LDL version 3.3.2, date: Mar 22, 2024 -------------------------------------------------------- Input file: Matrix/A01 name: Dense/0 n: 0 entries: 0 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input file: Matrix/A02 name: Dense/0 n: 0 entries: 0 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input file: Matrix/A03 name: Dense/1 n: 1 entries: 1 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 1 nz, number of nonzeros in A: 1 symmetry of A: 1.0000 number of nonzeros on diagonal: 1 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 72 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 1 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 1 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 0 -------------------------------------------------------- Input file: Matrix/A04 name: Dense/1 n: 1 entries: 2 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK, but jumbled n, dimension of A: 1 nz, number of nonzeros in A: 1 symmetry of A: 1.0000 number of nonzeros on diagonal: 1 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 104 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 1 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 1 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 8.32667e-17 -------------------------------------------------------- Input file: Matrix/A05 name: Dense/2 n: 2 entries: 4 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 2 nz, number of nonzeros in A: 4 symmetry of A: 1.0000 number of nonzeros on diagonal: 2 nonzeros in pattern of A+A' (excl. diagonal): 2 # dense rows/columns of A+A': 0 memory used, in bytes: 160 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 1 nonzeros in L (including diagonal): 3 # divide operations for LDL' or LU: 1 # multiply-subtract operations for LDL': 1 # multiply-subtract operations for LU: 1 max nz. in any column of L (incl. diagonal): 2 chol flop count for real A, sqrt counted as 1 flop: 5 LDL' flop count for real A: 3 LDL' flop count for complex A: 17 LU flop count for real A (with no pivoting): 3 LU flop count for complex A (with no pivoting): 17 Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 5.55112e-17 -------------------------------------------------------- Input file: Matrix/A06 name: Dense/2 n: 2 entries: 5 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK, but jumbled n, dimension of A: 2 nz, number of nonzeros in A: 4 symmetry of A: 1.0000 number of nonzeros on diagonal: 2 nonzeros in pattern of A+A' (excl. diagonal): 2 # dense rows/columns of A+A': 0 memory used, in bytes: 224 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 1 nonzeros in L (including diagonal): 3 # divide operations for LDL' or LU: 1 # multiply-subtract operations for LDL': 1 # multiply-subtract operations for LU: 1 max nz. in any column of L (incl. diagonal): 2 chol flop count for real A, sqrt counted as 1 flop: 5 LDL' flop count for real A: 3 LDL' flop count for complex A: 17 LU flop count for real A (with no pivoting): 3 LU flop count for complex A (with no pivoting): 17 Factorize PAP'=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 1 Flop count: 3 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input file: Matrix/A07 name: Dense/3 n: 3 entries: 9 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 3 nz, number of nonzeros in A: 9 symmetry of A: 1.0000 number of nonzeros on diagonal: 3 nonzeros in pattern of A+A' (excl. diagonal): 6 # dense rows/columns of A+A': 0 memory used, in bytes: 272 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 3 nonzeros in L (including diagonal): 6 # divide operations for LDL' or LU: 3 # multiply-subtract operations for LDL': 4 # multiply-subtract operations for LU: 5 max nz. in any column of L (incl. diagonal): 3 chol flop count for real A, sqrt counted as 1 flop: 14 LDL' flop count for real A: 11 LDL' flop count for complex A: 59 LU flop count for real A (with no pivoting): 13 LU flop count for complex A (with no pivoting): 67 Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.11022e-16 -------------------------------------------------------- Input file: Matrix/A08 name: Dense/3 n: 3 entries: 11 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK, but jumbled n, dimension of A: 3 nz, number of nonzeros in A: 9 symmetry of A: 1.0000 number of nonzeros on diagonal: 3 nonzeros in pattern of A+A' (excl. diagonal): 6 # dense rows/columns of A+A': 0 memory used, in bytes: 392 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 3 nonzeros in L (including diagonal): 6 # divide operations for LDL' or LU: 3 # multiply-subtract operations for LDL': 4 # multiply-subtract operations for LU: 5 max nz. in any column of L (incl. diagonal): 3 chol flop count for real A, sqrt counted as 1 flop: 14 LDL' flop count for real A: 11 LDL' flop count for complex A: 59 LU flop