SUBROUTINE PSGESV( N, NRHS, A, IA, JA, DESCA, IPIV, B, IB, JB, \$ DESCB, INFO ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * Jan 30, 2006 * * .. Scalar Arguments .. INTEGER IA, IB, INFO, JA, JB, N, NRHS * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCB( * ), IPIV( * ) REAL A( * ), B( * ) * .. * * Purpose * ======= * * PSGESV computes the solution to a real system of linear equations * * sub( A ) * X = sub( B ), * * where sub( A ) = A(IA:IA+N-1,JA:JA+N-1) is an N-by-N distributed * matrix and X and sub( B ) = B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS * distributed matrices. * * The LU decomposition with partial pivoting and row interchanges is * used to factor sub( A ) as sub( A ) = P * L * U, where P is a permu- * tation matrix, L is unit lower triangular, and U is upper triangular. * L and U are stored in sub( A ). The factored form of sub( A ) is then * used to solve the system of equations sub( A ) * X = sub( B ). * * 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 * * This routine requires square block decomposition ( MB_A = 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. * * NRHS (global input) INTEGER * The number of right hand sides, i.e., the number of columns * of the distributed submatrix sub( B ). NRHS >= 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 N-by-N distributed matrix * sub( A ) to be factored. On exit, this array contains the * local pieces of the factors L and U from the factorization * sub( A ) = P*L*U; the unit diagonal elements of L are not * stored. * * 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 output) INTEGER array, dimension ( LOCr(M_A)+MB_A ) * This array contains the pivoting information. * IPIV(i) -> The global row local row i was swapped with. * This array is tied to the distributed matrix A. * * B (local input/local output) REAL pointer into the * local memory to an array of dimension * (LLD_B,LOCc(JB+NRHS-1)). On entry, the right hand side * distributed matrix sub( B ). On exit, if INFO = 0, sub( B ) * is overwritten by the solution distributed matrix X. * * IB (global input) INTEGER * The row index in the global array B indicating the first * row of sub( B ). * * JB (global input) INTEGER * The column index in the global array B indicating the * first column of sub( B ). * * DESCB (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix B. * * 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,JA+K-1) is exactly zero. * The factorization has been completed, but the factor U * is exactly singular, so the solution 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 ) * .. * .. Local Scalars .. INTEGER IAROW, IBROW, ICOFFA, ICTXT, IROFFA, IROFFB, \$ MYCOL, MYROW, NPCOL, NPROW * .. * .. Local Arrays .. INTEGER IDUM1( 1 ), IDUM2( 1 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK2MAT, PSGETRF, \$ PSGETRS, PXERBLA * .. * .. External Functions .. INTEGER INDXG2P EXTERNAL INDXG2P * .. * .. Intrinsic Functions .. INTRINSIC 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 = -(600+CTXT_) ELSE CALL CHK1MAT( N, 1, N, 1, IA, JA, DESCA, 6, INFO ) CALL CHK1MAT( N, 1, NRHS, 2, IB, JB, DESCB, 11, INFO ) IF( INFO.EQ.0 ) THEN IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), \$ NPROW ) IBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ), \$ NPROW ) IROFFA = MOD( IA-1, DESCA( MB_ ) ) ICOFFA = MOD( JA-1, DESCA( NB_ ) ) IROFFB = MOD( IB-1, DESCB( MB_ ) ) IF( IROFFA.NE.0 ) THEN INFO = -4 ELSE IF( ICOFFA.NE.0 ) THEN INFO = -5 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN INFO = -(600+NB_) ELSE IF( IBROW.NE.IAROW .OR. ICOFFA.NE.IROFFB ) THEN INFO = -9 ELSE IF( DESCB( MB_ ).NE.DESCA( NB_ ) ) THEN INFO = -(1100+NB_) ELSE IF( ICTXT.NE.DESCB( CTXT_ ) ) THEN INFO = -(1100+CTXT_) END IF END IF CALL PCHK2MAT( N, 1, N, 1, IA, JA, DESCA, 6, N, 1, NRHS, 2, \$ IB, JB, DESCB, 11, 0, IDUM1, IDUM2, INFO ) END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PSGESV', -INFO ) RETURN END IF * * Compute the LU factorization of sub( A ). * CALL PSGETRF( N, N, A, IA, JA, DESCA, IPIV, INFO ) * IF( INFO.EQ.0 ) THEN * * Solve the system sub( A ) * X = sub( B ), overwriting sub( B ) * with X. * CALL PSGETRS( 'No transpose', N, NRHS, A, IA, JA, DESCA, IPIV, \$ B, IB, JB, DESCB, INFO ) * END IF * RETURN * * End of PSGESV * END