LAPACK: SRC/cla_hercond_c.f Source File

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00001       REAL FUNCTION CLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV, C,
00002      $                             CAPPLY, INFO, WORK, RWORK )
00003 *
00004 *     -- LAPACK routine (version 3.2.1)                                 --
00005 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
00006 *     -- Jason Riedy of Univ. of California Berkeley.                 --
00007 *     -- April 2009                                                   --
00008 *
00009 *     -- LAPACK is a software package provided by Univ. of Tennessee, --
00010 *     -- Univ. of California Berkeley and NAG Ltd.                    --
00011 *
00012       IMPLICIT NONE
00013 *     ..
00014 *     .. Scalar Arguments ..
00015       CHARACTER          UPLO
00016       LOGICAL            CAPPLY
00017       INTEGER            N, LDA, LDAF, INFO
00018 *     ..
00019 *     .. Array Arguments ..
00020       INTEGER            IPIV( * )
00021       COMPLEX            A( LDA, * ), AF( LDAF, * ), WORK( * )
00022       REAL               C ( * ), RWORK( * )
00023 *     ..
00024 *
00025 *  Purpose
00026 *  =======
00027 *
00028 *     CLA_HERCOND_C computes the infinity norm condition number of
00029 *     op(A) * inv(diag(C)) where C is a REAL vector.
00030 *
00031 *  Arguments
00032 *  =========
00033 *
00034 *     UPLO    (input) CHARACTER*1
00035 *       = 'U':  Upper triangle of A is stored;
00036 *       = 'L':  Lower triangle of A is stored.
00037 *
00038 *     N       (input) INTEGER
00039 *     The number of linear equations, i.e., the order of the
00040 *     matrix A.  N >= 0.
00041 *
00042 *     A       (input) COMPLEX array, dimension (LDA,N)
00043 *     On entry, the N-by-N matrix A
00044 *
00045 *     LDA     (input) INTEGER
00046 *     The leading dimension of the array A.  LDA >= max(1,N).
00047 *
00048 *     AF      (input) COMPLEX array, dimension (LDAF,N)
00049 *     The block diagonal matrix D and the multipliers used to
00050 *     obtain the factor U or L as computed by CHETRF.
00051 *
00052 *     LDAF    (input) INTEGER
00053 *     The leading dimension of the array AF.  LDAF >= max(1,N).
00054 *
00055 *     IPIV    (input) INTEGER array, dimension (N)
00056 *     Details of the interchanges and the block structure of D
00057 *     as determined by CHETRF.
00058 *
00059 *     C       (input) REAL array, dimension (N)
00060 *     The vector C in the formula op(A) * inv(diag(C)).
00061 *
00062 *     CAPPLY  (input) LOGICAL
00063 *     If .TRUE. then access the vector C in the formula above.
00064 *
00065 *     INFO    (output) INTEGER
00066 *       = 0:  Successful exit.
00067 *     i > 0:  The ith argument is invalid.
00068 *
00069 *     WORK    (input) COMPLEX array, dimension (2*N).
00070 *     Workspace.
00071 *
00072 *     RWORK   (input) REAL array, dimension (N).
00073 *     Workspace.
00074 *
00075 *  =====================================================================
00076 *
00077 *     .. Local Scalars ..
00078       INTEGER            KASE, I, J
00079       REAL               AINVNM, ANORM, TMP
00080       LOGICAL            UP
00081       COMPLEX            ZDUM
00082 *     ..
00083 *     .. Local Arrays ..
00084       INTEGER            ISAVE( 3 )
00085 *     ..
00086 *     .. External Functions ..
00087       LOGICAL            LSAME
00088       EXTERNAL           LSAME
00089 *     ..
00090 *     .. External Subroutines ..
00091       EXTERNAL           CLACN2, CHETRS, XERBLA
00092 *     ..
00093 *     .. Intrinsic Functions ..
00094       INTRINSIC          ABS, MAX
00095 *     ..
00096 *     .. Statement Functions ..
00097       REAL               CABS1
00098 *     ..
00099 *     .. Statement Function Definitions ..
00100       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
00101 *     ..
00102 *     .. Executable Statements ..