count for real A (with no pivoting): 13 LU flop count for complex A (with no pivoting): 67 Factorize PAP'=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 Factorize A=LDL' and solve Ax=b Nz in L: 3 Flop count: 11 relative maxnorm of residual: 1.38778e-16 -------------------------------------------------------- Input file: Matrix/A09 name: HB/can_24 n: 24 entries: 160 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 3032 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input file: Matrix/A10 name: HB/can_24 n: 24 entries: 188 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK, but jumbled n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 4736 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 Factorize PAP'=LDL' and solve Ax=b Nz in L: 96 Flop count: 632 Ax=b not solved since D(1,1) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 146 Flop count: 1360 Ax=b not solved since D(5,5) is zero. -------------------------------------------------------- Input file: Matrix/A11 name: FIDAP/ex5 n: 27 entries: 279 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 27 nz, number of nonzeros in A: 279 symmetry of A: 1.0000 number of nonzeros on diagonal: 27 nonzeros in pattern of A+A' (excl. diagonal): 252 # dense rows/columns of A+A': 0 memory used, in bytes: 4360 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 126 nonzeros in L (including diagonal): 153 # divide operations for LDL' or LU: 126 # multiply-subtract operations for LDL': 414 # multiply-subtract operations for LU: 702 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 981 LDL' flop count for real A: 954 LDL' flop count for complex A: 4446 LU flop count for real A (with no pivoting): 1530 LU flop count for complex A (with no pivoting): 6750 Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 2.59625e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.72848e-10 -------------------------------------------------------- Input file: Matrix/A12 name: FIDAP/ex5 n: 27 entries: 325 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK, but jumbled n, dimension of A: 27 nz, number of nonzeros in A: 279 symmetry of A: 1.0000 number of nonzeros on diagonal: 27 nonzeros in pattern of A+A' (excl. diagonal): 252 # dense rows/columns of A+A': 0 memory used, in bytes: 7184 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 126 nonzeros in L (including diagonal): 153 # divide operations for LDL' or LU: 126 # multiply-subtract operations for LDL': 414 # multiply-subtract operations for LU: 702 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 981 LDL' flop count for real A: 954 LDL' flop count for complex A: 4446 LU flop count for real A (with no pivoting): 1530 LU flop count for complex A (with no pivoting): 6750 Factorize PAP'=LDL' and solve Ax=b Nz in L: 126 Flop count: 954 relative maxnorm of residual: 3.27418e-10 Factorize A=LDL' and solve Ax=b Nz in L: 276 Flop count: 4206 relative maxnorm of residual: 2.32376e-10 -------------------------------------------------------- Input file: Matrix/A13 name: HB/bcsstk01 n: 48 entries: 400 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 400 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 352 # dense rows/columns of A+A': 0 memory used, in bytes: 6832 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 441 nonzeros in L (including diagonal): 489 # divide operations for LDL' or LU: 441 # multiply-subtract operations for LDL': 2760 # multiply-subtract operations for LU: 5079 max nz. in any column of L (incl. diagonal): 20 chol flop count for real A, sqrt counted as 1 flop: 6009 LDL' flop count for real A: 5961 LDL' flop count for complex A: 26049 LU flop count for real A (with no pivoting): 10599 LU flop count for complex A (with no pivoting): 44601 Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.38712e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 2.27374e-13 -------------------------------------------------------- Input file: Matrix/A14 name: HB/bcsstk01 n: 48 entries: 472 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 400 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 352 # dense rows/columns of A+A': 0 memory used, in bytes: 11000 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 441 nonzeros in L (including diagonal): 489 # divide operations for LDL' or LU: 441 # multiply-subtract operations for LDL': 2760 # multiply-subtract operations for LU: 5079 max nz. in any column of L (incl. diagonal): 20 chol flop count for real A, sqrt counted as 1 flop: 6009 LDL' flop count for real A: 5961 LDL' flop count for complex A: 26049 LU flop count for real A (with no pivoting): 10599 LU flop count for complex A (with no pivoting): 44601 Factorize PAP'=LDL' and solve Ax=b Nz in L: 441 Flop count: 5961 relative maxnorm of residual: 2.27374e-13 Factorize