SUBROUTINE PZTRTRI( UPLO, DIAG, N, A, IA, JA, DESCA, INFO ) * * -- ScaLAPACK routine (version 1.7) -- * 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( * ) COMPLEX*16 A( * ) * .. * * Purpose * ======= * * PZTRTRI computes the inverse of a upper or lower triangular * distributed matrix sub( A ) = 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 * ========= * * UPLO (global input) CHARACTER * Specifies whether the distributed matrix sub( A ) is upper * or lower triangular: * = 'U': Upper triangular, * = 'L': Lower triangular. * * DIAG (global input) CHARACTER * Specifies whether or not the distributed matrix sub( A ) * is unit triangular: * = 'N': Non-unit triangular, * = 'U': 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) COMPLEX*16 pointer into the * local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). * On entry, 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 to be inverted, 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. * On exit, the (triangular) inverse of the original matrix. * * 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 (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, A(IA+K-1,JA+K-1) is exactly zero. The * triangular matrix sub( A ) is singular and its * inverse can 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 ) COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL NOUNIT, UPPER INTEGER I, ICOFF, ICTXT, IROFF, ICURCOL, ICURROW, $ IDUMMY, II, IOFFA, J, JB, JJ, JN, LDA, MYCOL, $ MYROW, NN, NPCOL, NPROW * .. * .. Local Arrays .. INTEGER IDUM1( 2 ), IDUM2( 2 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, IGAMX2D, INFOG2L, $ PCHK1MAT, PXERBLA, PZTRTI2, PZTRMM, $ PZTRSM * .. * .. External Functions .. LOGICAL LSAME INTEGER ICEIL EXTERNAL ICEIL, LSAME * .. * .. Intrinsic Functions .. INTRINSIC ICHAR, MIN, MOD * .. * .. Executable Statements .. * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * * Test input parameters * INFO = 0 IF( NPROW.EQ.-1 ) THEN INFO = -(700+CTXT_) ELSE UPPER = LSAME( UPLO, 'U' ) NOUNIT = LSAME( DIAG, 'N' ) * CALL CHK1MAT( N, 3, N, 3, IA, JA, DESCA, 7, INFO ) IF( INFO.EQ.0 ) THEN IROFF = MOD( IA-1, DESCA( MB_ ) ) ICOFF = MOD( JA-1, DESCA( NB_ ) ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -2 ELSE IF( IROFF.NE.ICOFF .OR. IROFF.NE.0 ) THEN INFO = -6 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN INFO = -(700+NB_) END IF END IF * IF( UPPER ) THEN IDUM1( 1 ) = ICHAR( 'U' ) ELSE IDUM1( 1 ) = ICHAR( 'L' ) END IF IDUM2( 1 ) = 1 IF( NOUNIT ) THEN IDUM1( 2 ) = ICHAR( 'N' ) ELSE IDUM1( 2 ) = ICHAR( 'U' ) END IF IDUM2( 2 ) = 2 * CALL PCHK1MAT( N, 3, N, 3, IA, JA, DESCA, 7, 2, IDUM1, IDUM2, $ INFO ) END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PZTRTRI', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Check for singularity if non-unit. * JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) IF( NOUNIT ) THEN CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, $ II, JJ, ICURROW, ICURCOL ) * * Handle first block separately * JB = JN-JA+1 LDA = DESCA( LLD_ ) IF( MYROW.EQ.ICURROW .AND. MYCOL.EQ.ICURCOL ) THEN IOFFA = II+(JJ-1)*LDA DO 10 I = 0, JB-1 IF( A( IOFFA ).EQ.ZERO .AND. INFO.EQ.0 ) $ INFO = I + 1 IOFFA = IOFFA + LDA + 1 10 CONTINUE END IF IF( MYROW.EQ.ICURROW ) $ II = II + JB IF( MYCOL.EQ.ICURCOL ) $ JJ = JJ + JB ICURROW = MOD( ICURROW+1, NPROW ) ICURCOL = MOD( ICURCOL+1, NPCOL ) * * Loop over remaining blocks of columns * DO 30 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) IF( MYROW.EQ.ICURROW .AND. MYCOL.EQ.ICURCOL ) THEN IOFFA = II+(JJ-1)*LDA DO 20 I = 0, JB-1 IF( A( IOFFA ).EQ.ZERO .AND. INFO.EQ.0 ) $ INFO = J + I - JA + 1 IOFFA = IOFFA + LDA + 1 20 CONTINUE END IF IF( MYROW.EQ.ICURROW ) $ II = II + JB IF( MYCOL.EQ.ICURCOL ) $ JJ = JJ + JB ICURROW = MOD( ICURROW+1, NPROW ) ICURCOL = MOD( ICURCOL+1, NPCOL ) 30 CONTINUE CALL IGAMX2D( ICTXT, 'All', ' ', 1, 1, INFO, 1, IDUMMY, $ IDUMMY, -1, -1, MYCOL ) IF( INFO.NE.0 ) $ RETURN END IF * * Use blocked code * IF( UPPER ) THEN * * Compute inverse of upper triangular matrix * JB = JN-JA+1 * * Handle first block of column separately * CALL PZTRTI2( UPLO, DIAG, JB, A, IA, JA, DESCA, INFO ) * * Loop over remaining block of columns * DO 40 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( DESCA( NB_ ), JA+N-J ) I = IA + J - JA * * Compute rows 1:j-1 of current block column * CALL PZTRMM( 'Left', UPLO, 'No transpose', DIAG, J-JA, JB, $ ONE, A, IA, JA, DESCA, A, IA, J, DESCA ) CALL PZTRSM( 'Right', UPLO, 'No transpose', DIAG, J-JA, $ JB, -ONE, A, I, J, DESCA, A, IA, J, DESCA ) * * Compute inverse of current diagonal block * CALL PZTRTI2( UPLO, DIAG, JB, A, I, J, DESCA, INFO ) * 40 CONTINUE * ELSE * * Compute inverse of lower triangular matrix * NN = ( ( JA+N-2 ) / DESCA( NB_ ) )*DESCA( NB_ ) + 1 DO 50 J = NN, JN+1, -DESCA( NB_ ) JB = MIN( DESCA( NB_ ), JA+N-J ) I = IA + J - JA IF( J+JB.LE.JA+N-1 ) THEN * * Compute rows j+jb:ja+n-1 of current block column * CALL PZTRMM( 'Left', UPLO, 'No transpose', DIAG, $ JA+N-J-JB, JB, ONE, A, I+JB, J+JB, DESCA, $ A, I+JB, J, DESCA ) CALL PZTRSM( 'Right', UPLO, 'No transpose', DIAG, $ JA+N-J-JB, JB, -ONE, A, I, J, DESCA, $ A, I+JB, J, DESCA ) END IF * * Compute inverse of current diagonal block * CALL PZTRTI2( UPLO, DIAG, JB, A, I, J, DESCA, INFO ) * 50 CONTINUE * * Handle the last block of columns separately * JB = JN-JA+1 IF( JA+JB.LE.JA+N-1 ) THEN * * Compute rows ja+jb:ja+n-1 of current block column * CALL PZTRMM( 'Left', UPLO, 'No transpose', DIAG, N-JB, JB, $ ONE, A, IA+JB, JA+JB, DESCA, A, IA+JB, JA, $ DESCA ) CALL PZTRSM( 'Right', UPLO, 'No transpose', DIAG, N-JB, JB, $ -ONE, A, IA, JA, DESCA, A, IA+JB, JA, DESCA ) END IF * * Compute inverse of current diagonal block * CALL PZTRTI2( UPLO, DIAG, JB, A, IA, JA, DESCA, INFO ) * END IF * RETURN * * End PZTRTRI * END