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R (equation.9.15) 837 0 R (equation.9.16) 838 0 R] /Limits [(equation.9.11) (equation.9.16)] >> endobj -1020 0 obj << -/Names [(equation.9.17) 821 0 R (equation.9.18) 828 0 R (equation.9.19) 829 0 R (equation.9.20) 838 0 R (equation.9.21) 839 0 R (equation.9.22) 840 0 R] +1039 0 obj << +/Names [(equation.9.17) 839 0 R (equation.9.18) 846 0 R (equation.9.19) 847 0 R (equation.9.20) 857 0 R (equation.9.21) 858 0 R (equation.9.22) 859 0 R] /Limits [(equation.9.17) (equation.9.22)] >> endobj -1021 0 obj << -/Names [(equation.9.23) 841 0 R (equation.9.24) 842 0 R (equation.9.25) 851 0 R (equation.9.26) 852 0 R (equation.9.27) 853 0 R (equation.9.28) 863 0 R] +1040 0 obj << +/Names [(equation.9.23) 860 0 R (equation.9.24) 861 0 R (equation.9.25) 870 0 R (equation.9.26) 871 0 R (equation.9.27) 872 0 R (equation.9.28) 881 0 R] /Limits [(equation.9.23) (equation.9.28)] >> endobj -1022 0 obj << -/Names [(equation.9.29) 865 0 R (equation.9.30) 866 0 R (equation.9.31) 867 0 R (equation.9.32) 876 0 R (equation.9.33) 877 0 R (equation.9.34) 878 0 R] +1041 0 obj << +/Names [(equation.9.29) 883 0 R (equation.9.30) 884 0 R (equation.9.31) 885 0 R (equation.9.32) 894 0 R (equation.9.33) 895 0 R (equation.9.34) 896 0 R] /Limits [(equation.9.29) (equation.9.34)] >> endobj -1023 0 obj << -/Names [(equation.9.35) 888 0 R (equation.9.36) 889 0 R (equation.9.37) 901 0 R (equation.9.38) 902 0 R (equation.9.39) 915 0 R (equation.9.40) 916 0 R] +1042 0 obj << +/Names [(equation.9.35) 906 0 R (equation.9.36) 907 0 R (equation.9.37) 919 0 R (equation.9.38) 920 0 R (equation.9.39) 934 0 R (equation.9.40) 935 0 R] /Limits [(equation.9.35) (equation.9.40)] >> endobj -1024 0 obj << -/Names [(equation.9.41) 917 0 R (equation.9.42) 926 0 R (equation.9.43) 927 0 R (equation.9.44) 938 0 R (equation.9.45) 954 0 R (equation.9.46) 955 0 R] +1043 0 obj << +/Names [(equation.9.41) 936 0 R (equation.9.42) 945 0 R (equation.9.43) 946 0 R (equation.9.44) 956 0 R (equation.9.45) 972 0 R (equation.9.46) 973 0 R] /Limits [(equation.9.41) (equation.9.46)] >> endobj -1025 0 obj << -/Names [(equation.9.47) 956 0 R (equation.9.48) 964 0 R (equation.9.49) 965 0 R (equation.9.5) 793 0 R (equation.9.50) 966 0 R (equation.9.51) 967 0 R] +1044 0 obj << +/Names [(equation.9.47) 974 0 R (equation.9.48) 982 0 R (equation.9.49) 983 0 R (equation.9.5) 811 0 R (equation.9.50) 984 0 R (equation.9.51) 985 0 R] /Limits [(equation.9.47) (equation.9.51)] >> endobj -1026 0 obj << -/Names [(equation.9.6) 794 0 R (equation.9.7) 795 0 R (equation.9.8) 796 0 R (equation.9.9) 805 0 R (figure.1) 717 0 R (figure.2) 733 0 R] +1045 0 obj << +/Names [(equation.9.6) 812 0 R (equation.9.7) 813 0 R (equation.9.8) 814 0 R (equation.9.9) 823 0 R (figure.1) 735 0 R (figure.2) 752 0 R] /Limits [(equation.9.6) (figure.2)] >> endobj -1027 0 obj << -/Names [(figure.3) 879 0 R (figure.4) 900 0 R (figure.5) 918 0 R (figure.6) 937 0 R (page.1) 520 0 R (page.10) 679 0 R] +1046 0 obj << +/Names [(figure.3) 897 0 R (figure.4) 918 0 R (figure.5) 937 0 R (figure.6) 