A=LDL' and solve Ax=b Nz in L: 829 Flop count: 20103 relative maxnorm of residual: 3.83693e-13 -------------------------------------------------------- Input file: Matrix/A15 name: HB/bcsstm01 n: 48 entries: 24 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 24 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 3456 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 48 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 48 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input file: Matrix/A16 name: HB/bcsstm01 n: 48 entries: 26 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 24 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 4056 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 48 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 48 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 Ax=b not solved since D(3,3) is zero. -------------------------------------------------------- Input file: Matrix/A17 name: Pothen/mesh1e1 n: 48 entries: 306 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 48 nz, number of nonzeros in A: 306 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 258 # dense rows/columns of A+A': 0 memory used, in bytes: 5928 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 288 nonzeros in L (including diagonal): 336 # divide operations for LDL' or LU: 288 # multiply-subtract operations for LDL': 1171 # multiply-subtract operations for LU: 2054 max nz. in any column of L (incl. diagonal): 13 chol flop count for real A, sqrt counted as 1 flop: 2678 LDL' flop count for real A: 2630 LDL' flop count for complex A: 11960 LU flop count for real A (with no pivoting): 4396 LU flop count for complex A (with no pivoting): 19024 Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.96745e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 6.93889e-16 -------------------------------------------------------- Input file: Matrix/A18 name: Pothen/mesh1e1 n: 48 entries: 359 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK, but jumbled n, dimension of A: 48 nz, number of nonzeros in A: 306 symmetry of A: 1.0000 number of nonzeros on diagonal: 48 nonzeros in pattern of A+A' (excl. diagonal): 258 # dense rows/columns of A+A': 0 memory used, in bytes: 9192 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 288 nonzeros in L (including diagonal): 336 # divide operations for LDL' or LU: 288 # multiply-subtract operations for LDL': 1171 # multiply-subtract operations for LU: 2054 max nz. in any column of L (incl. diagonal): 13 chol flop count for real A, sqrt counted as 1 flop: 2678 LDL' flop count for real A: 2630 LDL' flop count for complex A: 11960 LU flop count for real A (with no pivoting): 4396 LU flop count for complex A (with no pivoting): 19024 Factorize PAP'=LDL' and solve Ax=b Nz in L: 288 Flop count: 2630 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 511 Flop count: 7383 relative maxnorm of residual: 5.55112e-16 -------------------------------------------------------- Input file: Matrix/A19 name: Bai/bfwb62 n: 62 entries: 342 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 62 nz, number of nonzeros in A: 342 symmetry of A: 1.0000 number of nonzeros on diagonal: 62 nonzeros in pattern of A+A' (excl. diagonal): 280 # dense rows/columns of A+A': 0 memory used, in bytes: 7152 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 226 nonzeros in L (including diagonal): 288 # divide operations for LDL' or LU: 226 # multiply-subtract operations for LDL': 623 # multiply-subtract operations for LU: 1020 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 1534 LDL' flop count for real A: 1472 LDL' flop count for complex A: 7018 LU flop count for real A (with no pivoting): 2266 LU flop count for complex A (with no pivoting): 10194 Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.55112e-16 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 1.11022e-15 -------------------------------------------------------- Input file: Matrix/A20 name: Bai/bfwb62 n: 62 entries: 407 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK, but jumbled n, dimension of A: 62 nz, number of nonzeros in A: 342 symmetry of A: 1.0000 number of nonzeros on diagonal: 62 nonzeros in pattern of A+A' (excl. diagonal): 280 # dense rows/columns of A+A': 0 memory used, in bytes: 10912 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 226 nonzeros in L (including diagonal): 288 # divide operations for LDL' or LU: 226 # multiply-subtract operations for LDL': 623 # multiply-subtract operations for LU: 1020 max nz. in any column of L (incl. diagonal): 9 chol flop count for real A, sqrt counted as 1 flop: 1534 LDL' flop count for real A: 1472 LDL' flop count for complex A: 7018 LU flop count for real A (with no pivoting): 2266 LU flop count for complex A (with no