00103 *
00104       CLA_HERCOND_C = 0.0E+0
00105 *
00106       INFO = 0
00107       IF( N.LT.0 ) THEN
00108          INFO = -2
00109       END IF
00110       IF( INFO.NE.0 ) THEN
00111          CALL XERBLA( 'CLA_HERCOND_C', -INFO )
00112          RETURN
00113       END IF
00114       UP = .FALSE.
00115       IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
00116 *
00117 *     Compute norm of op(A)*op2(C).
00118 *
00119       ANORM = 0.0E+0
00120       IF ( UP ) THEN
00121          DO I = 1, N
00122             TMP = 0.0E+0
00123             IF ( CAPPLY ) THEN
00124                DO J = 1, I
00125                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00126                END DO
00127                DO J = I+1, N
00128                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00129                END DO
00130             ELSE
00131                DO J = 1, I
00132                   TMP = TMP + CABS1( A( J, I ) )
00133                END DO
00134                DO J = I+1, N
00135                   TMP = TMP + CABS1( A( I, J ) )
00136                END DO
00137             END IF
00138             RWORK( I ) = TMP
00139             ANORM = MAX( ANORM, TMP )
00140          END DO
00141       ELSE
00142          DO I = 1, N
00143             TMP = 0.0E+0
00144             IF ( CAPPLY ) THEN
00145                DO J = 1, I
00146                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00147                END DO
00148                DO J = I+1, N
00149                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00150                END DO
00151             ELSE
00152                DO J = 1, I
00153                   TMP = TMP + CABS1( A( I, J ) )
00154                END DO
00155                DO J = I+1, N
00156                   TMP = TMP + CABS1( A( J, I ) )
00157                END DO
00158             END IF
00159             RWORK( I ) = TMP
00160             ANORM = MAX( ANORM, TMP )
00161          END DO
00162       END IF
00163 *
00164 *     Quick return if possible.
00165 *
00166       IF( N.EQ.0 ) THEN
00167          CLA_HERCOND_C = 1.0E+0
00168          RETURN
00169       ELSE IF( ANORM .EQ. 0.0E+0 ) THEN
00170          RETURN
00171       END IF
00172 *
00173 *     Estimate the norm of inv(op(A)).
00174 *
00175       AINVNM = 0.0E+0
00176 *
00177       KASE = 0
00178    10 CONTINUE
00179       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00180       IF( KASE.NE.0 ) THEN
00181          IF( KASE.EQ.2 ) THEN
00182 *
00183 *           Multiply by R.
00184 *
00185             DO I = 1, N
00186                WORK( I ) = WORK( I ) * RWORK( I )
00187             END DO
00188 *
00189             IF ( UP ) THEN
00190                CALL CHETRS( 'U', N, 1, AF, LDAF, IPIV,
00191      $            WORK, N, INFO )
00192             ELSE
00193                CALL CHETRS( 'L', N, 1, AF, LDAF, IPIV,
00194      $            WORK, N, INFO )
00195             ENDIF
00196 *
00197 *           Multiply by inv(C).
00198 *
00199             IF ( CAPPLY ) THEN
00200                DO I = 1, N
00201                   WORK( I ) = WORK( I ) * C( I )
00202                END DO
00203             END IF
00204          ELSE
00205 *
00206 *           Multiply by inv(C').
00207 *
00208             IF ( CAPPLY ) THEN
00209                DO I = 1, N
00210                   WORK( I ) = WORK( I ) * C( I )
00211                END DO
00212             END IF
00213 *
00214             IF ( UP ) THEN
00215                CALL CHETRS( 'U', N, 1, AF, LDAF, IPIV,
00216      $            WORK, N, INFO )
00217             ELSE
00218                CALL CHETRS( 'L', N, 1, AF, LDAF, IPIV,
00219      $            WORK, N, INFO )
00220             END IF
00221 *
00222 *           Multiply by R.
00223 *
00224             DO I = 1, N
00225                WORK( I ) = WORK( I ) * RWORK( I )
00226             END DO
00227          END IF
00228          GO TO 10
00229       END IF
00230 *
00231 *     Compute the estimate of the reciprocal condition number.
00232 *
00233       IF( AINVNM .NE. 0.0E+0 )
00234      $   CLA_HERCOND_C = 1.0E+0 / AINVNM
00235 *
00236       RETURN
00237 *
00238       END