| 1 |
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| 2 | #include <stdio.h>
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| 3 | #include <stdlib.h>
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| 4 | #include <math.h>
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| 5 |
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| 6 | typedef double real;
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| 7 | typedef int integer;
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| 8 |
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| 9 | #define r_sign(a,b) ((*b<0.0)?-fabs(*a):fabs(*a))
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| 10 | #define min(a,b) (((a)<(b))?(a):(b))
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| 11 | #define max(a,b) (((a)>(b))?(a):(b))
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| 12 | #define dmax(a,b) (((a)>(b))?(a):(b))
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| 13 |
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| 14 | int
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| 15 | sing_(double *q, int *lq, int *iq, double *s, double *p,
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| 16 | int *lp, int *ip, double *a, int *la, int *m, int *n, double *w);
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| 17 |
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| 18 | static int
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| 19 | bidag2_(double *d, double *b, double *q, int *lq, int *iq,
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| 20 | double *p, int *lp, int *ip, double *a, int *la, int *m, int *n);
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| 21 | static int
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| 22 | hsr1_(double *a, int *la, int *n);
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| 23 | static int
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| 24 | hsr2_(double *a, int *la, int *n);
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| 25 | static int
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| 26 | hsr3_(double *a, int *la, int *m, int *n);
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| 27 | static int
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| 28 | hsr4_(double *a, int *la, int *m, int *n);
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| 29 | static int
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| 30 | hsr5_(double *a, int *la, int *m, int *n);
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| 31 | static int
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| 32 | singb_(double *d, int *n, double *u, int *iu,
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| 33 | double *q, int *lq, int *mq, int *iq,
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| 34 | double *p, int *lp, int *mp, int *ip, double *e, double *f);
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| 35 | static int
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| 36 | sng0_(double *q, int *lq, int *m, double *p, int *lp, int *n,
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| 37 | int *l, int *j, int *k, double *x, double *y);
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| 38 | static int
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| 39 | sft_(double *s, double *a, double *b, double *c,
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| 40 | double *d, double *e2, double *e1, double *e0, double *f2, double *f1);
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| 41 | static int
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| 42 | sng1_(double *q, int *lq, int *m, double *p,
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| 43 | int *lp, int *n, int *l, int *j, int *k, double *x, double *y);
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| 44 | static int
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| 45 | scl_(double *d, double *u, int *n, double *q,
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| 46 | int *lq, int *mq, double *p, int *lp, int *mp,
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| 47 | double *e, double *f, double *b,
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| 48 | int *j, int *k, int *jl,
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| 49 | int *jr);
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| 50 | static int
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| 51 | eig3_(double *ea, double *eb, double *a, double *b, double *y, double *z);
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| 52 | static int
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| 53 | sort2_(double *x, double *y, double *w, int *n);
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| 54 | static int
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| 55 | fgv_(double *x, double *y, double *s, double *p, double *q,
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| 56 | double *a, double *b);
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| 57 |
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| 58 | #ifdef TEST
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| 59 |
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| 60 | main(int argc, char**argv)
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| 61 | {
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| 62 | int i,j;
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| 63 | double *tmp;
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| 64 |
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| 65 | int m = atoi(argv[1]);
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| 66 | int n = atoi(argv[2]);
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| 67 |
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| 68 | int l = ((m<n)?m:n);
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| 69 |
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| 70 | double *q = (double*)malloc(sizeof(double)*m*m);
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| 71 | double *s = (double*)malloc(sizeof(double)*n);
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| 72 | double *p = (double*)malloc(sizeof(double)*n*n);
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| 73 | double *a = (double*)malloc(sizeof(double)*n*m);
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| 74 | double *w = (double*)malloc(sizeof(double)*3*m);
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| 75 |
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| 76 | int lq = m;
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| 77 | int lp = n;
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| 78 | int iq = 3;
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| 79 | int ip = 3;
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| 80 | int la = lq;
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| 81 |
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| 82 | tmp = a;
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| 83 | for (i=0; i<m; i++) {
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| 84 | for (j=0; j<n; j++) {
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| 85 | *tmp++ = drand48() * ((drand48()<0.5)?1.0:-1.0);
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| 86 | /* *tmp++ = 1.0; */
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| 87 | }
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| 88 | }
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| 89 |
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| 90 | printf("A:\n");
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| 91 | for (i=0; i<m; i++) {
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| 92 | for (j=0; j<n; j++) {
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| 93 | printf(" % 6.4f", a[j*m + i]);
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| 94 | }
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| 95 | printf("\n");
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| 96 | }
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| 97 |
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| 98 | sing_(q, &lq, &iq, s, p,
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| 99 | &lp, &ip, a, &la, &m, &n, w);
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| 100 |
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| 101 | printf("Q:\n");
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| 102 | for (i=0; i<m; i++) {
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| 103 | for (j=0; j<m; j++) {
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| 104 | printf(" % 6.4f",q[j*m+i]);
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| 105 | }
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| 106 | printf("\n");
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| 107 | }
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| 108 |
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| 109 | printf("P:\n");
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| 110 | for (i=0; i<n; i++) {
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| 111 | for (j=0; j<n; j++) {
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| 112 | printf(" % 6.4f",p[j*n+i]);
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| 113 | }
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| 114 | printf("\n");
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| 115 | }
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| 116 |
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| 117 | printf("S:\n");
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| 118 | tmp = s;
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| 119 | for (j=0; j<l; j++) {
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| 120 | printf(" % 6.4f",*tmp++);
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| 121 | }
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| 122 | printf("\n");
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| 123 |
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| 124 | printf("QQt:\n");
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| 125 | for (i=0; i<m; i++) {
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| 126 | for (j=0; j<m; j++) {
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| 127 | int k;
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| 128 | double tmp = 0.0;
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| 129 | for (k=0; k<m; k++) {
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| 130 | tmp += q[k*m+i]*q[k*m+j];
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| 131 | }
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| 132 | printf(" % 6.4f",tmp);
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| 133 | }
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| 134 | printf("\n");
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| 135 | }
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| 136 |
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| 137 | printf("QtQ:\n");
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| 138 | for (i=0; i<m; i++) {
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| 139 | for (j=0; j<m; j++) {
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| 140 | int k;
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| 141 | double tmp = 0.0;
