SUBROUTINE PSTRTI2( UPLO, DIAG, N, A, IA, JA, DESCA, INFO ) * * -- ScaLAPACK routine (version 1.5) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER IA, INFO, JA, N * .. * .. Array Arguments .. INTEGER DESCA( * ) REAL A( * ) * .. * * Purpose * ======= * * PSTRTI2 computes the inverse of a real upper or lower triangular * block matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). This matrix should be * contained in one and only one process memory space (local operation). * * 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 * ========= * * UPLO (global input) CHARACTER*1 * = 'U': sub( A ) is upper triangular; * = 'L': sub( A ) is lower triangular. * * DIAG (global input) CHARACTER*1 * = 'N': sub( A ) is non-unit triangular * = 'U': sub( A ) is unit triangular * * 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)), * this array contains the local pieces of the triangular matrix * sub( A ). If UPLO = 'U', the leading N-by-N upper triangular * part of the matrix sub( A ) contains the upper triangular * matrix, and the strictly lower triangular part of sub( A ) * is not referenced. If UPLO = 'L', the leading N-by-N lower * triangular part of the matrix sub( A ) contains the lower * triangular matrix, and the strictly upper triangular part * of sub( A ) is not referenced. If DIAG = 'U', the diagonal * elements of sub( A ) are also not referenced and are assumed * to be 1. On exit, the (triangular) inverse of the original * matrix, in the same storage format. * * 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. * * INFO (local 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 ) REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. LOGICAL NOUNIT, UPPER INTEGER IACOL, IAROW, ICTXT, ICURR, IDIAG, IIA, IOFFA, $ JJA, LDA, MYCOL, MYROW, NA, NPCOL, NPROW REAL AJJ * .. * .. External Subroutines .. EXTERNAL BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT, INFOG2L, $ PXERBLA, SSCAL, STRMV * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. 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 = -(700+CTXT_) ELSE CALL CHK1MAT( N, 3, N, 3, IA, JA, DESCA, 7, INFO ) UPPER = LSAME( UPLO, 'U' ) NOUNIT = LSAME( DIAG, 'N' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -2 END IF END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PSTRTI2', -INFO ) CALL BLACS_ABORT( ICTXT, 1 ) RETURN END IF * * Compute local indexes * CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, $ IAROW, IACOL ) * IF( MYROW.EQ.IAROW .AND. MYCOL.EQ.IACOL ) THEN * LDA = DESCA( LLD_ ) * IF( UPPER ) THEN * IOFFA = IIA + ( JJA - 1 ) * LDA ICURR = IOFFA + LDA * IF( NOUNIT ) THEN * * Compute inverse of upper non-unit triangular matrix. * A( IOFFA ) = ONE / A( IOFFA ) IDIAG = ICURR + 1 DO 10 NA = 1, N-1 A( IDIAG ) = ONE / A( IDIAG ) AJJ = -A( IDIAG ) * * Compute elements 1:j-1 of j-th column. * CALL STRMV( 'Upper', 'No transpose', DIAG, NA, $ A( IOFFA ), LDA, A( ICURR ), 1 ) CALL SSCAL( NA, AJJ, A( ICURR ), 1 ) IDIAG = IDIAG + LDA + 1 ICURR = ICURR + LDA 10 CONTINUE * ELSE * * Compute inverse of upper unit triangular matrix. * DO 20 NA = 1, N-1 * * Compute elements 1:j-1 of j-th column. * CALL STRMV( 'Upper', 'No transpose', DIAG, NA, $ A( IOFFA ), LDA, A( ICURR ), 1 ) CALL SSCAL( NA, -ONE, A( ICURR ), 1 ) ICURR = ICURR + LDA 20 CONTINUE * END IF * ELSE * ICURR = IIA + N - 1 + ( JJA + N - 2 ) * LDA IOFFA = ICURR - LDA * IF( NOUNIT ) THEN * * Compute inverse of lower non-unit triangular matrix. * A( ICURR ) = ONE / A( ICURR ) IDIAG = IOFFA - 1 DO 30 NA = 1, N-1 A( IDIAG ) = ONE / A( IDIAG ) AJJ = -A( IDIAG ) * * Compute elements j+1:n of j-th column. * CALL STRMV( 'Lower', 'No transpose', DIAG, NA, $ A( ICURR ), LDA, A( IOFFA ), 1 ) CALL SSCAL( NA, AJJ, A( IOFFA ), 1 ) ICURR = IDIAG IDIAG = IDIAG - LDA - 1 IOFFA = IDIAG + 1 30 CONTINUE * ELSE * * Compute inverse of lower unit triangular matrix. * DO 40 NA = 1, N-1 * * Compute elements j+1:n of j-th column. * CALL STRMV( 'Lower', 'No transpose', DIAG, NA, $ A( ICURR ), LDA, A( IOFFA ), 1 ) CALL SSCAL( NA, -ONE, A( IOFFA ), 1 ) ICURR = ICURR - LDA - 1 IOFFA = ICURR - LDA 40 CONTINUE * END IF * END IF * END IF * * End of PSTRTI2 * END