955 0 R (page.1) 529 0 R (page.10) 687 0 R] /Limits [(figure.3) (page.10)] >> endobj -1028 0 obj << -/Names [(page.11) 694 0 R (page.12) 699 0 R (page.13) 704 0 R (page.14) 710 0 R (page.15) 716 0 R (page.16) 721 0 R] +1047 0 obj << +/Names [(page.11) 692 0 R (page.12) 700 0 R (page.13) 712 0 R (page.14) 718 0 R (page.15) 723 0 R (page.16) 728 0 R] /Limits [(page.11) (page.16)] >> endobj -1029 0 obj << -/Names [(page.17) 732 0 R (page.18) 737 0 R (page.19) 745 0 R (page.2) 585 0 R (page.20) 753 0 R (page.21) 759 0 R] +1048 0 obj << +/Names [(page.17) 734 0 R (page.18) 739 0 R (page.19) 750 0 R (page.2) 595 0 R (page.20) 756 0 R (page.21) 764 0 R] /Limits [(page.17) (page.21)] >> endobj -1030 0 obj << -/Names [(page.22) 766 0 R (page.23) 772 0 R (page.24) 777 0 R (page.25) 781 0 R (page.26) 792 0 R (page.27) 804 0 R] +1049 0 obj << +/Names [(page.22) 771 0 R (page.23) 777 0 R (page.24) 784 0 R (page.25) 790 0 R (page.26) 796 0 R (page.27) 800 0 R] /Limits [(page.22) (page.27)] >> endobj -1031 0 obj << -/Names [(page.28) 818 0 R (page.29) 827 0 R (page.3) 627 0 R (page.30) 837 0 R (page.31) 850 0 R (page.32) 862 0 R] +1050 0 obj << +/Names [(page.28) 810 0 R (page.29) 822 0 R (page.3) 637 0 R (page.30) 836 0 R (page.31) 845 0 R (page.32) 856 0 R] /Limits [(page.28) (page.32)] >> endobj -1032 0 obj << -/Names [(page.33) 875 0 R (page.34) 887 0 R (page.35) 899 0 R (page.36) 914 0 R (page.37) 925 0 R (page.38) 936 0 R] +1051 0 obj << +/Names [(page.33) 869 0 R (page.34) 880 0 R (page.35) 893 0 R (page.36) 905 0 R (page.37) 917 0 R (page.38) 933 0 R] /Limits [(page.33) (page.38)] >> endobj -1033 0 obj << -/Names [(page.39) 946 0 R (page.4) 635 0 R (page.40) 953 0 R (page.41) 963 0 R (page.42) 971 0 R (page.5) 641 0 R] -/Limits [(page.39) (page.5)] +1052 0 obj << +/Names [(page.39) 944 0 R (page.4) 645 0 R (page.40) 954 0 R (page.41) 964 0 R (page.42) 971 0 R (page.43) 981 0 R] +/Limits [(page.39) (page.43)] >> endobj -1034 0 obj << -/Names [(page.6) 648 0 R (page.7) 658 0 R (page.8) 666 0 R (page.9) 673 0 R (section*.1) 525 0 R (section*.10) 683 0 R] -/Limits [(page.6) (section*.10)] +1053 0 obj << +/Names [(page.44) 990 0 R (page.5) 651 0 R (page.6) 658 0 R (page.7) 668 0 R (page.8) 676 0 R (page.9) 682 0 R] +/Limits [(page.44) (page.9)] >> endobj -1035 0 obj << -/Names [(section*.11) 684 0 R (section*.12) 685 0 R (section*.13) 686 0 R (section*.14) 687 0 R (section*.15) 688 0 R (section*.16) 689 0 R] -/Limits [(section*.11) (section*.16)] +1054 0 obj << +/Names [(section*.1) 534 0 R (section*.10) 701 0 R (section*.11) 702 0 R (section*.12) 703 0 R (section*.13) 704 0 R (section*.14) 705 0 R] +/Limits [(section*.1) (section*.14)] >> endobj -1036 0 obj << -/Names [(section*.17) 690 0 R (section*.18) 695 0 R (section*.19) 700 0 R (section*.2) 636 0 R (section*.20) 705 0 R (section*.21) 722 0 R] -/Limits [(section*.17) (section*.21)] +1055 0 obj << +/Names [(section*.15) 706 0 R (section*.16) 707 0 R (section*.17) 708 0 R (section*.18) 713 0 R (section*.19) 719 0 R (section*.2) 646 0 R] +/Limits [(section*.15) (section*.2)] >> endobj -1037 0 obj << -/Names [(section*.22) 746 0 R (section*.23) 761 0 R (section*.24) 768 0 R (section*.3) 642 0 R (section*.4) 649 0 R (section*.5) 659 0 R] -/Limits [(section*.22) (section*.5)] +1056 0 obj << +/Names [(section*.20) 724 0 R (section*.21) 740 0 R (section*.22) 765 0 R (section*.23) 779 0 R (section*.24) 786 0 R (section*.3) 652 0 R] +/Limits [(section*.20) (section*.3)] >> endobj -1038 0 obj << -/Names [(section*.6) 660 0 R (section*.7) 668 0 R (section*.8) 680 0 R (section*.9) 682 0 R (section.1) 6 0 R (section.2) 18 0 R] -/Limits [(section*.6) (section.2)] +1057 0 obj << +/Names [(section*.4) 659 0 R (section*.5) 669 0 R (section*.6) 670 0 R (section*.7) 678 0 R (section*.8) 694 0 R (section*.9) 696 0 R] +/Limits [(section*.4) (section*.9)] >> endobj -1039 0 obj << -/Names [(section.3) 22 0 R (section.4) 26 0 R (section.5) 66 0 R (section.6) 106 0 R (section.7) 110 0 R (section.8) 114 0 R] -/Limits [(section.3) (section.8)] +1058 0 obj << +/Names [(section.1) 6 0 R (section.2) 18 0 R (section.3) 22 0 R (section.4) 26 0 R (section.5) 74 0 R (section.6) 114 0 R] +/Limits [(section.1) (section.6)] >> endobj -1040 0 obj << -/Names [(section.9) 138 0 R (subsection.1.1) 10 0 R (subsection.1.2) 14 0 R (subsection.4.1) 30 0 R (subsection.4.2) 34 0 R (subsection.4.3) 38 0 R] -/Limits [(section.9) (subsection.4.3)] +1059 0 obj << +/Names [(section.7) 118 0 R (section.8) 122 0 R (section.9) 146 0 R (subsection.1.1) 10 0 R (subsection.1.2) 14 0 R (subsection.4.1) 30 0 R] +/Limits [(section.7) (subsection.4.1)] >> endobj -1041 0 obj << -/Names [(subsection.4.4) 42 0 R (subsection.4.5) 46 0 R (subsection.4.6) 50 0 R (subsection.4.7) 54 0 R (subsection.5.1) 70 0 R (subsection.5.2) 90 0 R] -/Limits [(subsection.4.4) (subsection.5.2)] +1060 0 obj << +/Names [(subsection.4.2) 34 0 R (subsection.4.3) 38 0 R (subsection.4.4) 42 0 R (subsection.4.5) 46 0 R (subsection.4.6) 58 0 R (subsection.4.7) 62 0 R] +/Limits [(subsection.4.2) (subsection.4.7)] >> endobj -1042 0 obj << -/Names [(subsection.8.1) 118 0 R (subsection.8.2) 122 0 R (subsection.8.3) 126 0 R (subsection.9.1) 142 0 R (subsection.9.2) 166 0 R (subsection.9.3) 226 0 R] -/Limits [(subsection.8.1) (subsection.9.3)] +1061 0 obj << +/Names [(subsection.5.1) 78 0 R (subsection.5.2) 98 0 R (subsection.8.1) 126 0 R (subsection.8.2) 130 0 R (subsection.8.3) 134 0 R (subsection.9.1) 150 0 R] +/Limits [(subsection.5.1) (subsection.9.1)] >> endobj -1043 0 obj << -/Names [(subsection.9.4) 266 0 R (subsection.9.5) 330 0 R (subsection.9.6) 346 0 R (subsection.9.7) 430 0 R (subsection.9.8) 466 0 R (subsubsection.4.7.1) 58 0 R] -/Limits [(subsection.9.4) (subsubsection.4.7.1)] +1062 0 obj << +/Names [(subsection.9.2) 174 0 R (subsection.9.3) 234 0 R (subsection.9.4) 274 0 R (subsection.9.5) 338 0 R (subsection.9.6) 354 0 R (subsection.9.7) 438 0 R] +/Limits [(subsection.9.2) (subsection.9.7)] >> endobj -1044 0 obj << -/Names [(subsubsection.4.7.2) 62 0 R (subsubsection.5.1.1) 74 0 R (subsubsection.5.1.2) 78 0 R (subsubsection.5.1.3) 82 0 R (subsubsection.5.1.4) 86 0 R (subsubsection.5.2.1) 