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| 142 | for (k=0; k<m; k++) {
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| 143 | tmp += q[i*m+k]*q[j*m+k];
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| 144 | }
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| 145 | printf(" % 6.4f",tmp);
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| 146 | }
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| 147 | printf("\n");
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| 148 | }
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| 149 |
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| 150 | printf("PPt:\n");
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| 151 | for (i=0; i<n; i++) {
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| 152 | for (j=0; j<n; j++) {
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| 153 | int k;
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| 154 | double tmp = 0.0;
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| 155 | for (k=0; k<l; k++) {
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| 156 | tmp += p[k*n+i]*p[k*n+j];
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| 157 | }
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| 158 | printf(" % 6.4f",tmp);
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| 159 | }
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| 160 | printf("\n");
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| 161 | }
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| 162 |
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| 163 | printf("PtP:\n");
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| 164 | for (i=0; i<n; i++) {
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| 165 | for (j=0; j<n; j++) {
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| 166 | int k;
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| 167 | double tmp = 0.0;
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| 168 | for (k=0; k<l; k++) {
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| 169 | tmp += p[i*n+k]*p[j*n+k];
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| 170 | }
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| 171 | printf(" % 6.4f",tmp);
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| 172 | }
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| 173 | printf("\n");
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| 174 | }
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| 175 |
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| 176 | printf("QSPt:\n");
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| 177 | for (i=0; i<m; i++) {
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| 178 | for (j=0; j<n; j++) {
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| 179 | int k;
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| 180 | double tmp = 0.0;
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| 181 | for (k=0; k<l; k++) {
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| 182 | tmp += q[k*m+i]*s[k]*p[k*n+j];
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| 183 | }
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| 184 | printf(" % 6.4f",tmp);
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| 185 | }
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| 186 | printf("\n");
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| 187 | }
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| 188 |
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| 189 |
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| 190 | return 0;
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| 191 | }
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| 192 |
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| 193 | #endif /* TEST */
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| 194 |
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| 195 | /* ________________________________________________________ */
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| 196 | /* | | */
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| 197 | /* |COMPUTE SINGULAR VALUE DECOMPOSITION OF A GENERAL MATRIX| */
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| 198 | /* | A = Q TIMES DIAGONAL MATRIX TIMES P TRANSPOSE | */
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| 199 | /* | | */
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| 200 | /* | INPUT: | */
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| 201 | /* | | */
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| 202 | /* | S --ARRAY WITH AT LEAST N ELEMENTS | */
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| 203 | /* | | */
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| 204 | /* | LQ --LEADING (ROW) DIMENSION OF ARRAY Q | */
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| 205 | /* | | */
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| 206 | /* | IQ --AN INTEGER WHICH INDICATES WHICH COL- | */
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| 207 | /* | UMNS OF Q TO COMPUTE (= 0 MEANS NONE, | */
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| 208 | /* | = 1 MEANS FIRST L, = 2 MEANS LAST M-L, | */
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| 209 | /* | = 3 MEANS ALL M WHERE L = MIN(M,N)) | */
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| 210 | /* | | */
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| 211 | /* | LP --LEADING (ROW) DIMENSION OF ARRAY P | */
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| 212 | /* | | */
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| 213 | /* | IP --AN INTEGER (LIKE IQ) WHICH INDICATES | */
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| 214 | /* | WHICH COLUMNS OF P TO COMPUTE | */
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| 215 | /* | | */
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| 216 | /* | A --ARRAY CONTAINING COEFFICIENT MATRIX | */
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| 217 | /* | | */
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| 218 | /* | LA --LEADING (ROW) DIMENSION OF ARRAY A | */
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| 219 | /* | | */
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| 220 | /* | M --ROW DIMENSION OF MATRIX STORED IN A | */
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| 221 | /* | | */
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| 222 | /* | N --COLUMN DIMENSION OF MATRIX STORED IN A | */
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| 223 | /* | | */
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| 224 | /* | W --WORK ARRAY(LENGTH AT LEAST MAX(M,3L-1))| */
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| 225 | /* | | */
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| 226 | /* | OUTPUT: | */
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| 227 | /* | | */
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| 228 | /* | Q --Q FACTOR IN THE SINGULAR VALUE DECOMP. | */
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| 229 | /* | | */
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| 230 | /* | S --SINGULAR VALUES IN DECREASING ORDER | */
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| 231 | /* | | */
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| 232 | /* | P --P FACTOR IN THE SINGULAR VALUE DECOMP. | */
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| 233 | /* | | */
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| 234 | /* | A --THE HOUSEHOLDER VECTORS USED IN THE | */
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| 235 | /* | REDUCTION PROCESS | */
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| 236 | /* | | */
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| 237 | /* | NOTE: | */
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| 238 | /* | | */
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| 239 | /* | EITHER P OR Q CAN BE IDENTIFIED WITH A BUT NOT | */
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| 240 | /* | BOTH. WHEN EITHER P OR Q ARE IDENTIFIED WITH A,| */
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| 241 | /* | THE HOUSEHOLDER VECTORS IN A ARE DESTROYED. IF | */
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| 242 | /* | IQ = 2, Q MUST HAVE M COLUMNS EVEN THOUGH THE | */
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| 243 | /* | OUTPUT ARRAY HAS JUST M-L COLUMNS. SIMILARLY IF| */
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| 244 | /* | IP = 2, P MUST HAVE N COLUMNS EVEN THOUGH THE | */
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| 245 | /* | OUTPUT ARRAY HAS JUST N-L COLUMNS. | */
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| 246 | /* | | */
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| 247 | /* | BUILTIN FUNCTIONS: MIN0 | */
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| 248 | /* | PACKAGE SUBROUTINES: BIDAG2,EIG3,FGV,HSR1-HSR5,SCL, | */
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| 249 | /* | SFT,SINGB,SNG0,SNG1,SORT2 | */
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| 250 | /* |________________________________________________________| */
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| 251 |
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| 252 | int
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| 253 | sing_(real *q, int *lq, int *iq, double *s, double *p,
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| 254 | int *lp, int *ip, double *a, int *la, int *m, int *n, double *w)
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| 255 | {
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| 256 | /* System generated locals */
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| 257 | integer a_dim1, a_offset, q_dim1, q_offset, p_dim1, p_offset, i__1;
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| 258 |
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| 259 | /* Local variables */
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| 260 | static integer i, l;
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| 261 | static integer jl, iu, jr;
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| 262 |
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| 263 | /* Parameter adjustments */
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| 264 | --w;
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| 265 | a_dim1 = *la;
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| 266 | a_offset = a_dim1 + 1;
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| 267 | a -= a_offset;
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| 268 | p_dim1 = *lp;
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| 269 | p_offset = p_dim1 + 1;
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| 270 | p -= p_offset;
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| 271 | --s;
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| 272 | q_dim1 = *lq;
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| 273 | q_offset = q_dim1 + 1;
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| 274 | q -= q_offset;
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| 275 |
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| 276 | /* Function Body */
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| 277 | if (*iq >= 0) {
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| 278 | goto L20;
