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SUBROUTINE PSINVCHK( MATTYP, N, A, IA, JA, DESCA, IASEED, ANORM,
$ FRESID, RCOND, WORK )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 28, 2001
*
* .. Scalar Arguments ..
INTEGER IA, IASEED, JA, N
REAL ANORM, FRESID, RCOND
* ..
* .. Array Arguments ..
CHARACTER*3 MATTYP
INTEGER DESCA( * )
REAL A( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PSINVCHK computes the scaled residual
*
* || sub( A ) * inv( sub( A ) ) - I || / ( || sub( A ) || * N * eps ),
*
* where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1). to check the result
* returned by the matrix inversion routines.
*
* 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
* =========
*
* MATTYP (global input) CHARACTER*3
* The type of the distributed matrix to be generated:
* if MATTYP = 'GEN' then GENeral matrix,
* if MATTYP = 'UTR' then Upper TRiangular matrix,
* if MATTYP = 'LTR' then Lower TRiangular matrix,
* if MATTYP = 'UPD' then (Upper) symmetric Positive Definite,
* if MATTYP = 'LPD' then (Lower) symmetric Positive Definite,
*
* N (global input) INTEGER
* The number of rows and columns to be operated on, i.e. the
* order of the distributed submatrix sub( A ). N >= 0.
*
* A (local input) REAL pointer into the local memory
* to an array of local dimension (LLD_A, LOCc(JA+N-1)). On
* entry, sub( A ) contains the distributed matrix inverse
* computed by PSGETRI, PSPOTRI or PSTRTRI.
*
* 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.
*
* IASEED (global input) INTEGER
* Seed for the random generation of sub( A ).
*
* ANORM (global input) REAL
* The 1-norm of the original matrix sub( A ).
*
* FRESID (global output) REAL
* The inversion residual.
*
* RCOND (global output) REAL
* The condition number of the original distributed matrix.
* RCOND = || sub( A ) ||.|| sub( A )^{-1} || where ||A||
* denotes the 1-norm of A.
*
* WORK (local workspace) REAL array, dimension
* MAX(2*LOCr(N_A+MOD(IA-1,MB_A))*MB_A, LDW)
* where LDW is the workspace requirement for the norm computa-
* tions, see PSLANGE, PSLANSY and PSLANTR.
*
* =====================================================================
*
* .. 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 )
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
CHARACTER AFORM, DIAG, UPLO
INTEGER ICTXT, ICURCOL, ICURROW, II, IIA, IPW, IROFF,
$ IW, J, JB, JJA, JN, KK, MYCOL, MYROW, NP,
$ NPCOL, NPROW
REAL AUXNORM, EPS, NRMINVAXA, TEMP
* ..
* .. Local Arrays ..
INTEGER DESCW( DLEN_ )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DESCSET, INFOG2L, PSGEMM,
$ PSLASET, PSMATGEN, PSSYMM, PSTRMM
* ..
* .. External Functions ..
LOGICAL LSAMEN
INTEGER ICEIL, NUMROC
REAL PSLAMCH, PSLANGE, PSLANSY, PSLANTR
EXTERNAL ICEIL, LSAMEN, NUMROC, PSLAMCH, PSLANGE,
$ PSLANSY, PSLANTR
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, MOD
* ..
* .. Executable Statements ..
