/* ========================================================================== */ /* === UMFPACK_report_info ================================================== */ /* ========================================================================== */ /* -------------------------------------------------------------------------- */ /* UMFPACK Copyright (c) Timothy A. Davis, CISE, */ /* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */ /* web: http://www.cise.ufl.edu/research/sparse/umfpack */ /* -------------------------------------------------------------------------- */ /* User-callable. Prints the Info array. See umfpack_report_info.h for details. */ #include "umf_internal.h" #define PRINT_INFO(format,x) \ { \ if (SCALAR_IS_NAN (x) || (!SCALAR_IS_LTZERO (x))) \ { \ PRINTF ((format, x)) ; \ } \ } /* RATIO macro uses a double relop, but ignore NaN case: */ #define RATIO(a,b,c) (((b) == 0) ? (c) : (((double) a)/((double) b))) /* ========================================================================== */ /* === print_ratio ========================================================== */ /* ========================================================================== */ PRIVATE void print_ratio ( char *what, char *format, double estimate, double actual ) { if (estimate < 0 && actual < 0) /* double relop, but ignore Nan case */ { return ; } PRINTF ((" %-27s", what)) ; if (estimate >= 0) /* double relop, but ignore Nan case */ { PRINTF ((format, estimate)) ; } else { PRINTF ((" -")) ; } if (actual >= 0) /* double relop, but ignore Nan case */ { PRINTF ((format, actual)) ; } else { PRINTF ((" -")) ; } if (estimate >= 0 && actual >= 0) /* double relop, but ignore Nan case */ { PRINTF ((" %5.0f%%\n", 100 * RATIO (actual, estimate, 1))) ; } else { PRINTF ((" -\n")) ; } } /* ========================================================================== */ /* === UMFPACK_report_info ================================================== */ /* ========================================================================== */ GLOBAL void UMFPACK_report_info ( const double Control [UMFPACK_CONTROL], const double Info [UMFPACK_INFO] ) { double lnz_est, unz_est, lunz_est, lnz, unz, lunz, tsym, tnum, fnum, tsolve, fsolve, ttot, ftot, twsym, twnum, twsolve, twtot, n2 ; Int n_row, n_col, n_inner, prl, is_sym ; /* ---------------------------------------------------------------------- */ /* get control settings and status to determine what to print */ /* ---------------------------------------------------------------------- */ prl = GET_CONTROL (UMFPACK_PRL, UMFPACK_DEFAULT_PRL) ; if (!Info || prl < 2) { /* no output generated if Info is (double *) NULL */ /* or if prl is less than 2 */ return ; } /* ---------------------------------------------------------------------- */ /* print umfpack version */ /* ---------------------------------------------------------------------- */ PRINTF (("UMFPACK V%d.%d.