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| 279 | }
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| 280 | L10:
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| 281 | fprintf(stderr,"ERROR: INPUT PARAMETER IQ FOR SUBROUTINE SING\n");
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| 282 | fprintf(stderr,"EITHER LESS THAN 0 OR GREATER THAN 3\n");
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| 283 | abort();
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| 284 | L20:
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| 285 | if (*iq > 3) {
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| 286 | goto L10;
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| 287 | }
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| 288 | jl = 0;
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| 289 | if (*iq == 0) {
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| 290 | goto L30;
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| 291 | }
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| 292 | if (*iq == 2) {
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| 293 | goto L30;
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| 294 | }
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| 295 | jl = 1;
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| 296 | L30:
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| 297 | if (*ip >= 0) {
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| 298 | goto L50;
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| 299 | }
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| 300 | L40:
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| 301 | fprintf(stderr,"ERROR: INPUT PARAMETER IP FOR SUBROUTINE SING\n");
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| 302 | fprintf(stderr,"EITHER LESS THAN 0 OR GREATER THAN 3\n");
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| 303 | abort();
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| 304 | L50:
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| 305 | if (*ip > 3) {
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| 306 | goto L40;
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| 307 | }
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| 308 | jr = 0;
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| 309 | if (*ip == 0) {
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| 310 | goto L60;
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| 311 | }
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| 312 | if (*ip == 2) {
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| 313 | goto L60;
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| 314 | }
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| 315 | jr = 1;
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| 316 | L60:
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| 317 | bidag2_(&s[1], &w[1], &q[q_offset], lq, iq, &p[p_offset], lp, ip, &a[
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| 318 | a_offset], la, m, n);
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| 319 | l = min(*m,*n);
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| 320 | if (l > 1) {
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| 321 | goto L80;
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| 322 | }
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| 323 | if (s[1] >= (double)0.) {
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| 324 | return 0;
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| 325 | }
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| 326 | s[1] = -(double)s[1];
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| 327 | if ((real) jl == (double)0.) {
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| 328 | return 0;
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| 329 | }
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| 330 | i__1 = *m;
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| 331 | for (i = 1; i <= i__1; ++i) {
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| 332 | /* L70: */
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| 333 | q[i + q_dim1] = -(double)q[i + q_dim1];
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| 334 | }
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| 335 | return 0;
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| 336 | L80:
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| 337 | iu = 0;
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| 338 | if (*m >= *n) {
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| 339 | goto L90;
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| 340 | }
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| 341 | iu = 1;
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| 342 | L90:
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| 343 | singb_(&s[1], &l, &w[1], &iu, &q[q_offset], lq, m, &jl, &p[p_offset], lp,
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| 344 | n, &jr, &w[l], &w[l + l]);
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| 345 | return 0;
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| 346 | } /* sing_ */
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| 347 |
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| 348 |
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| 349 | /* ________________________________________________________ */
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| 350 | /* | | */
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| 351 | /* | REDUCE A GENERAL MATRIX A TO BIDIAGONAL FORM | */
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| 352 | /* | A = Q TIMES BIDIAGONAL MATRIX TIMES P TRANSPOSE | */
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| 353 | /* | | */
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| 354 | /* | INPUT: | */
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| 355 | /* | | */
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| 356 | /* | D --ARRAY WITH AT LEAST N ELEMENTS | */
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| 357 | /* | | */
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| 358 | /* | B --ARRAY WITH AT LEAST M ELEMENTS | */
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| 359 | /* | | */
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| 360 | /* | LQ --LEADING (ROW) DIMENSION OF ARRAY Q | */
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| 361 | /* | | */
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| 362 | /* | IQ --AN INTEGER WHICH INDICATES WHICH COL- | */
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| 363 | /* | UMNS OF Q TO COMPUTE (= 0 MEANS NONE, | */
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| 364 | /* | = 1 MEANS FIRST L, = 2 MEANS LAST M-L, | */
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| 365 | /* | = 3 MEANS ALL M WHERE L = MIN(M,N)) | */
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| 366 | /* | | */
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| 367 | /* | LP --LEADING (ROW) DIMENSION OF ARRAY P | */
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| 368 | /* | | */
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| 369 | /* | IP --AN INTEGER (LIKE IQ) WHICH INDICATES | */
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| 370 | /* | WHICH COLUMNS OF P TO COMPUTE | */
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| 371 | /* | | */
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| 372 | /* | A --ARRAY CONTAINING COEFFICIENT MATRIX | */
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| 373 | /* | | */
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| 374 | /* | LA --LEADING (ROW) DIMENSION OF ARRAY A | */
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| 375 | /* | | */
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| 376 | /* | M --ROW DIMENSION OF MATRIX STORED IN A | */
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| 377 | /* | | */
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| 378 | /* | N --COLUMN DIMENSION OF MATRIX STORED IN A | */
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| 379 | /* | | */
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| 380 | /* | OUTPUT: | */
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| 381 | /* | | */
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| 382 | /* | D --DIAGONAL OF BIDIAGONAL FORM | */
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| 383 | /* | | */
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| 384 | /* | B --SUPERDIAGONAL (IF M .GE. N) OR SUBDIAG-| */
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| 385 | /* | ONAL (IF M .LT. N) OF BIDIAGONAL FORM | */
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| 386 | /* | | */
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| 387 | /* | A --THE HOUSEHOLDER VECTORS USED IN THE | */
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|---|
| 388 | /* | REDUCTION PROCESS | */
|
|---|
| 389 | /* | | */
|
|---|
| 390 | /* | Q --THE Q FACTOR IN THE BIDIAGONALIZATION | */
|
|---|
| 391 | /* | | */
|
|---|
| 392 | /* | P --THE P FACTOR IN THE BIDIAGONALIZATION | */
|
|---|
| 393 | /* | | */
|
|---|
| 394 | /* | NOTE: | */
|
|---|
| 395 | /* | | */
|
|---|
| 396 | /* | EITHER P OR Q CAN BE IDENTIFIED WITH A BUT NOT | */
|
|---|
| 397 | /* | BOTH. WHEN EITHER P OR Q ARE IDENTIFIED WITH A,| */
|
|---|
| 398 | /* | THEN THE HOUSEHOLDER VECTORS IN A ARE DESTROYED| */
|
|---|
| 399 | /* | | */
|
|---|
| 400 | /* | BUILTIN FUNCTIONS: ABS,MIN0,SQRT | */
|
|---|
| 401 | /* | PACKAGE SUBROUTINES: HSR1-HSR5 | */
|
|---|
| 402 | /* |________________________________________________________| */
|
|---|
| 403 |
|
|---|
| 404 | static int
|
|---|
| 405 | bidag2_(double *d, double *b, double *q, int *lq, int *iq,
|
|---|
| 406 | double *p, int *lp, int *ip, double *a, int *la, int *m, int *n)
|
|---|
| 407 | {
|
|---|
| 408 | /* System generated locals */
|
|---|
| 409 | integer a_dim1, a_offset, q_dim1, q_offset, p_dim1, p_offset, i__1, i__2;
|
|---|
| 410 | real r__1;
|
|---|
| 411 |
|
|---|
| 412 | /* Local variables */
|
|---|
| 413 | static integer h, i, j, k, l;
|
|---|
| 414 | static real r, s, t, u;
|
|---|
| 415 | static integer jp, jq;
|
|---|
| 416 |
|
|---|
| 417 | /* Parameter adjustments */
|
|---|
| 418 | a_dim1 = *la;
|
|---|
| 419 | a_offset = a_dim1 + 1;
|
|---|
| 420 | a -= a_offset;
|
|---|
| 421 | p_dim1 = *lp;
|
|---|
| 422 | p_offset = p_dim1 + 1;
|
|---|
| 423 | p -= p_offset;
|
|---|
| 424 | q_dim1 = *lq;
|
|---|
| 425 | q_offset = q_dim1 + 1;
|
|---|
| 426 | q -= q_offset;
|
|---|
| 427 | --b;
|
|---|
| 428 | --d;
|
|---|
| 429 |
|
|---|
| 430 | /* Function Body */
|
|---|
| 431 | l = min(*m,*n);
|
|---|
| 432 | if (*iq >= 0) {
|
|---|
| 433 | goto L20;
|
|---|
| 434 | }
|
|---|
| 435 | L10:
|
|---|
| 436 | fprintf(stderr,"ERROR: INPUT PARAMETER IQ FOR SUBROUTINE BIDAG2\n");
|
|---|
| 437 | fprintf(stderr,"EITHER LESS THAN 0 OR GREATER THAN 3\n");
|
|---|
| 438 | abort();
|
|---|
| 439 | L20:
|
|---|
| 440 | if (*iq > 3) {
|
|---|
| 441 | goto L10;
|
|---|
| 442 | }
|
|---|
| 443 | jq = *iq;
|
|---|
| 444 | if (*iq <= 1) {
|
|---|
| 445 | goto L30;
|
|---|
| 446 | }
|
|---|
| 447 | if (*iq == 3) {
|
|---|
| 448 | goto L30;
|
|---|
| 449 | }
|
|---|
| 450 | if (*m == l) {
|
|---|
| 451 | jq = 0;
|
|---|
| 452 | }
|
|---|
| 453 | L30:
|
|---|
| 454 | if (*ip >= 0) {
