SUBROUTINE PSLACON( N, V, IV, JV, DESCV, X, IX, JX, DESCX, ISGN, $ EST, KASE ) * * -- ScaLAPACK auxiliary routine (version 1.5) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. INTEGER IV, IX, JV, JX, KASE, N REAL EST * .. * .. Array Arguments .. INTEGER DESCV( * ), DESCX( * ), ISGN( * ) REAL V( * ), X( * ) * .. * * Purpose * ======= * * PSLACON estimates the 1-norm of a square, real distributed matrix A. * Reverse communication is used for evaluating matrix-vector products. * X and V are aligned with the distributed matrix A, this information * is implicitly contained within IV, IX, DESCV, and DESCX. * * Notes * ===== * * Each global data object is described by an associated description * vector. This vector stores the information required to establish * the mapping between an object element and its corresponding process * and memory location. * * Let A be a generic term for any 2D block cyclicly distributed array. * Such a global array has an associated description vector DESCA. * In the following comments, the character _ should be read as * "of the global array". * * NOTATION STORED IN EXPLANATION * --------------- -------------- -------------------------------------- * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, * DTYPE_A = 1. * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating * the BLACS process grid A is distribu- * ted over. The context itself is glo- * bal, but the handle (the integer * value) may vary. * M_A (global) DESCA( M_ ) The number of rows in the global * array A. * N_A (global) DESCA( N_ ) The number of columns in the global * array A. * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute * the rows of the array. * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute * the columns of the array. * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first * row of the array A is distributed. * CSRC_A (global) DESCA( CSRC_ ) The process column over which the * first column of the array A is * distributed. * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local * array. LLD_A >= MAX(1,LOCr(M_A)). * * Let K be the number of rows or columns of a distributed matrix, * and assume that its process grid has dimension p x q. * LOCr( K ) denotes the number of elements of K that a process * would receive if K were distributed over the p processes of its * process column. * Similarly, LOCc( K ) denotes the number of elements of K that a * process would receive if K were distributed over the q processes of * its process row. * The values of LOCr() and LOCc() may be determined via a call to the * ScaLAPACK tool function, NUMROC: * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). * An upper bound for these quantities may be computed by: * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A * * Arguments * ========= * * N (global input) INTEGER * The length of the distributed vectors V and X. N >= 0. * * V (local workspace) REAL pointer into the local * memory to an array of dimension LOCr(N+MOD(IV-1,MB_V)). On * the final return, V = A*W, where EST = norm(V)/norm(W) * (W is not returned). * * IV (global input) INTEGER * The row index in the global array V indicating the first * row of sub( V ). * * JV (global input) INTEGER * The column index in the global array V indicating the * first column of sub( V ). * * DESCV (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix V. * * X (local input/local output) REAL