94 0 R] -/Limits [(subsubsection.4.7.2) (subsubsection.5.2.1)] +1063 0 obj << +/Names [(subsection.9.8) 474 0 R (subsubsection.4.5.1) 50 0 R (subsubsection.4.5.2) 54 0 R (subsubsection.4.7.1) 66 0 R (subsubsection.4.7.2) 70 0 R (subsubsection.5.1.1) 82 0 R] +/Limits [(subsection.9.8) (subsubsection.5.1.1)] >> endobj -1045 0 obj << -/Names [(subsubsection.5.2.2) 98 0 R (subsubsection.5.2.3) 102 0 R (subsubsection.8.3.1) 130 0 R (subsubsection.8.3.2) 134 0 R (subsubsection.9.1.1) 146 0 R (subsubsection.9.1.2) 150 0 R] -/Limits [(subsubsection.5.2.2) (subsubsection.9.1.2)] +1064 0 obj << +/Names [(subsubsection.5.1.2) 86 0 R (subsubsection.5.1.3) 90 0 R (subsubsection.5.1.4) 94 0 R (subsubsection.5.2.1) 102 0 R (subsubsection.5.2.2) 106 0 R (subsubsection.5.2.3) 110 0 R] +/Limits [(subsubsection.5.1.2) (subsubsection.5.2.3)] >> endobj -1046 0 obj << -/Names [(subsubsection.9.1.3) 154 0 R (subsubsection.9.1.4) 158 0 R (subsubsection.9.1.5) 162 0 R (subsubsection.9.2.1) 170 0 R (subsubsection.9.2.10) 206 0 R (subsubsection.9.2.11) 210 0 R] -/Limits [(subsubsection.9.1.3) (subsubsection.9.2.11)] +1065 0 obj << +/Names [(subsubsection.8.3.1) 138 0 R (subsubsection.8.3.2) 142 0 R (subsubsection.9.1.1) 154 0 R (subsubsection.9.1.2) 158 0 R (subsubsection.9.1.3) 162 0 R (subsubsection.9.1.4) 166 0 R] +/Limits [(subsubsection.8.3.1) (subsubsection.9.1.4)] >> endobj -1047 0 obj << -/Names [(subsubsection.9.2.12) 214 0 R (subsubsection.9.2.13) 218 0 R (subsubsection.9.2.14) 222 0 R (subsubsection.9.2.2) 174 0 R (subsubsection.9.2.3) 178 0 R (subsubsection.9.2.4) 182 0 R] -/Limits [(subsubsection.9.2.12) (subsubsection.9.2.4)] +1066 0 obj << +/Names [(subsubsection.9.1.5) 170 0 R (subsubsection.9.2.1) 178 0 R (subsubsection.9.2.10) 214 0 R (subsubsection.9.2.11) 218 0 R (subsubsection.9.2.12) 222 0 R (subsubsection.9.2.13) 226 0 R] +/Limits [(subsubsection.9.1.5) (subsubsection.9.2.13)] >> endobj -1048 0 obj << -/Names [(subsubsection.9.2.5) 186 0 R (subsubsection.9.2.6) 190 0 R (subsubsection.9.2.7) 194 0 R (subsubsection.9.2.8) 198 0 R (subsubsection.9.2.9) 202 0 R (subsubsection.9.3.1) 230 0 R] -/Limits [(subsubsection.9.2.5) (subsubsection.9.3.1)] +1067 0 obj << +/Names [(subsubsection.9.2.14) 230 0 R (subsubsection.9.2.2) 182 0 R (subsubsection.9.2.3) 186 0 R (subsubsection.9.2.4) 190 0 R (subsubsection.9.2.5) 194 0 R (subsubsection.9.2.6) 198 0 R] +/Limits [(subsubsection.9.2.14) (subsubsection.9.2.6)] >> endobj -1049 0 obj << -/Names [(subsubsection.9.3.2) 234 0 R (subsubsection.9.3.3) 238 0 R (subsubsection.9.3.4) 242 0 R (subsubsection.9.3.5) 246 0 R (subsubsection.9.3.6) 250 0 R (subsubsection.9.3.7) 254 0 R] -/Limits [(subsubsection.9.3.2) (subsubsection.9.3.7)] +1068 0 obj << +/Names [(subsubsection.9.2.7) 202 0 R (subsubsection.9.2.8) 206 0 R (subsubsection.9.2.9) 210 0 R (subsubsection.9.3.1) 238 0 R (subsubsection.9.3.2) 242 0 R (subsubsection.9.3.3) 246 0 R] +/Limits [(subsubsection.9.2.7) (subsubsection.9.3.3)] >> endobj -1050 0 obj << -/Names [(subsubsection.9.3.8) 258 0 R (subsubsection.9.3.9) 262 0 R (subsubsection.9.4.1) 270 0 R (subsubsection.9.4.10) 306 0 R (subsubsection.9.4.11) 310 0 R (subsubsection.9.4.12) 314 0 R] -/Limits [(subsubsection.9.3.8) (subsubsection.9.4.12)] +1069 0 obj << +/Names [(subsubsection.9.3.4) 250 0 R (subsubsection.9.3.5) 254 0 R (subsubsection.9.3.6) 258 0 R (subsubsection.9.3.7) 262 0 R (subsubsection.9.3.8) 266 0 R (subsubsection.9.3.9) 270 0 R] +/Limits [(subsubsection.9.3.4) (subsubsection.9.3.9)] >> endobj -1051 0 obj << -/Names [(subsubsection.9.4.13) 318 0 R (subsubsection.9.4.14) 322 0 R (subsubsection.9.4.15) 326 0 R (subsubsection.9.4.2) 274 0 R (subsubsection.9.4.3) 278 0 R (subsubsection.9.4.4) 282 0 R] -/Limits [(subsubsection.9.4.13) (subsubsection.9.4.4)] +1070 0 obj << +/Names [(subsubsection.9.4.1) 278 0 R (subsubsection.9.4.10) 314 0 R (subsubsection.9.4.11) 318 0 R (subsubsection.9.4.12) 322 0 R (subsubsection.9.4.13) 326 0 R (subsubsection.9.4.14) 330 0 R] +/Limits [(subsubsection.9.4.1) (subsubsection.9.4.14)] >> endobj -1052 0 obj << -/Names [(subsubsection.9.4.5) 286 0 R (subsubsection.9.4.6) 290 0 R (subsubsection.9.4.7) 294 0 R (subsubsection.9.4.8) 298 0 R (subsubsection.9.4.9) 302 0 R (subsubsection.9.5.1) 334 0 R] -/Limits [(subsubsection.9.4.5) (subsubsection.9.5.1)] +1071 0 obj << +/Names [(subsubsection.9.4.15) 334 0 R (subsubsection.9.4.2) 282 0 R (subsubsection.9.4.3) 286 0 R (subsubsection.9.4.4) 290 0 R (subsubsection.9.4.5) 294 0 R (subsubsection.9.4.6) 298 0 R] +/Limits [(subsubsection.9.4.15) (subsubsection.9.4.6)] >> endobj -1053 0 obj << -/Names [(subsubsection.9.5.2) 338 0 R (subsubsection.9.5.3) 342 0 R (subsubsection.9.6.1) 350 0 R (subsubsection.9.6.10) 386 0 R (subsubsection.9.6.11) 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+299822 %%EOF diff --git a/doc/fvn.tex b/doc/fvn.tex index d3f69f4..c79c589 100644 --- a/doc/fvn.tex +++ b/doc/fvn.tex @@ -277,24 +277,26 @@ end program \end{verbatim} -\subsection{Sparse solving} -By interfacing Tim Davis's SuiteSparse from university of Florida \url{http://www.cise.ufl.edu/research/sparse/SuiteSparse/} which is a reference for this kind of problems, fvn provides simple subroutines for solving linear sparse systems. +\subsection{Sparse matrix} +By interfacing Tim Davis's SuiteSparse from university of Florida \url{http://www.cise.ufl.edu/research/sparse/SuiteSparse/} which is a reference for this kind of problems, fvn provides simple subroutines for solving linear sparse systems and calculating determinants. +\subsubsection{Sparse solving} The provided routines solves the equation $Ax=B$ where A is sparse and given in its triplet form. \begin{verbatim} Module : fvn_sparse -call fvn_sparse_solve(n,nz,T,Ti,Tj,B,x,status) +call fvn_sparse_solve(n,nz,T,Ti,Tj,B,x,status,det) \end{verbatim} \begin{itemize} - \item For this family of subroutine the two letters (zl,zi,dl,di) of the specific interface name decribe the arguments's type. z is for complex(8), d for real(8), l for integer(8) and i for integer(4) - \item n (in) is an integer equal to the matrix rank - \item nz (in) is an integer equal to the number