|
|---|
| 455 | goto L50;
|
|---|
| 456 | }
|
|---|
| 457 | L40:
|
|---|
| 458 | fprintf(stderr,"ERROR: INPUT PARAMETER IP FOR SUBROUTINE BIDAG2\n");
|
|---|
| 459 | fprintf(stderr,"EITHER LESS THAN 0 OR GREATER THAN 3\n");
|
|---|
| 460 | abort();
|
|---|
| 461 | L50:
|
|---|
| 462 | if (*ip > 3) {
|
|---|
| 463 | goto L40;
|
|---|
| 464 | }
|
|---|
| 465 | jp = *ip;
|
|---|
| 466 | if (*ip <= 1) {
|
|---|
| 467 | goto L60;
|
|---|
| 468 | }
|
|---|
| 469 | if (*ip == 3) {
|
|---|
| 470 | goto L60;
|
|---|
| 471 | }
|
|---|
| 472 | if (*n == l) {
|
|---|
| 473 | jp = 0;
|
|---|
| 474 | }
|
|---|
| 475 | L60:
|
|---|
| 476 | k = 1;
|
|---|
| 477 | h = 2;
|
|---|
| 478 | if (*m < *n) {
|
|---|
| 479 | goto L330;
|
|---|
| 480 | }
|
|---|
| 481 | if (*m > 1) {
|
|---|
| 482 | goto L70;
|
|---|
| 483 | }
|
|---|
| 484 | d[1] = a[a_dim1 + 1];
|
|---|
| 485 | if (*iq > 0) {
|
|---|
| 486 | q[q_dim1 + 1] = (double)1.;
|
|---|
| 487 | }
|
|---|
| 488 | if (*ip > 0) {
|
|---|
| 489 | p[p_dim1 + 1] = (double)1.;
|
|---|
| 490 | }
|
|---|
| 491 | return 0;
|
|---|
| 492 | L70:
|
|---|
| 493 | j = k;
|
|---|
| 494 | k = h;
|
|---|
| 495 | i__1 = *m;
|
|---|
| 496 | for (i = k; i <= i__1; ++i) {
|
|---|
| 497 | /* L80: */
|
|---|
| 498 | if (a[i + j * a_dim1] != (double)0.) {
|
|---|
| 499 | goto L110;
|
|---|
| 500 | }
|
|---|
| 501 | }
|
|---|
| 502 | d[j] = a[j + j * a_dim1];
|
|---|
| 503 | a[j + j * a_dim1] = (double)0.;
|
|---|
| 504 | i__1 = *n;
|
|---|
| 505 | for (i = k; i <= i__1; ++i) {
|
|---|
| 506 | /* L90: */
|
|---|
| 507 | d[i] = a[j + i * a_dim1];
|
|---|
| 508 | }
|
|---|
| 509 | if (jq == 0) {
|
|---|
| 510 | goto L200;
|
|---|
| 511 | }
|
|---|
| 512 | i__1 = *m;
|
|---|
| 513 | for (i = j; i <= i__1; ++i) {
|
|---|
| 514 | /* L100: */
|
|---|
| 515 | q[i + j * q_dim1] = (double)0.;
|
|---|
| 516 | }
|
|---|
| 517 | goto L200;
|
|---|
| 518 | L110:
|
|---|
| 519 | t = (r__1 = a[j + j * a_dim1], fabs(r__1));
|
|---|
| 520 | if (t != (double)0.) {
|
|---|
| 521 | u = (double)1. / t;
|
|---|
| 522 | }
|
|---|
| 523 | r = (double)1.;
|
|---|
| 524 | i__1 = *m;
|
|---|
| 525 | for (l = i; l <= i__1; ++l) {
|
|---|
| 526 | s = (r__1 = a[l + j * a_dim1], fabs(r__1));
|
|---|
| 527 | if (s <= t) {
|
|---|
| 528 | goto L120;
|
|---|
| 529 | }
|
|---|
| 530 | u = (double)1. / s;
|
|---|
| 531 | /* Computing 2nd power */
|
|---|
| 532 | r__1 = t * u;
|
|---|
| 533 | r = r * (r__1 * r__1) + (double)1.;
|
|---|
| 534 | t = s;
|
|---|
| 535 | goto L130;
|
|---|
| 536 | L120:
|
|---|
| 537 | /* Computing 2nd power */
|
|---|
| 538 | r__1 = s * u;
|
|---|
| 539 | r += r__1 * r__1;
|
|---|
| 540 | L130:
|
|---|
| 541 | ;
|
|---|
| 542 | }
|
|---|
| 543 | s = t * sqrt(r);
|
|---|
| 544 | r = a[j + j * a_dim1];
|
|---|
| 545 | u = (double)1. / sqrt(s * (s + fabs(r)));
|
|---|
| 546 | if (r < (double)0.) {
|
|---|
| 547 | s = -(double)s;
|
|---|
| 548 | }
|
|---|
| 549 | d[j] = -(double)s;
|
|---|
| 550 | a[j + j * a_dim1] = u * (r + s);
|
|---|
| 551 | i__1 = *m;
|
|---|
| 552 | for (i = k; i <= i__1; ++i) {
|
|---|
| 553 | /* L140: */
|
|---|
| 554 | a[i + j * a_dim1] *= u;
|
|---|
| 555 | }
|
|---|
| 556 | if (jq == 0) {
|
|---|
| 557 | goto L160;
|
|---|
| 558 | }
|
|---|
| 559 | i__1 = *m;
|
|---|
| 560 | for (i = j; i <= i__1; ++i) {
|
|---|
| 561 | /* L150: */
|
|---|
| 562 | q[i + j * q_dim1] = a[i + j * a_dim1];
|
|---|
| 563 | }
|
|---|
| 564 | L160:
|
|---|
| 565 | if (k > *n) {
|
|---|
| 566 | goto L620;
|
|---|
| 567 | }
|
|---|
| 568 | i__1 = *n;
|
|---|
| 569 | for (l = k; l <= i__1; ++l) {
|
|---|
| 570 | t = (double)0.;
|
|---|
| 571 | i__2 = *m;
|
|---|
| 572 | for (i = j; i <= i__2; ++i) {
|
|---|
| 573 | /* L170: */
|
|---|
| 574 | t += a[i + j * a_dim1] * a[i + l * a_dim1];
|
|---|
| 575 | }
|
|---|
| 576 | a[j + l * a_dim1] -= t * a[j + j * a_dim1];
|
|---|
| 577 | d[l] = a[j + l * a_dim1];
|
|---|
| 578 | i__2 = *m;
|
|---|
| 579 | for (i = k; i <= i__2; ++i) {
|
|---|
| 580 | /* L180: */
|
|---|
| 581 | a[i + l * a_dim1] -= t * a[i + j * a_dim1];
|
|---|
| 582 | }
|
|---|
| 583 | /* L190: */
|
|---|
| 584 | }
|
|---|
| 585 | L200:
|
|---|
| 586 | h = k + 1;
|
|---|
| 587 | if (k < *n) {
|
|---|
| 588 | goto L210;
|
|---|
| 589 | }
|
|---|
| 590 | if (k > *n) {
|
|---|
| 591 | goto L620;
|
|---|
| 592 | }
|
|---|
| 593 | if (*m == *n) {
|
|---|
| 594 | goto L610;
|
|---|
| 595 | }
|
|---|
| 596 | b[j] = a[j + *n * a_dim1];
|
|---|
| 597 | goto L70;
|
|---|
| 598 | L210:
|
|---|
| 599 | i__1 = *n;
|
|---|
| 600 | for (i = h; i <= i__1; ++i) {
|
|---|
| 601 | /* L220: */
|
|---|
| 602 | if (d[i] != (double)0.) {
|
|---|
| 603 | goto L240;
|
|---|
| 604 | }
|
|---|
| 605 | }
|
|---|
| 606 | b[j] = d[k];
|
|---|
| 607 | a[j + k * a_dim1] = (double)0.;
|
|---|
| 608 | if (*ip == 0) {
|
|---|
| 609 | goto L70;
|
|---|
| 610 | }
|
|---|
| 611 | i__1 = *n;
|
|---|
| 612 | for (i = k; i <= i__1; ++i) {
|
|---|
| 613 | /* L230: */
|
|---|
| 614 | p[i + j * p_dim1] = (double)0.;
|
|---|
| 615 | }
|
|---|
| 616 | goto L70;
|
|---|
| 617 | L240:
|
|---|
| 618 | t = (r__1 = d[k], fabs(r__1));
|
|---|
| 619 | if (t != (double)0.) {
|
|---|
| 620 | u = (double)1. / t;
|
|---|
| 621 | }
|
|---|
| 622 | r = (double)1.;
|
|---|
| 623 | i__1 = *n;
|
|---|
| 624 | for (l = i; l <= i__1; ++l) {
|
|---|
| 625 | s = (r__1 = d[l], fabs(r__1));
|
|---|
| 626 | if (s <= t) {
|
|---|
| 627 | goto L250;
|
|---|
| 628 | }
|
|---|
| 629 | u = (double)1. / s;
|
|---|
| 630 | /* Computing 2nd power */
|
|---|
| 631 | r__1 = t * u;
|
|---|
| 632 | r = r * (r__1 * r__1) + (double)1.;
|
|---|
| 633 | t = s;
|
|---|
| 634 | goto L260;
|
|---|
| 635 | L250:
|
|---|
| 636 | /* Computing 2nd power */
|
|---|
| 637 | r__1 = s * u;
|
|---|
| 638 | r += r__1 * r__1;
|
|---|
| 639 | L260:
|
|---|
| 640 | ;
|
|---|
| 641 | }
|
|---|
| 642 | s = t * sqrt(r);
|
|---|
| 643 | r = d[k];
|
|---|
| 644 | u = (double)1. / sqrt(s * (s + fabs(r)));
|
|---|
| 645 | if (r < (double)0.) {
|
|---|
| 646 | s = -(double)s;
|
|---|
| 647 | }
|
|---|
| 648 | d[k] = u * (r + s);
|
|---|
| 649 | i__1 = *n;
|
|---|
| 650 | for (i = h; i <= i__1; ++i) {
|
|---|
| 651 | /* L270: */
|
|---|
| 652 | d[i] *= u;
|
|---|
| 653 | }
|
|---|
| 654 | if (*ip == 0) {
|
|---|
| 655 | goto L290;
|
|---|
| 656 | }
|
|---|
| 657 | i__1 = *n;
|
|---|
| 658 | for (i = k; i <= i__1; ++i) {
|
|---|
| 659 | /* L280: */
|
|---|
| 660 | p[i + j * p_dim1] = d[i];
|
|---|
| 661 | }
|
|---|
| 662 | L290:
|
|---|
| 663 | b[j] = -(double)s;
|
|---|
| 664 | i__1 = *m;
|
|---|
| 665 | for (i = k; i <= i__1; ++i) {
|
|---|
| 666 | /* L300: */
|
|---|
| 667 | b[i] = (double)0.;
|
|---|
| 668 | }
|
|---|
| 669 | i__1 = *n;
|
|---|
| 670 | for (l = k; l <= i__1; ++l) {
|
|---|
| 671 | t = d[l];
|
|---|
| 672 | a[j + l * a_dim1] = t;
|
|---|
| 673 | i__2 = *m;
|
|---|
| 674 | for (i = k; i <= i__2; ++i) {
|
|---|
| 675 | /* L310: */
|
|---|
| 676 | b[i] += t * a[i + l * a_dim1];
|
|---|
| 677 | }
|
|---|
| 678 | }
|
|---|
| 679 | i__2 = *n;
|
|---|
| 680 | for (l = k; l <= i__2; ++l) {
|
|---|
| 681 | t = d[l];
|
|---|
| 682 | i__1 = *m;
|
|---|
| 683 | for (i = k; i <= i__1; ++i) {
|
|---|
| 684 | /* L320: */
|
|---|
| 685 | a[i + l * a_dim1] -= t * b[i];
|
|---|
| 686 | }
|
|---|
| 687 | }
|
|---|
| 688 | goto L70;
|
|---|
| 689 | L330:
|
|---|
| 690 | i__1 = *n;
|
|---|
| 691 | for (i = k; i <= i__1; ++i) {
|
|---|
| 692 | /* L340: */
|
|---|
| 693 | d[i] = a[k + i * a_dim1];
|
|---|
| 694 | }
|
|---|
| 695 | L350:
|
|---|
| 696 | j = k;
|
|---|
| 697 | k = h;
|
|---|
| 698 | i__1 = *n;
|
|---|
| 699 | for (i = k; i <= i__1; ++i) {
|
|---|
| 700 | /* L360: */
|
|---|
| 701 | if (d[i] != (double)0.) {
|
|---|
| 702 | goto L370;
|
|---|
| 703 | }
|
|---|
| 704 | }
|
|---|
| 705 | u = d[j];
|
|---|
| 706 | d[j] = (double)0.;
|
|---|
| 707 | goto L440;
|
|---|
| 708 | L370:
|
|---|
| 709 | t = (r__1 = d[j], fabs(r__1));
|
|---|
| 710 | if (t != (double)0.) {
|
|---|
| 711 | u = (double)1. / t;
|
|---|
| 712 | }
|
|---|
| 713 | r = (double)1.;
|
|---|
| 714 | i__1 = *n;
|
|---|
| 715 | for (l = i; l <= i__1; ++l) {
|
|---|
| 716 | s = (r__1 = d[l], fabs(r__1));
|
|---|
| 717 | if (s <= t) {
|
|---|
| 718 | goto L380;
|
|---|
| 719 | }
|
|---|
| 720 | u = (double)1. / s;
|
|---|
| 721 | /* Computing 2nd power */
|
|---|
| 722 | r__1 = t * u;
|
|---|
| 723 | r = r * (r__1 * r__1) + (double)1.;
|
|---|
| 724 | t = s;
|
|---|
| 725 | goto L390;
|
|---|
| 726 | L380:
|
|---|
| 727 | /* Computing 2nd power */
|
|---|
| 728 | r__1 = s * u;
|
|---|
| 729 | r += r__1 * r__1;
|
|---|
| 730 | L390:
|
|---|
| 731 | ;
|
|---|
| 732 | }
|
|---|
| 733 | s = t * sqrt(r);
|
|---|
| 734 | r = d[j];
|
|---|
| 735 | u = (double)1. / sqrt(s * (s + fabs(r)));
|
|---|
| 736 | if (r < (double)0.) {
|
|---|
| 737 | s = -(double)s;
|
|---|
| 738 | }
|
|---|
| 739 | d[j] = u * (r + s);
|
|---|
| 740 | i__1 = *n;
|
|---|
| 741 | for (i = k; i <= i__1; ++i) {
|
|---|
| 742 | /* L400: */
|
|---|
| 743 | d[i] *= u;
|
|---|
| 744 | }
|
|---|
| 745 | u = -(double)s;
|
|---|
| 746 | if (k > *m) {
|
|---|
| 747 | goto L470;
|
|---|
| 748 | }
|
|---|
| 749 | i__1 = *m;
|
|---|
| 750 | for (i = k; i <= i__1; ++i) {
|
|---|
| 751 | /* L410: */
|
|---|
| 752 | b[i] = (double)0.;
|
|---|
| 753 | }
|
|---|
| 754 | i__1 = *n;
|
|---|
| 755 | for (l = j; l <= i__1; ++l) {
|
|---|
| 756 | t = d[l];
|
|---|
| 757 | a[j + l * a_dim1] = t;
|
|---|
| 758 | i__2 = *m;
|
|---|
| 759 | for (i = k; i <= i__2; ++i) {
|
|---|
| 760 | /* L420: */
|
|---|
| 761 | b[i] += t * a[i + l * a_dim1];
|
|---|
| 762 | }
|
|---|
| 763 | }
|
|---|
| 764 | i__2 = *n;
|
|---|
| 765 | for (l = j; l <= i__2; ++l) {
|
|---|
| 766 | t = d[l];
|
|---|
| 767 | i__1 = *m;
|
|---|
| 768 | for (i = k; i <= i__1; ++i) {
|
|---|
| 769 | /* L430: */
|
|---|
| 770 | a[i + l * a_dim1] -= t * b[i];
|
|---|
| 771 | }
|
|---|
| 772 | }
|
|---|
| 773 | L440:
|
|---|
| 774 | h = k + 1;
|
|---|
| 775 | if (*ip == 0) {
|
|---|
| 776 | goto L460;
|
|---|
| 777 | }
|
|---|
| 778 | i__1 = *n;
|
|---|
| 779 | for (i = j; i <= i__1; ++i) {
|
|---|
| 780 | /* L450: */
|
|---|
| 781 | p[i + j * p_dim1] = d[i];
|
|---|
| 782 | }
|
|---|
| 783 | L460:
|
|---|
| 784 | d[j] = u;
|
|---|
| 785 | if (k < *m) {
|
|---|
| 786 | goto L490;
|
|---|
| 787 | }
|
|---|
| 788 | if (k > *m) {
|
|---|
| 789 | goto L620;
|
|---|
| 790 | }
|
|---|
| 791 | b[j] = a[*m + j * a_dim1];
|
|---|
| 792 | goto L330;
|
|---|
| 793 | L470:
|
|---|
| 794 | i__1 = *n;
|
|---|
| 795 | for (i = j; i <= i__1; ++i) {
|
|---|
| 796 | /* L480: */
|
|---|
| 797 | a[j + i * a_dim1] = d[i];
|
|---|
| 798 | }
|
|---|
| 799 | goto L440;
|
|---|
| 800 | L490:
|
|---|
| 801 | i__1 = *m;
|
|---|
| 802 | for (i = h; i <= i__1; ++i) {
|
|---|
| 803 | /* L500: */
|
|---|
| 804 | if (a[i + j * a_dim1] != (double)0.) {
|
|---|
| 805 | goto L520;
|
|---|
| 806 | }
|
|---|
| 807 | }
|
|---|
| 808 | b[j] = a[k + j * a_dim1];
|
|---|
| 809 | a[k + j * a_dim1] = (double)0.;
|
|---|
| 810 | if (*iq == 0) {
|
|---|
| 811 | goto L330;
|
|---|
| 812 | }
|
|---|
| 813 | i__1 = *m;
|
|---|
| 814 | for (i = k; i <= i__1; ++i) {
|
|---|
| 815 | /* L510: */
|
|---|
| 816 | q[i + j * q_dim1] = (double)0.;
|
|---|
| 817 | }
|
|---|
| 818 | goto L330;
|
|---|
| 819 | L520:
|
|---|
| 820 | t = (r__1 = a[k + j * a_dim1], fabs(r__1));
|
|---|
| 821 | if (t != (double)0.) {
|
|---|
| 822 | u = (double)1. / t;
|
|---|
| 823 | }
|
|---|
| 824 | r = (double)1.;
|
|---|
| 825 | i__1 = *m;
|
|---|
