LAPACK: SRC/zla_gbrcond_c.f Source File

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00001       DOUBLE PRECISION FUNCTION ZLA_GBRCOND_C( TRANS, N, KL, KU, AB, 
00002      $                                         LDAB, AFB, LDAFB, IPIV,
00003      $                                         C, CAPPLY, INFO, WORK,
00004      $                                         RWORK )
00005 *
00006 *     -- LAPACK routine (version 3.2.1)                               --
00007 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
00008 *     -- Jason Riedy of Univ. of California Berkeley.                 --
00009 *     -- April 2009                                                   --
00010 *
00011 *     -- LAPACK is a software package provided by Univ. of Tennessee, --
00012 *     -- Univ. of California Berkeley and NAG Ltd.                    --
00013 *
00014       IMPLICIT NONE
00015 *     ..
00016 *     .. Scalar Arguments ..
00017       CHARACTER          TRANS
00018       LOGICAL            CAPPLY
00019       INTEGER            N, KL, KU, KD, KE, LDAB, LDAFB, INFO
00020 *     ..
00021 *     .. Array Arguments ..
00022       INTEGER            IPIV( * )
00023       COMPLEX*16         AB( LDAB, * ), AFB( LDAFB, * ), WORK( * )
00024       DOUBLE PRECISION   C( * ), RWORK( * )
00025 *
00026 *
00027 *  Purpose
00028 *  =======
00029 *
00030 *     ZLA_GBRCOND_C Computes the infinity norm condition number of
00031 *     op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
00032 *
00033 *  Arguments
00034 *  =========
00035 *
00036 *     TRANS   (input) CHARACTER*1
00037 *     Specifies the form of the system of equations:
00038 *       = 'N':  A * X = B     (No transpose)
00039 *       = 'T':  A**T * X = B  (Transpose)
00040 *       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
00041 *
00042 *     N       (input) INTEGER
00043 *     The number of linear equations, i.e., the order of the
00044 *     matrix A.  N >= 0.
00045 *
00046 *     KL      (input) INTEGER
00047 *     The number of subdiagonals within the band of A.  KL >= 0.
00048 *
00049 *     KU      (input) INTEGER
00050 *     The number of superdiagonals within the band of A.  KU >= 0.
00051 *
00052 *     AB      (input) COMPLEX*16 array, dimension (LDAB,N)
00053 *     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
00054 *     The j-th column of A is stored in the j-th column of the
00055 *     array AB as follows:
00056 *     AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
00057 *
00058 *     LDAB    (input) INTEGER
00059 *     The leading dimension of the array AB.  LDAB >= KL+KU+1.
00060 *
00061 *     AFB     (input) COMPLEX*16 array, dimension (LDAFB,N)
00062 *     Details of the LU factorization of the band matrix A, as
00063 *     computed by ZGBTRF.  U is stored as an upper triangular
00064 *     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
00065 *     and the multipliers used during the factorization are stored
00066 *     in rows KL+KU+2 to 2*KL+KU+1.
00067 *
00068 *     LDAFB   (input) INTEGER
00069 *     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
00070 *
00071 *     IPIV    (input) INTEGER array, dimension (N)
00072 *     The pivot indices from the factorization A = P*L*U
00073 *     as computed by ZGBTRF; row i of the matrix was interchanged
00074 *     with row IPIV(i).
00075 *
00076 *     C       (input) DOUBLE PRECISION array, dimension (N)
00077 *     The vector C in the formula op(A) * inv(diag(C)).
00078 *
00079 *     CAPPLY  (input) LOGICAL
00080 *     If .TRUE. then access the vector C in the formula above.
00081 *
00082 *     INFO    (output) INTEGER
00083 *       = 0:  Successful exit.
00084 *     i > 0:  The ith argument is invalid.
00085 *
00086 *     WORK    (input) COMPLEX*16 array, dimension (2*N).
00087 *     Workspace.
00088 *
00089 *     RWORK   (input) DOUBLE PRECISION array, dimension (N).
00090 *     Workspace.
00091 *
00092 *  =====================================================================
00093 *
00094 *     .. Local Scalars ..
00095       LOGICAL            NOTRANS
00096       INTEGER            KASE, I, J
00097       DOUBLE PRECISION   AINVNM, ANORM, TMP
00098       COMPLEX*16         ZDUM
00099 *     ..
00100 *     .. Local Arrays ..
00101       INTEGER            ISAVE( 3 )
00102 *     ..
00103 *     .. External Functions ..
00104       LOGICAL            LSAME
00105       EXTERNAL           LSAME
00106 *     ..
00107 *     .. External Subroutines ..
00108       EXTERNAL           ZLACN2, ZGBTRS, XERBLA
00109 *     ..
