SUBROUTINE PSGETRI( N, A, IA, JA, DESCA, IPIV, WORK, LWORK, $ IWORK, LIWORK, INFO ) * * -- ScaLAPACK routine (version 1.7.4) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * v1.7.4: May 10, 2006 * v1.7: May 1, 1997 * * .. Scalar Arguments .. INTEGER IA, INFO, JA, LIWORK, LWORK, N * .. * .. Array Arguments .. INTEGER DESCA( * ), IPIV( * ), IWORK( * ) REAL A( * ), WORK( * ) * .. * * Purpose * ======= * * PSGETRI computes the inverse of a distributed matrix using the LU * factorization computed by PSGETRF. This method inverts U and then * computes the inverse of sub( A ) = A(IA:IA+N-1,JA:JA+N-1) denoted * InvA by solving the system InvA*L = inv(U) for InvA. * * 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 number of rows and columns to be operated on, i.e. the * order of the distributed submatrix sub( A ). N >= 0. * * A (local input/local output) REAL pointer into the * local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). * On entry, the local pieces of the L and U obtained by the * factorization sub( A ) = P*L*U computed by PSGETRF. On * exit, if INFO = 0, sub( A ) contains the inverse of the * original distributed matrix sub( A ). * * 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. * * IPIV (local input) INTEGER array, dimension LOCr(M_A)+MB_A * keeps track of the pivoting information. IPIV(i) is the * global row index the local row i was swapped with. This * array is tied to the distributed matrix A. * * WORK (local workspace/local output) REAL 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 = LOCr(N+MOD(IA-1,MB_A))*NB_A. WORK is used to keep a * copy of at most an entire column block of sub( A ). * * 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 used as workspace for * physically transposing the pivots. * LIWORK is local input and must be at least * if NPROW == NPCOL then * LIWORK = LOCc( N_A + MOD(JA-1, NB_A) ) + NB_A, * else * LIWORK = LOCc( N_A + MOD(JA-1, NB_A) ) + * MAX( CEIL(CEIL(LOCr(M_A)/MB_A)/(LCM/NPROW)), * NB_A ) * where LCM is the least common multiple of process * rows and columns (NPROW and NPCOL). * end if * * 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. * > 0: If INFO = K, U(IA+K-1,IA+K-1) is exactly zero; the * matrix is singular and its inverse could not be * computed. * * ===================================================================== * * .. 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 .. LOGICAL LQUERY INTEGER I, IACOL, IAROW, ICOFF, ICTXT, IROFF, IW, J, $ JB, JN, LCM, LIWMIN, LWMIN, MP, MYCOL, MYROW, $ NN, NP, NPCOL, NPROW, NQ * .. * .. Local Arrays .. INTEGER DESCW( DLEN_ ), IDUM1( 2 ), IDUM2( 2 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, DESCSET, PCHK1MAT, $ PSGEMM, PSLACPY, PSLASET, PSLAPIV, $ PSTRSM, PSTRTRI, PXERBLA * .. * .. External Functions .. INTEGER ICEIL, ILCM, INDXG2P, NUMROC EXTERNAL ICEIL, ILCM, INDXG2P, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, MOD, REAL * .. * .. 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 = -(500+CTXT_) ELSE CALL CHK1MAT( N, 1, N, 1, IA, JA, DESCA, 5, INFO ) IF( INFO.EQ.0 ) THEN IROFF = MOD( IA-1, DESCA( MB_ ) ) ICOFF = MOD( JA-1, DESCA( NB_ ) ) IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), $ NPROW ) NP = NUMROC( N+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) LWMIN = NP * DESCA( NB_ ) * MP = NUMROC( DESCA( M_ ), DESCA( MB_ ), MYROW, $ DESCA( RSRC_ ), NPROW ) NQ = NUMROC( DESCA( N_ ), DESCA( NB_ ), MYCOL, $ DESCA( CSRC_ ), NPCOL ) IF( NPROW.EQ.NPCOL ) THEN LIWMIN = NQ + DESCA( NB_ ) ELSE * * Use the formula for the workspace given in PxLAPIV * to compute the minimum size LIWORK for IWORK * * The formula in PxLAPIV is * LDW = LOCc( M_P + MOD(IP-1, MB_P) ) + * MB_P * CEIL( CEIL(LOCr(M_P)/MB_P) / (LCM/NPROW) ) * * where * M_P is the global length of the