| 826 | for (l = i; l <= i__1; ++l) {
|
|---|
| 827 | s = (r__1 = a[l + j * a_dim1], fabs(r__1));
|
|---|
| 828 | if (s <= t) {
|
|---|
| 829 | goto L530;
|
|---|
| 830 | }
|
|---|
| 831 | u = (double)1. / s;
|
|---|
| 832 | /* Computing 2nd power */
|
|---|
| 833 | r__1 = t * u;
|
|---|
| 834 | r = r * (r__1 * r__1) + (double)1.;
|
|---|
| 835 | t = s;
|
|---|
| 836 | goto L540;
|
|---|
| 837 | L530:
|
|---|
| 838 | /* Computing 2nd power */
|
|---|
| 839 | r__1 = s * u;
|
|---|
| 840 | r += r__1 * r__1;
|
|---|
| 841 | L540:
|
|---|
| 842 | ;
|
|---|
| 843 | }
|
|---|
| 844 | s = t * sqrt(r);
|
|---|
| 845 | r = a[k + j * a_dim1];
|
|---|
| 846 | u = (double)1. / sqrt(s * (s + fabs(r)));
|
|---|
| 847 | if (r < (double)0.) {
|
|---|
| 848 | s = -(double)s;
|
|---|
| 849 | }
|
|---|
| 850 | b[j] = -(double)s;
|
|---|
| 851 | a[k + j * a_dim1] = u * (r + s);
|
|---|
| 852 | i__1 = *m;
|
|---|
| 853 | for (i = h; i <= i__1; ++i) {
|
|---|
| 854 | /* L550: */
|
|---|
| 855 | a[i + j * a_dim1] *= u;
|
|---|
| 856 | }
|
|---|
| 857 | if (*iq == 0) {
|
|---|
| 858 | goto L570;
|
|---|
| 859 | }
|
|---|
| 860 | i__1 = *m;
|
|---|
| 861 | for (i = k; i <= i__1; ++i) {
|
|---|
| 862 | /* L560: */
|
|---|
| 863 | q[i + j * q_dim1] = a[i + j * a_dim1];
|
|---|
| 864 | }
|
|---|
| 865 | L570:
|
|---|
| 866 | i__1 = *n;
|
|---|
| 867 | for (l = k; l <= i__1; ++l) {
|
|---|
| 868 | t = (double)0.;
|
|---|
| 869 | i__2 = *m;
|
|---|
| 870 | for (i = k; i <= i__2; ++i) {
|
|---|
| 871 | /* L580: */
|
|---|
| 872 | t += a[i + j * a_dim1] * a[i + l * a_dim1];
|
|---|
| 873 | }
|
|---|
| 874 | a[k + l * a_dim1] -= t * a[k + j * a_dim1];
|
|---|
| 875 | d[l] = a[k + l * a_dim1];
|
|---|
| 876 | i__2 = *m;
|
|---|
| 877 | for (i = h; i <= i__2; ++i) {
|
|---|
| 878 | /* L590: */
|
|---|
| 879 | a[i + l * a_dim1] -= t * a[i + j * a_dim1];
|
|---|
| 880 | }
|
|---|
| 881 | /* L600: */
|
|---|
| 882 | }
|
|---|
| 883 | goto L350;
|
|---|
| 884 | L610:
|
|---|
| 885 | d[*n] = a[*n + *n * a_dim1];
|
|---|
| 886 | b[*n - 1] = a[*n - 1 + *n * a_dim1];
|
|---|
| 887 | L620:
|
|---|
| 888 | if (jq == 0) {
|
|---|
| 889 | goto L650;
|
|---|
| 890 | }
|
|---|
| 891 | if (*n > *m) {
|
|---|
| 892 | goto L640;
|
|---|
| 893 | }
|
|---|
| 894 | if (*n == *m) {
|
|---|
| 895 | goto L630;
|
|---|
| 896 | }
|
|---|
| 897 | if (jq == 1) {
|
|---|
| 898 | hsr3_(&q[q_offset], lq, m, n);
|
|---|
| 899 | }
|
|---|
| 900 | if (jq == 2) {
|
|---|
| 901 | hsr4_(&q[q_offset], lq, m, n);
|
|---|
| 902 | }
|
|---|
| 903 | if (jq == 3) {
|
|---|
| 904 | hsr5_(&q[q_offset], lq, m, n);
|
|---|
| 905 | }
|
|---|
| 906 | goto L650;
|
|---|
| 907 | L630:
|
|---|
| 908 | hsr2_(&q[q_offset], lq, m);
|
|---|
| 909 | goto L650;
|
|---|
| 910 | L640:
|
|---|
| 911 | hsr1_(&q[q_offset], lq, m);
|
|---|
| 912 | L650:
|
|---|
| 913 | if (jp == 0) {
|
|---|
| 914 | return 0;
|
|---|
| 915 | }
|
|---|
| 916 | if (*n <= *m) {
|
|---|
| 917 | goto L660;
|
|---|
| 918 | }
|
|---|
| 919 | if (jp == 1) {
|
|---|
| 920 | hsr3_(&p[p_offset], lp, n, m);
|
|---|
| 921 | }
|
|---|
| 922 | if (jp == 2) {
|
|---|
| 923 | hsr4_(&p[p_offset], lp, n, m);
|
|---|
| 924 | }
|
|---|
| 925 | if (jp == 3) {
|
|---|
| 926 | hsr5_(&p[p_offset], lp, n, m);
|
|---|
| 927 | }
|
|---|
| 928 | return 0;
|
|---|
| 929 | L660:
|
|---|
| 930 | hsr1_(&p[p_offset], lp, n);
|
|---|
| 931 | return 0;
|
|---|
| 932 | } /* bidag2_ */
|
|---|
| 933 |
|
|---|
| 934 |
|
|---|
| 935 | static int
|
|---|
| 936 | hsr1_(double *a, int *la, int *n)
|
|---|
| 937 | {
|
|---|
| 938 | /* System generated locals */
|
|---|
| 939 | integer a_dim1, a_offset, i__1;
|
|---|
| 940 |
|
|---|
| 941 | /* Local variables */
|
|---|
| 942 | static integer i, j, k, l, m;
|
|---|
| 943 | static real s;
|
|---|
| 944 |
|
|---|
| 945 | /* Parameter adjustments */
|
|---|
| 946 | a_dim1 = *la;
|
|---|
| 947 | a_offset = a_dim1 + 1;
|
|---|
| 948 | a -= a_offset;
|
|---|
| 949 |
|
|---|
| 950 | /* Function Body */
|
|---|
| 951 | a[a_dim1 + 1] = (double)1.;
|
|---|
| 952 | if (*n == 1) {
|
|---|
| 953 | return 0;
|
|---|
| 954 | }
|
|---|
| 955 | a[(a_dim1 << 1) + 1] = (double)0.;
|
|---|
| 956 | if (*n > 2) {
|
|---|
| 957 | goto L10;
|
|---|
| 958 | }
|
|---|
| 959 | a[a_dim1 + 2] = (double)0.;
|
|---|
| 960 | a[(a_dim1 << 1) + 2] = (double)1.;
|
|---|
| 961 | return 0;
|
|---|
| 962 | L10:
|
|---|
| 963 | l = *n - 2;
|
|---|
| 964 | m = *n - 1;
|
|---|
| 965 | k = *n;
|
|---|
| 966 | s = a[k + l * a_dim1];
|
|---|
| 967 | a[*n + *n * a_dim1] = (double)1. - s * a[*n + l * a_dim1];
|
|---|
| 968 | a[m + *n * a_dim1] = -(double)s * a[m + l * a_dim1];
|
|---|
| 969 | L20:
|
|---|
| 970 | j = m;
|
|---|
| 971 | m = l;
|
|---|
| 972 | --l;
|
|---|
| 973 | if (l == 0) {
|
|---|
| 974 | goto L50;
|
|---|
| 975 | }
|
|---|
| 976 | s = (double)0.;
|
|---|
| 977 | i__1 = *n;
|
|---|
| 978 | for (i = j; i <= i__1; ++i) {
|
|---|
| 979 | /* L30: */
|
|---|
| 980 | s += a[i + l * a_dim1] * a[i + k * a_dim1];
|
|---|
| 981 | }
|
|---|
| 982 | a[m + k * a_dim1] = -(double)s * a[m + l * a_dim1];
|
|---|
| 983 | i__1 = *n;
|
|---|
| 984 | for (i = j; i <= i__1; ++i) {
|
|---|
| 985 | /* L40: */
|
|---|
| 986 | a[i + k * a_dim1] -= s * a[i + l * a_dim1];
|
|---|
| 987 | }
|
|---|
| 988 | goto L20;
|
|---|
| 989 | L50:
|
|---|
| 990 | a[k * a_dim1 + 1] = (double)0.;
|
|---|
| 991 | --k;
|
|---|
| 992 | m = k;
|
|---|
| 993 | l = k - 1;
|
|---|
| 994 | s = -(double)a[m + l * a_dim1];
|
|---|
| 995 | i__1 = *n;
|
|---|
| 996 | for (i = k; i <= i__1; ++i) {
|
|---|
| 997 | /* L60: */
|
|---|
| 998 | a[i + k * a_dim1] = s * a[i + l * a_dim1];
|
|---|
| 999 | }
|
|---|
| 1000 | a[k + k * a_dim1] += (double)1.;
|
|---|
| 1001 | if (l > 1) {
|
|---|
| 1002 | goto L20;
|
|---|
| 1003 | }
|
|---|
| 1004 | i__1 = *n;
|
|---|
| 1005 | for (i = 2; i <= i__1; ++i) {
|
|---|
| 1006 | /* L70: */
|
|---|
| 1007 | a[i + a_dim1] = (double)0.;
|
|---|
| 1008 | }
|
|---|
| 1009 | return 0;
|
|---|
| 1010 | } /* hsr1_ */
|
|---|
| 1011 |
|
|---|
| 1012 | static int
|
|---|
| 1013 | hsr2_(double *a, int *la, int *n)
|
|---|
| 1014 | {
|
|---|
| 1015 | /* System generated locals */
|
|---|
| 1016 | integer a_dim1, a_offset, i__1;
|
|---|
| 1017 |
|
|---|
| 1018 | /* Local variables */
|
|---|
| 1019 | static integer i, j, k, l, m;
|
|---|
| 1020 | static real s;
|
|---|
| 1021 |
|
|---|
| 1022 | /* Parameter adjustments */
|
|---|
| 1023 | a_dim1 = *la;
|
|---|
| 1024 | a_offset = a_dim1 + 1;
|
|---|
| 1025 | a -= a_offset;
|
|---|
| 1026 |
|
|---|
| 1027 | /* Function Body */
|
|---|
| 1028 | if (*n > 1) {
|
|---|
| 1029 | goto L10;
|
|---|
| 1030 | }
|
|---|
| 1031 | a[a_dim1 + 1] = (double)1.;
|
|---|
| 1032 | return 0;
|
|---|
| 1033 | L10:
|
|---|
| 1034 | l = *n - 2;
|
|---|
| 1035 | m = *n - 1;
|
|---|
| 1036 | k = *n;
|
|---|
| 1037 | s = a[*n + m * a_dim1];
|
|---|
| 1038 | a[*n + *n * a_dim1] = (double)1. - s * a[*n + m * a_dim1];
|
|---|
| 1039 | a[m + *n * a_dim1] = -(double)s * a[m + m * a_dim1];
|
|---|
| 1040 | L20:
|
|---|
| 1041 | j = m;
|
|---|
| 1042 | --m;
|
|---|
| 1043 | if (m == 0) {
|
|---|
| 1044 | goto L50;
|
|---|
| 1045 | }
|
|---|
| 1046 | s = (double)0.;
|
|---|
| 1047 | i__1 = *n;
|
|---|
| 1048 | for (i = j; i <= i__1; ++i) {
|
|---|
| 1049 | /* L30: */
|
|---|
| 1050 | s += a[i + m * a_dim1] * a[i + k * a_dim1];
|
|---|
| 1051 | }
|
|---|
| 1052 | a[m + k * a_dim1] = -(double)s * a[m + m * a_dim1];
|
|---|
| 1053 | i__1 = *n;
|
|---|
| 1054 | for (i = j; i <= i__1; ++i) {
|
|---|
| 1055 | /* L40: */
|
|---|
| 1056 | a[i + k * a_dim1] -= s * a[i + m * a_dim1];
|
|---|
| 1057 | }
|
|---|
| 1058 | goto L20;
|
|---|
| 1059 | L50:
|
|---|
| 1060 | --k;
|
|---|
| 1061 | m = k;
|
|---|
| 1062 | s = -(double)a[k + k * a_dim1];
|
|---|
| 1063 | i__1 = *n;
|
|---|
| 1064 | for (i = k; i <= i__1; ++i) {
|
|---|
| 1065 | /* L60: */
|
|---|
| 1066 | a[i + k * a_dim1] = s * a[i + k * a_dim1];
|
|---|
| 1067 | }
|
|---|
| 1068 | a[k + k * a_dim1] += (double)1.;
|
|---|
| 1069 | if (k > 1) {
|
|---|
| 1070 | goto L20;
|
|---|
| 1071 | }
|
|---|
| 1072 | return 0;
|
|---|
| 1073 | } /* hsr2_ */
|
|---|
| 1074 |
|
|---|
| 1075 | static int
|
|---|
| 1076 | hsr3_(double *a, int *la, int *m, int *n)
|
|---|
| 1077 | {
|
|---|
| 1078 | /* System generated locals */
|
|---|
| 1079 | integer a_dim1, a_offset, i__1;
|
|---|
| 1080 |
|
|---|
| 1081 | /* Local variables */
|
|---|
| 1082 | static integer i, j, k, l;
|
|---|
| 1083 | static real s;
|
|---|
| 1084 |
|
|---|
| 1085 | /* Parameter adjustments */
|
|---|
| 1086 | a_dim1 = *la;
|
|---|
| 1087 | a_offset = a_dim1 + 1;
|
|---|
| 1088 | a -= a_offset;
|
|---|
| 1089 |
|
|---|
| 1090 | /* Function Body */
|
|---|
| 1091 | k = *n;
|
|---|
| 1092 | if (*m >= *n) {
|
|---|
| 1093 | goto L10;
|
|---|
| 1094 | }
|
|---|
| 1095 | fprintf(stderr,"ERROR: ARGUMENT M MUST BE .GE. N IN SUBROUTINE HSR3\n");
|
|---|
| 1096 | abort();
|
|---|
| 1097 | L10:
|
|---|
| 1098 | s = -(double)a[k + k * a_dim1];
|
|---|
| 1099 | i__1 = *m;
|
|---|
| 1100 | for (i = k; i <= i__1; ++i) {
|
|---|
| 1101 | /* L20: */
|
|---|
| 1102 | a[i + k * a_dim1] = s * a[i + k * a_dim1];
|
|---|
| 1103 | }
|
|---|
| 1104 | a[k + k * a_dim1] += (double)1.;
|
|---|
| 1105 | if (k == 1) {
|
|---|
| 1106 | return 0;
|
|---|
| 1107 | }
|
|---|
| 1108 | l = k;
|
|---|
| 1109 | L30:
|
|---|
| 1110 | j = l;
|
|---|
| 1111 | --l;
|
|---|
| 1112 | if (l == 0) {
|
|---|
| 1113 | goto L60;
|
|---|
| 1114 | }
|
|---|
| 1115 | s = (double)0.;
|
|---|
| 1116 | i__1 = *m;
|
|---|
| 1117 | for (i = j; i <= i__1; ++i) {
|
|---|
| 1118 | /* L40: */
|
|---|
| 1119 | s += a[i + l * a_dim1] * a[i + k * a_dim1];
|
|---|
| 1120 | }
|
|---|
| 1121 | a[l + k * a_dim1] = -(double)s * a[l + l * a_dim1];
|
|---|
| 1122 | i__1 = *m;
|
|---|
| 1123 | for (i = j; i <= i__1; ++i) {
|
|---|
| 1124 | /* L50: */
|
|---|
| 1125 | a[i + k * a_dim1] -= s * a[i + l * a_dim1];
|
|---|
| 1126 | }
|
|---|
| 1127 | goto L30;
|
|---|
| 1128 | L60:
|
|---|
| 1129 | --k;
|
|---|
| 1130 | goto L10;
|
|---|
| 1131 | } /* hsr3_ */
|
|---|
| 1132 |
|
|---|
| 1133 | static int
|
|---|
| 1134 | hsr4_(double *a, int *la, int *m, int *n)
|
|---|
| 1135 | {
|
|---|
| 1136 | /* System generated locals */
|
|---|
| 1137 | integer a_dim1, a_offset, i__1, i__2;
|
|---|
| 1138 |
|
|---|
| 1139 | /* Local variables */
|
|---|
| 1140 | static integer i, j, k, l;
|
|---|
| 1141 | static real s;
|
|---|
| 1142 |
|
|---|
| 1143 | /* Parameter adjustments */
|
|---|
| 1144 | a_dim1 = *la;
|
|---|
| 1145 | a_offset = a_dim1 + 1;
|
|---|
| 1146 | a -= a_offset;
|
|---|
| 1147 |
|
|---|
| 1148 | /* Function Body */
|
|---|
| 1149 | k = *m;
|
|---|
| 1150 | if (*m > *n) {
|
|---|
| 1151 | goto L10;
|
|---|
| 1152 | }
|
|---|
| 1153 | fprintf(stderr,"ERROR: ARGUMENT M MUST BE .GE. N IN SUBROUTINE HSR4\n");
|
|---|
| 1154 | abort();
|
|---|
| 1155 | L10:
|
|---|
| 1156 | s = -(double)a[k + *n * a_dim1];
|
|---|
| 1157 | i__1 = *m;
|
|---|
| 1158 | for (i = *n; i <= i__1; ++i) {
|
|---|
| 1159 | /* L20: */
|
|---|
| 1160 | a[i + k * a_dim1] = s * a[i + *n * a_dim1];
|
|---|
| 1161 | }
|
|---|
| 1162 | a[k + k * a_dim1] += (double)1.;
|
|---|
| 1163 | l = *n;
|
|---|
| 1164 | L30:
|
|---|
| 1165 | j = l;
|
|---|
| 1166 | --l;
|
|---|
| 1167 | if (l == 0) {
|
|---|
| 1168 | goto L60;
|
|---|
| 1169 | }
|
|---|
| 1170 | s = (double)0.;
|
|---|
| 1171 | i__1 = *m;
|
|---|
| 1172 | for (i = j; i <= i__1; ++i) {
|
|---|
| 1173 | /* L40: */
|
|---|