of non-zero elements - \item T(nz) (in) is a complex/real array containing the non-zero elements - \item Ti(nz),Tj(nz) (in) are the indexes of the corresponding element of T in the original matrix. - \item B(n) (in) is a complex/real array containing the second member of the equation. - \item x(n) (out) is a complex/real array containing the solution - \item status (out) is an integer which contain non-zero is something went wrong + \item For this family of subroutines the two letters (zl,zi,dl,di) of the specific interface name decribe the arguments's type. z is for complex(8), d for real(8), l for integer(8) and i for integer(4) + \item \texttt{n} (in) is an integer equal to the matrix rank + \item \texttt{nz} (in) is an integer equal to the number of non-zero elements + \item \texttt{T(nz)} (in) is a complex/real array containing the non-zero elements + \item \textt{Ti(nz)},\texttt{Tj(nz)} (in) are the indexes of the corresponding element of \texttt{T} in the original matrix. + \item \texttt{B(n)} (in) is a complex/real array containing the second member of the equation. + \item \texttt{x(n)} (out) is a complex/real array containing the solution + \item \texttt{status} (out) is an integer which contain non-zero is something went wrong + \item \texttt{det} (out), is an optional real(8) array of dimension 2 for dl and di specific interface (real systems) and dimension 3 for zl and zi interface (complex systems) \end{itemize} @@ -350,10 +352,102 @@ write(*,*) x end program +\end{verbatim} + +If optional parameter \texttt{det} is given, the routine will also calculates the matrix determinant and returns it on a mantissa + exponent form, that is the actual determinant will be $det(1).10^{det(2)}$ for real problems and $(det(1)+i.det(2)).10^{det(3)}$ for complex problems. This is given in this form as the determinant can be considerably higher/lower than the biggest/lowest usable double precision real. There's an example of how to use this in following paragraph. +\subsubsection{Sparse determinant} +The provided subroutines calculates the determinant of a matrix given in its triplet form. +\begin{verbatim} +Module : fvn_sparse +call fvn_sparse_det(n,nz,T,Ti,Tj,det,status) \end{verbatim} +\begin{itemize} + \item For this family of subroutines the two letters (zl,zi,dl,di) of the specific interface name decribe the arguments's type. z is for complex(8), d for real(8), l for integer(8) and i for integer(4) + \item \texttt{n} (in) is an integer equal to the matrix rank + \item \texttt{nz} (in) is an integer equal to the number of non-zero elements + \item \texttt{T(nz)} (in) is a complex/real array containing the non-zero elements + \item \textt{Ti(nz)},\texttt{Tj(nz)} (in) are the indexes of the corresponding element of \texttt{T} in the original matrix. + \item \texttt{det} (out), a real(8) array of dimension 2 for dl and di specific interface (real systems) and dimension 3 for zl and zi interface (complex systems) +\item \texttt{status} (out) is an integer which contain non-zero is something went wrong +\end{itemize} + +The