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eis_trbak1.c
Go to the documentation of this file.00001 /* trbak1.f -- translated by f2c (version 19961017). 00002 You must link the resulting object file with the libraries: 00003 -lf2c -lm (in that order) 00004 */ 00005 00006 #include "f2c.h" 00007 00008 /* Subroutine */ int trbak1_(integer *nm, integer *n, doublereal *a, 00009 doublereal *e, integer *m, doublereal *z__) 00010 { 00011 /* System generated locals */ 00012 integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2, i__3; 00013 00014 /* Local variables */ 00015 static integer i__, j, k, l; 00016 static doublereal s; 00017 00018 00019 00020 /* THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE TRBAK1, */ 00021 /* NUM. MATH. 11, 181-195(1968) BY MARTIN, REINSCH, AND WILKINSON. */ 00022 /* HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 212-226(1971). */ 00023 00024 /* THIS SUBROUTINE FORMS THE EIGENVECTORS OF A REAL SYMMETRIC */ 00025 /* MATRIX BY BACK TRANSFORMING THOSE OF THE CORRESPONDING */ 00026 /* SYMMETRIC TRIDIAGONAL MATRIX DETERMINED BY TRED1. */ 00027 00028 /* ON INPUT */ 00029 00030 /* NM MUST BE SET TO THE ROW DIMENSION OF TWO-DIMENSIONAL */ 00031 /* ARRAY PARAMETERS AS DECLARED IN THE CALLING PROGRAM */ 00032 /* DIMENSION STATEMENT. */ 00033 00034 /* N IS THE ORDER OF THE MATRIX. */ 00035 00036 /* A CONTAINS INFORMATION ABOUT THE ORTHOGONAL TRANS- */ 00037 /* FORMATIONS USED IN THE REDUCTION BY TRED1 */ 00038 /* IN ITS STRICT LOWER TRIANGLE. */ 00039 00040 /* E CONTAINS THE SUBDIAGONAL ELEMENTS OF THE TRIDIAGONAL */ 00041 /* MATRIX IN ITS LAST N-1 POSITIONS. E(1) IS ARBITRARY. */ 00042 00043 /* M IS THE NUMBER OF EIGENVECTORS TO BE BACK TRANSFORMED. */ 00044 00045 /* Z CONTAINS THE EIGENVECTORS TO BE BACK TRANSFORMED */ 00046 /* IN ITS FIRST M COLUMNS. */ 00047 00048 /* ON OUTPUT */ 00049 00050 /* Z CONTAINS THE TRANSFORMED EIGENVECTORS */ 00051 /* IN ITS FIRST M COLUMNS. */ 00052 00053 /* NOTE THAT TRBAK1 PRESERVES VECTOR EUCLIDEAN NORMS. */ 00054 00055 /* QUESTIONS AND COMMENTS SHOULD BE DIRECTED TO BURTON S. GARBOW, */ 00056 /* MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY 00057 */ 00058 00059 /* THIS VERSION DATED AUGUST 1983. */ 00060 00061 /* ------------------------------------------------------------------ 00062 */ 00063 00064 /* Parameter adjustments */ 00065 --e; 00066 a_dim1 = *nm; 00067 a_offset = a_dim1 + 1; 00068 a -= a_offset; 00069 z_dim1 = *nm; 00070 z_offset = z_dim1 + 1; 00071 z__ -= z_offset; 00072 00073 /* Function Body */ 00074 if (*m == 0) { 00075 goto L200; 00076 } 00077 if (*n == 1) { 00078 goto L200; 00079 } 00080 00081 i__1 = *n; 00082 for (i__ = 2; i__ <= i__1; ++i__) { 00083 l = i__ - 1; 00084 if (e[i__] == 0.) { 00085 goto L140; 00086 } 00087 00088 i__2 = *m; 00089 for (j = 1; j <= i__2; ++j) { 00090 s = 0.; 00091 00092 i__3 = l; 00093 for (k = 1; k <= i__3; ++k) { 00094 /* L110: */ 00095 s += a[i__ + k * a_dim1] * z__[k + j * z_dim1]; 00096 } 00097 /* .......... DIVISOR BELOW IS NEGATIVE OF H FORMED IN TRED1. 00098 */ 00099 /* DOUBLE DIVISION AVOIDS POSSIBLE UNDERFLOW ...... 00100 .... */ 00101 s = s / a[i__ + l * a_dim1] / e[i__]; 00102 00103 i__3 = l; 00104 for (k = 1; k <= i__3; ++k) { 00105 /* L120: */ 00106 z__[k + j * z_dim1] += s * a[i__ + k * a_dim1]; 00107 } 00108 00109 /* L130: */ 00110 } 00111 00112 L140: 00113 ; 00114 } 00115 00116 L200: 00117 return 0; 00118 } /* trbak1_ */ 00119