| 1174 | s += a[i + l * a_dim1] * a[i + k * a_dim1];
|
|---|
| 1175 | }
|
|---|
| 1176 | a[l + k * a_dim1] = -(double)s * a[l + l * a_dim1];
|
|---|
| 1177 | i__1 = *m;
|
|---|
| 1178 | for (i = j; i <= i__1; ++i) {
|
|---|
| 1179 | /* L50: */
|
|---|
| 1180 | a[i + k * a_dim1] -= s * a[i + l * a_dim1];
|
|---|
| 1181 | }
|
|---|
| 1182 | goto L30;
|
|---|
| 1183 | L60:
|
|---|
| 1184 | --k;
|
|---|
| 1185 | if (k > *n) {
|
|---|
| 1186 | goto L10;
|
|---|
| 1187 | }
|
|---|
| 1188 | k = *m - *n;
|
|---|
| 1189 | i__1 = k;
|
|---|
| 1190 | for (j = 1; j <= i__1; ++j) {
|
|---|
| 1191 | i__2 = *m;
|
|---|
| 1192 | for (i = 1; i <= i__2; ++i) {
|
|---|
| 1193 | /* L70: */
|
|---|
| 1194 | a[i + j * a_dim1] = a[i + (j + *n) * a_dim1];
|
|---|
| 1195 | }
|
|---|
| 1196 | }
|
|---|
| 1197 | return 0;
|
|---|
| 1198 | } /* hsr4_ */
|
|---|
| 1199 |
|
|---|
| 1200 | /* ________________________________________________________ */
|
|---|
| 1201 | /* | | */
|
|---|
| 1202 | /* | PACKAGE SUBROUTINES: HSR3 | */
|
|---|
| 1203 | /* |________________________________________________________| */
|
|---|
| 1204 |
|
|---|
| 1205 | static int
|
|---|
| 1206 | hsr5_(double *a, int *la, int *m, int *n)
|
|---|
| 1207 | {
|
|---|
| 1208 | /* System generated locals */
|
|---|
| 1209 | integer a_dim1, a_offset, i__1;
|
|---|
| 1210 |
|
|---|
| 1211 | /* Local variables */
|
|---|
| 1212 | static integer i, j, k, l;
|
|---|
| 1213 | static real s;
|
|---|
| 1214 |
|
|---|
| 1215 | /* Parameter adjustments */
|
|---|
| 1216 | a_dim1 = *la;
|
|---|
| 1217 | a_offset = a_dim1 + 1;
|
|---|
| 1218 | a -= a_offset;
|
|---|
| 1219 |
|
|---|
| 1220 | /* Function Body */
|
|---|
| 1221 | if (*m >= *n) {
|
|---|
| 1222 | goto L10;
|
|---|
| 1223 | }
|
|---|
| 1224 | fprintf(stderr,"ERROR: ARGUMENT M MUST BE .GE. N IN SUBROUTINE HSR5\n");
|
|---|
| 1225 | abort();
|
|---|
| 1226 | L10:
|
|---|
| 1227 | if (*m == *n) {
|
|---|
| 1228 | goto L90;
|
|---|
| 1229 | }
|
|---|
| 1230 | k = *m;
|
|---|
| 1231 | L20:
|
|---|
| 1232 | s = -(double)a[k + *n * a_dim1];
|
|---|
| 1233 | i__1 = *m;
|
|---|
| 1234 | for (i = *n; i <= i__1; ++i) {
|
|---|
| 1235 | /* L30: */
|
|---|
| 1236 | a[i + k * a_dim1] = s * a[i + *n * a_dim1];
|
|---|
| 1237 | }
|
|---|
| 1238 | a[k + k * a_dim1] += (double)1.;
|
|---|
| 1239 | l = *n;
|
|---|
| 1240 | L40:
|
|---|
| 1241 | j = l;
|
|---|
| 1242 | --l;
|
|---|
| 1243 | if (l == 0) {
|
|---|
| 1244 | goto L70;
|
|---|
| 1245 | }
|
|---|
| 1246 | s = (double)0.;
|
|---|
| 1247 | i__1 = *m;
|
|---|
| 1248 | for (i = j; i <= i__1; ++i) {
|
|---|
| 1249 | /* L50: */
|
|---|
| 1250 | s += a[i + l * a_dim1] * a[i + k * a_dim1];
|
|---|
| 1251 | }
|
|---|
| 1252 | a[l + k * a_dim1] = -(double)s * a[l + l * a_dim1];
|
|---|
| 1253 | i__1 = *m;
|
|---|
| 1254 | for (i = j; i <= i__1; ++i) {
|
|---|
| 1255 | /* L60: */
|
|---|
| 1256 | a[i + k * a_dim1] -= s * a[i + l * a_dim1];
|
|---|
| 1257 | }
|
|---|
| 1258 | goto L40;
|
|---|
| 1259 | L70:
|
|---|
| 1260 | --k;
|
|---|
| 1261 | if (k > *n) {
|
|---|
| 1262 | goto L20;
|
|---|
| 1263 | }
|
|---|
| 1264 | L90:
|
|---|
| 1265 | hsr3_(&a[a_offset], la, m, n);
|
|---|
| 1266 | return 0;
|
|---|
| 1267 | } /* hsr5_ */
|
|---|
| 1268 |
|
|---|
| 1269 | /* ________________________________________________________ */
|
|---|
| 1270 | /* | | */
|
|---|
| 1271 | /* | COMPUTE SINGULAR VALUE DECOMPOSITION OF A BIDIAGONAL | */
|
|---|
| 1272 | /* | MATRIX: A = Q TIMES DIAGONAL MATRIX TIMES P TRANSPOSE | */
|
|---|
| 1273 | /* | | */
|
|---|
| 1274 | /* | INPUT: | */
|
|---|
| 1275 | /* | | */
|
|---|
| 1276 | /* | D --DIAGONAL | */
|
|---|
| 1277 | /* | | */
|
|---|
| 1278 | /* | N --DIMENSION OF BIDIAGONAL MATRIX | */
|
|---|
| 1279 | /* | | */
|
|---|
| 1280 | /* | U --OFF DIAGONAL | */
|
|---|
| 1281 | /* | | */
|
|---|
| 1282 | /* | IU --= 0 IF U IS SUPERDIAGONAL AND = 1 IF | */
|
|---|
| 1283 | /* | U IS SUBDIAGONAL | */
|
|---|
| 1284 | /* | | */
|
|---|
| 1285 | /* | Q --EITHER A SEGMENT OF AN IDENTITY MATRIX | */
|
|---|
| 1286 | /* | OR A SEGMENT OF THE MATRIX USED TO | */
|
|---|
| 1287 | /* | BIDIAGONALIZE THE COEFFICIENT MATRIX | */
|
|---|
| 1288 | /* | | */
|
|---|
| 1289 | /* | LQ --LEADING (ROW) DIMENSION OF ARRAY Q | */
|
|---|
| 1290 | /* | | */
|
|---|
| 1291 | /* | MQ --NUMBER OF MATRIX ELEMENTS CONTAINED IN | */
|
|---|
| 1292 | /* | EACH COLUMN OF Q | */
|
|---|
| 1293 | /* | | */
|
|---|
| 1294 | /* | IQ --AN INTEGER WHICH INDICATES WHETHER | */
|
|---|
| 1295 | /* | COLUMNS OF Q TO BE PROCESSED (= 0 MEANS| */
|
|---|
| 1296 | /* | NO AND = 1 MEANS YES) | */
|
|---|
| 1297 | /* | | */
|
|---|
| 1298 | /* | LP --LEADING (ROW) DIMENSION OF ARRAY P | */
|
|---|
| 1299 | /* | | */
|
|---|
| 1300 | /* | MP --NUMBER OF MATRIX ELEMENTS CONTAINED IN | */
|
|---|
| 1301 | /* | EACH COLUMN OF P | */
|
|---|
| 1302 | /* | | */
|
|---|
| 1303 | /* | IP --AN INTEGER DEFINED LIKE IQ | */
|
|---|
| 1304 | /* | | */
|
|---|
| 1305 | /* | E --WORK ARRAY WITH AT LEAST N ELEMENTS | */
|
|---|
| 1306 | /* | | */
|
|---|
| 1307 | /* | F --WORK ARRAY WITH AT LEAST N ELEMENTS | */
|
|---|
| 1308 | /* | | */
|
|---|
| 1309 | /* | OUTPUT: | */
|
|---|
| 1310 | /* | | */
|
|---|
| 1311 | /* | Q --Q FACTOR IN THE SINGULAR VALUE DECOMP. | */
|
|---|
| 1312 | /* | | */
|
|---|
| 1313 | /* | D --SINGULAR VALUES IN DECREASING ORDER | */
|
|---|
| 1314 | /* | | */
|
|---|
| 1315 | /* | P --P FACTOR IN THE SINGULAR VALUE DECOMP. | */
|
|---|
| 1316 | /* | | */
|
|---|
| 1317 | /* | BUILTIN FUNCTIONS: ABS,AMAX1,SIGN,SQRT | */
|
|---|
| 1318 | /* | PACKAGE SUBROUTINES: EIG3,FGV,HSR1-HSR5,SCL,SFT, | */
|
|---|
| 1319 | /* | SNG0,SNG1,SORT2 | */
|
|---|
| 1320 | /* |________________________________________________________| */
|
|---|
| 1321 |
|
|---|
| 1322 | static int
|
|---|
| 1323 | singb_(double *d, int *n, double *u, int *iu,
|
|---|
| 1324 | double *q, int *lq, int *mq, int *iq,
|
|---|
| 1325 | double *p, int *lp, int *mp, int *ip, double *e, double *f)
|
|---|
| 1326 | {
|
|---|
| 1327 | int one = 1;
|
|---|
| 1328 |
|
|---|
| 1329 | /* System generated locals */
|
|---|
| 1330 | integer q_dim1, q_offset, p_dim1, p_offset, i__1, i__2;
|
|---|
| 1331 | real r__1, r__2;
|
|---|
| 1332 |
|
|---|
| 1333 | /* Local variables */
|
|---|
| 1334 | static real b, c;
|
|---|
| 1335 | static integer g, h, i, j, k, l, m;
|
|---|
| 1336 | static real r, s, t, v, w, x, y, z;
|
|---|
| 1337 | static integer j0, k2, l1;
|
|---|
| 1338 | static real t0, t1, t2, t3;
|
|---|
| 1339 | static integer id, jl, ll, jr, ns;
|
|---|
| 1340 |
|
|---|
| 1341 | /* Parameter adjustments */
|
|---|
| 1342 | --f;
|
|---|
| 1343 | --e;
|
|---|
| 1344 | p_dim1 = *lp;
|
|---|
| 1345 | p_offset = p_dim1 + 1;
|
|---|
| 1346 | p -= p_offset;
|
|---|
| 1347 | q_dim1 = *lq;
|
|---|
| 1348 | q_offset = q_dim1 + 1;
|
|---|
| 1349 | q -= q_offset;
|
|---|
| 1350 | --u;
|
|---|
| 1351 | --d;
|
|---|
| 1352 |
|
|---|
| 1353 | /* Function Body */
|
|---|
| 1354 | if (*n > 1) {
|
|---|
| 1355 | goto L10;
|
|---|
| 1356 | }
|
|---|
| 1357 | if (*iq == 1) {
|
|---|
| 1358 | q[q_dim1 + 1] = (double)1.;
|
|---|
| 1359 | }
|
|---|
| 1360 | if (*ip == 1) {
|
|---|
| 1361 | p[p_dim1 + 1] = (double)1.;
|
|---|
| 1362 | }
|
|---|
| 1363 | if (d[1] >= (double)0.) {
|
|---|
| 1364 | return 0;
|
|---|
| 1365 | }
|
|---|
| 1366 | d[1] = -(double)d[1];
|
|---|
| 1367 | if (*iq == 1) {
|
|---|
| 1368 | q[q_dim1 + 1] = (double)-1.;
|
|---|
| 1369 | }
|
|---|
| 1370 | return 0;
|
|---|
| 1371 | L10:
|
|---|
| 1372 | jl = *iq;
|
|---|
| 1373 | if (jl == 0) {
|
|---|
| 1374 | jl = 3;
|
|---|
| 1375 | }
|
|---|
| 1376 | if (jl != 3) {
|
|---|
| 1377 | jl = 1;
|
|---|
| 1378 | }
|
|---|
| 1379 | jr = *ip;
|
|---|
| 1380 | if (jr == 0) {
|
|---|
| 1381 | jr = 3;
|
|---|
| 1382 | }
|
|---|
| 1383 | if (jr != 3) {
|
|---|
| 1384 | jr = 2;
|
|---|
| 1385 | }
|
|---|
| 1386 | if (*iu == 0) {
|
|---|
| 1387 | goto L20;
|
|---|
| 1388 | }
|
|---|
| 1389 | i = jl;
|
|---|
| 1390 | jl = jr;
|
|---|
| 1391 | jr = i;
|
|---|
| 1392 | L20:
|
|---|
| 1393 | j = 0;
|
|---|
| 1394 | l = *n - 1;
|
|---|
| 1395 | k2 = *n - 2;
|
|---|
| 1396 | i__1 = l;
|
|---|
| 1397 | for (i = 1; i <= i__1; ++i) {
|
|---|
| 1398 | e[i] = (double)1.;
|
|---|
| 1399 | f[i] = (double)1.;
|
|---|
| 1400 | if (u[i] == (double)0.) {
|
|---|
| 1401 | j = i;
|
|---|
| 1402 | }
|
|---|
| 1403 | /* L30: */
|
|---|
| 1404 | if (d[i] == (double)0.) {
|
|---|
| 1405 | j = i;
|
|---|
| 1406 | }
|
|---|
| 1407 | }
|
|---|
| 1408 | e[*n] = (double)1.;
|
|---|
| 1409 | f[*n] = (double)1.;
|
|---|
| 1410 | b = (double)3.5527136788005009e-15;
|
|---|
| 1411 | t = (double)1.;
|
|---|
| 1412 | L40:
|
|---|
| 1413 | t *= (double).5;
|
|---|
| 1414 | s = t + (double)1.;
|
|---|
| 1415 | if (s > (double)1.) {
|
|---|
| 1416 | goto L40;
|
|---|
| 1417 | }
|
|---|
| 1418 | t0 = (double)1. / (t + t);
|
|---|
| 1419 | /* Computing 2nd power */
|
|---|
| 1420 | r__1 = t + t;
|
|---|
| 1421 | t2 = r__1 * r__1;
|
|---|
| 1422 | ns = *n * 50;
|
|---|
| 1423 | l1 = 0;
|
|---|
| 1424 | k = *n;
|
|---|
| 1425 | ll = 0;
|
|---|
| 1426 | goto L70;
|
|---|
| 1427 | L50:
|
|---|
| 1428 | j = 0;
|
|---|
| 1429 | i__1 = l;
|
|---|
| 1430 | for (i = 1; i <= i__1; ++i) {
|
|---|
| 1431 | if (u[i] == (double)0.) {
|
|---|
| 1432 | j = i;
|
|---|
| 1433 | }
|
|---|
| 1434 | /* L60: */
|
|---|
| 1435 | if (d[i] == (double)0.) {
|
|---|
| 1436 | j = i;
|
|---|
| 1437 | }
|
|---|
| 1438 | }
|
|---|
| 1439 | L70:
|
|---|
| 1440 | if (j == 0) {
|
|---|
| 1441 | goto L140;
|
|---|
| 1442 | }
|
|---|
| 1443 | if (u[j] == (double)0.) {
|
|---|
| 1444 | goto L140;
|
|---|
| 1445 | }
|
|---|
| 1446 | /* ------------------------------- */
|
|---|
| 1447 | /* |*** ZERO DIAGONAL ELEMENT ***| */
|
|---|
| 1448 | /* ------------------------------- */
|
|---|
| 1449 | i = j;
|
|---|
| 1450 | v = u[j];
|
|---|
| 1451 | u[j] = (double)0.;
|
|---|
| 1452 | s = -(double)v * (r__1 = e[j], fabs(r__1));
|
|---|
| 1453 | /* --------------------------- */
|
|---|
| 1454 | /* |*** PROCESS LEFT SIDE ***| */
|
|---|
| 1455 | /* --------------------------- */
|
|---|
| 1456 | L80:
|
|---|
| 1457 | h = i;
|
|---|
| 1458 | ++i;
|
|---|
| 1459 | r = (r__1 = e[i], fabs(r__1)) * d[i];
|
|---|
| 1460 | fgv_(&x, &y, &t, &r, &s, &e[j], &e[i]);
|
|---|
| 1461 | if (t == (double)1.) {
|
|---|
| 1462 | goto L90;
|
|---|
| 1463 | }
|
|---|
| 1464 | d[i] -= y * v;
|
|---|
| 1465 | sng0_(&q[q_offset], lq, mq, &p[p_offset], lp, mp, &jl, &j, &i, &x, &y);
|
|---|
| 1466 | if (i == k) {
|
|---|
| 1467 | goto L100;
|
|---|
| 1468 | }
|
|---|
| 1469 | v = x * u[i];
|
|---|
| 1470 | s = -(double)v * (r__1 = e[j], fabs(r__1));
|
|---|
| 1471 | goto L80;
|
|---|
| 1472 | L90:
|
|---|
| 1473 | d[i] = d[i] * y - v;
|
|---|
| 1474 | sng1_(&q[q_offset], lq, mq, &p[p_offset], lp, mp, &jl, &j, &i, &x, &y);
|
|---|
| 1475 | if (i == k) {
|
|---|
| 1476 | goto L100;
|
|---|
| 1477 | }
|
|---|
| 1478 | v = u[i];
|
|---|
| 1479 | u[i] = v * y;
|
|---|
| 1480 | s = -(double)v * (r__1 = e[j], fabs(r__1));
|
|---|
| 1481 | goto L80;
|
|---|
| 1482 | L100:
|
|---|
| 1483 | if (j == 1) {
|
|---|
| 1484 | goto L130;
|
|---|
| 1485 | }
|
|---|
| 1486 | i = j - 1;
|
|---|
| 1487 | s = u[i];
|
|---|
| 1488 | u[i] = (double)0.;
|
|---|
| 1489 | /* ---------------------------- */
|
|---|
| 1490 | /* |*** PROCESS RIGHT SIDE ***| */
|
|---|
| 1491 | /* ---------------------------- */
|
|---|
| 1492 | L110:
|
|---|
| 1493 | h = i;
|
|---|
| 1494 | --i;
|
|---|