pointer into the * local memory to an array of dimension * LOCr(N+MOD(IX-1,MB_X)). On an intermediate return, X * should be overwritten by * A * X, if KASE=1, * A' * X, if KASE=2, * PSLACON must be re-called with all the other parameters * unchanged. * * IX (global input) INTEGER * The row index in the global array X indicating the first * row of sub( X ). * * JX (global input) INTEGER * The column index in the global array X indicating the * first column of sub( X ). * * DESCX (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix X. * * ISGN (local workspace) INTEGER array, dimension * LOCr(N+MOD(IX-1,MB_X)). ISGN is aligned with X and V. * * * EST (global output) REAL * An estimate (a lower bound) for norm(A). * * KASE (local input/local output) INTEGER * On the initial call to PSLACON, KASE should be 0. * On an intermediate return, KASE will be 1 or 2, indicating * whether X should be overwritten by A * X or A' * X. * On the final return from PSLACON, KASE will again be 0. * * Further Details * =============== * * The serial version SLACON has been contributed by Nick Higham, * University of Manchester. It was originally named SONEST, dated * March 16, 1988. * * Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of * a real or complex matrix, with applications to condition estimation", * ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988. * * ===================================================================== * * .. Parameters .. INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, $ LLD_, MB_, M_, NB_, N_, RSRC_ PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) INTEGER ITMAX PARAMETER ( ITMAX = 5 ) REAL ZERO, ONE, TWO PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0 ) * .. * .. Local Scalars .. INTEGER I, ICTXT, IFLAG, IIVX, IMAXROW, IOFFVX, IROFF, $ ITER, IVXCOL, IVXROW, J, JLAST, JJVX, JUMP, $ K, MYCOL, MYROW, NP, NPCOL, NPROW REAL ALTSGN, ESTOLD, JLMAX, TEMP, XMAX * .. * .. Local Arrays .. REAL WORK( 2 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, IGSUM2D, INFOG2L, PSAMAX, $ PSASUM, PSELGET, SGEBR2D, $ SGEBS2D, SCOPY * .. * .. External Functions .. INTEGER INDXG2L, INDXG2P, INDXL2G, NUMROC EXTERNAL INDXG2L, INDXG2P, INDXL2G, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC ABS, MOD, NINT, REAL, SIGN * .. * .. Save statement .. SAVE * .. * .. Executable Statements .. * * Get grid parameters. * ICTXT = DESCX( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * CALL INFOG2L( IX, JX, DESCX, NPROW, NPCOL, MYROW, MYCOL, $ IIVX, JJVX, IVXROW, IVXCOL ) IF( MYCOL.NE.IVXCOL ) $ RETURN IROFF = MOD( IX-1, DESCX( MB_ ) ) NP = NUMROC( N+IROFF, DESCX( MB_ ), MYROW, IVXROW, NPROW ) IF( MYROW.EQ.IVXROW ) $ NP = NP - IROFF IOFFVX = IIVX + (JJVX-1)*DESCX( LLD_ ) * IF( KASE.EQ.0 ) THEN DO 10 I = IOFFVX, IOFFVX+NP-1 X( I ) = ONE / REAL( N ) 10 CONTINUE KASE = 1 JUMP = 1 RETURN END IF * GO TO ( 20, 40, 70, 110, 140 )JUMP * * ................ ENTRY (JUMP = 1) * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X * 20 CONTINUE IF( N.EQ.1 ) THEN IF( MYROW.EQ.IVXROW ) THEN V( IOFFVX ) = X( IOFFVX ) EST = ABS( V( IOFFVX ) ) CALL SGEBS2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1 ) ELSE CALL SGEBR2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1, $ IVXROW, MYCOL ) END IF * ... QUIT GO TO 150 END IF CALL PSASUM( N, EST, X, IX, JX, DESCX, 1 ) IF( DESCX( M_ ).EQ.1 .AND. N.EQ.1 ) THEN IF( MYROW.EQ.IVXROW ) THEN CALL SGEBS2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1 ) ELSE CALL SGEBR2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1, $ IVXROW, MYCOL ) END IF END IF * DO 30 I = IOFFVX, IOFFVX+NP-1 X( I ) = SIGN( ONE, X( I ) ) ISGN( I ) = NINT( X( I ) ) 30 CONTINUE KASE = 2 JUMP = 2 RETURN * * ................ ENTRY (JUMP = 2) * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X * 40 CONTINUE CALL PSAMAX( N, XMAX, J, X, IX, JX, DESCX, 1 ) IF( DESCX( M_ ).EQ.1 .AND. N.EQ.1 ) THEN IF( MYROW.EQ.IVXROW ) THEN WORK( 1 ) = XMAX WORK( 2 ) = REAL( J ) CALL SGEBS2D( ICTXT, 'Columnwise', ' ', 2, 1, WORK, 2 ) ELSE CALL SGEBR2D( ICTXT, 'Columnwise', ' ', 2, 1, WORK, 2, $ IVXROW, MYCOL ) XMAX = WORK( 1 ) J = NINT( WORK( 2 ) ) END IF END IF ITER = 2 * * MAIN LOOP - ITERATIONS 2, 3,...,ITMAX * 50 CONTINUE DO 60 I = IOFFVX, IOFFVX+NP-1 X( I ) = ZERO 60 CONTINUE IMAXROW = INDXG2P( J, DESCX( MB_ ), MYROW, DESCX( RSRC_ ), NPROW ) IF( MYROW.EQ.IMAXROW ) THEN I = INDXG2L( J, DESCX( MB_ ), MYROW, DESCX( RSRC_ ), NPROW ) X( I ) = ONE END IF KASE = 1 JUMP = 3 RETURN * * ................ ENTRY (JUMP = 3) * X HAS BEEN OVERWRITTEN BY A*X * 70 CONTINUE CALL SCOPY( NP, X( IOFFVX ), 1, V( IOFFVX ), 1 ) ESTOLD = EST CALL PSASUM( N, EST, V, IV, JV, DESCV, 1 ) IF( DESCV( M_ ).EQ.1 .AND. N.EQ.1 ) THEN IF( MYROW.EQ.IVXROW ) THEN CALL SGEBS2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1 ) ELSE CALL SGEBR2D( ICTXT, 'Columnwise', ' ', 1, 1, EST, 1, $ IVXROW, MYCOL ) END IF END IF IFLAG = 0 DO 80 I = IOFFVX, IOFFVX+NP-1 IF( NINT( SIGN( ONE, X( I ) ) ).NE.ISGN( I ) ) THEN IFLAG = 1 GO TO 90 END IF 80 CONTINUE * 90 CONTINUE CALL IGSUM2D( ICTXT, 'C', ' ', 1, 1, IFLAG, 1, -1, MYCOL ) * * REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED. * ALONG WITH IT, TEST FOR CYCLING. * IF( IFLAG.EQ.0 .OR. EST.LE.ESTOLD ) $ GO TO 120 * DO 100 I = IOFFVX, IOFFVX+NP-1 X( I ) = SIGN( ONE, X( I ) ) ISGN( I ) = NINT( X( I ) ) 100 CONTINUE KASE = 2 JUMP = 4 RETURN * * ................ ENTRY (JUMP = 4) * X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X * 110 CONTINUE JLAST = J CALL PSAMAX( N, XMAX, J, X, IX, JX, DESCX, 1 ) IF( DESCX( M_ ).EQ.1 .AND. N.EQ.1 ) THEN IF( MYROW.EQ.IVXROW ) THEN WORK( 1 ) = XMAX WORK( 2 ) = REAL( J ) CALL SGEBS2D( ICTXT, 'Columnwise', ' ', 2, 1, WORK, 2 ) ELSE CALL SGEBR2D( ICTXT, 'Columnwise', ' ', 2, 1, WORK, 2, $ IVXROW, MYCOL ) XMAX = WORK( 1 ) J = NINT( WORK( 2 ) ) END IF END IF CALL PSELGET( 'Columnwise', ' ', JLMAX, X, JLAST, JX, DESCX ) IF( ( JLMAX.NE.ABS( XMAX ) ).AND.( ITER.LT.ITMAX ) ) THEN ITER = ITER + 1 GO TO 50 END IF * * ITERATION COMPLETE. FINAL STAGE. * 120 CONTINUE DO 130 I = IOFFVX, IOFFVX+NP-1 K = INDXL2G( I-IOFFVX+IIVX, DESCX( MB_ ), MYROW, $ DESCX( RSRC_ ), NPROW )-IX+1 IF( MOD( K, 2 ).EQ.0 ) THEN ALTSGN = -ONE ELSE ALTSGN = ONE END IF X( I ) = ALTSGN*( ONE+REAL( K-1 ) / REAL( N-1 ) ) 130 CONTINUE KASE = 1 JUMP = 5 RETURN * * ................ ENTRY (JUMP = 5) * X HAS BEEN OVERWRITTEN BY A*X * 140 CONTINUE CALL PSASUM( N, TEMP, X, IX, JX, DESCX, 1 ) IF( DESCX( M_ ).EQ.1 .AND. N.EQ.1 ) THEN IF( MYROW.EQ.IVXROW ) THEN CALL SGEBS2D( ICTXT, 'Columnwise', ' ', 1, 1, TEMP, 1 ) ELSE CALL SGEBR2D( ICTXT, 'Columnwise', ' ', 1, 1, TEMP, 1, $ IVXROW, MYCOL ) END IF END IF TEMP = TWO*( TEMP / REAL( 3*N ) ) IF( TEMP.GT.EST ) THEN CALL SCOPY( NP, X( IOFFVX ), 1, V( IOFFVX ), 1 ) EST = TEMP END IF * 150 CONTINUE KASE = 0 * RETURN * * End of PSLACON * END