SUBROUTINE PDTRCON( NORM, UPLO, DIAG, N, A, IA, JA, DESCA, RCOND, \$ WORK, LWORK, IWORK, LIWORK, INFO ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 25, 2001 * * * .. Scalar Arguments .. CHARACTER DIAG, NORM, UPLO INTEGER IA, JA, INFO, LIWORK, LWORK, N DOUBLE PRECISION RCOND * .. * .. Array Arguments .. INTEGER DESCA( * ), IWORK( * ) DOUBLE PRECISION A( * ), WORK( * ) * .. * * Purpose * ======= * * PDTRCON estimates the reciprocal of the condition number of a * triangular distributed matrix A(IA:IA+N-1,JA:JA+N-1), in either the * 1-norm or the infinity-norm. * * The norm of A(IA:IA+N-1,JA:JA+N-1) is computed and an estimate is * obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), then the reciprocal * of the condition number is computed as * RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1) ) * * norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ). * * 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 * ========= * * NORM (global input) CHARACTER * Specifies whether the 1-norm condition number or the * infinity-norm condition number is required: * = '1' or 'O': 1-norm; * = 'I': Infinity-norm. * * UPLO (global input) CHARACTER * = 'U': A(IA:IA+N-1,JA:JA+N-1) is upper triangular; * = 'L': A(IA:IA+N-1,JA:JA+N-1) is lower triangular. * * DIAG (global input) CHARACTER * = 'N': A(IA:IA+N-1,JA:JA+N-1) is non-unit triangular; * = 'U': A(IA:IA+N-1,JA:JA+N-1) is unit triangular. * * N (global input) INTEGER * The order of the distributed matrix A(IA:IA+N-1,JA:JA+N-1). * N >= 0. * * A (local input) DOUBLE PRECISION pointer into the local memory * to an array of dimension ( LLD_A, LOCc(JA+N-1) ). This array * contains the local pieces of the triangular distributed * matrix A(IA:IA+N-1,JA:JA+N-1). If UPLO = 'U', the leading * N-by-N upper triangular part of this distributed matrix con- * tains the upper triangular matrix, and its strictly lower * triangular part is not referenced. If UPLO = 'L', the * leading N-by-N lower triangular part of this ditributed * matrix contains the lower triangular matrix, and the strictly * upper triangular part is not referenced. If DIAG = 'U', the * diagonal elements of A(IA:IA+N-1,JA:JA+N-1) are also not * referenced and are assumed to be 1. * * IA (global input) INTEGER * The row index in the global array A indicating the first * row of sub( A ). * * JA (global input) INTEGER * The column index in the global array A indicating the * first column of sub( A ). * * DESCA (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix A. * * RCOND (global output) DOUBLE PRECISION * The reciprocal of the condition number of the distributed * matrix A(IA:IA+N-1,JA:JA+N-1), computed as * RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1) ) * * norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ). * * WORK (local workspace/local output) DOUBLE PRECISION array, * dimension (LWORK) * On exit, WORK(1) returns the minimal and optimal LWORK. * * LWORK (local or global input) INTEGER * The dimension of the array WORK. * LWORK is local input and must be at least * LWORK >= 2*LOCr(N+MOD(IA-1,MB_A)) + LOCc(N+MOD(JA-1,NB_A)) * + MAX( 2, MAX( NB_A*MAX( 1, CEIL(NPROW-1,NPCOL) ), * LOCc(N+MOD(JA-1,NB_A)) + * NB_A*MAX( 1, CEIL(NPCOL-1,NPROW) ) ). * * If LWORK = -1, then