pivot vector * MP = DESCA( M_ ) + DESCA( MB_ ) * NPROW * I_P is IA * I_P = IA * MB_P is the block size use for the block cyclic distribution of the * pivot vector * MB_P = DESCA (MB_ ) * LOCc ( . ) * NUMROC ( . , DESCA ( NB_ ), MYCOL, DESCA ( CSRC_ ), NPCOL ) * LOCr ( . ) * NUMROC ( . , DESCA ( MB_ ), MYROW, DESCA ( RSRC_ ), NPROW ) * CEIL ( X / Y ) * ICEIL( X, Y ) * LCM * LCM = ILCM( NPROW, NPCOL ) * LCM = ILCM( NPROW, NPCOL ) LIWMIN = NUMROC( DESCA( M_ ) + DESCA( MB_ ) * NPROW $ + MOD ( IA - 1, DESCA( MB_ ) ), DESCA ( NB_ ), $ MYCOL, DESCA( CSRC_ ), NPCOL ) + $ MAX ( DESCA( MB_ ) * ICEIL ( ICEIL( $ NUMROC( DESCA( M_ ) + DESCA( MB_ ) * NPROW, $ DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), $ DESCA( MB_ ) ), LCM / NPROW ), DESCA( NB_ ) ) * END IF * WORK( 1 ) = REAL( LWMIN ) IWORK( 1 ) = LIWMIN LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) IF( IROFF.NE.ICOFF .OR. IROFF.NE.0 ) THEN INFO = -4 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN INFO = -(500+NB_) ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -8 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN INFO = -10 END IF END IF IF( LWORK.EQ.-1 ) THEN IDUM1( 1 ) = -1 ELSE IDUM1( 1 ) = 1 END IF IDUM2( 1 ) = 8 IF( LIWORK.EQ.-1 ) THEN IDUM1( 2 ) = -1 ELSE IDUM1( 2 ) = 1 END IF IDUM2( 2 ) = 10 CALL PCHK1MAT( N, 1, N, 1, IA, JA, DESCA, 5, 2, IDUM1, IDUM2, $ INFO ) END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PSGETRI', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Form inv(U). If INFO > 0 from PSTRTRI, then U is singular, * and the inverse is not computed. * CALL PSTRTRI( 'Upper', 'Non-unit', N, A, IA, JA, DESCA, INFO ) IF( INFO.GT.0 ) $ RETURN * * Define array descriptor for working array WORK * JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) NN = ( ( JA+N-2 ) / DESCA( NB_ ) ) * DESCA( NB_ ) + 1 IACOL = INDXG2P( NN, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), NPCOL ) CALL DESCSET( DESCW, N+IROFF, DESCA( NB_ ), DESCA( MB_ ), $ DESCA( NB_ ), IAROW, IACOL, ICTXT, MAX( 1, NP ) ) IW = IROFF + 1 * * Solve the equation inv(A)*L=inv(U) for inv(A) using blocked code. * DO 10 J = NN, JN+1, -DESCA( NB_ ) JB = MIN( DESCA( NB_ ), JA+N-J ) I = IA + J - JA * * Copy current block column of L to WORK and replace with zeros. * CALL PSLACPY( 'Lower', JA+N-1-J, JB, A, I+1, J, DESCA, $ WORK, IW+J-JA+1, 1, DESCW ) CALL PSLASET( 'Lower', JA+N-1-J, JB, ZERO, ZERO, A, I+1, J, $ DESCA ) * * Compute current block column of inv(A). * IF( J+JB.LE.JA+N-1 ) $ CALL PSGEMM( 'No transpose', 'No transpose', N, JB, $ JA+N-J-JB, -ONE, A, IA, J+JB, DESCA, WORK, $ IW+J+JB-JA, 1, DESCW, ONE, A, IA, J, DESCA ) CALL PSTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB, $ ONE, WORK, IW+J-JA, 1, DESCW, A, IA, J, DESCA ) DESCW( CSRC_ ) = MOD( DESCW( CSRC_ ) + NPCOL - 1, NPCOL ) * 10 CONTINUE * * Handle the last block of columns separately * JB = JN-JA+1 * * Copy current block column of L to WORK and replace with zeros. * CALL PSLACPY( 'Lower', N-1, JB, A, IA+1, JA, DESCA, WORK, IW+1, $ 1, DESCW ) CALL PSLASET( 'Lower', N-1, JB, ZERO, ZERO, A, IA+1, JA, DESCA ) * * Compute current block column of inv(A). * IF( JA+JB.LE.JA+N-1 ) $ CALL PSGEMM( 'No transpose', 'No transpose', N, JB, $ N-JB, -ONE, A, IA, JA+JB, DESCA, WORK, IW+JB, 1, $ DESCW, ONE, A, IA, JA, DESCA ) CALL PSTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB, $ ONE, WORK, IW, 1, DESCW, A, IA, JA, DESCA ) * * Use the row pivots and apply them to the columns of the global * matrix. * CALL DESCSET( DESCW, DESCA( M_ ) + DESCA( MB_ )*NPROW, 1, $ DESCA( MB_ ), 1, DESCA( RSRC_ ), MYCOL, ICTXT, $ MP+DESCA( MB_ ) ) CALL PSLAPIV( 'Backward', 'Columns', 'Column', N, N, A, IA, $ JA, DESCA, IPIV, IA, 1, DESCW, IWORK ) * WORK( 1 ) = REAL( LWMIN ) IWORK( 1 ) = LIWMIN * RETURN * * End of PSGETRI * END