*
EPS = PSLAMCH( DESCA( CTXT_ ), 'eps' )
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Compute the condition number
*
IF( LSAMEN( 1, MATTYP( 1:1 ), 'U' ) ) THEN
UPLO = 'U'
ELSE
UPLO = 'L'
END IF
*
IF( LSAMEN( 3, MATTYP, 'GEN' ) ) THEN
*
AFORM = 'N'
DIAG = 'D'
AUXNORM = PSLANGE( '1', N, N, A, IA, JA, DESCA, WORK )
*
ELSE IF( LSAMEN( 2, MATTYP( 2:3 ), 'TR' ) ) THEN
*
AFORM = 'N'
DIAG = 'D'
AUXNORM = PSLANTR( '1', UPLO, 'Non unit', N, N, A, IA, JA,
$ DESCA, WORK )
ELSE IF( LSAMEN( 2, MATTYP( 2:3 ), 'PD' ) ) THEN
*
AFORM = 'S'
DIAG = 'D'
AUXNORM = PSLANSY( '1', UPLO, N, A, IA, JA, DESCA, WORK )
*
END IF
RCOND = ANORM*AUXNORM
*
* Compute inv(A)*A
*
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA,
$ ICURROW, ICURCOL )
*
* Define array descriptor for working array WORK
*
IROFF = MOD( IA-1, DESCA( MB_ ) )
NP = NUMROC( N+IROFF, DESCA( MB_ ), MYROW, ICURROW, NPROW )
CALL DESCSET( DESCW, N+IROFF, DESCA( NB_ ), DESCA( MB_ ),
$ DESCA( NB_ ), ICURROW, ICURCOL, DESCA( CTXT_ ),
$ MAX( 1, NP ) )
IPW = DESCW( LLD_ ) * DESCW( NB_ ) + 1
*
IF( MYROW.EQ.ICURROW ) THEN
II = IROFF + 1
NP = NP - IROFF
ELSE
II = 1
END IF
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
JB = JN - JA + 1
*
* Handle first block separately, regenerate a block of columns of A
*
IW = IROFF + 1
IF( MYCOL.EQ.ICURCOL ) THEN
IF( LSAMEN( 2, MATTYP( 2:3 ), 'TR' ) ) THEN
CALL PSMATGEN( ICTXT, AFORM, DIAG, DESCA( M_ ), DESCA( N_ ),
$ DESCW( MB_ ), DESCW( NB_ ), WORK,
$ DESCW( LLD_ ), DESCA( RSRC_ ),
$ DESCA( CSRC_ ), IASEED, IIA-1, NP,
$ JJA-1, JB, MYROW, MYCOL, NPROW, NPCOL )
IF( LSAMEN( 3, MATTYP, 'UTR' ) ) THEN
CALL PSLASET( 'Lower', N-1, JB, ZERO, ZERO, WORK, IW+1,
$ 1, DESCW )
ELSE
CALL PSLASET( 'Upper', JB-1, JB-1, ZERO, ZERO, WORK, IW,
$ 2, DESCW )
END IF
ELSE
CALL PSMATGEN( ICTXT, AFORM, DIAG, DESCA( M_ ), DESCA( N_ ),
$ DESCW( MB_ ), DESCW( NB_ ), WORK( IPW ),
$ DESCW( LLD_ ), DESCA( RSRC_ ),
$ DESCA( CSRC_ ), IASEED,
$ IIA-1, NP, JJA-1, JB, MYROW, MYCOL, NPROW,
$ NPCOL )
END IF
END IF
*
* Multiply A^{-1}*A
*
IF( LSAMEN( 3, MATTYP, 'GEN' ) ) THEN
*
CALL PSGEMM( 'No tranpose', 'No transpose', N, JB, N, ONE, A,
$ IA, JA, DESCA, WORK( IPW ), IW, 1, DESCW, ZERO,
$ WORK, IW, 1, DESCW )
*
ELSE IF( LSAMEN( 2, MATTYP( 2:3 ), 'TR' ) ) THEN
*
CALL PSTRMM( 'Left', UPLO, 'No tranpose', 'Non unit', N, JB,
$ ONE, A, IA, JA, DESCA, WORK, IW, 1, DESCW )
*
ELSE IF( LSAMEN( 2, MATTYP( 2:3 ), 'PD' ) ) THEN
*
CALL PSSYMM( 'Left', UPLO, N, JB, ONE, A, IA, JA, DESCA,
$ WORK( IPW ), IW, 1, DESCW, ZERO, WORK, IW, 1,
$ DESCW )
*
END IF
*
