ScaLAPACK  2.0.2
ScaLAPACK: Scalable Linear Algebra PACKage
pdpocon.f
Go to the documentation of this file.
00001       SUBROUTINE PDPOCON( UPLO, N, A, IA, JA, DESCA, ANORM, RCOND, WORK,
00002      $                    LWORK, IWORK, LIWORK, INFO )
00003 *
00004 *  -- ScaLAPACK routine (version 1.7) --
00005 *     University of Tennessee, Knoxville, Oak Ridge National Laboratory,
00006 *     and University of California, Berkeley.
00007 *     May 25, 2001
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          UPLO
00011       INTEGER            IA, INFO, JA, LIWORK, LWORK, N
00012       DOUBLE PRECISION   ANORM, RCOND
00013 *     ..
00014 *     .. Array Arguments ..
00015       INTEGER            DESCA( * ), IWORK( * )
00016       DOUBLE PRECISION   A( * ), WORK( * )
00017 *     ..
00018 *
00019 *  Purpose
00020 *  =======
00021 *
00022 *  PDPOCON estimates the reciprocal of the condition number (in the
00023 *  1-norm) of a real symmetric positive definite distributed matrix
00024 *  using the Cholesky factorization A = U**T*U or A = L*L**T computed by
00025 *  PDPOTRF.
00026 *
00027 *  An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and
00028 *  the reciprocal of the condition number is computed as
00029 *             RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1)      ) *
00030 *                           norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ).
00031 *
00032 *  Notes
00033 *  =====
00034 *
00035 *  Each global data object is described by an associated description
00036 *  vector.  This vector stores the information required to establish
00037 *  the mapping between an object element and its corresponding process
00038 *  and memory location.
00039 *
00040 *  Let A be a generic term for any 2D block cyclicly distributed array.
00041 *  Such a global array has an associated description vector DESCA.
00042 *  In the following comments, the character _ should be read as
00043 *  "of the global array".
00044 *
00045 *  NOTATION        STORED IN      EXPLANATION
00046 *  --------------- -------------- --------------------------------------
00047 *  DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
00048 *                                 DTYPE_A = 1.
00049 *  CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
00050 *                                 the BLACS process grid A is distribu-
00051 *                                 ted over. The context itself is glo-
00052 *                                 bal, but the handle (the integer
00053 *                                 value) may vary.
00054 *  M_A    (global) DESCA( M_ )    The number of rows in the global
00055 *                                 array A.
00056 *  N_A    (global) DESCA( N_ )    The number of columns in the global
00057 *                                 array A.
00058 *  MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
00059 *                                 the rows of the array.
00060 *  NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
00061 *                                 the columns of the array.
00062 *  RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
00063 *                                 row of the array A is distributed.
00064 *  CSRC_A (global) DESCA( CSRC_ ) The process column over which the
00065 *                                 first column of the array A is
00066 *                                 distributed.
00067 *  LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
00068 *                                 array.  LLD_A >= MAX(1,LOCr(M_A)).
00069 *
00070 *  Let K be the number of rows or columns of a distributed matrix,
00071 *  and assume that its process grid has dimension p x q.
00072 *  LOCr( K ) denotes the number of elements of K that a process
00073 *  would receive if K were distributed over the p processes of its
00074 *  process column.
00075 *  Similarly, LOCc( K ) denotes the number of elements of K that a
00076 *  process would receive if K were distributed over the q processes of
00077 *  its process row.
00078 *  The values of LOCr() and LOCc() may be determined via a call to the
00079 *  ScaLAPACK tool function, NUMROC:
00080 *          LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
00081 *          LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
00082 *  An upper bound for these quantities may be computed by:
00083 *          LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
00084 *          LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
00085 *
00086 *  Arguments
00087 *  =========
00088 *
00089 *  UPLO    (global input) CHARACTER
00090 *          Specifies whether the factor stored in
00091 *          A(IA:IA+N-1,JA:JA+N-1) is upper or lower triangular.
00092 *          = 'U':  Upper triangular
00093 *          = 'L':  Lower triangular
00094 *
00095 *  N       (global input) INTEGER
00096 *          The order of the distributed matrix A(IA:IA+N-1,JA:JA+N-1).
00097 *          N >= 0.
00098 *
00099 *  A       (local input) DOUBLE PRECISION pointer into the local memory
00100 *          to an array of dimension ( LLD_A, LOCc(JA+N-1) ). On entry,
00101 *          this array contains the local pieces of the factors L or U
00102 *          from the Cholesky factorization A(IA:IA+N-1,JA:JA+N-1) = U'*U
00103 *          or L*L', as computed by PDPOTRF.
00104 *
00105 *  IA      (global input) INTEGER
00106 *          The row index in the global array A indicating the first
00107 *          row of sub( A ).