00110 *     .. Intrinsic Functions ..
00111       INTRINSIC          ABS, MAX
00112 *     ..
00113 *     .. Statement Functions ..
00114       DOUBLE PRECISION   CABS1
00115 *     ..
00116 *     .. Statement Function Definitions ..
00117       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00118 *     ..
00119 *     .. Executable Statements ..
00120       ZLA_GBRCOND_C = 0.0D+0
00121 *
00122       INFO = 0
00123       NOTRANS = LSAME( TRANS, 'N' )
00124       IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
00125      $     LSAME( TRANS, 'C' ) ) THEN
00126          INFO = -1
00127       ELSE IF( N.LT.0 ) THEN
00128          INFO = -2
00129       ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN
00130          INFO = -3
00131       ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
00132          INFO = -4
00133       ELSE IF( LDAB.LT.KL+KU+1 ) THEN
00134          INFO = -6
00135       ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
00136          INFO = -8
00137       END IF
00138       IF( INFO.NE.0 ) THEN
00139          CALL XERBLA( 'ZLA_GBRCOND_C', -INFO )
00140          RETURN
00141       END IF
00142 *
00143 *     Compute norm of op(A)*op2(C).
00144 *
00145       ANORM = 0.0D+0
00146       KD = KU + 1
00147       KE = KL + 1
00148       IF ( NOTRANS ) THEN
00149          DO I = 1, N
00150             TMP = 0.0D+0
00151             IF ( CAPPLY ) THEN
00152                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00153                   TMP = TMP + CABS1( AB( KD+I-J, J ) ) / C( J )
00154                END DO
00155             ELSE
00156                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00157                   TMP = TMP + CABS1( AB( KD+I-J, J ) )
00158                END DO
00159             END IF
00160             RWORK( I ) = TMP
00161             ANORM = MAX( ANORM, TMP )
00162          END DO
00163       ELSE
00164          DO I = 1, N
00165             TMP = 0.0D+0
00166             IF ( CAPPLY ) THEN
00167                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00168                   TMP = TMP + CABS1( AB( KE-I+J, I ) ) / C( J )
00169                END DO
00170             ELSE
00171                DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00172                   TMP = TMP + CABS1( AB( KE-I+J, I ) )
00173                END DO
00174             END IF
00175             RWORK( I ) = TMP
00176             ANORM = MAX( ANORM, TMP )
00177          END DO
00178       END IF
00179 *
00180 *     Quick return if possible.
00181 *
00182       IF( N.EQ.0 ) THEN
00183          ZLA_GBRCOND_C = 1.0D+0
00184          RETURN
00185       ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
00186          RETURN
00187       END IF
00188 *
00189 *     Estimate the norm of inv(op(A)).
00190 *
00191       AINVNM = 0.0D+0
00192 *
00193       KASE = 0
00194    10 CONTINUE
00195       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00196       IF( KASE.NE.0 ) THEN
00197          IF( KASE.EQ.2 ) THEN
00198 *
00199 *           Multiply by R.
00200 *
00201             DO I = 1, N
00202                WORK( I ) = WORK( I ) * RWORK( I )
00203             END DO
00204 *
00205             IF ( NOTRANS ) THEN
00206                CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
00207      $              IPIV, WORK, N, INFO )
00208             ELSE
00209                CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
00210      $              LDAFB, IPIV, WORK, N, INFO )
00211             ENDIF
00212 *
00213 *           Multiply by inv(C).
00214 *
00215             IF ( CAPPLY ) THEN
00216                DO I = 1, N
00217                   WORK( I ) = WORK( I ) * C( I )
00218                END DO
00219             END IF
00220          ELSE
00221 *
00222 *           Multiply by inv(C').
00223 *
00224             IF ( CAPPLY ) THEN
00225                DO I = 1, N
00226                   WORK( I ) = WORK( I ) * C( I )
00227                END DO
00228             END IF
00229 *
00230             IF ( NOTRANS ) THEN
00231                CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
00232      $              LDAFB, IPIV,  WORK, N, INFO )
00233             ELSE
00234                CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
00235      $              IPIV, WORK, N, INFO )
00236             END IF
00237 *
00238 *           Multiply by R.
00239 *
00240             DO I = 1, N
00241                WORK( I ) = WORK( I ) * RWORK( I )
00242             END DO
00243          END IF
00244          GO TO 10
00245       END IF
00246 *
00247 *     Compute the estimate of the reciprocal condition number.
00248 *
00249       IF( AINVNM .NE. 0.0D+0 )
00250      $   ZLA_GBRCOND_C = 1.0D+0 / AINVNM
00251 *
00252       RETURN
00253 *
00254       END