* * SUBROUTINE PSGSEPCHK( IBTYPE, MS, NV, A, IA, JA, DESCA, B, IB, JB, $ DESCB, THRESH, Q, IQ, JQ, DESCQ, C, IC, JC, $ DESCC, W, WORK, LWORK, TSTNRM, RESULT ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * April 15, 1997 * * .. Scalar Arguments .. INTEGER IA, IB, IBTYPE, IC, IQ, JA, JB, JC, JQ, LWORK, $ MS, NV, RESULT REAL THRESH, TSTNRM * .. * .. Array Arguments .. * INTEGER DESCA( * ), DESCB( * ), DESCC( * ), DESCQ( * ) REAL A( * ), B( * ), C( * ), Q( * ), W( * ), $ WORK( * ) * .. * * * Purpose * ======= * * PSGSEPCHK checks a decomposition of the form * * A Q = B Q D or * A B Q = Q D or * B A Q = Q D * * where A is a symmetric matrix, B is * symmetric positive definite, Q is orthogonal, and D is diagonal. * * One of the following test ratios is computed: * * IBTYPE = 1: TSTNRM = | A Q - B Q D | / ( |A| |Q| n ulp ) * * IBTYPE = 2: TSTNRM = | A B Q - Q D | / ( |A| |Q| n ulp ) * * IBTYPE = 3: TSTNRM = | B A Q - Q D | / ( |A| |Q| n ulp ) * * * 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 * ========= * * MP = number of local rows in A, B and Q * MQ = number of local columns in A * NQ = number of local columns in B and Q * * IBTYPE (input) INTEGER * The form of the symmetric generalized eigenproblem. * = 1: A*Q = (lambda)*B*Q * = 2: A*B*Q = (lambda)*Q * = 3: B*A*Q = (lambda)*Q * * MS (global input) INTEGER * Matrix size. * The number of global rows in A, B, C and Q * Also, the number of columns in A * * NV (global input) INTEGER * Number of eigenvectors * The number of global columns in C and Q. * * A (local input) REAL pointer to an * array in local memory of dimension (LLD_A, LOCc(JA+N-1)). * This array contains the local pieces of the M-by-N * distributed test matrix A * * IA (global input) INTEGER * A's global row index, which points to the beginning of the * submatrix which is to be operated on. * * JA (global input) INTEGER * A's global column index, which points to the beginning of * the submatrix which is to be operated on. * * DESCA (global and local input) INTEGER array of dimension 8 * The array descriptor for the distributed matrix A. * * B (local input) REAL pointer to an * array in local memory of dimension (LLD_B, LOCc(JB+N-1)). * This array contains the local pieces of the M-by-N * distributed test matrix B * * IB (global input) INTEGER * B's global row index, which points to the beginning of the * submatrix which is to be operated on. * * JB (global input) INTEGER * B's global column index, which points to the beginning of * the submatrix which is to be operated on. * * DESCB (global and local input) INTEGER array of dimension 8 * The array descriptor for the distributed matrix B. * * THRESH (input) REAL * A test will count as "failed" if the "error", computed as * described below, exceeds THRESH. Note that the error * is scaled to be O(1), so THRESH should be a reasonably * small multiple of 1, e.g., 10 or 100. In particular, * it should not depend on the precision (single vs. double) * or the size of the matrix. It must be at least zero. * * Q (local input) REAL array * global dimension (MS, NV), * local dimension (DESCA( DLEN_ ), NQ) * * Contains the eigenvectors as computed by PSSYEVX * * IQ (global input) INTEGER * Q's global row index, which points to the beginning of the * submatrix which is to be operated on. * * JQ (global input) INTEGER * Q's global column index, which points to the beginning of * the submatrix which is to be operated on. * * DESCQ (global and local input) INTEGER array of dimension 8 * The array descriptor for the distributed matrix Q. * * C (local workspace) REAL array, * global dimension (MS, NV), * local dimension (DESCA( DLEN_ ), MQ) * * Accumulator for computing AQ -QL * * IC (global input) INTEGER * C's global row index, which points to the beginning of the * submatrix which is to be operated on. * * JC (global input) INTEGER * C's global