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_ */