LAPACK: SRC/zla_gercond_c.f Source File

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00001       DOUBLE PRECISION FUNCTION ZLA_GERCOND_C( TRANS, N, A, LDA, AF, 
00002      $                                         LDAF, IPIV, C, CAPPLY,
00003      $                                         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 Aguments ..
00016       CHARACTER          TRANS
00017       LOGICAL            CAPPLY
00018       INTEGER            N, LDA, LDAF, INFO
00019 *     ..
00020 *     .. Array Arguments ..
00021       INTEGER            IPIV( * )
00022       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), WORK( * )
00023       DOUBLE PRECISION   C( * ), RWORK( * )
00024 *     ..
00025 *
00026 *  Purpose
00027 *  =======
00028 *
00029 *     ZLA_GERCOND_C computes the infinity norm condition number of
00030 *     op(A) * inv(diag(C)) where C is a DOUBLE PRECISION 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 *     A       (input) COMPLEX*16 array, dimension (LDA,N)
00046 *     On entry, the N-by-N matrix A
00047 *
00048 *     LDA     (input) INTEGER
00049 *     The leading dimension of the array A.  LDA >= max(1,N).
00050 *
00051 *     AF      (input) COMPLEX*16 array, dimension (LDAF,N)
00052 *     The factors L and U from the factorization
00053 *     A = P*L*U as computed by ZGETRF.
00054 *
00055 *     LDAF    (input) INTEGER
00056 *     The leading dimension of the array AF.  LDAF >= max(1,N).
00057 *
00058 *     IPIV    (input) INTEGER array, dimension (N)
00059 *     The pivot indices from the factorization A = P*L*U
00060 *     as computed by ZGETRF; row i of the matrix was interchanged
00061 *     with row IPIV(i).
00062 *
00063 *     C       (input) DOUBLE PRECISION array, dimension (N)
00064 *     The vector C in the formula op(A) * inv(diag(C)).
00065 *
00066 *     CAPPLY  (input) LOGICAL
00067 *     If .TRUE. then access the vector C in the formula above.
00068 *
00069 *     INFO    (output) INTEGER
00070 *       = 0:  Successful exit.
00071 *     i > 0:  The ith argument is invalid.
00072 *
00073 *     WORK    (input) COMPLEX*16 array, dimension (2*N).
00074 *     Workspace.
00075 *
00076 *     RWORK   (input) DOUBLE PRECISION array, dimension (N).
00077 *     Workspace.
00078 *
00079 *  =====================================================================
00080 *
00081 *     .. Local Scalars ..
00082       LOGICAL            NOTRANS
00083       INTEGER            KASE, I, J
00084       DOUBLE PRECISION   AINVNM, ANORM, TMP
00085       COMPLEX*16         ZDUM
00086 *     ..
00087 *     .. Local Arrays ..
00088       INTEGER            ISAVE( 3 )
00089 *     ..
00090 *     .. External Functions ..
00091       LOGICAL            LSAME
00092       EXTERNAL           LSAME
00093 *     ..
00094 *     .. External Subroutines ..
00095       EXTERNAL           ZLACN2, ZGETRS, XERBLA
00096 *     ..
00097 *     .. Intrinsic Functions ..
00098       INTRINSIC          ABS, MAX, REAL, DIMAG
00099 *     ..
00100 *     .. Statement Functions ..
00101       DOUBLE PRECISION   CABS1
00102 *     ..
00103 *     .. Statement Function Definitions ..
00104       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00105 *     ..
00106 *     .. Executable Statements ..
00107       ZLA_GERCOND_C = 0.0D+0
00108 *
00109       INFO = 0
00110       NOTRANS = LSAME( TRANS, 'N' )
00111       IF ( .NOT. NOTRANS .AND. .NOT. LSAME( TRANS, 'T' ) .AND. .NOT.
00112      $     LSAME( TRANS, 'C' ) ) THEN
00113       ELSE IF( N.LT.0 ) THEN
00114          INFO = -2
00115       END IF
00116       IF( INFO.NE.0 ) THEN
00117          CALL XERBLA( 'ZLA_GERCOND_C', -INFO )
00118          RETURN
00119       END IF
00120 *
00121 *     Compute norm of op(A)*op2(C).
00122 *
00123       ANORM = 0.0D+0
00124       IF ( NOTRANS ) THEN
00125          DO I = 1, N
00126             TMP = 0.0D+0
00127             IF ( CAPPLY ) THEN
00128                DO J = 1, N
00129                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00130                END DO
00131             ELSE
00132                DO J = 1, N
00133                   TMP = TMP + CABS1( A( I, J ) )
00134                END DO
00135             END IF
00136             RWORK( I ) = TMP
00137             ANORM = MAX( ANORM, TMP )
00138          END DO
00139       ELSE
00140          DO I = 1, N
00141             TMP = 0.0D+0
00142             IF ( CAPPLY ) THEN
00143                DO J = 1, N
00144                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00145                END DO
00146             ELSE
00147                DO J = 1, N
00148                   TMP = TMP + CABS1( A( J, I ) )
00149                END DO
00150             END IF
00151             RWORK( I ) = TMP
00152             ANORM = MAX( ANORM, TMP )
00153          END DO
00154       END IF
00155 *
00156 *     Quick return if possible.
00157 *
00158       IF( N.EQ.0 ) THEN
00159          ZLA_GERCOND_C = 1.0D+0
00160          RETURN
00161       ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
00162          RETURN
00163       END IF
00164 *
00165 *     Estimate the norm of inv(op(A)).
00166 *
00167       AINVNM = 0.0D+0
00168 *
00169       KASE = 0
00170    10 CONTINUE
00171       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00172       IF( KASE.NE.0 ) THEN
00173          IF( KASE.EQ.2 ) THEN
00174 *
00175 *           Multiply by R.
00176 *
00177             DO I = 1, N
00178                WORK( I ) = WORK( I ) * RWORK( I )
00179             END DO
00180 *
00181             IF (NOTRANS) THEN
00182                CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
00183      $            WORK, N, INFO )
00184             ELSE
00185                CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
00186      $            WORK, N, INFO )
00187             ENDIF
00188 *
00189 *           Multiply by inv(C).
00190 *
00191             IF ( CAPPLY ) THEN
00192                DO I = 1, N
00193                   WORK( I ) = WORK( I ) * C( I )
00194                END DO
00195             END IF
00196          ELSE
00197 *
00198 *           Multiply by inv(C').
00199 *
00200             IF ( CAPPLY ) THEN
00201                DO I = 1, N
00202                   WORK( I ) = WORK( I ) * C( I )
00203                END DO
00204             END IF
00205 *
00206             IF ( NOTRANS ) THEN
00207                CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV,
00208      $            WORK, N, INFO )
00209             ELSE
00210                CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
00211      $            WORK, N, INFO )
00212             END IF
00213 *
00214 *           Multiply by R.
00215 *
00216             DO I = 1, N
00217                WORK( I ) = WORK( I ) * RWORK( I )
00218             END DO
00219          END IF
00220          GO TO 10
00221       END IF
00222 *
00223 *     Compute the estimate of the reciprocal condition number.
00224 *
00225       IF( AINVNM .NE. 0.0D+0 )
00226      $   ZLA_GERCOND_C = 1.0D+0 / AINVNM
00227 *
00228       RETURN
00229 *
00230       END