LWORK is global input and a workspace * query is assumed; the routine only calculates the minimum * and optimal size for all work arrays. Each of these * values is returned in the first entry of the corresponding * work array, and no error message is issued by PXERBLA. * * IWORK (local workspace/local output) INTEGER array, * dimension (LIWORK) * On exit, IWORK(1) returns the minimal and optimal LIWORK. * * LIWORK (local or global input) INTEGER * The dimension of the array IWORK. * LIWORK is local input and must be at least * LIWORK >= LOCr(N+MOD(IA-1,MB_A)). * * If LIWORK = -1, then LIWORK is global input and a workspace * query is assumed; the routine only calculates the minimum * and optimal size for all work arrays. Each of these * values is returned in the first entry of the corresponding * work array, and no error message is issued by PXERBLA. * * * INFO (global output) INTEGER * = 0: successful exit * < 0: If the i-th argument is an array and the j-entry had * an illegal value, then INFO = -(i*100+j), if the i-th * argument is a scalar and had an illegal value, then * INFO = -i. * * ===================================================================== * * .. 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 ) DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY, NOUNIT, ONENRM, UPPER CHARACTER CBTOP, COLCTOP, NORMIN, ROWCTOP INTEGER IACOL, IAROW, ICOFF, ICTXT, IIA, IPN, IPV, IPW, \$ IPX, IROFF, IV, IX, IXX, JJA, JV, JX, KASE, \$ KASE1, LIWMIN, LWMIN, MYCOL, MYROW, NP, NPCOL, \$ NPMOD, NPROW, NQ, NQMOD DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM DOUBLE PRECISION WMAX * .. * .. Local Arrays .. INTEGER DESCV( DLEN_ ), DESCX( DLEN_ ), IDUM1( 5 ), \$ IDUM2( 5 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, DESCSET, DGEBR2D, \$ DGEBS2D, INFOG2L, PCHK1MAT, PDAMAX, \$ PDLATRS, PDLACON, PDRSCL, PB_TOPGET, \$ PB_TOPSET, PXERBLA * .. * .. External Functions .. LOGICAL LSAME INTEGER ICEIL, INDXG2P, NUMROC DOUBLE PRECISION PDLAMCH, PDLANTR EXTERNAL ICEIL, INDXG2P, LSAME, NUMROC, PDLAMCH, \$ PDLANTR * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, ICHAR, MAX, MOD * .. * .. Executable Statements .. * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * * Test the input parameters * INFO = 0 IF( NPROW.EQ.-1 ) THEN INFO = -( 800 + CTXT_ ) ELSE CALL CHK1MAT( N, 4, N, 4, IA, JA, DESCA, 8, INFO ) IF( INFO.EQ.0 ) THEN UPPER = LSAME( UPLO, 'U' ) ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) NOUNIT = LSAME( DIAG, 'N' ) IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), \$ NPROW ) IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), \$ NPCOL ) NPMOD = NUMROC( N + MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ), \$ MYROW, IAROW, NPROW ) NQMOD = NUMROC( N + MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ), \$ MYCOL, IACOL, NPCOL ) LWMIN = 2*NPMOD + NQMOD + \$ MAX( 2, MAX( DESCA( NB_ )* \$ MAX( 1, ICEIL( NPROW-1, NPCOL ) ), NQMOD + \$ DESCA( NB_ )* \$ MAX( 1, ICEIL( NPCOL-1, NPROW ) ) ) ) WORK( 1 ) = DBLE( LWMIN ) LIWMIN = NPMOD IWORK( 1 ) = LIWMIN LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) * IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -3 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -11 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN INFO = -13 END IF END IF * IF( ONENRM ) THEN IDUM1( 1 ) = ICHAR( '1' ) ELSE IDUM1( 1 ) = ICHAR( 'I' ) END IF IDUM2( 1 ) = 1 IF( UPPER ) THEN IDUM1( 2 ) = ICHAR( 'U' ) ELSE IDUM1( 2 ) = ICHAR( 'L' ) END IF IDUM2( 2 ) = 2 IF( NOUNIT ) THEN IDUM1( 3 ) = ICHAR( 'N' ) ELSE IDUM1( 3 ) = ICHAR( 'U' ) END IF IDUM2( 3 ) = 3 IF( LWORK.EQ.