%d (%s), Info:\n", UMFPACK_MAIN_VERSION, UMFPACK_SUB_VERSION, UMFPACK_SUBSUB_VERSION, UMFPACK_DATE)) ; #ifndef NDEBUG PRINTF (( "**** Debugging enabled (UMFPACK will be exceedingly slow!) *****************\n" )) ; #endif /* ---------------------------------------------------------------------- */ /* print run-time options */ /* ---------------------------------------------------------------------- */ #ifdef DINT PRINTF ((" matrix entry defined as: double\n")) ; PRINTF ((" Int (generic integer) defined as: int\n")) ; #endif #ifdef DLONG PRINTF ((" matrix entry defined as: double\n")) ; PRINTF ((" Int (generic integer) defined as: UF_long\n")) ; #endif #ifdef ZINT PRINTF ((" matrix entry defined as: double complex\n")) ; PRINTF ((" Int (generic integer) defined as: int\n")) ; #endif #ifdef ZLONG PRINTF ((" matrix entry defined as: double complex\n")) ; PRINTF ((" Int (generic integer) defined as: UF_long\n")) ; #endif /* ---------------------------------------------------------------------- */ /* print compile-time options */ /* ---------------------------------------------------------------------- */ PRINTF ((" BLAS library used: ")) ; #ifdef NBLAS PRINTF (("none. UMFPACK will be slow.\n")) ; #else PRINTF (("Fortran BLAS. size of BLAS integer: "ID"\n", (Int) (sizeof (BLAS_INT)))) ; #endif PRINTF ((" MATLAB: ")) ; #ifdef MATLAB_MEX_FILE PRINTF (("yes.\n")) ; #else #ifdef MATHWORKS PRINTF (("yes.\n")) ; #else PRINTF (("no.\n")) ; #endif #endif PRINTF ((" CPU timer: ")) ; #ifdef NO_TIMER PRINTF (("none.\n")) ; #else #ifndef NPOSIX PRINTF (("POSIX times ( ) routine.\n")) ; #else #ifdef GETRUSAGE PRINTF (("getrusage ( ) routine.\n")) ; #else PRINTF (("ANSI clock ( ) routine.\n")) ; #endif #endif #endif /* ---------------------------------------------------------------------- */ /* print n and nz */ /* ---------------------------------------------------------------------- */ n_row = (Int) Info [UMFPACK_NROW] ; n_col = (Int) Info [UMFPACK_NCOL] ; n_inner = MIN (n_row, n_col) ; PRINT_INFO (" number of rows in matrix A: "ID"\n", n_row) ; PRINT_INFO (" number of columns in matrix A: "ID"\n", n_col) ; PRINT_INFO (" entries in matrix A: "ID"\n", (Int) Info [UMFPACK_NZ]) ; PRINT_INFO (" memory usage reported in: "ID"-byte Units\n", (Int) Info [UMFPACK_SIZE_OF_UNIT]) ; PRINT_INFO (" size of int: "ID" bytes\n", (Int) Info [UMFPACK_SIZE_OF_INT]) ; PRINT_INFO (" size of UF_long: "ID" bytes\n", (Int) Info [UMFPACK_SIZE_OF_LONG]) ; PRINT_INFO (" size of pointer: "ID" bytes\n", (Int) Info [UMFPACK_SIZE_OF_POINTER]) ; PRINT_INFO (" size of numerical entry: "ID" bytes\n", (Int) Info [UMFPACK_SIZE_OF_ENTRY]) ; /* ---------------------------------------------------------------------- */ /* symbolic parameters */ /* ---------------------------------------------------------------------- */ if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_SYMMETRIC) { PRINTF (("\n strategy used: symmetric\n")) ; } else if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_UNSYMMETRIC) { PRINTF (("\n strategy used: unsymmetric\n")) ; } else if (Info [UMFPACK_STRATEGY_USED] == UMFPACK_STRATEGY_2BY2) { PRINTF (("\n strategy used: symmetric 2-by-2\n")); } if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_AMD) { PRINTF ((" ordering used: amd on A+A'\n")) ; } else