00108 *
00109 *  JA      (global input) INTEGER
00110 *          The column index in the global array A indicating the
00111 *          first column of sub( A ).
00112 *
00113 *  DESCA   (global and local input) INTEGER array of dimension DLEN_.
00114 *          The array descriptor for the distributed matrix A.
00115 *
00116 *  ANORM   (global input) DOUBLE PRECISION
00117 *          The 1-norm (or infinity-norm) of the symmetric distributed
00118 *          matrix A(IA:IA+N-1,JA:JA+N-1).
00119 *
00120 *  RCOND   (global output) DOUBLE PRECISION
00121 *          The reciprocal of the condition number of the distributed
00122 *          matrix A(IA:IA+N-1,JA:JA+N-1), computed as
00123 *             RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1)      ) *
00124 *                           norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ).
00125 *
00126 *  WORK    (local workspace/local output) DOUBLE PRECISION array,
00127 *                                                   dimension (LWORK)
00128 *          On exit, WORK(1) returns the minimal and optimal LWORK.
00129 *
00130 *  LWORK   (local or global input) INTEGER
00131 *          The dimension of the array WORK.
00132 *          LWORK is local input and must be at least
00133 *          LWORK >= 2*LOCr(N+MOD(IA-1,MB_A)) + 2*LOCc(N+MOD(JA-1,NB_A))+
00134 *          MAX( 2, MAX(NB_A*CEIL(NPROW-1,NPCOL),LOCc(N+MOD(JA-1,NB_A)) +
00135 *          NB_A*CEIL(NPCOL-1,NPROW)) ).
00136 *
00137 *          If LWORK = -1, then LWORK is global input and a workspace
00138 *          query is assumed; the routine only calculates the minimum
00139 *          and optimal size for all work arrays. Each of these
00140 *          values is returned in the first entry of the corresponding
00141 *          work array, and no error message is issued by PXERBLA.
00142 *
00143 *  IWORK   (local workspace/local output) INTEGER array,
00144 *                                                 dimension (LIWORK)
00145 *          On exit, IWORK(1) returns the minimal and optimal LIWORK.
00146 *
00147 *  LIWORK  (local or global input) INTEGER
00148 *          The dimension of the array IWORK.
00149 *          LIWORK is local input and must be at least
00150 *          LIWORK >= LOCr(N+MOD(IA-1,MB_A)).
00151 *
00152 *          If LIWORK = -1, then LIWORK is global input and a workspace
00153 *          query is assumed; the routine only calculates the minimum
00154 *          and optimal size for all work arrays. Each of these
00155 *          values is returned in the first entry of the corresponding
00156 *          work array, and no error message is issued by PXERBLA.
00157 *
00158 *
00159 *  INFO    (global output) INTEGER
00160 *          = 0:  successful exit
00161 *          < 0:  If the i-th argument is an array and the j-entry had
00162 *                an illegal value, then INFO = -(i*100+j), if the i-th
00163 *                argument is a scalar and had an illegal value, then
00164 *                INFO = -i.
00165 *
00166 *  =====================================================================
00167 *
00168 *     .. Parameters ..
00169       INTEGER            BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
00170      $                   LLD_, MB_, M_, NB_, N_, RSRC_
00171       PARAMETER          ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
00172      $                     CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
00173      $                     RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
00174       DOUBLE PRECISION   ONE, ZERO
00175       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00176 *     ..
00177 *     .. Local Scalars ..
00178       LOGICAL            LQUERY, UPPER
00179       CHARACTER          CBTOP, COLCTOP, NORMIN, ROWCTOP
00180       INTEGER            IACOL, IAROW, ICOFF, ICTXT, IIA, IPNL, IPNU,
00181      $                   IPV, IPW, IPX, IROFF, IV, IX, IXX, JJA, JV,
00182      $                   JX, KASE, LIWMIN, LWMIN, MYCOL, MYROW, NP,
00183      $                   NPCOL, NPROW, NPMOD, NQ, NQMOD
00184       DOUBLE PRECISION   AINVNM, SCALE, SL, SU, SMLNUM
00185       DOUBLE PRECISION   WMAX
00186 *     ..
00187 *     .. Local Arrays ..
00188       INTEGER            DESCV( DLEN_ ), DESCX( DLEN_ ), IDUM1( 3 ),
00189      $                   IDUM2( 3 )
00190 *     ..
00191 *     .. External Subroutines ..
00192       EXTERNAL           BLACS_GRIDINFO, CHK1MAT, DESCSET, DGEBR2D,
00193      $                   DGEBS2D, INFOG2L, PCHK1MAT, PDAMAX,
00194      $                   PDLATRS, PDLACON, PDRSCL, PB_TOPGET,
00195      $                   PB_TOPSET, PXERBLA
00196 *     ..
