
00020 *     .. Array Arguments ..
00021       INTEGER            IPIV( * )
00022       COMPLEX            AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
00023       REAL               C( * ), RWORK( * )
00024 *     ..
00025 *
00026 *  Purpose
00027 *  =======
00028 *
00029 *     CLA_GBRCOND_C Computes the infinity norm condition number of
00030 *     op(A) * inv(diag(C)) where C is a REAL vector.
00031 *
00032 *  Arguments
00033 *  =========
00034 *
00035 *     TRANS   (input) CHARACTER*1
00036 *     Specifies the form of the system of equations:
00037 *       = 'N':  A * X = B     (No transpose)
00038 *       = 'T':  A**T * X = B  (Transpose)
00039 *       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
00040 *
00041 *     N       (input) INTEGER
00042 *     The number of linear equations, i.e., the order of the
00043 *     matrix A.  N >= 0.
00044 *
00045 *     KL      (input) INTEGER
00046 *     The number of subdiagonals within the band of A.  KL >= 0.
00047 *
00048 *     KU      (input) INTEGER
00049 *     The number of superdiagonals within the band of A.  KU >= 0.
00050 *
00051 *     AB      (input) COMPLEX array, dimension (LDAB,N)
00052 *     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
00053 *     The j-th column of A is stored in the j-th column of the
00054 *     array AB as follows:
00055 *     AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
00056 *
00057 *     LDAB    (input) INTEGER
00058 *     The leading dimension of the array AB.  LDAB >= KL+KU+1.
00059 *
00060 *     AFB     (input) COMPLEX array, dimension (LDAFB,N)
00061 *     Details of the LU factorization of the band matrix A, as
00062 *     computed by CGBTRF.  U is stored as an upper triangular
00063 *     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
00064 *     and the multipliers used during the factorization are stored
00065 *     in rows KL+KU+2 to 2*KL+KU+1.
00066 *
00067 *     LDAFB   (input) INTEGER
00068 *     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
00069 *
00070 *     IPIV    (input) INTEGER array, dimension (N)
00071 *     The pivot indices from the factorization A = P*L*U
00072 *     as computed by CGBTRF; row i of the matrix was interchanged
00073 *     with row IPIV(i).
00074 *
00075 *     C       (input) REAL array, dimension (N)
00076 *     The vector C in the formula op(A) * inv(diag(C)).
00077 *
00078 *     CAPPLY  (input) LOGICAL
00079 *     If .TRUE. then access the vector C in the formula above.
00080 *
00081 *     INFO    (output) INTEGER
00082 *       = 0:  Successful exit.
00083 *     i > 0:  The ith argument is invalid.
00084 *
00085 *     WORK    (input) COMPLEX array, dimension (2*N).
00086 *     Workspace.
00087 *
00088 *     RWORK   (input) REAL array, dimension (N).
00089 *     Workspace.
00090 *
00091 *  =====================================================================
00092 *
00093 *     .. Local Scalars ..
00094       LOGICAL            NOTRANS
00095       INTEGER            KASE, I, J
00096       REAL               AINVNM, ANORM, TMP
00097       COMPLEX            ZDUM
00098 *     ..
00099 *     .. Local Arrays ..
00100       INTEGER            ISAVE( 3 )
00101 *     ..
00102 *     .. External Functions ..
00103       LOGICAL            LSAME
00104       EXTERNAL           LSAME
00105 *     ..
00106 *     .. External Subroutines ..
00107       EXTERNAL           CLACN2, CGBTRS, XERBLA
00108 *     ..
00109 *     .. Intrinsic Functions ..
00110       INTRINSIC          ABS, MAX
00111 *     ..
00112 *     .. Statement Functions ..
00113       REAL               CABS1
00114 *     ..
00115 *     .. Statement Function Definitions ..
00116       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00117 *     ..
00118 *     .. Executable Statements ..