-1 ) THEN IDUM1( 4 ) = -1 ELSE IDUM1( 4 ) = 1 END IF IDUM2( 4 ) = 11 IF( LIWORK.EQ.-1 ) THEN IDUM1( 5 ) = -1 ELSE IDUM1( 5 ) = 1 END IF IDUM2( 5 ) = 13 CALL PCHK1MAT( N, 4, N, 4, IA, JA, DESCA, 8, 5, IDUM1, IDUM2, \$ INFO ) END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PDTRCON', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) THEN RCOND = ONE RETURN END IF * CALL PB_TOPGET( ICTXT, 'Combine', 'Columnwise', COLCTOP ) CALL PB_TOPGET( ICTXT, 'Combine', 'Rowwise', ROWCTOP ) CALL PB_TOPSET( ICTXT, 'Combine', 'Columnwise', '1-tree' ) CALL PB_TOPSET( ICTXT, 'Combine', 'Rowwise', '1-tree' ) * RCOND = ZERO SMLNUM = PDLAMCH( ICTXT, 'Safe minimum' )*DBLE( MAX( 1, N ) ) CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, \$ IAROW, IACOL ) IROFF = MOD( IA-1, DESCA( MB_ ) ) ICOFF = MOD( JA-1, DESCA( NB_ ) ) NP = NUMROC( N+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) IV = IROFF + 1 IX = IV JV = ICOFF + 1 JX = JV * IPX = 1 IPV = IPX + NP IPN = IPV + NP IPW = IPN + NQ * CALL DESCSET( DESCV, N+IROFF, 1, DESCA( MB_ ), 1, IAROW, MYCOL, \$ ICTXT, MAX( 1, NP ) ) CALL DESCSET( DESCX, N+IROFF, 1, DESCA( MB_ ), 1, IAROW, MYCOL, \$ ICTXT, MAX( 1, NP ) ) * * Compute the norm of the triangular matrix A. * ANORM = PDLANTR( NORM, UPLO, DIAG, N, N, A, IA, JA, DESCA, WORK ) * * Continue only if ANORM > 0. * IF( ANORM.GT.ZERO ) THEN * * Estimate the norm of the inverse of A. * AINVNM = ZERO NORMIN = 'N' IF( ONENRM ) THEN KASE1 = 1 ELSE KASE1 = 2 END IF KASE = 0 10 CONTINUE CALL PDLACON( N, WORK( IPV ), IV, JV, DESCV, WORK( IPX ), \$ IX, JX, DESCX, IWORK, AINVNM, KASE ) IF( KASE.NE.0 ) THEN IF( KASE.EQ.KASE1 ) THEN * * Multiply by inv(A). * DESCX( CSRC_ ) = IACOL CALL PDLATRS( UPLO, 'No transpose', DIAG, NORMIN, \$ N, A, IA, JA, DESCA, WORK( IPX ), IX, JX, \$ DESCX, SCALE, WORK( IPN ), WORK( IPW ) ) DESCX( CSRC_ ) = MYCOL ELSE * * Multiply by inv(A'). * DESCX( CSRC_ ) = IACOL CALL PDLATRS( UPLO, 'Transpose', DIAG, NORMIN, \$ N, A, IA, JA, DESCA, WORK( IPX ), IX, JX, \$ DESCX, SCALE, WORK( IPN ), WORK( IPW ) ) DESCX( CSRC_ ) = MYCOL END IF NORMIN = 'Y' * * Multiply by 1/SCALE if doing so will not cause overflow. * IF( SCALE.NE.ONE ) THEN CALL PDAMAX( N, WMAX, IXX, WORK( IPX ), IX, JX, \$ DESCX, 1 ) IF( DESCX( M_ ).EQ.1 .AND. N.EQ.1 ) THEN CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', \$ CBTOP ) IF( MYROW.EQ.IAROW ) THEN CALL DGEBS2D( ICTXT, 'Column', CBTOP, 1, 1, WMAX, \$ 1 ) ELSE CALL DGEBR2D( ICTXT, 'Column', CBTOP, 1, 1, WMAX, \$ 1, IAROW, MYCOL ) END IF END IF IF( SCALE.LT.ABS( WMAX )*SMLNUM .OR. SCALE.EQ.ZERO ) \$ GO TO 20 CALL PDRSCL( N, SCALE, WORK( IPX ), IX, JX, DESCX, 1 ) END IF GO TO 10 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM.NE.ZERO ) \$ RCOND = ( ONE / ANORM ) / AINVNM END IF * 20 CONTINUE * CALL PB_TOPSET( ICTXT, 'Combine', 'Columnwise', COLCTOP ) CALL PB_TOPSET( ICTXT, 'Combine', 'Rowwise', ROWCTOP ) * RETURN * * End of PDTRCON * END