SUBROUTINE PZPOTRF( UPLO, 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 25, 2001 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER IA, INFO, JA, N * .. * .. Array Arguments .. INTEGER DESCA( * ) COMPLEX*16 A( * ) * .. * * Purpose * ======= * * PZPOTRF computes the Cholesky factorization of an N-by-N complex * hermitian positive definite distributed matrix sub( A ) denoting * A(IA:IA+N-1, JA:JA+N-1). * * The factorization has the form * * sub( A ) = U' * U , if UPLO = 'U', or * * sub( A ) = L * L', if UPLO = 'L', * * where U is an upper triangular matrix and L is lower triangular. * * 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 * ========= * * UPLO (global input) CHARACTER * = 'U': Upper triangle of sub( A ) is stored; * = 'L': Lower triangle of sub( A ) is stored. * * 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 * N-by-N Hermitian distributed matrix sub( A ) to be factored. * If UPLO = 'U', the leading N-by-N upper triangular part of * sub( A ) contains the upper triangular part of the matrix, * and its strictly lower triangular part is not referenced. * If UPLO = 'L', the leading N-by-N lower triangular part of * sub( A ) contains the lower triangular part of the distribu- * ted matrix, and its strictly upper triangular part is not * referenced. On exit, if UPLO = 'U', the upper triangular * part of the distributed matrix contains the Cholesky factor * U, if UPLO = 'L', the lower triangular part of the distribu- * ted matrix contains the Cholesky factor L. * * 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, the leading minor of order K, * A(IA:IA+K-1,JA:JA+K-1) is not positive definite, and * the factorization could not be completed. * * ===================================================================== * * .. 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 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER CHARACTER COLBTOP, ROWBTOP INTEGER I, ICOFF, ICTXT, IROFF, J, JB, JN, MYCOL, $ MYROW, NPCOL, NPROW * .. * .. Local Arrays .. INTEGER IDUM1( 1 ), IDUM2( 1 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK1MAT, PB_TOPGET, $ PB_TOPSET, PXERBLA, PZPOTF2, PZHERK, $ 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 the input parameters * INFO = 0 IF( NPROW.EQ.-1 ) THEN INFO = -(600+CTXT_) ELSE CALL CHK1MAT( N, 2, N, 2, IA, JA, DESCA, 6, INFO ) UPPER = LSAME( UPLO, 'U' ) 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( IROFF.NE.0 ) THEN INFO = -4 ELSE IF( ICOFF.NE.0 ) THEN INFO = -5 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN INFO = -(600+NB_) END IF END IF IF( UPPER ) THEN IDUM1( 1 ) = ICHAR( 'U' ) ELSE IDUM1( 1 ) = ICHAR( 'L' ) END IF IDUM2( 1 ) = 1 CALL PCHK1MAT( N, 2, N, 2, IA, JA, DESCA, 6, 1, IDUM1, IDUM2, $ INFO ) END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PZPOTRF', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * IF( UPPER ) THEN * * Split-ring topology for the communication along process * columns, 1-tree topology along process rows. * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'S-ring' ) * * A is upper triangular, compute Cholesky factorization A = U'*U. * * Handle the first block of columns separately * JN = MIN( ICEIL( JA, DESCA( NB_ ) )*DESCA(NB_), JA+N-1 ) JB = JN - JA + 1 * * Perform unblocked Cholesky factorization on JB block * CALL PZPOTF2( UPLO, JB, A, IA, JA, DESCA, INFO ) IF( INFO.NE.0 ) $ GO TO 30 * IF( JB+1.LE.N ) THEN * * Form the row panel of U using the triangular solver * CALL PZTRSM( 'Left', UPLO, 'Conjugate transpose', $ 'Non-Unit', JB, N-JB, CONE, A, IA, JA, DESCA, $ A, IA, JA+JB, DESCA ) * * Update the trailing matrix, A = A - U'*U * CALL PZHERK( UPLO, 'Conjugate transpose', N-JB, JB, -ONE, A, $ IA, JA+JB, DESCA, ONE, A, IA+JB, JA+JB, DESCA ) END IF * * Loop over remaining block of columns * DO 10 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( N-J+JA, DESCA( NB_ ) ) I = IA + J - JA * * Perform unblocked Cholesky factorization on JB block * CALL PZPOTF2( UPLO, JB, A, I, J, DESCA, INFO ) IF( INFO.NE.0 ) THEN INFO = INFO + J - JA GO TO 30 END IF * IF( J-JA+JB+1.LE.N ) THEN * * Form the row panel of U using the triangular solver * CALL PZTRSM( 'Left', UPLO, 'Conjugate transpose', $ 'Non-Unit', JB, N-J-JB+JA, CONE, A, I, J, $ DESCA, A, I, J+JB, DESCA ) * * Update the trailing matrix, A = A - U'*U * CALL PZHERK( UPLO, 'Conjugate transpose', N-J-JB+JA, JB, $ -ONE, A, I, J+JB, DESCA, ONE, A, I+JB, $ J+JB, DESCA ) END IF 10 CONTINUE * ELSE * * 1-tree topology for the communication along process columns, * Split-ring topology along process rows. * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', 'S-ring' ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' ) * * A is lower triangular, compute Cholesky factorization A = L*L' * (right-looking) * * Handle the first block of columns separately * JN = MIN( ICEIL( JA, DESCA( NB_ ) )*DESCA( NB_ ), JA+N-1 ) JB = JN - JA + 1 * * Perform unblocked Cholesky factorization on JB block * CALL PZPOTF2( UPLO, JB, A, IA, JA, DESCA, INFO ) IF( INFO.NE.0 ) $ GO TO 30 * IF( JB+1.LE.N ) THEN * * Form the column panel of L using the triangular solver * CALL PZTRSM( 'Right', UPLO, 'Conjugate transpose', $ 'Non-Unit', N-JB, JB, CONE, A, IA, JA, DESCA, $ A, IA+JB, JA, DESCA ) * * Update the trailing matrix, A = A - L*L' * CALL PZHERK( UPLO, 'No Transpose', N-JB, JB, -ONE, A, IA+JB, $ JA, DESCA, ONE, A, IA+JB, JA+JB, DESCA ) * END IF * DO 20 J = JN+1, JA+N-1, DESCA( NB_ ) JB = MIN( N-J+JA, DESCA( NB_ ) ) I = IA + J - JA * * Perform unblocked Cholesky factorization on JB block * CALL PZPOTF2( UPLO, JB, A, I, J, DESCA, INFO ) IF( INFO.NE.0 ) THEN INFO = INFO + J - JA GO TO 30 END IF * IF( J-JA+JB+1.LE.N ) THEN * * Form the column panel of L using the triangular solver * CALL PZTRSM( 'Right', UPLO, 'Conjugate transpose', $ 'Non-Unit', N-J-JB+JA, JB, CONE, A, I, J, $ DESCA, A, I+JB, J, DESCA ) * * Update the trailing matrix, A = A - L*L' * CALL PZHERK( UPLO, 'No Transpose', N-J-JB+JA, JB, -ONE, $ A, I+JB, J, DESCA, ONE, A, I+JB, J+JB, $ DESCA ) * END IF 20 CONTINUE * END IF * 30 CONTINUE * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * RETURN * * End of PZPOTRF * END