| 1495 | r = d[h];
|
|---|
| 1496 | fgv_(&x, &y, &t, &r, &s, &f[h], &f[j]);
|
|---|
| 1497 | if (t == (double)1.) {
|
|---|
| 1498 | goto L120;
|
|---|
| 1499 | }
|
|---|
| 1500 | d[h] = r + x * s;
|
|---|
| 1501 | sng0_(&q[q_offset], lq, mq, &p[p_offset], lp, mp, &jr, &h, &j, &x, &y);
|
|---|
| 1502 | if (h == 1) {
|
|---|
| 1503 | goto L130;
|
|---|
| 1504 | }
|
|---|
| 1505 | s = -(double)y * u[i];
|
|---|
| 1506 | goto L110;
|
|---|
| 1507 | L120:
|
|---|
| 1508 | d[h] = x * r + s;
|
|---|
| 1509 | sng1_(&q[q_offset], lq, mq, &p[p_offset], lp, mp, &jr, &h, &j, &x, &y);
|
|---|
| 1510 | if (h == 1) {
|
|---|
| 1511 | goto L130;
|
|---|
| 1512 | }
|
|---|
| 1513 | s = -(double)u[i];
|
|---|
| 1514 | u[i] = x * u[i];
|
|---|
| 1515 | goto L110;
|
|---|
| 1516 | L130:
|
|---|
| 1517 | scl_(&d[1], &u[1], n, &q[q_offset], lq, mq, &p[p_offset], lp, mp, &e[1], &
|
|---|
| 1518 | f[1], &b, &one, &k, &jl, &jr);
|
|---|
| 1519 | L140:
|
|---|
| 1520 | ++j;
|
|---|
| 1521 | if (j == k) {
|
|---|
| 1522 | goto L320;
|
|---|
| 1523 | }
|
|---|
| 1524 | s = (double)0.;
|
|---|
| 1525 | t = (double)0.;
|
|---|
| 1526 | /* ----------------------------- */
|
|---|
| 1527 | /* |*** SET ERROR TOLERANCE ***| */
|
|---|
| 1528 | /* ----------------------------- */
|
|---|
| 1529 | i__1 = l;
|
|---|
| 1530 | for (i = j; i <= i__1; ++i) {
|
|---|
| 1531 | x = (r__1 = d[i] * e[i] * (d[i] * f[i]), fabs(r__1));
|
|---|
| 1532 | y = (r__1 = u[i] * e[i] * (u[i] * f[i + 1]), fabs(r__1));
|
|---|
| 1533 | /* Computing MAX */
|
|---|
| 1534 | r__1 = max(s,x);
|
|---|
| 1535 | s = dmax(r__1,y);
|
|---|
| 1536 | /* L150: */
|
|---|
| 1537 | t = t + x + y;
|
|---|
| 1538 | }
|
|---|
| 1539 | x = (r__1 = e[k] * d[k] * (f[k] * d[k]), fabs(r__1));
|
|---|
| 1540 | s = dmax(s,x);
|
|---|
| 1541 | t3 = s * t2;
|
|---|
| 1542 | t += x;
|
|---|
| 1543 | if (t == (double)0.) {
|
|---|
| 1544 | t = (double)1.;
|
|---|
| 1545 | }
|
|---|
| 1546 | t1 = t0 / t;
|
|---|
| 1547 | goto L280;
|
|---|
| 1548 | L160:
|
|---|
| 1549 | ++ll;
|
|---|
| 1550 | if (ll > ns) {
|
|---|
| 1551 | goto L530;
|
|---|
| 1552 | }
|
|---|
| 1553 | if (l > j) {
|
|---|
| 1554 | goto L170;
|
|---|
| 1555 | }
|
|---|
| 1556 | s = (double)0.;
|
|---|
| 1557 | t = (double)0.;
|
|---|
| 1558 | goto L180;
|
|---|
| 1559 | L170:
|
|---|
| 1560 | s = u[k2];
|
|---|
| 1561 | t = e[k2];
|
|---|
| 1562 | /* ----------------------- */
|
|---|
| 1563 | /* |*** COMPUTE SHIFT ***| */
|
|---|
| 1564 | /* ----------------------- */
|
|---|
| 1565 | L180:
|
|---|
| 1566 | sft_(&c, &d[k], &d[l], &u[l], &s, &e[k], &e[l], &t, &f[k], &f[l]);
|
|---|
| 1567 | v = (r__1 = e[j], fabs(r__1));
|
|---|
| 1568 | w = (r__1 = f[j], fabs(r__1));
|
|---|
| 1569 | t = d[j] * w;
|
|---|
| 1570 | r = t * (d[j] * v) - c;
|
|---|
| 1571 | s = t * (u[j] * v);
|
|---|
| 1572 | id = 1;
|
|---|
| 1573 | j0 = j;
|
|---|
| 1574 | i = j;
|
|---|
| 1575 | h = j - 1;
|
|---|
| 1576 | L190:
|
|---|
| 1577 | g = h;
|
|---|
| 1578 | h = i;
|
|---|
| 1579 | ++i;
|
|---|
| 1580 | z = (r__1 = f[i], fabs(r__1));
|
|---|
| 1581 | /* ---------------------------- */
|
|---|
| 1582 | /* |*** PROCESS RIGHT SIDE ***| */
|
|---|
| 1583 | /* ---------------------------- */
|
|---|
| 1584 | fgv_(&x, &y, &t, &r, &s, &f[h], &f[i]);
|
|---|
| 1585 | v = d[h];
|
|---|
| 1586 | if (t == (double)1.) {
|
|---|
| 1587 | goto L210;
|
|---|
| 1588 | }
|
|---|
| 1589 | if (h == j) {
|
|---|
| 1590 | goto L200;
|
|---|
| 1591 | }
|
|---|
| 1592 | t = u[g] + x * s;
|
|---|
| 1593 | u[g] = t;
|
|---|
| 1594 | if ((r__1 = t * e[g] * (t * f[h]), fabs(r__1)) > t3) {
|
|---|
| 1595 | goto L200;
|
|---|
| 1596 | }
|
|---|
| 1597 | j = h;
|
|---|
| 1598 | id = 1;
|
|---|
| 1599 | L200:
|
|---|
| 1600 | r = v + x * u[h];
|
|---|
| 1601 | s = x * d[i];
|
|---|
| 1602 | u[h] -= y * v;
|
|---|
| 1603 | sng0_(&q[q_offset], lq, mq, &p[p_offset], lp, mp, &jr, &h, &i, &x, &y);
|
|---|
| 1604 | goto L230;
|
|---|
| 1605 | L210:
|
|---|
| 1606 | if (h == j) {
|
|---|
| 1607 | goto L220;
|
|---|
| 1608 | }
|
|---|
| 1609 | t = x * u[g] + s;
|
|---|
| 1610 | u[g] = t;
|
|---|
| 1611 | if ((r__1 = t * e[g] * (t * f[h]), fabs(r__1)) > t3) {
|
|---|
| 1612 | goto L220;
|
|---|
| 1613 | }
|
|---|
| 1614 | j = h;
|
|---|
| 1615 | id = 1;
|
|---|
| 1616 | L220:
|
|---|
| 1617 | r = x * v + u[h];
|
|---|
| 1618 | s = d[i];
|
|---|
| 1619 | u[h] = y * u[h] - v;
|
|---|
| 1620 | d[i] = y * s;
|
|---|
| 1621 | sng1_(&q[q_offset], lq, mq, &p[p_offset], lp, mp, &jr, &h, &i, &x, &y);
|
|---|
| 1622 | /* --------------------------- */
|
|---|
| 1623 | /* |*** PROCESS LEFT SIDE ***| */
|
|---|
| 1624 | /* --------------------------- */
|
|---|
| 1625 | L230:
|
|---|
| 1626 | fgv_(&x, &y, &t, &r, &s, &e[h], &e[i]);
|
|---|
| 1627 | if (t == (double)1.) {
|
|---|
| 1628 | goto L250;
|
|---|
| 1629 | }
|
|---|
| 1630 | t = r + x * s;
|
|---|
| 1631 | d[h] = t;
|
|---|
| 1632 | if ((r__1 = t * e[h] * (t * f[h]), fabs(r__1)) > t3) {
|
|---|
| 1633 | goto L240;
|
|---|
| 1634 | }
|
|---|
| 1635 | id = 0;
|
|---|
| 1636 | j = h;
|
|---|
| 1637 | L240:
|
|---|
| 1638 | r = u[h] + x * d[i];
|
|---|
| 1639 | d[i] -= y * u[h];
|
|---|
| 1640 | u[h] = r;
|
|---|
| 1641 | sng0_(&q[q_offset], lq, mq, &p[p_offset], lp, mp, &jl, &h, &i, &x, &y);
|
|---|
| 1642 | if (i == k) {
|
|---|
| 1643 | goto L270;
|
|---|
| 1644 | }
|
|---|
| 1645 | s = x * u[i];
|
|---|
| 1646 | goto L190;
|
|---|
| 1647 | L250:
|
|---|
| 1648 | t = s + x * r;
|
|---|
| 1649 | d[h] = t;
|
|---|
| 1650 | if ((r__1 = t * e[h] * (t * f[h]), fabs(r__1)) > t3) {
|
|---|
| 1651 | goto L260;
|
|---|
| 1652 | }
|
|---|
| 1653 | id = 0;
|
|---|
| 1654 | j = h;
|
|---|
| 1655 | L260:
|
|---|
| 1656 | r = d[i] + x * u[h];
|
|---|
| 1657 | d[i] = y * d[i] - u[h];
|
|---|
| 1658 | u[h] = r;
|
|---|
| 1659 | sng1_(&q[q_offset], lq, mq, &p[p_offset], lp, mp, &jl, &h, &i, &x, &y);
|
|---|
| 1660 | if (i == k) {
|
|---|
| 1661 | goto L270;
|
|---|
| 1662 | }
|
|---|
| 1663 | s = u[i];
|
|---|
| 1664 | u[i] = s * y;
|
|---|
| 1665 | goto L190;
|
|---|
| 1666 | L270:
|
|---|
| 1667 | scl_(&d[1], &u[1], n, &q[q_offset], lq, mq, &p[p_offset], lp, mp, &e[1], &
|
|---|
| 1668 | f[1], &b, &j0, &k, &jl, &jr);
|
|---|
| 1669 | if (id == 0) {
|
|---|
| 1670 | goto L70;
|
|---|
| 1671 | }
|
|---|
| 1672 | L280:
|
|---|
| 1673 | w = e[l];
|
|---|
| 1674 | x = e[k];
|
|---|
| 1675 | y = f[l];
|
|---|
| 1676 | z = f[k];
|
|---|
| 1677 | r = (r__1 = x * d[k] * (z * d[k]), fabs(r__1));
|
|---|
| 1678 | s = (r__1 = w * d[l] * (y * d[l]), fabs(r__1));
|
|---|
| 1679 | t = (r__1 = x * u[l] * (y * u[l]), fabs(r__1));
|
|---|
| 1680 | /* ------------------------------ */
|
|---|
| 1681 | /* |*** TEST FOR CONVERGENCE ***| */
|
|---|
| 1682 | /* ------------------------------ */
|
|---|
| 1683 | if (s * t1 * (t * t1) > (double)1.) {
|
|---|
| 1684 | goto L160;
|
|---|
| 1685 | }
|
|---|
| 1686 | ++l1;
|
|---|
| 1687 | if (l1 > 40) {
|
|---|
| 1688 | goto L290;
|
|---|
| 1689 | }
|
|---|
| 1690 | if (t == (double)0.) {
|
|---|
| 1691 | goto L290;
|
|---|
| 1692 | }
|
|---|
| 1693 | r += t;
|
|---|
| 1694 | if (s / r * (t / r) > t2) {
|
|---|
| 1695 | goto L160;
|
|---|
| 1696 | }
|
|---|
| 1697 | L290:
|
|---|
| 1698 | l1 = 0;
|
|---|
| 1699 | if (s > r) {
|
|---|
| 1700 | goto L310;
|
|---|
| 1701 | }
|
|---|
| 1702 | r = -(double)d[k] * fabs(x);
|
|---|
| 1703 | s = u[l] * fabs(w);
|
|---|
| 1704 | fgv_(&w, &y, &t, &r, &s, &e[l], &e[k]);
|
|---|
| 1705 | x = e[k];
|
|---|
| 1706 | if (t == (double)1.) {
|
|---|
| 1707 | goto L300;
|
|---|
| 1708 | }
|
|---|
| 1709 | d[k] -= y * u[l];
|
|---|
| 1710 | sng0_(&q[q_offset], lq, mq, &p[p_offset], lp, mp, &jl, &l, &k, &w, &y);
|
|---|
| 1711 | goto L310;
|
|---|
| 1712 | L300:
|
|---|
| 1713 | d[l] *= w;
|
|---|
| 1714 | d[k] = y * d[k] - u[l];
|
|---|
| 1715 | sng1_(&q[q_offset], lq, mq, &p[p_offset], lp, mp, &jl, &l, &k, &w, &y);
|
|---|
| 1716 | L310:
|
|---|
| 1717 | r__1 = sqrt((fabs(x)));
|
|---|
| 1718 | r__2 = sqrt((fabs(z)));
|
|---|
| 1719 | t = r_sign(&r__1, &x) * d[k] * r_sign(&r__2, &z);
|
|---|
| 1720 | if (t < (double)0.) {
|
|---|
| 1721 | e[k] = -(double)e[k];
|
|---|
| 1722 | }
|
|---|
| 1723 | d[k] = fabs(t);
|
|---|
| 1724 | k = l;
|
|---|
| 1725 | l = k2;
|
|---|
| 1726 | --k2;
|
|---|
| 1727 | if (k > j) {
|
|---|
| 1728 | goto L280;
|
|---|
| 1729 | }
|
|---|
| 1730 | L320:
|
|---|
| 1731 | x = e[k];
|
|---|
| 1732 | z = f[k];
|
|---|
| 1733 | r__1 = sqrt((fabs(x)));
|
|---|
| 1734 | r__2 = sqrt((fabs(z)));
|
|---|
| 1735 | t = r_sign(&r__1, &x) * d[k] * r_sign(&r__2, &z);
|
|---|
| 1736 | if (t < (double)0.) {
|
|---|
| 1737 | e[k] = -(double)e[k];
|
|---|
| 1738 | }
|
|---|
| 1739 | d[k] = fabs(t);
|
|---|
| 1740 | k = l;
|
|---|
| 1741 | l = k2;
|
|---|
| 1742 | --k2;
|
|---|
| 1743 | if (k > 1) {
|
|---|
| 1744 | goto L50;
|
|---|
| 1745 | }
|
|---|
| 1746 | if (k == 0) {
|
|---|
| 1747 | goto L330;
|
|---|
| 1748 | }
|
|---|
| 1749 | goto L320;
|
|---|
| 1750 | /* ------------------------- */
|
|---|
| 1751 | /* |*** RESCALE P AND Q ***| */
|
|---|
| 1752 | /* ------------------------- */
|
|---|
| 1753 | L330:
|
|---|
| 1754 | switch ((int)jl) {
|
|---|
| 1755 | case 1: goto L340;
|
|---|
| 1756 | case 2: goto L360;
|
|---|
| 1757 | case 3: goto L380;
|
|---|
| 1758 | }
|
|---|
| 1759 | L340:
|
|---|
| 1760 | i__1 = *n;
|
|---|
| 1761 | for (j = 1; j <= i__1; ++j) {
|
|---|
| 1762 | t = e[j];
|
|---|
| 1763 | r__1 = sqrt((fabs(t)));
|
|---|
| 1764 | t = r_sign(&r__1, &t);
|
|---|
| 1765 | i__2 = *mq;
|
|---|
| 1766 | for (i = 1; i <= i__2; ++i) {
|
|---|
| 1767 | /* L350: */
|
|---|
| 1768 | q[i + j * q_dim1] *= t;
|
|---|
| 1769 | }
|
|---|
| 1770 | }
|
|---|
| 1771 | goto L380;
|
|---|
| 1772 | L360:
|
|---|
| 1773 | i__2 = *n;
|
|---|
| 1774 | for (j = 1; j <= i__2; ++j) {
|
|---|
| 1775 | t = e[j];
|
|---|
| 1776 | r__1 = sqrt((fabs(t)));
|
|---|
| 1777 | t = r_sign(&r__1, &t);
|
|---|
| 1778 | i__1 = *mp;
|
|---|
| 1779 | for (i = 1; i <= i__1; ++i) {
|
|---|
| 1780 | /* L370: */
|
|---|
| 1781 | p[i + j * p_dim1] *= t;
|
|---|
| 1782 | }
|
|---|
| 1783 | }
|
|---|
| 1784 | L380:
|
|---|
| 1785 | switch ((int)jr) {
|
|---|
| 1786 | case 1: goto L390;
|
|---|
| 1787 | case 2: goto L410;
|
|---|
| 1788 | case 3: goto L430;
|
|---|
| 1789 | }
|
|---|
| 1790 | L390:
|
|---|
| 1791 | i__1 = *n;
|
|---|
| 1792 | for (j = 1; j <= i__1; ++j) {
|
|---|
| 1793 | t = f[j];
|
|---|
| 1794 | r__1 = sqrt((fabs(t)));
|
|---|
| 1795 | t = r_sign(&r__1, &t);
|
|---|
| 1796 | i__2 = *mq;
|
|---|
| 1797 | for (i = 1; i <= i__2; ++i) {
|
|---|
| 1798 | /* L400: */
|
|---|
| 1799 | q[i + j * q_dim1] *= t;
|
|---|
| 1800 | }
|
|---|
| 1801 | }
|
|---|
| 1802 | goto L430;
|
|---|
| 1803 | L410:
|
|---|
| 1804 | i__2 = *n;
|
|---|
| 1805 | for (j = 1; j <= i__2; ++j) {
|
|---|
| 1806 | t = f[j];
|
|---|
| 1807 | r__1 = sqrt((fabs(t)));
|
|---|
| 1808 | t = r_sign(&r__1, &t);
|
|---|
| 1809 | i__1 = *mp;
|
|---|
| 1810 | for (i = 1; i <= i__1; ++i) {
|
|---|
| 1811 | /* L420: */
|
|---|
| 1812 | p[i + j * p_dim1] *= t;
|
|---|
| 1813 | }
|
|---|
| 1814 | }
|
|---|
| 1815 | /* -------------------------------- */
|
|---|
| 1816 | /* |*** REORDER THE EIGENPAIRS ***| */
|
|---|
| 1817 | /* -------------------------------- */
|
|---|
| 1818 | L430:
|
|---|
| 1819 | sort2_(&d[1], &e[1], &f[1], n);
|
|---|
| 1820 | i__1 = *n;
|
|---|
| 1821 | for (i = 1; i <= i__1; ++i) {
|
|---|
| 1822 | j = e[i];
|
|---|
| 1823 | /* L440: */
|
|---|
| 1824 | f[j] = (real) i;