* subtract the identity matrix to the diagonal block of these cols
*
IF( MYROW.EQ.ICURROW .AND. MYCOL.EQ.ICURCOL ) THEN
DO 10 KK = 0, JB-1
WORK( II+KK*(DESCW(LLD_)+1) ) =
$ WORK( II+KK*(DESCW( LLD_ )+1) )-ONE
10 CONTINUE
END IF
*
NRMINVAXA = PSLANGE( '1', N, JB, WORK, IW, 1, DESCW, WORK( IPW ) )
*
IF( MYROW.EQ.ICURROW )
$ II = II + JB
IF( MYCOL.EQ.ICURCOL )
$ JJA = JJA + JB
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
DESCW( CSRC_ ) = ICURCOL
*
DO 30 J = JN+1, JA+N-1, DESCA( NB_ )
*
JB = MIN( N-J+JA, DESCA( NB_ ) )
*
* regenerate a block of columns of A
*
IF( MYCOL.EQ.ICURCOL ) THEN
IF( LSAMEN( 2, MATTYP( 2:3 ), 'TR' ) ) THEN
CALL PSMATGEN( ICTXT, AFORM, DIAG, DESCA( M_ ),
$ DESCA( N_ ), DESCW( MB_ ), DESCW( NB_ ),
$ WORK, DESCW( LLD_ ), DESCA( RSRC_ ),
$ DESCA( CSRC_ ),
$ IASEED, IIA-1, NP, JJA-1, JB, MYROW,
$ MYCOL, NPROW, NPCOL )
IF( LSAMEN( 3, MATTYP, 'UTR' ) ) THEN
CALL PSLASET( 'Lower', JA+N-J-1, JB, ZERO, ZERO,
$ WORK, IW+J-JA+1, 1, DESCW )
ELSE
CALL PSLASET( 'All', J-JA, JB, ZERO, ZERO, WORK, IW,
$ 1, DESCW )
CALL PSLASET( 'Upper', JB-1, JB-1, ZERO, ZERO,
$ WORK, IW+J-JA, 2, DESCW )
END IF
ELSE
CALL PSMATGEN( ICTXT, AFORM, DIAG, DESCA( M_ ),
$ DESCA( N_ ), DESCW( MB_ ), DESCW( NB_ ),
$ WORK( IPW ), DESCW( LLD_ ),
$ DESCA( RSRC_ ), DESCA( CSRC_ ), IASEED,
$ IIA-1, NP,
$ JJA-1, JB, MYROW, MYCOL, NPROW, NPCOL )
END IF
END IF
*
* Multiply A^{-1}*A
*
IF( LSAMEN( 3, MATTYP, 'GEN' ) ) THEN
*
CALL PSGEMM( 'No tranpose', 'No transpose', N, JB, N, ONE,
$ A, IA, JA, DESCA, WORK( IPW ), IW, 1, DESCW,
$ ZERO, WORK, IW, 1, DESCW )
*
ELSE IF( LSAMEN( 2, MATTYP(2:3), 'TR' ) ) THEN
*
CALL PSTRMM( 'Left', UPLO, 'No tranpose', 'Non unit', N, JB,
$ ONE, A, IA, JA, DESCA, WORK, IW, 1, DESCW )
*
ELSE IF( LSAMEN( 2, MATTYP( 2:3 ), 'PD' ) ) THEN
*
CALL PSSYMM( 'Left', UPLO, N, JB, ONE, A, IA, JA, DESCA,
$ WORK(IPW), IW, 1, DESCW, ZERO, WORK, IW, 1,
$ DESCW )
*
END IF
*
* subtract the identity matrix to the diagonal block of these
* cols
*
IF( MYROW.EQ.ICURROW .AND. MYCOL.EQ.ICURCOL ) THEN
DO 20 KK = 0, JB-1
WORK( II+KK*(DESCW( LLD_ )+1) ) =
$ WORK( II+KK*(DESCW( LLD_ )+1) ) - ONE
20 CONTINUE
END IF
*
* Compute the 1-norm of these JB cols
*
TEMP = PSLANGE( '1', N, JB, WORK, IW, 1, DESCW, WORK( IPW ) )
NRMINVAXA = MAX( TEMP, NRMINVAXA )
*
IF( MYROW.EQ.ICURROW )
$ II = II + JB
IF( MYCOL.EQ.ICURCOL )
$ JJA = JJA + JB
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
DESCW( CSRC_ ) = ICURCOL
*
30 CONTINUE
*
* Compute the scaled residual
*
FRESID = NRMINVAXA / ( N * EPS * ANORM )
*
RETURN
*
* End of PSINVCHK
*
END
|