00197 *     .. External Functions ..
00198       LOGICAL            LSAME
00199       INTEGER            ICEIL, INDXG2P, NUMROC
00200       DOUBLE PRECISION   PDLAMCH
00201       EXTERNAL           ICEIL, INDXG2P, LSAME, NUMROC, PDLAMCH
00202 *     ..
00203 *     .. Intrinsic Functions ..
00204       INTRINSIC          ABS, DBLE, ICHAR, MAX, MOD
00205 *     ..
00206 *     .. Executable Statements ..
00207 *
00208 *     Get grid parameters
00209 *
00210       ICTXT = DESCA( CTXT_ )
00211       CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
00212 *
00213 *     Test the input parameters
00214 *
00215       INFO = 0
00216       IF( NPROW.EQ.-1 ) THEN
00217          INFO = -(600+CTXT_)
00218       ELSE
00219          CALL CHK1MAT( N, 2, N, 2, IA, JA, DESCA, 6, INFO )
00220          IF( INFO.EQ.0 ) THEN
00221             UPPER = LSAME( UPLO, 'U' )
00222             IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),
00223      $                       NPROW )
00224             IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
00225      $                       NPCOL )
00226             NPMOD = NUMROC( N + MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),
00227      $                      MYROW, IAROW, NPROW )
00228             NQMOD = NUMROC( N + MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),
00229      $                      MYCOL, IACOL, NPCOL )
00230             LWMIN = 2*NPMOD + 2*NQMOD +
00231      $              MAX( 2, MAX( DESCA( NB_ )*
00232      $                   MAX( 1, ICEIL( NPROW-1, NPCOL ) ), NQMOD +
00233      $                   DESCA( NB_ )*
00234      $                   MAX( 1, ICEIL( NPCOL-1, NPROW ) ) ) )
00235             WORK( 1 ) = DBLE( LWMIN )
00236             LIWMIN = NPMOD
00237             IWORK( 1 ) = LIWMIN
00238             LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
00239 *
00240             IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00241                INFO = -1
00242             ELSE IF( ANORM.LT.ZERO ) THEN
00243                INFO = -7
00244             ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
00245                INFO = -10
00246             ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
00247                IWORK( 1 ) = LIWMIN
00248                INFO = -12
00249             END IF
00250          END IF
00251 *
00252          IF( UPPER ) THEN
00253             IDUM1( 1 ) = ICHAR( 'U' )
00254          ELSE
00255             IDUM1( 1 ) = ICHAR( 'L' )
00256          END IF
00257          IDUM2( 1 ) = 1
00258          IF( LWORK.EQ.-1 ) THEN
00259             IDUM1( 2 ) = -1
00260          ELSE
00261             IDUM1( 2 ) = 1
00262          END IF
00263          IDUM2( 2 ) = 10
00264          IF( LIWORK.EQ.-1 ) THEN
00265             IDUM1( 3 ) = -1
00266          ELSE
00267             IDUM1( 3 ) = 1
00268          END IF
00269          IDUM2( 3 ) = 12
00270          CALL PCHK1MAT( N, 2, N, 2, IA, JA, DESCA, 6, 3, IDUM1, IDUM2,
00271      $                  INFO )
00272       END IF
00273 *
00274       IF( INFO.NE.0 ) THEN
00275          CALL PXERBLA( ICTXT, 'PDPOCON', -INFO )
00276          RETURN
00277       ELSE IF( LQUERY ) THEN
00278          RETURN
00279       END IF
00280 *
00281 *     Quick return if possible
00282 *
00283       RCOND = ZERO
00284       IF( N.EQ.0 ) THEN
00285          RCOND = ONE
00286          RETURN
00287       ELSE IF( ANORM.EQ.ZERO ) THEN
00288          RETURN
00289       ELSE IF( N.EQ.1 ) THEN
00290          RCOND = ONE
00291          RETURN
00292       END IF
00293 *
00294       CALL PB_TOPGET( ICTXT, 'Combine', 'Columnwise', COLCTOP )
00295       CALL PB_TOPGET( ICTXT, 'Combine', 'Rowwise',    ROWCTOP )
00296       CALL PB_TOPSET( ICTXT, 'Combine', 'Columnwise', '1-tree' )
00297       CALL PB_TOPSET( ICTXT, 'Combine', 'Rowwise',    '1-tree' )
00298 *
00299       SMLNUM = PDLAMCH( ICTXT, 'Safe minimum' )
00300       IROFF = MOD( IA-1, DESCA( MB_ ) )
00301       ICOFF = MOD( JA-1, DESCA( NB_ ) )
00302       CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA,
00303      $              IAROW, IACOL )
00304       NP = NUMROC( N+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW )
00305       NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL )
00306       IV = IROFF + 1
00307       IX = IV
00308       JV = ICOFF + 1
00309       JX = JV
00310 *
00311       IPX  = 1
00312       IPV  = IPX + NP
00313       IPNL = IPV + NP
00314       IPNU = IPNL + NQ
00315       IPW  = IPNU + NQ
00316 *
00317       CALL DESCSET( DESCV, N+IROFF, 1, DESCA( MB_ ), 1, IAROW, MYCOL,
00318      $              ICTXT, MAX( 1, NP ) )
00319       CALL DESCSET( DESCX, N+IROFF, 1, DESCA( MB_ ), 1, IAROW, MYCOL,
00320      $              ICTXT, MAX( 1, NP ) )
00321 *
00322 *     Estimate the 1-norm (or I-norm) of inv(A).
