LAPACK 3.3.1 Linear Algebra PACKage

# zla_gbrcond_x.f

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```00001       DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB,
00002      \$                                         LDAB, AFB, LDAFB, IPIV,
00003      \$                                         X, INFO, WORK, 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       INTEGER            N, KL, KU, KD, KE, LDAB, LDAFB, INFO
00018 *     ..
00019 *     .. Array Arguments ..
00020       INTEGER            IPIV( * )
00021       COMPLEX*16         AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
00022      \$                   X( * )
00023       DOUBLE PRECISION   RWORK( * )
00024 *
00025 *
00026 *  Purpose
00027 *  =======
00028 *
00029 *     ZLA_GBRCOND_X Computes the infinity norm condition number of
00030 *     op(A) * diag(X) where X is a COMPLEX*16 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*16 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*16 array, dimension (LDAFB,N)
00061 *     Details of the LU factorization of the band matrix A, as
00062 *     computed by ZGBTRF.  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 ZGBTRF; row i of the matrix was interchanged
00073 *     with row IPIV(i).
00074 *
00075 *     X       (input) COMPLEX*16 array, dimension (N)
00076 *     The vector X in the formula op(A) * diag(X).
00077 *
00078 *     INFO    (output) INTEGER
00079 *       = 0:  Successful exit.
00080 *     i > 0:  The ith argument is invalid.
00081 *
00082 *     WORK    (input) COMPLEX*16 array, dimension (2*N).
00083 *     Workspace.
00084 *
00085 *     RWORK   (input) DOUBLE PRECISION array, dimension (N).
00086 *     Workspace.
00087 *
00088 *  =====================================================================
00089 *
00090 *     .. Local Scalars ..
00091       LOGICAL            NOTRANS
00092       INTEGER            KASE, I, J
00093       DOUBLE PRECISION   AINVNM, ANORM, TMP
00094       COMPLEX*16         ZDUM
00095 *     ..
00096 *     .. Local Arrays ..
00097       INTEGER            ISAVE( 3 )
00098 *     ..
00099 *     .. External Functions ..
00100       LOGICAL            LSAME
00101       EXTERNAL           LSAME
00102 *     ..
00103 *     .. External Subroutines ..
00104       EXTERNAL           ZLACN2, ZGBTRS, XERBLA
00105 *     ..
00106 *     .. Intrinsic Functions ..
00107       INTRINSIC          ABS, MAX
00108 *     ..
00109 *     .. Statement Functions ..
00110       DOUBLE PRECISION   CABS1
00111 *     ..
00112 *     .. Statement Function Definitions ..
00113       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00114 *     ..
00115 *     .. Executable Statements ..
00116 *
00117       ZLA_GBRCOND_X = 0.0D+0
00118 *
00119       INFO = 0
00120       NOTRANS = LSAME( TRANS, 'N' )
00121       IF ( .NOT. NOTRANS .AND. .NOT. LSAME(TRANS, 'T') .AND. .NOT.
00122      \$     LSAME( TRANS, 'C' ) ) THEN
00123          INFO = -1
00124       ELSE IF( N.LT.0 ) THEN
00125          INFO = -2
00126       ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN
00127          INFO = -3
00128       ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
00129          INFO = -4
00130       ELSE IF( LDAB.LT.KL+KU+1 ) THEN
00131          INFO = -6
00132       ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
00133          INFO = -8
00134       END IF
00135       IF( INFO.NE.0 ) THEN
00136          CALL XERBLA( 'ZLA_GBRCOND_X', -INFO )
00137          RETURN
00138       END IF
00139 *
00140 *     Compute norm of op(A)*op2(C).
00141 *
00142       KD = KU + 1
00143       KE = KL + 1
00144       ANORM = 0.0D+0
00145       IF ( NOTRANS ) THEN
00146          DO I = 1, N
00147             TMP = 0.0D+0
00148             DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00149                TMP = TMP + CABS1( AB( KD+I-J, J) * X( J ) )
00150             END DO
00151             RWORK( I ) = TMP
00152             ANORM = MAX( ANORM, TMP )
00153          END DO
00154       ELSE
00155          DO I = 1, N
00156             TMP = 0.0D+0
00157             DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
00158                TMP = TMP + CABS1( AB( KE-I+J, I ) * X( J ) )
00159             END DO
00160             RWORK( I ) = TMP
00161             ANORM = MAX( ANORM, TMP )
00162          END DO
00163       END IF
00164 *
00165 *     Quick return if possible.
00166 *
00167       IF( N.EQ.0 ) THEN
00168          ZLA_GBRCOND_X = 1.0D+0
00169          RETURN
00170       ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
00171          RETURN
00172       END IF
00173 *
00174 *     Estimate the norm of inv(op(A)).
00175 *
00176       AINVNM = 0.0D+0
00177 *
00178       KASE = 0
00179    10 CONTINUE
00180       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00181       IF( KASE.NE.0 ) THEN
00182          IF( KASE.EQ.2 ) THEN
00183 *
00184 *           Multiply by R.
00185 *
00186             DO I = 1, N
00187                WORK( I ) = WORK( I ) * RWORK( I )
00188             END DO
00189 *
00190             IF ( NOTRANS ) THEN
00191                CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
00192      \$              IPIV, WORK, N, INFO )
00193             ELSE
00194                CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
00195      \$              LDAFB, IPIV, WORK, N, INFO )
00196             ENDIF
00197 *
00198 *           Multiply by inv(X).
00199 *
00200             DO I = 1, N
00201                WORK( I ) = WORK( I ) / X( I )
00202             END DO
00203          ELSE
00204 *
00205 *           Multiply by inv(X**H).
00206 *
00207             DO I = 1, N
00208                WORK( I ) = WORK( I ) / X( I )
00209             END DO
00210 *
00211             IF ( NOTRANS ) THEN
00212                CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
00213      \$              LDAFB, IPIV, WORK, N, INFO )
00214             ELSE
00215                CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
00216      \$              IPIV, WORK, N, INFO )
00217             END IF
00218 *
00219 *           Multiply by R.
00220 *
00221             DO I = 1, N
00222                WORK( I ) = WORK( I ) * RWORK( I )
00223             END DO
00224          END IF
00225          GO TO 10
00226       END IF
00227 *
00228 *     Compute the estimate of the reciprocal condition number.
00229 *
00230       IF( AINVNM .NE. 0.0D+0 )
00231      \$   ZLA_GBRCOND_X = 1.0D+0 / AINVNM
00232 *
00233       RETURN
00234 *
00235       END
```