LAPACK: SRC/zla_syrcond_c.f Source File

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00001       DOUBLE PRECISION FUNCTION ZLA_SYRCOND_C( UPLO, 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 Arguments ..
00016       CHARACTER          UPLO
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_SYRCOND_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 *     UPLO    (input) CHARACTER*1
00036 *       = 'U':  Upper triangle of A is stored;
00037 *       = 'L':  Lower triangle of A is stored.
00038 *
00039 *     N       (input) INTEGER
00040 *     The number of linear equations, i.e., the order of the
00041 *     matrix A.  N >= 0.
00042 *
00043 *     A       (input) COMPLEX*16 array, dimension (LDA,N)
00044 *     On entry, the N-by-N matrix A
00045 *
00046 *     LDA     (input) INTEGER
00047 *     The leading dimension of the array A.  LDA >= max(1,N).
00048 *
00049 *     AF      (input) COMPLEX*16 array, dimension (LDAF,N)
00050 *     The block diagonal matrix D and the multipliers used to
00051 *     obtain the factor U or L as computed by ZSYTRF.
00052 *
00053 *     LDAF    (input) INTEGER
00054 *     The leading dimension of the array AF.  LDAF >= max(1,N).
00055 *
00056 *     IPIV    (input) INTEGER array, dimension (N)
00057 *     Details of the interchanges and the block structure of D
00058 *     as determined by ZSYTRF.
00059 *
00060 *     C       (input) DOUBLE PRECISION array, dimension (N)
00061 *     The vector C in the formula op(A) * inv(diag(C)).
00062 *
00063 *     CAPPLY  (input) LOGICAL
00064 *     If .TRUE. then access the vector C in the formula above.
00065 *
00066 *     INFO    (output) INTEGER
00067 *       = 0:  Successful exit.
00068 *     i > 0:  The ith argument is invalid.
00069 *
00070 *     WORK    (input) COMPLEX*16 array, dimension (2*N).
00071 *     Workspace.
00072 *
00073 *     RWORK   (input) DOUBLE PRECISION array, dimension (N).
00074 *     Workspace.
00075 *
00076 *  =====================================================================
00077 *
00078 *     .. Local Scalars ..
00079       INTEGER            KASE
00080       DOUBLE PRECISION   AINVNM, ANORM, TMP
00081       INTEGER            I, J
00082       LOGICAL            UP
00083       COMPLEX*16         ZDUM
00084 *     ..
00085 *     .. Local Arrays ..
00086       INTEGER            ISAVE( 3 )
00087 *     ..
00088 *     .. External Functions ..
00089       LOGICAL            LSAME
00090       EXTERNAL           LSAME
00091 *     ..
00092 *     .. External Subroutines ..
00093       EXTERNAL           ZLACN2, ZSYTRS, XERBLA
00094 *     ..
00095 *     .. Intrinsic Functions ..
00096       INTRINSIC          ABS, MAX
00097 *     ..
00098 *     .. Statement Functions ..
00099       DOUBLE PRECISION CABS1
00100 *     ..
00101 *     .. Statement Function Definitions ..
00102       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
00103 *     ..
00104 *     .. Executable Statements ..
00105 *
00106       ZLA_SYRCOND_C = 0.0D+0
00107 *
00108       INFO = 0
00109       IF( N.LT.0 ) THEN
00110          INFO = -2
00111       END IF
00112       IF( INFO.NE.0 ) THEN
00113          CALL XERBLA( 'ZLA_SYRCOND_C', -INFO )
00114          RETURN
00115       END IF
00116       UP = .FALSE.
00117       IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
00118 *
00119 *     Compute norm of op(A)*op2(C).
00120 *
00121       ANORM = 0.0D+0
00122       IF ( UP ) THEN
00123          DO I = 1, N
00124             TMP = 0.0D+0
00125             IF ( CAPPLY ) THEN
00126                DO J = 1, I
00127                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00128                END DO
00129                DO J = I+1, N
00130                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00131                END DO
00132             ELSE
00133                DO J = 1, I
00134                   TMP = TMP + CABS1( A( J, I ) )
00135                END DO
00136                DO J = I+1, N
00137                   TMP = TMP + CABS1( A( I, J ) )
00138                END DO
00139             END IF
00140             RWORK( I ) = TMP
00141             ANORM = MAX( ANORM, TMP )
00142          END DO
00143       ELSE
00144          DO I = 1, N
00145             TMP = 0.0D+0
00146             IF ( CAPPLY ) THEN
00147                DO J = 1, I
00148                   TMP = TMP + CABS1( A( I, J ) ) / C( J )
00149                END DO
00150                DO J = I+1, N
00151                   TMP = TMP + CABS1( A( J, I ) ) / C( J )
00152                END DO
00153             ELSE
00154                DO J = 1, I
00155                   TMP = TMP + CABS1( A( I, J ) )
00156                END DO
00157                DO J = I+1, N
00158                   TMP = TMP + CABS1( A( J, I ) )
00159                END DO
00160             END IF
00161             RWORK( I ) = TMP
00162             ANORM = MAX( ANORM, TMP )
00163          END DO
00164       END IF
00165 *
00166 *     Quick return if possible.
00167 *
00168       IF( N.EQ.0 ) THEN
00169          ZLA_SYRCOND_C = 1.0D+0
00170          RETURN
00171       ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
00172          RETURN
00173       END IF
00174 *
00175 *     Estimate the norm of inv(op(A)).
00176 *
00177       AINVNM = 0.0D+0
00178 *
00179       KASE = 0
00180    10 CONTINUE
00181       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00182       IF( KASE.NE.0 ) THEN
00183          IF( KASE.EQ.2 ) THEN
00184 *
00185 *           Multiply by R.
00186 *
00187             DO I = 1, N
00188                WORK( I ) = WORK( I ) * RWORK( I )
00189             END DO
00190 *
00191             IF ( UP ) THEN
00192                CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
00193      $            WORK, N, INFO )
00194             ELSE
00195                CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
00196      $            WORK, N, INFO )
00197             ENDIF
00198 *
00199 *           Multiply by inv(C).
00200 *
00201             IF ( CAPPLY ) THEN
00202                DO I = 1, N
00203                   WORK( I ) = WORK( I ) * C( I )
00204                END DO
00205             END IF
00206          ELSE
00207 *
00208 *           Multiply by inv(C').
00209 *
00210             IF ( CAPPLY ) THEN
00211                DO I = 1, N
00212                   WORK( I ) = WORK( I ) * C( I )
00213                END DO
00214             END IF
00215 *
00216             IF ( UP ) THEN
00217                CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
00218      $            WORK, N, INFO )
00219             ELSE
00220                CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
00221      $            WORK, N, INFO )
00222             END IF
00223 *
00224 *           Multiply by R.
00225 *
00226             DO I = 1, N
00227                WORK( I ) = WORK( I ) * RWORK( I )
00228             END DO
00229          END IF
00230          GO TO 10
00231       END IF
00232 *
00233 *     Compute the estimate of the reciprocal condition number.
00234 *
00235       IF( AINVNM .NE. 0.0D+0 )
00236      $   ZLA_SYRCOND_C = 1.0D+0 / AINVNM
00237 *
00238       RETURN
00239 *
00240       END