00323 *
00324       AINVNM = ZERO
00325       KASE   = 0
00326       NORMIN = 'N'
00327 *
00328    10 CONTINUE
00329       CALL PDLACON( N, WORK( IPV ), IV, JV, DESCV, WORK( IPX ), IX, JX,
00330      $              DESCX, IWORK, AINVNM, KASE )
00331       IF( KASE.NE.0 ) THEN
00332          IF( UPPER ) THEN
00333 *
00334 *           Multiply by inv(U').
00335 *
00336             DESCX( CSRC_ ) = IACOL
00337             CALL PDLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN,
00338      $                    N, A, IA, JA, DESCA, WORK( IPX ), IX, JX,
00339      $                    DESCX, SL, WORK( IPNL ), WORK( IPW ) )
00340             DESCX( CSRC_ ) = MYCOL
00341             NORMIN = 'Y'
00342 *
00343 *           Multiply by inv(U).
00344 *
00345             DESCX( CSRC_ ) = IACOL
00346             CALL PDLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN,
00347      $                    N, A, IA, JA, DESCA, WORK( IPX ), IX, JX,
00348      $                    DESCX, SU, WORK( IPNU ), WORK( IPW ) )
00349             DESCX( CSRC_ ) = MYCOL
00350          ELSE
00351 *
00352 *           Multiply by inv(L).
00353 *
00354             DESCX( CSRC_ ) = IACOL
00355             CALL PDLATRS( 'Lower', 'No transpose', 'Non-unit', NORMIN,
00356      $                    N, A, IA, JA, DESCA, WORK( IPX ), IX, JX,
00357      $                    DESCX, SL, WORK( IPNL ), WORK( IPW ) )
00358             DESCX( CSRC_ ) = MYCOL
00359             NORMIN = 'Y'
00360 *
00361 *           Multiply by inv(L').
00362 *
00363             DESCX( CSRC_ ) = IACOL
00364             CALL PDLATRS( 'Lower', 'Transpose', 'Non-unit', NORMIN,
00365      $                    N, A, IA, JA, DESCA, WORK( IPX ), IX, JX,
00366      $                    DESCX, SU, WORK( IPNU ), WORK( IPW ) )
00367             DESCX( CSRC_ ) = MYCOL
00368          END IF
00369 *
00370 *        Multiply by 1/SCALE if doing so will not cause overflow.
00371 *
00372          SCALE = SL*SU
00373          IF( SCALE.NE.ONE ) THEN
00374             CALL PDAMAX( N, WMAX, IXX, WORK( IPX ), IX, JX, DESCX, 1 )
00375             IF( DESCX( M_ ).EQ.1 .AND. N.EQ.1 ) THEN
00376                CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', CBTOP )
00377                IF( MYROW.EQ.IAROW ) THEN
00378                   CALL DGEBS2D( ICTXT, 'Column', CBTOP, 1, 1, WMAX, 1 )
00379                ELSE
00380                   CALL DGEBR2D( ICTXT, 'Column', CBTOP, 1, 1, WMAX, 1,
00381      $                          IAROW, MYCOL )
00382                END IF
00383             END IF
00384             IF( SCALE.LT.ABS( WMAX )*SMLNUM .OR. SCALE.EQ.ZERO )
00385      $         GO TO 20
00386             CALL PDRSCL( N, SCALE, WORK( IPX ), IX, JX, DESCX, 1 )
00387          END IF
00388          GO TO 10
00389       END IF
00390 *
00391 *     Compute the estimate of the reciprocal condition number.
00392 *
00393       IF( AINVNM.NE.ZERO )
00394      $   RCOND = ( ONE / AINVNM ) / ANORM
00395 *
00396    20 CONTINUE
00397 *
00398       CALL PB_TOPSET( ICTXT, 'Combine', 'Columnwise', COLCTOP )
00399       CALL PB_TOPSET( ICTXT, 'Combine', 'Rowwise',    ROWCTOP )
00400 *
00401       RETURN
00402 *
00403 *     End of PDPOCON
00404 *
00405       END