00119       CLA_GBRCOND_C = 0.0E+0
00120 *
00121       INFO = 0
00122       NOTRANS = LSAME( TRANS, 'N' )
00123       IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
00124      $     LSAME( TRANS, 'C' ) ) THEN
00125          INFO = -1
00126       ELSE IF( N.LT.0 ) THEN
00127          INFO = -2
00128       ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN
00129          INFO = -3
00130       ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
00131          INFO = -4
00132       ELSE IF( LDAB.LT.KL+KU+1 ) THEN
00133          INFO = -6
00134       ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
00135          INFO = -8
00136       END IF
00137       IF( INFO.NE.0 ) THEN
00138          CALL XERBLA( 'CLA_GBRCOND_C', -INFO )
00139          RETURN
00140       END IF
00141 *
00142 *     Compute norm of op(A)*op2(C).
00143 *
00144       ANORM = 0.0E+0
00145       KD = KU + 1
00146       KE = KL + 1
00147       IF ( NOTRANS ) THEN
00148          DO I = 1, N
00149             TMP = 0.0E+0
00150             IF ( CAPPLY ) THEN
00151                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00152                   TMP = TMP + CABS1( AB( KD+I-J, J ) ) / C( J )
00153                END DO
00154             ELSE
00155                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00156                   TMP = TMP + CABS1( AB( KD+I-J, J ) )
00157                END DO
00158             END IF
00159             RWORK( I ) = TMP
00160             ANORM = MAX( ANORM, TMP )
00161          END DO
00162       ELSE
00163          DO I = 1, N
00164             TMP = 0.0E+0
00165             IF ( CAPPLY ) THEN
00166                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00167                   TMP = TMP + CABS1( AB( KE-I+J, I ) ) / C( J )
00168                END DO
00169             ELSE
00170                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00171                   TMP = TMP + CABS1( AB( KE-I+J, I ) )
00172                END DO
00173             END IF
00174             RWORK( I ) = TMP
00175             ANORM = MAX( ANORM, TMP )
00176          END DO
00177       END IF
00178 *
00179 *     Quick return if possible.
00180 *
00181       IF( N.EQ.0 ) THEN
00182          CLA_GBRCOND_C = 1.0E+0
00183          RETURN
00184       ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
00185          RETURN
00186       END IF
00187 *
00188 *     Estimate the norm of inv(op(A)).
00189 *
00190       AINVNM = 0.0E+0
00191 *
00192       KASE = 0
00193    10 CONTINUE
00194       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00195       IF( KASE.NE.0 ) THEN
00196          IF( KASE.EQ.2 ) THEN
00197 *
00198 *           Multiply by R.
00199 *
00200             DO I = 1, N
00201                WORK( I ) = WORK( I ) * RWORK( I )
00202             END DO
00203 *
00204             IF ( NOTRANS ) THEN
00205                CALL CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
00206      $              IPIV, WORK, N, INFO )
00207             ELSE
00208                CALL CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
00209      $              LDAFB, IPIV, WORK, N, INFO )
00210             ENDIF
00211 *
00212 *           Multiply by inv(C).
00213 *
00214             IF ( CAPPLY ) THEN
00215                DO I = 1, N
00216                   WORK( I ) = WORK( I ) * C( I )
00217                END DO
00218             END IF
00219          ELSE
00220 *
00221 *           Multiply by inv(C').
00222 *
00223             IF ( CAPPLY ) THEN
00224                DO I = 1, N
00225                   WORK( I ) = WORK( I ) * C( I )
00226                END DO
00227             END IF
00228 *
00229             IF ( NOTRANS ) THEN
00230                CALL CGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
00231      $              LDAFB, IPIV,  WORK, N, INFO )
00232             ELSE
00233                CALL CGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
00234      $              IPIV, WORK, N, INFO )
00235             END IF
00236 *
00237 *           Multiply by R.
00238 *
00239             DO I = 1, N
00240                WORK( I ) = WORK( I ) * RWORK( I )
00241             END DO
00242          END IF
00243          GO TO 10
00244       END IF
00245 *
00246 *     Compute the estimate of the reciprocal condition number.
00247 *
00248       IF( AINVNM .NE. 0.0E+0 )
00249      $   CLA_GBRCOND_C = 1.0E+0 / AINVNM
00250 *
00251       RETURN
00252 *
00253       END