if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_COLAMD) { PRINTF ((" ordering used: colamd on A\n")) ; } else if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_GIVEN) { PRINTF ((" ordering used: provided by user\n")) ; } if (Info [UMFPACK_QFIXED] == 1) { PRINTF ((" modify Q during factorization: no\n")) ; } else if (Info [UMFPACK_QFIXED] == 0) { PRINTF ((" modify Q during factorization: yes\n")) ; } if (Info [UMFPACK_DIAG_PREFERRED] == 0) { PRINTF ((" prefer diagonal pivoting: no\n")) ; } else if (Info [UMFPACK_DIAG_PREFERRED] == 1) { PRINTF ((" prefer diagonal pivoting: yes\n")) ; } /* ---------------------------------------------------------------------- */ /* singleton statistics */ /* ---------------------------------------------------------------------- */ PRINT_INFO (" pivots with zero Markowitz cost: %0.f\n", Info [UMFPACK_COL_SINGLETONS] + Info [UMFPACK_ROW_SINGLETONS]) ; PRINT_INFO (" submatrix S after removing zero-cost pivots:\n" " number of \"dense\" rows: %.0f\n", Info [UMFPACK_NDENSE_ROW]) ; PRINT_INFO (" number of \"dense\" columns: %.0f\n", Info [UMFPACK_NDENSE_COL]) ; PRINT_INFO (" number of empty rows: %.0f\n", Info [UMFPACK_NEMPTY_ROW]) ; PRINT_INFO (" number of empty columns %.0f\n", Info [UMFPACK_NEMPTY_COL]) ; is_sym = Info [UMFPACK_S_SYMMETRIC] ; if (is_sym > 0) { PRINTF ((" submatrix S square and diagonal preserved\n")) ; } else if (is_sym == 0) { PRINTF ((" submatrix S not square or diagonal not preserved\n")); } /* ---------------------------------------------------------------------- */ /* statistics from amd_aat */ /* ---------------------------------------------------------------------- */ n2 = Info [UMFPACK_N2] ; if (n2 >= 0) { PRINTF ((" pattern of square submatrix S:\n")) ; } PRINT_INFO (" number rows and columns %.0f\n", n2) ; PRINT_INFO (" symmetry of nonzero pattern: %.6f\n", Info [UMFPACK_PATTERN_SYMMETRY]) ; PRINT_INFO (" nz in S+S' (excl. diagonal): %.0f\n", Info [UMFPACK_NZ_A_PLUS_AT]) ; PRINT_INFO (" nz on diagonal of matrix S: %.0f\n", Info [UMFPACK_NZDIAG]) ; if (Info [UMFPACK_NZDIAG] >= 0 && n2 > 0) { PRINTF ((" fraction of nz on diagonal: %.6f\n", Info [UMFPACK_NZDIAG] / n2)) ; } /* ---------------------------------------------------------------------- */ /* statistics from 2-by-2 permutation */ /* ---------------------------------------------------------------------- */ PRINT_INFO (" 2-by-2 pivoting to place large entries on diagonal:\n" " # of small diagonal entries of S: %.0f\n", Info [UMFPACK_2BY2_NWEAK]) ; PRINT_INFO (" # unmatched: %.0f\n", Info [UMFPACK_2BY2_UNMATCHED]) ; PRINT_INFO (" symmetry of P2*S: %.6f\n", Info [UMFPACK_2BY2_PATTERN_SYMMETRY]) ; PRINT_INFO (" nz in P2*S+(P2*S)' (excl. diag.): %.0f\n", Info [UMFPACK_2BY2_NZ_PA_PLUS_PAT]) ; PRINT_INFO (" nz on diagonal of P2*S: %.0f\n", Info [UMFPACK_2BY2_NZDIAG]) ; if (Info [UMFPACK_2BY2_NZDIAG] >= 0 && n2 > 0) { PRINTF ((" fraction of nz on diag of P2*S: %.6f\n", Info [UMFPACK_2BY2_NZDIAG] / n2)) ; } /* ---------------------------------------------------------------------- */ /* statistics from AMD */ /* ---------------------------------------------------------------------- */ if (Info [UMFPACK_ORDERING_USED] == UMFPACK_ORDERING_AMD) { double dmax = Info [UMFPACK_SYMMETRIC_DMAX] ; PRINTF ((" AMD statistics, for strict diagonal pivoting:\n")) ; PRINT_INFO (" est. flops for LU factorization: %.5e\n", Info [UMFPACK_SYMMETRIC_FLOPS]) ; PRINT_INFO (" est. nz in L+U (incl. diagonal): %.0f\n", Info [UMFPACK_SYMMETRIC_LUNZ]) ; PRINT_INFO (" est. largest front (# entries): %.0f\n", dmax*dmax) ; PRINT_INFO (" est. max nz in any column of L: %.0f\n", dmax) ; PRINT_INFO ( " number of \"dense\" rows/columns in S+S': %.0f\n", Info [UMFPACK_SYMMETRIC_NDENSE]) ; } /* ---------------------------------------------------------------------- */ /* symbolic factorization */ /* ---------------------------------------------------------------------- */ tsym = Info [UMFPACK_SYMBOLIC_TIME] ; twsym = Info [UMFPACK_SYMBOLIC_WALLTIME] ; PRINT_INFO (" symbolic factorization defragmentations: %.0f\n", Info [UMFPACK_SYMBOLIC_DEFRAG]) ; PRINT_INFO (" symbolic memory usage (Units): %.0f\n", Info [UMFPACK_SYMBOLIC_PEAK_MEMORY]) ; PRINT_INFO (" symbolic memory usage (MBytes): %.1f\n", MBYTES (Info [UMFPACK_SYMBOLIC_PEAK_MEMORY])) ; PRINT_INFO (" Symbolic size (Units): %.0f\n", Info [UMFPACK_SYMBOLIC_SIZE]) ; PRINT_INFO (" Symbolic size (MBytes): %.0f\n", MBYTES (Info [UMFPACK_SYMBOLIC_SIZE])) ; PRINT_INFO (" symbolic factorization CPU time (sec): %.2f\n", tsym) ; PRINT_INFO (" symbolic factorization wallclock time(sec): %.2f\n", twsym) ; /* ---------------------------------------------------------------------- */ /* scaling, from numerical factorization */ /* ---------------------------------------------------------------------- */ if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_NONE) { PRINTF (("\n matrix scaled: no\n")) ; } else if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_SUM) { PRINTF (("\n matrix scaled: yes ")) ; PRINTF (("(divided each row by sum of abs values in each row)\n")) ; PRINTF ((" minimum sum (abs (rows of A)): %.5e\n", Info [UMFPACK_RSMIN])) ; PRINTF ((" maximum sum (abs (rows of A)): %.5e\n", Info [UMFPACK_RSMAX])) ; } else if (Info [UMFPACK_WAS_SCALED] == UMFPACK_SCALE_MAX) { PRINTF (("\n matrix scaled: yes ")) ; PRINTF (("(divided each row by max abs value in each row)\n")) ; PRINTF ((" minimum max (abs (rows of A)): %.5e\n", Info [UMFPACK_RSMIN])) ; PRINTF ((" maximum max (abs (rows of A)): %.5e\n", Info [UMFPACK_RSMAX])) ; } /* ---------------------------------------------------------------------- */ /* estimate/actual in symbolic/numeric factorization */ /* ---------------------------------------------------------------------- */ /* double relop, but ignore NaN case: */ if (Info [UMFPACK_SYMBOLIC_DEFRAG] >= 0 /* UMFPACK_*symbolic called */ || Info [UMFPACK_NUMERIC_DEFRAG] >= 0) /* UMFPACK_numeric called */ { PRINTF (("\n symbolic/numeric factorization: upper bound")) ; PRINTF ((" actual %%\n")) ; PRINTF ((" variable-sized part of Numeric object:\n")) ; } print_ratio (" initial size (Units)", " %20.0f", Info [UMFPACK_VARIABLE_INIT_ESTIMATE], Info [UMFPACK_VARIABLE_INIT]) ; print_ratio (" peak size (Units)", " %20.0f", Info [UMFPACK_VARIABLE_PEAK_ESTIMATE], Info [UMFPACK_VARIABLE_PEAK]) ; print_ratio (" final size (Units)", " %20.0f", Info [UMFPACK_VARIABLE_FINAL_ESTIMATE], Info [UMFPACK_VARIABLE_FINAL]) ; print_ratio ("Numeric final size (Units)", " %20.0f", Info [UMFPACK_NUMERIC_SIZE_ESTIMATE], Info [UMFPACK_NUMERIC_SIZE]) ; print_ratio ("Numeric final size (MBytes)", " %20.1f", MBYTES (Info [UMFPACK_NUMERIC_SIZE_ESTIMATE]), MBYTES (Info [UMFPACK_NUMERIC_SIZE])) ; print_ratio ("peak memory usage (Units)", " %20.0f", Info [UMFPACK_PEAK_MEMORY_ESTIMATE], Info [UMFPACK_PEAK_MEMORY]) ; print_ratio ("peak memory usage (MBytes)", " %20.1f", MBYTES (Info [UMFPACK_PEAK_MEMORY_ESTIMATE]), MBYTES (Info [UMFPACK_PEAK_MEMORY])) ; print_ratio ("numeric factorization flops", " %20.5e", Info [UMFPACK_FLOPS_ESTIMATE], Info [UMFPACK_FLOPS]) ; lnz_est = Info [UMFPACK_LNZ_ESTIMATE] ; unz_est = Info [UMFPACK_UNZ_ESTIMATE] ; if (lnz_est >= 0 && unz_est >= 0) /* double relop, but ignore NaN case */ { lunz_est = lnz_est + unz_est - n_inner ; } else { lunz_est = EMPTY ; } lnz = Info [UMFPACK_LNZ] ; unz = Info [UMFPACK_UNZ] ; if (lnz >= 0 && unz >= 0) /* double relop, but ignore NaN case */ { lunz = lnz + unz - n_inner ; } else { lunz = EMPTY ; } print_ratio ("nz in L (incl diagonal)", " %20.0f", lnz_est, lnz) ; print_ratio ("nz in U (incl diagonal)", " %20.0f", unz_est, unz) ; print_ratio ("nz in L+U (incl diagonal)", " %20.0f", lunz_est, lunz) ; print_ratio ("largest front (# entries)", " %20.0f", Info [UMFPACK_MAX_FRONT_SIZE_ESTIMATE], Info [UMFPACK_MAX_FRONT_SIZE]) ; print_ratio ("largest # rows in front", " %20.0f", Info [UMFPACK_MAX_FRONT_NROWS_ESTIMATE], Info [UMFPACK_MAX_FRONT_NROWS]) ; print_ratio ("largest # columns in front", " %20.0f", Info [UMFPACK_MAX_FRONT_NCOLS_ESTIMATE], Info [UMFPACK_MAX_FRONT_NCOLS]) ; /* ---------------------------------------------------------------------- */ /* numeric factorization */ /* ---------------------------------------------------------------------- */ tnum = Info [UMFPACK_NUMERIC_TIME] ; twnum = Info [UMFPACK_NUMERIC_WALLTIME] ; fnum = Info [UMFPACK_FLOPS] ; PRINT_INFO ("\n initial allocation ratio used: %0.3g\n", Info [UMFPACK_ALLOC_INIT_USED]) ; PRINT_INFO (" # of forced updates due to frontal growth: %.0f\n", Info [UMFPACK_FORCED_UPDATES]) ; PRINT_INFO (" number of off-diagonal pivots: %.0f\n", Info [UMFPACK_NOFF_DIAG]) ; PRINT_INFO (" nz in L (incl diagonal), if none dropped %.0f\n", Info [UMFPACK_ALL_LNZ]) ; PRINT_INFO (" nz in U (incl diagonal), if none dropped %.0f\n", Info [UMFPACK_ALL_UNZ]) ; PRINT_INFO (" number of small entries dropped %.0f\n", Info [UMFPACK_NZDROPPED]) ; PRINT_INFO (" nonzeros on diagonal of U: %.0f\n", Info [UMFPACK_UDIAG_NZ]) ; PRINT_INFO (" min abs. value on diagonal of U: %.2e\n", Info [UMFPACK_UMIN]) ; PRINT_INFO (" max abs. value on diagonal of U: %.2e\n", Info [UMFPACK_UMAX]) ; PRINT_INFO (" estimate of reciprocal of condition number: %.2e\n", Info [UMFPACK_RCOND]) ; PRINT_INFO (" indices in compressed pattern: %.0f\n", Info [UMFPACK_COMPRESSED_PATTERN]) ; PRINT_INFO (" numerical values stored in Numeric object: %.0f\n", Info [UMFPACK_LU_ENTRIES]) ; PRINT_INFO (" numeric factorization defragmentations: %.0f\n", Info [UMFPACK_NUMERIC_DEFRAG]) ; PRINT_INFO (" numeric factorization reallocations: %.0f\n", Info [UMFPACK_NUMERIC_REALLOC]) ; PRINT_INFO (" costly numeric factorization reallocations: %.0f\n", Info [UMFPACK_NUMERIC_COSTLY_REALLOC]) ; PRINT_INFO (" numeric factorization CPU time (sec): %.2f\n", tnum) ; PRINT_INFO (" numeric factorization wallclock time (sec): %.2f\n", twnum) ; #define TMIN 0.001 if (tnum > TMIN && fnum > 0) { PRINT_INFO ( " numeric factorization mflops (CPU time): %.2f\n", 1e-6 * fnum / tnum) ; } if (twnum > TMIN && fnum > 0) { PRINT_INFO ( " numeric factorization mflops (wallclock): %.2f\n", 1e-6 * fnum / twnum) ; } ttot = EMPTY ; ftot = fnum ; if (tsym >= TMIN && tnum >= 0) { ttot = tsym + tnum ; PRINT_INFO (" symbolic + numeric CPU time (sec): %.2f\n", ttot) ; if (ftot > 0 && ttot > TMIN) { PRINT_INFO ( " symbolic + numeric mflops (CPU time): %.2f\n", 1e-6 * ftot / ttot) ; } } twtot = EMPTY ; if (twsym >= TMIN && twnum >= TMIN) { twtot = twsym + twnum ; PRINT_INFO (" symbolic + numeric wall clock time (sec): %.2f\n", twtot) ; if (ftot > 0 && twtot > TMIN) { PRINT_INFO ( " symbolic + numeric mflops (wall clock): %.2f\n", 1e-6 * ftot / twtot) ; } } /* ---------------------------------------------------------------------- */ /* solve */ /* ---------------------------------------------------------------------- */ tsolve = Info [UMFPACK_SOLVE_TIME] ; twsolve = Info [UMFPACK_SOLVE_WALLTIME] ; fsolve = Info [UMFPACK_SOLVE_FLOPS] ; PRINT_INFO ("\n solve flops: %.5e\n", fsolve) ; PRINT_INFO (" iterative refinement steps taken: %.0f\n", Info [UMFPACK_IR_TAKEN]) ; PRINT_INFO (" iterative refinement steps attempted: %.0f\n", Info [UMFPACK_IR_ATTEMPTED]) ; PRINT_INFO (" sparse backward error omega1: %.2e\n", Info [UMFPACK_OMEGA1]) ; PRINT_INFO (" sparse backward error omega2: %.2e\n", Info [UMFPACK_OMEGA2]) ; PRINT_INFO (" solve CPU time (sec): %.2f\n", tsolve) ; PRINT_INFO (" solve wall clock time (sec): %.2f\n", twsolve) ; if (fsolve > 0 && tsolve > TMIN) { PRINT_INFO ( " solve mflops (CPU time): %.2f\n", 1e-6 * fsolve / tsolve) ; } if (fsolve > 0 && twsolve > TMIN) { PRINT_INFO ( " solve mflops (wall clock time): %.2f\n", 1e-6 * fsolve / twsolve) ; } if (ftot >= 0 && fsolve >= 0) { ftot += fsolve ; PRINT_INFO ( "\n total symbolic + numeric + solve flops: %.5e\n", ftot) ; } if (tsolve >= TMIN) { if (ttot >= TMIN && ftot >= 0) { ttot += tsolve ; PRINT_INFO ( " total symbolic + numeric + solve CPU time: %.2f\n", ttot) ; if (ftot > 0 && ttot > TMIN) { PRINT_INFO ( " total symbolic + numeric + solve mflops (CPU): %.2f\n", 1e-6 * ftot / ttot) ; } } } if (twsolve >= TMIN) { if (twtot >= TMIN && ftot >= 0) { twtot += tsolve ; PRINT_INFO ( " total symbolic+numeric+solve wall clock time: %.2f\n", twtot) ; if (ftot > 0 && twtot > TMIN) { PRINT_INFO ( " total symbolic+numeric+solve mflops(wallclock) %.2f\n", 1e-6 * ftot / twtot) ; } } } PRINTF (("\n")) ; }