pivoting): 10194 Factorize PAP'=LDL' and solve Ax=b Nz in L: 226 Flop count: 1472 relative maxnorm of residual: 5.68434e-14 Factorize A=LDL' and solve Ax=b Nz in L: 662 Flop count: 11350 relative maxnorm of residual: 2.15827e-12 -------------------------------------------------------- Input file: Matrix/A21 name: HB/bcsstk02 n: 66 entries: 4356 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 66 nz, number of nonzeros in A: 4356 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 4290 # dense rows/columns of A+A': 0 memory used, in bytes: 45936 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 2145 nonzeros in L (including diagonal): 2211 # divide operations for LDL' or LU: 2145 # multiply-subtract operations for LDL': 47905 # multiply-subtract operations for LU: 93665 max nz. in any column of L (incl. diagonal): 66 chol flop count for real A, sqrt counted as 1 flop: 98021 LDL' flop count for real A: 97955 LDL' flop count for complex A: 402545 LU flop count for real A (with no pivoting): 189475 LU flop count for complex A (with no pivoting): 768625 Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 7.50219e-13 -------------------------------------------------------- Input file: Matrix/A22 name: HB/bcsstk02 n: 66 entries: 5175 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK, but jumbled n, dimension of A: 66 nz, number of nonzeros in A: 4356 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 4290 # dense rows/columns of A+A': 0 memory used, in bytes: 87872 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 2145 nonzeros in L (including diagonal): 2211 # divide operations for LDL' or LU: 2145 # multiply-subtract operations for LDL': 47905 # multiply-subtract operations for LU: 93665 max nz. in any column of L (incl. diagonal): 66 chol flop count for real A, sqrt counted as 1 flop: 98021 LDL' flop count for real A: 97955 LDL' flop count for complex A: 402545 LU flop count for real A (with no pivoting): 189475 LU flop count for complex A (with no pivoting): 768625 Factorize PAP'=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 Factorize A=LDL' and solve Ax=b Nz in L: 2145 Flop count: 97955 relative maxnorm of residual: 8.59759e-13 -------------------------------------------------------- Input file: Matrix/A23 name: HB/bcsstm02 n: 66 entries: 66 -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK n, dimension of A: 66 nz, number of nonzeros in A: 66 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 4752 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 66 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 66 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input file: Matrix/A24 name: HB/bcsstm02 n: 66 entries: 72 (jumbled version) -------------------------------------------------------- AMD version 3.3.2, Mar 22, 2024: approximate minimum degree ordering dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes size of AMD integer: 8 AMD version 3.3.2, Mar 22, 2024, results: status: OK, but jumbled n, dimension of A: 66 nz, number of nonzeros in A: 66 symmetry of A: 1.0000 number of nonzeros on diagonal: 66 nonzeros in pattern of A+A' (excl. diagonal): 0 # dense rows/columns of A+A': 0 memory used, in bytes: 5864 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 0 nonzeros in L (including diagonal): 66 # divide operations for LDL' or LU: 0 # multiply-subtract operations for LDL': 0 # multiply-subtract operations for LU: 0 max nz. in any column of L (incl. diagonal): 1 chol flop count for real A, sqrt counted as 1 flop: 66 LDL' flop count for real A: 0 LDL' flop count for complex A: 0 LU flop count for real A (with no pivoting): 0 LU flop count for complex A (with no pivoting): 0 Factorize PAP'=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 Factorize A=LDL' and solve Ax=b Nz in L: 0 Flop count: 0 relative maxnorm of residual: 2.22045e-16 -------------------------------------------------------- Input file: Matrix/A25 name: Dense/0 n: 0 entries: 0 (invalid matrix, Ap [0] = 1) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input file: Matrix/A26 name: Dense/2 n: 2 entries: 4 (invalid perm, P[1]=99) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input file: Matrix/A27 name: Dense/3 n: 3 entries: 9 (invalid perm) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input file: Matrix/A28 name: Dense/3 n: 3 entries: 9 (invalid Ap) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input file: Matrix/A29 name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation -------------------------------------------------------- Input file: Matrix/A30 name: Dense/3 n: 3 entries: 9 (invalid Ai) -------------------------------------------------------- ldlamd: invalid matrix and/or permutation Largest residual during all tests: 3.27418e-10 ldlamd: all tests passed