matrix determinant is returned on a mantissa + exponent form, that is the actual determinant will be $det(1).10^{det(2)}$ for real problems and $(det(1)+i.det(2)).10^{det(3)}$ for complex problems. This is given in this form as the determinant can be considerably higher/lower than the biggest/lowest usable double precision real. + +Here are the possibly returned errors in \texttt{status} parameter : +\begin{itemize} + \item \texttt{0} : no errors + \item \texttt{-1}: out of memory + \item \texttt{1} : singular matrix + \item \texttt{2} : determinant underflow, the ``natural'' form of the determinant $det(1).10^{det(2)}$ or $(det(1)+i.det(2)).10^{det(3)}$ will underflow. + \item \texttt{3} : determinant overflow, the ``natural'' form of the determinant (as above) will overflow +\end{itemize} + + +And here's an example using this + +\begin{verbatim} +program test_sparse +use fvn +implicit none +integer(kind=sp_kind), parameter :: nz=12 +integer(kind=sp_kind), parameter :: n=5 +complex(kind=dp_kind),dimension(nz) :: A +complex(kind=dp_kind),dimension(n,n) :: As +integer(kind=sp_kind),dimension(nz) :: Ti,Tj +complex(kind=dp_kind),dimension(n) :: B,x +integer(kind=sp_kind) :: status,i +real(kind=dp_kind),dimension(3) :: det +character(len=80) :: fmcmplx + +fmcmplx='(5("(",f8.5,",",f8.5,") "))' + +! Description of the matrix in triplet form +A = (/ (2.,-1.),(3.,2.),(3.,1.),(-1.,5.),(4.,-7.),(4.,0.),(-3.,-4.),(1.,3.),(2.,0.),(2.,-2.),(6.,4.),(1.,0.) /) +B = (/ (8.,3.), (45.,1.), (-3.,-2.), (3.,0.), (19.,2.) /) +Ti = (/ 1,2,1,3,5,2,3,4,5,3,2,5 /) +Tj = (/ 1,1,2,2,2,3,3,3,3,4,5,5 /) + +! Reconstruction of the matrix in standard form +As=0. +do i=1,nz + As(Ti(i),Tj(i))=A(i) +end do + +write(*,*) "Matrix in standard representation :" +do i=1,5 + write(*,fmcmplx) As(i,:) +end do +write(*,*) +write(*,*) "Standard determinant : ",fvn_det(5,As) +write(*,*) +write(*,*) "Right hand side :" +write(*,fmcmplx) B + +! can use either specific interface, fvn_zi_sparse_det +! either generic one fvn_sparse_det +call fvn_zi_sparse_det(n,nz,A,Ti,Tj,det,status) +write(*,*) +write(*,*) "Sparse Det = ",cmplx(det(1),det(2),kind=dp_kind)*10**det(3) +! can use either specific interface fvn_zi_sparse_solve +! either generic one fvn_sparse_solve +! parameter det is optional +call fvn_zi_sparse_solve(n,nz,A,Ti,Tj,B,x,status,det) +write(*,*) +write(*,*) "Sparse Det as solve option= ",cmplx(det(1),det(2),kind=dp_kind)*10**det(3) +write(*,*) +write(*,*) "Solution :" +write(*,fmcmplx) x +write(*,*) +write(*,*) "Product matrix Solution :" +write(*,fmcmplx) matmul(As,x) +end program + +\end{verbatim} + + \subsection{Identity matrix} \begin{verbatim} Module : use fvn_linear diff --git a/fvn_sparse/fvn_sparse.f90 b/fvn_sparse/fvn_sparse.f90 index 6e32712..2fd3f2b 100644 --- a/fvn_sparse/fvn_sparse.f90 +++ b/fvn_sparse/fvn_sparse.f90 @@ -101,7 +101,9 @@ if (present(det) ) then call umfpack_zl_get_determinant(det(1),det(2),det(3),numeric,info,status) ! info(1) should be zero if (info(1) /= 0) then - write(*,*) "Problem during sparse determinant, returned code : ",info(1) + if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning + write(*,*) "Problem during sparse determinant, returned code : ",info(1) + endif status=info(1) endif endif @@ -208,7 +210,9 @@ if (present(det) ) then call umfpack_zi_get_determinant(det(1),det(2),det(3),numeric,info,status) ! info(1) should be zero if (info(1) /= 0) then - write(*,*) "Problem during sparse determinant, returned code : ",info(1) + if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning + write(*,*) "Problem during sparse determinant, returned code : ",info(1) + endif status=info(1) endif endif @@ -307,7 +311,9 @@ if (present(det) ) then call umfpack_dl_get_determinant(det(1),det(2),numeric,info,status) ! info(1) should be zero if (info(1) /= 0) then - write(*,*) "Problem during sparse determinant, returned code : ",info(1) + if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning + write(*,*) "Problem during sparse determinant, returned code : ",info(1) + endif status=info(1) endif endif @@ -400,7 +406,9 @@ if (present(det) ) then call umfpack_di_get_determinant(det(1),det(2),numeric,info,status) ! info(1) should be zero if (info(1) /= 0) then - write(*,*) "Problem during sparse determinant, returned code : ",info(1) + if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning + write(*,*) "Problem during sparse determinant, returned code : ",info(1) + endif status=info(1) endif endif @@ -491,7 +499,9 @@ call umfpack_zl_free_symbolic (symbolic) call umfpack_zl_get_determinant(det(1),det(2),det(3),numeric,info,status) ! info(1) should be zero if (info(1) /= 0) then - write(*,*) "Problem during sparse determinant, returned code : ",info(1) + if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning + write(*,*) "Problem during sparse determinant, returned code : ",info(1) + endif status=info(1) endif @@ -568,7 +578,9 @@ call umfpack_zi_free_symbolic (symbolic) call umfpack_zi_get_determinant(det(1),det(2),det(3),numeric,info,status) ! info(1) should be zero if (info(1) /= 0) then - write(*,*) "Problem during sparse determinant, returned code : ",info(1) + if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning + write(*,*) "Problem during sparse determinant, returned code : ",info(1) + endif status=info(1) endif @@ -636,7 +648,9 @@ call umfpack_dl_free_symbolic (symbolic) call umfpack_dl_get_determinant(det(1),det(2),numeric,info,status) ! info(1) should be zero if (info(1) /= 0) then - write(*,*) "Problem during sparse determinant, returned code : ",info(1) + if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning + write(*,*) "Problem during sparse determinant, returned code : ",info(1) + endif status=info(1) endif @@ -710,7 +724,9 @@ call umfpack_di_free_symbolic (symbolic) call umfpack_di_get_determinant(det(1),det(2),numeric,info,status) ! info(1) should be zero if (info(1) /= 0) then - write(*,*) "Problem during sparse determinant, returned code : ",info(1) + if ( (info(1) < 1) .or. (info(1) >3) ) then ! not a warning + write(*,*) "Problem during sparse determinant, returned code : ",info(1) + endif status=info(1) endif