column index, which points to the beginning of * the submatrix which is to be operated on. * * DESCC (global and local input) INTEGER array of dimension 8 * The array descriptor for the distributed matrix C. * * W (global input) REAL array, dimension (NV) * * Contains the computed eigenvalues * * WORK (local workspace) REAL array, * dimension (LWORK) * * LWORK (local input) INTEGER * The length of the array WORK. * LWORK >= NUMROC( NV, DESCA( NB_ ), MYCOL, 0, NPCOL ) * * TSTNRM (global output) REAL * * RESULT (global output) INTEGER * 0 if the test passes * 1 if the test fails * * .. Local Scalars .. * INTEGER I, INFO, MYCOL, MYROW, NPCOL, NPROW, NQ REAL ANORM, ULP * .. * .. Parameters .. INTEGER BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_, $ MB_, NB_, RSRC_, CSRC_, LLD_ 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, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) REAL CONE, CNEGONE, CZERO PARAMETER ( CONE = 1.0E+0, CNEGONE = -1.0E+0, $ CZERO = 0.0E+0 ) * .. * .. External Functions .. INTEGER NUMROC REAL PSLANGE, SLAMCH EXTERNAL NUMROC, PSLANGE, SLAMCH * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PSGEMM, PSSCAL, $ PXERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * This is just to keep ftnchek happy IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_* $ RSRC_.LT.0 )RETURN * RESULT = 0 * CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL ) * INFO = 0 CALL CHK1MAT( MS, 1, MS, 2, IA, JA, DESCA, 7, INFO ) CALL CHK1MAT( MS, 1, MS, 2, IB, JB, DESCB, 11, INFO ) CALL CHK1MAT( MS, 1, NV, 2, IQ, JQ, DESCQ, 16, INFO ) CALL CHK1MAT( MS, 1, NV, 2, IB, JB, DESCB, 20, INFO ) * IF( INFO.EQ.0 ) THEN * NQ = NUMROC( NV, DESCA( NB_ ), MYCOL, 0, NPCOL ) * IF( IQ.NE.1 ) THEN INFO = -14 ELSE IF( JQ.NE.1 ) THEN INFO = -15 ELSE IF( IA.NE.1 ) THEN INFO = -5 ELSE IF( JA.NE.1 ) THEN INFO = -6 ELSE IF( IB.NE.1 ) THEN INFO = -9 ELSE IF( JB.NE.1 ) THEN INFO = -10 ELSE IF( LWORK.LT.NQ ) THEN INFO = -23 END IF END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( DESCA( CTXT_ ), 'PSGSEPCHK', -INFO ) RETURN END IF * RESULT = 0 ULP = SLAMCH( 'Epsilon' ) * * Compute product of Max-norms of A and Q. * ANORM = PSLANGE( 'M', MS, MS, A, IA, JA, DESCA, WORK )* $ PSLANGE( 'M', MS, NV, Q, IQ, JQ, DESCQ, WORK ) IF( ANORM.EQ.ZERO ) $ ANORM = ONE * IF( IBTYPE.EQ.1 ) THEN * * Norm of AQ - BQD * * C = AQ * CALL PSGEMM( 'N', 'N', MS, NV, MS, CONE, A, IA, JA, DESCA, Q, $ IQ, JQ, DESCQ, CZERO, C, IC, JC, DESCC ) * * Q = QD * DO 10 I = 1, NV CALL PSSCAL( MS, W( I ), Q, IQ, JQ+I-1, DESCQ, 1 ) 10 CONTINUE * * C = C - BQ (i.e. AQ-BQD) * CALL PSGEMM( 'N', 'N', MS, NV, MS, CONE, B, IB, JB, DESCB, Q, $ IQ, JQ, DESCQ, CNEGONE, C, IC, JC, DESCC ) * TSTNRM = ( PSLANGE( 'M', MS, NV, C, IC, JC, DESCC, WORK ) / $ ANORM ) / ( MAX( MS, 1 )*ULP ) * * ELSE IF( IBTYPE.EQ.2 ) THEN * * Norm of ABQ - QD * * * C = BQ * CALL PSGEMM( 'N', 'N', MS, NV, MS, CONE, B, IB, JB, DESCB, Q, $ IQ, JQ, DESCQ, CZERO, C, IC, JC, DESCC ) * * Q = QD * DO 20 I = 1, NV CALL PSSCAL( MS, W( I ), Q, IQ, JQ+I-1, DESCQ, 1 ) 20 CONTINUE * * Q = AC - Q * CALL PSGEMM( 'N', 'N', MS, NV, MS, CONE, A, IA, JA, DESCA, C, $ IC, JC, DESCC, CNEGONE, Q, IQ, JQ, DESCQ ) * TSTNRM = ( PSLANGE( 'M', MS, NV, Q, IQ, JQ, DESCQ, WORK ) / $ ANORM ) / ( MAX( MS, 1 )*ULP ) * ELSE IF( IBTYPE.EQ.3 ) THEN * * Norm of BAQ - QD * * * C = AQ * CALL PSGEMM( 'N', 'N', MS, NV, MS, CONE, A, IA, JA, DESCA, Q, $ IQ, JQ, DESCQ, CZERO, C, IC, JC, DESCC ) * * Q = QD * DO 30 I = 1, NV CALL PSSCAL( MS, W( I ), Q, IQ, JQ+I-1, DESCQ, 1 ) 30 CONTINUE * * Q = BC - Q * CALL PSGEMM( 'N', 'N', MS, NV, MS, CONE, B, IB, JB, DESCB, C, $ IC, JC, DESCC, CNEGONE, Q, IQ, JQ, DESCQ ) * TSTNRM = ( PSLANGE( 'M', MS, NV, Q, IQ, JQ, DESCQ, WORK ) / $ ANORM ) / ( MAX( MS, 1 )*ULP ) * END IF * IF( TSTNRM.GT.THRESH .OR. ( TSTNRM-TSTNRM.NE.0.0E0 ) ) THEN RESULT = 1 END IF RETURN * * End of PSGSEPCHK * END