|
|---|
| 1825 | }
|
|---|
| 1826 | m = *n + 1;
|
|---|
| 1827 | i__1 = *n;
|
|---|
| 1828 | for (j = 1; j <= i__1; ++j) {
|
|---|
| 1829 | l = m - j;
|
|---|
| 1830 | k = e[l];
|
|---|
| 1831 | i = f[j];
|
|---|
| 1832 | e[i] = (real) k;
|
|---|
| 1833 | f[k] = (real) i;
|
|---|
| 1834 | t = d[j];
|
|---|
| 1835 | d[j] = d[k];
|
|---|
| 1836 | d[k] = t;
|
|---|
| 1837 | if (jl == 1) {
|
|---|
| 1838 | goto L450;
|
|---|
| 1839 | }
|
|---|
| 1840 | if (jr != 1) {
|
|---|
| 1841 | goto L480;
|
|---|
| 1842 | }
|
|---|
| 1843 | L450:
|
|---|
| 1844 | s = (double)0.;
|
|---|
| 1845 | i__2 = *mq;
|
|---|
| 1846 | for (i = 1; i <= i__2; ++i) {
|
|---|
| 1847 | t = q[i + k * q_dim1];
|
|---|
| 1848 | q[i + k * q_dim1] = q[i + j * q_dim1];
|
|---|
| 1849 | q[i + j * q_dim1] = t;
|
|---|
| 1850 | /* L460: */
|
|---|
| 1851 | s += t * t;
|
|---|
| 1852 | }
|
|---|
| 1853 | s = (double)1. / sqrt(s);
|
|---|
| 1854 | i__2 = *mq;
|
|---|
| 1855 | for (i = 1; i <= i__2; ++i) {
|
|---|
| 1856 | /* L470: */
|
|---|
| 1857 | q[i + j * q_dim1] = s * q[i + j * q_dim1];
|
|---|
| 1858 | }
|
|---|
| 1859 | L480:
|
|---|
| 1860 | if (jr == 2) {
|
|---|
| 1861 | goto L490;
|
|---|
| 1862 | }
|
|---|
| 1863 | if (jl != 2) {
|
|---|
| 1864 | goto L520;
|
|---|
| 1865 | }
|
|---|
| 1866 | L490:
|
|---|
| 1867 | s = (double)0.;
|
|---|
| 1868 | i__2 = *mp;
|
|---|
| 1869 | for (i = 1; i <= i__2; ++i) {
|
|---|
| 1870 | t = p[i + k * p_dim1];
|
|---|
| 1871 | p[i + k * p_dim1] = p[i + j * p_dim1];
|
|---|
| 1872 | p[i + j * p_dim1] = t;
|
|---|
| 1873 | /* L500: */
|
|---|
| 1874 | s += t * t;
|
|---|
| 1875 | }
|
|---|
| 1876 | s = (double)1. / sqrt(s);
|
|---|
| 1877 | i__2 = *mp;
|
|---|
| 1878 | for (i = 1; i <= i__2; ++i) {
|
|---|
| 1879 | /* L510: */
|
|---|
| 1880 | p[i + j * p_dim1] = s * p[i + j * p_dim1];
|
|---|
| 1881 | }
|
|---|
| 1882 | L520:
|
|---|
| 1883 | ;
|
|---|
| 1884 | }
|
|---|
| 1885 | e[1] = (real) (*n);
|
|---|
| 1886 | return 0;
|
|---|
| 1887 | L530:
|
|---|
| 1888 | k = *n - k + 1;
|
|---|
| 1889 | fprintf(stderr,"SINCE THE STOPPING CRITERION NOT SATISFIED\n");
|
|---|
| 1890 | fprintf(stderr,"AFTER %d ITERATIONS, WE STOP WHILE COMPUTING\n", ns);
|
|---|
| 1891 | fprintf(stderr,"EIGENVALUE NUMBER %d", k);
|
|---|
| 1892 | e[1] = (real) k;
|
|---|
| 1893 | return 0;
|
|---|
| 1894 | } /* singb_ */
|
|---|
| 1895 |
|
|---|
| 1896 | /* % */
|
|---|
| 1897 | static int
|
|---|
| 1898 | fgv_(double *x, double *y, double *s, double *p, double *q,
|
|---|
| 1899 | double *a, double *b)
|
|---|
| 1900 | {
|
|---|
| 1901 | /* System generated locals */
|
|---|
| 1902 | real r__1;
|
|---|
| 1903 |
|
|---|
| 1904 | /* Local variables */
|
|---|
| 1905 | static real c, r, t;
|
|---|
| 1906 |
|
|---|
| 1907 | if (fabs(*p) > fabs(*q)) {
|
|---|
| 1908 | goto L10;
|
|---|
| 1909 | }
|
|---|
| 1910 | if (*q == (double)0.) {
|
|---|
| 1911 | goto L110;
|
|---|
| 1912 | }
|
|---|
| 1913 | r = *a / *b;
|
|---|
| 1914 | *s = *p / *q;
|
|---|
| 1915 | t = fabs(r) * *s * *s;
|
|---|
| 1916 | if (t < (double)1.) {
|
|---|
| 1917 | goto L70;
|
|---|
| 1918 | }
|
|---|
| 1919 | t /= t + (double)1.;
|
|---|
| 1920 | r = *b / *a;
|
|---|
| 1921 | *s = *q / *p;
|
|---|
| 1922 | goto L20;
|
|---|
| 1923 | L10:
|
|---|
| 1924 | r = *b / *a;
|
|---|
| 1925 | *s = *q / *p;
|
|---|
| 1926 | t = fabs(r) * *s * *s;
|
|---|
| 1927 | if (t > (double)1.) {
|
|---|
| 1928 | goto L60;
|
|---|
| 1929 | }
|
|---|
| 1930 | t = (double)1. / (t + (double)1.);
|
|---|
| 1931 | L20:
|
|---|
| 1932 | r__1 = *a * t;
|
|---|
| 1933 | *a = r_sign(&r__1, p);
|
|---|
| 1934 | if (r_sign(&r, p) == r) {
|
|---|
| 1935 | goto L40;
|
|---|
| 1936 | }
|
|---|
| 1937 | *b = -(double)(r__1 = *b * t, fabs(r__1));
|
|---|
| 1938 | goto L50;
|
|---|
| 1939 | L40:
|
|---|
| 1940 | *b = (r__1 = *b * t, fabs(r__1));
|
|---|
| 1941 | L50:
|
|---|
| 1942 | *y = *s;
|
|---|
| 1943 | *x = fabs(r) * *s;
|
|---|
| 1944 | *s = (double)0.;
|
|---|
| 1945 | return 0;
|
|---|
| 1946 | L60:
|
|---|
| 1947 | t /= t + (double)1.;
|
|---|
| 1948 | r = *a / *b;
|
|---|
| 1949 | *s = *p / *q;
|
|---|
| 1950 | goto L80;
|
|---|
| 1951 | L70:
|
|---|
| 1952 | t = (double)1. / (t + (double)1.);
|
|---|
| 1953 | L80:
|
|---|
| 1954 | c = *a;
|
|---|
| 1955 | r__1 = *b * t;
|
|---|
| 1956 | *a = r_sign(&r__1, q);
|
|---|
| 1957 | if (r_sign(&r, q) == r) {
|
|---|
| 1958 | goto L90;
|
|---|
| 1959 | }
|
|---|
| 1960 | *b = -(double)(r__1 = c * t, fabs(r__1));
|
|---|
| 1961 | goto L100;
|
|---|
| 1962 | L90:
|
|---|
| 1963 | *b = (r__1 = c * t, fabs(r__1));
|
|---|
| 1964 | L100:
|
|---|
| 1965 | *y = *s;
|
|---|
| 1966 | *x = fabs(r) * *s;
|
|---|
| 1967 | *s = (double)1.;
|
|---|
| 1968 | return 0;
|
|---|
| 1969 | L110:
|
|---|
| 1970 | *x = (double)0.;
|
|---|
| 1971 | *y = (double)0.;
|
|---|
| 1972 | *s = (double)0.;
|
|---|
| 1973 | return 0;
|
|---|
| 1974 | } /* fgv_ */
|
|---|
| 1975 |
|
|---|
| 1976 | /* % */
|
|---|
| 1977 | static int
|
|---|
| 1978 | sng0_(double *q, int *lq, int *m, double *p, int *lp, int *n,
|
|---|
| 1979 | int *l, int *j, int *k, double *x, double *y)
|
|---|
| 1980 | {
|
|---|
| 1981 | /* System generated locals */
|
|---|
| 1982 | integer q_dim1, q_offset, p_dim1, p_offset, i__1;
|
|---|
| 1983 |
|
|---|
| 1984 | /* Local variables */
|
|---|
| 1985 | static integer i;
|
|---|
| 1986 | static real s, t;
|
|---|
| 1987 |
|
|---|
| 1988 | /* Parameter adjustments */
|
|---|
| 1989 | p_dim1 = *lp;
|
|---|
| 1990 | p_offset = p_dim1 + 1;
|
|---|
| 1991 | p -= p_offset;
|
|---|
| 1992 | q_dim1 = *lq;
|
|---|
| 1993 | q_offset = q_dim1 + 1;
|
|---|
| 1994 | q -= q_offset;
|
|---|
| 1995 |
|
|---|
| 1996 | /* Function Body */
|
|---|
| 1997 | switch ((int)*l) {
|
|---|
| 1998 | case 1: goto L10;
|
|---|
| 1999 | case 2: goto L30;
|
|---|
| 2000 | case 3: goto L50;
|
|---|
| 2001 | }
|
|---|
| 2002 | L10:
|
|---|
| 2003 | i__1 = *m;
|
|---|
| 2004 | for (i = 1; i <= i__1; ++i) {
|
|---|
| 2005 | t = q[i + *j * q_dim1];
|
|---|
| 2006 | s = q[i + *k * q_dim1];
|
|---|
| 2007 | q[i + *j * q_dim1] = t + *x * s;
|
|---|
| 2008 | /* L20: */
|
|---|
| 2009 | q[i + *k * q_dim1] = s - *y * t;
|
|---|
| 2010 | }
|
|---|
| 2011 | return 0;
|
|---|
| 2012 | L30:
|
|---|
| 2013 | i__1 = *n;
|
|---|
| 2014 | for (i = 1; i <= i__1; ++i) {
|
|---|
| 2015 | t = p[i + *j * p_dim1];
|
|---|
| 2016 | s = p[i + *k * p_dim1];
|
|---|
| 2017 | p[i + *j * p_dim1] = t + *x * s;
|
|---|
| 2018 | /* L40: */
|
|---|
| 2019 | p[i + *k * p_dim1] = s - *y * t;
|
|---|
| 2020 | }
|
|---|
| 2021 | L50:
|
|---|
| 2022 | return 0;
|
|---|
| 2023 | } /* sng0_ */
|
|---|
| 2024 |
|
|---|
| 2025 | /* % */
|
|---|
| 2026 | static int
|
|---|
| 2027 | sng1_(double *q, int *lq, int *m, double *p,
|
|---|
| 2028 | int *lp, int *n, int *l, int *j, int *k, double *x, double *y)
|
|---|
| 2029 | {
|
|---|
| 2030 | /* System generated locals */
|
|---|
| 2031 | integer q_dim1, q_offset, p_dim1, p_offset, i__1;
|
|---|
| 2032 |
|
|---|
| 2033 | /* Local variables */
|
|---|
| 2034 | static integer i;
|
|---|
| 2035 | static real s, t;
|
|---|
| 2036 |
|
|---|
| 2037 | /* Parameter adjustments */
|
|---|
| 2038 | p_dim1 = *lp;
|
|---|
| 2039 | p_offset = p_dim1 + 1;
|
|---|
| 2040 | p -= p_offset;
|
|---|
| 2041 | q_dim1 = *lq;
|
|---|
| 2042 | q_offset = q_dim1 + 1;
|
|---|
| 2043 | q -= q_offset;
|
|---|
| 2044 |
|
|---|
| 2045 | /* Function Body */
|
|---|
| 2046 | switch ((int)*l) {
|
|---|
| 2047 | case 1: goto L10;
|
|---|
| 2048 | case 2: goto L30;
|
|---|
| 2049 | case 3: goto L50;
|
|---|
| 2050 | }
|
|---|
| 2051 | L10:
|
|---|
| 2052 | i__1 = *m;
|
|---|
| 2053 | for (i = 1; i <= i__1; ++i) {
|
|---|
| 2054 | t = q[i + *j * q_dim1];
|
|---|
| 2055 | s = q[i + *k * q_dim1];
|
|---|
| 2056 | q[i + *j * q_dim1] = *x * t + s;
|
|---|
| 2057 | /* L20: */
|
|---|
| 2058 | q[i + *k * q_dim1] = *y * s - t;
|
|---|
| 2059 | }
|
|---|
| 2060 | return 0;
|
|---|
| 2061 | L30:
|
|---|
| 2062 | i__1 = *n;
|
|---|
| 2063 | for (i = 1; i <= i__1; ++i) {
|
|---|
| 2064 | t = p[i + *j * p_dim1];
|
|---|
| 2065 | s = p[i + *k * p_dim1];
|
|---|
| 2066 | p[i + *j * p_dim1] = *x * t + s;
|
|---|
| 2067 | /* L40: */
|
|---|
| 2068 | p[i + *k * p_dim1] = *y * s - t;
|
|---|
| 2069 | }
|
|---|
| 2070 | L50:
|
|---|
| 2071 | return 0;
|
|---|
| 2072 | } /* sng1_ */
|
|---|
| 2073 |
|
|---|
| 2074 | /* % */
|
|---|
| 2075 | static int
|
|---|
| 2076 | sft_(double *s, double *a, double *b, double *c,
|
|---|
| 2077 | double *d, double *e2, double *e1, double *e0, double *f2, double *f1)
|
|---|
| 2078 | {
|
|---|
| 2079 | static real w, x, y, z, g0, g1, g2, h1, h2;
|
|---|
| 2080 |
|
|---|
| 2081 | g0 = fabs(*e0);
|
|---|
| 2082 | g1 = fabs(*e1);
|
|---|
| 2083 | g2 = fabs(*e2);
|
|---|
| 2084 | h1 = fabs(*f1);
|
|---|
| 2085 | h2 = fabs(*f2);
|
|---|
| 2086 | w = *a * g2 * (*a * h2) + *c * g1 * (*c * h2);
|
|---|
| 2087 | x = *b * g1 * (*b * h1) + *d * g0 * (*d * h1);
|
|---|
| 2088 | y = *b * g1 * (*c * h1);
|
|---|
| 2089 | z = *b * g1 * (*c * h2);
|
|---|
| 2090 | eig3_(s, s, &x, &w, &y, &z);
|
|---|
| 2091 | return 0;
|
|---|
| 2092 | } /* sft_ */
|
|---|
| 2093 |
|
|---|
| 2094 | /* % */
|
|---|
| 2095 | static int
|
|---|
| 2096 | scl_(double *d, double *u, int *n, double *q,
|
|---|
| 2097 | int *lq, int *mq, double *p, int *lp, int *mp,
|
|---|
| 2098 | double *e, double *f, double *b,
|
|---|
| 2099 | int *j, int *k, int *jl,
|
|---|
| 2100 | int *jr)
|
|---|
| 2101 | {
|
|---|
| 2102 | /* System generated locals */
|
|---|
| 2103 | integer p_dim1, p_offset, q_dim1, q_offset, i__1, i__2;
|
|---|
| 2104 | real r__1, r__2;
|
|---|
| 2105 |
|
|---|
| 2106 | /* Local variables */
|
|---|
| 2107 | static integer h, i, l, m;
|
|---|
| 2108 | static real r, s, t, v;
|
|---|
| 2109 |
|
|---|
| 2110 | /* Parameter adjustments */
|
|---|
| 2111 | --f;
|
|---|
| 2112 | --e;
|
|---|
| 2113 | p_dim1 = *lp;
|
|---|
| 2114 | p_offset = p_dim1 + 1;
|
|---|
| 2115 | p -= p_offset;
|
|---|
| 2116 | q_dim1 = *lq;
|
|---|
| 2117 | q_offset = q_dim1 + 1;
|
|---|
| 2118 | q -= q_offset;
|
|---|
| 2119 | --u;
|
|---|
| 2120 | --d;
|
|---|
| 2121 |
|
|---|
| 2122 | /* Function Body */
|
|---|
| 2123 | t = (double)1.;
|
|---|
| 2124 | i__1 = *k;
|
|---|
| 2125 | for (i = *j; i <= i__1; ++i) {
|
|---|
| 2126 | if ((r__1 = e[i], fabs(r__1)) < t) {
|
|---|
| 2127 | t = (r__2 = e[i], fabs(r__2));
|
|---|
| 2128 | }
|
|---|
| 2129 | /* L10: */
|
|---|
| 2130 | if ((r__1 = f[i], fabs(r__1)) < t) {
|
|---|
| 2131 | t = (r__2 = f[i], fabs(r__2));
|
|---|
| 2132 | }
|
|---|
| 2133 | }
|
|---|
| 2134 | if (t > *b) {
|
|---|
| 2135 | return 0;
|
|---|
| 2136 | }
|
|---|
| 2137 | /* ---------------------------- */
|
|---|
| 2138 | /* |*** RESCALE THE MATRIX ***| */
|
|---|
| 2139 | /* ---------------------------- */
|
|---|
| 2140 | r = e[*j];
|
|---|
| 2141 | r__1 = sqrt((fabs(r)));
|
|---|
| 2142 | r = r_sign(&r__1, &r);
|
|---|
| 2143 | e[*j] = (double)1.;
|
|---|
| 2144 | s = f[*j];
|
|---|
| 2145 | r__1 = sqrt((fabs(s)));
|
|---|
| 2146 | s = r_sign(&r__1, &s);
|
|---|
| 2147 | f[*j] = (double)1.;
|
|---|
| 2148 | d[*j] = r * d[*j] * s;
|
|---|
| 2149 | t = r;
|
|---|
| 2150 | if (*jl == 1) {
|
|---|
| 2151 | goto L20;
|
|---|
| 2152 | }
|
|---|
| 2153 | if (*jr != 1) {
|
|---|
| 2154 | goto L40;
|
|---|
| 2155 | }
|
|---|
| 2156 | t = s;
|
|---|
| 2157 | L20:
|
|---|
| 2158 | i__1 = *mq;
|
|---|
| 2159 | for (i = 1; i <= i__1; ++i) {
|
|---|
| 2160 | /* L30: */
|
|---|
| 2161 | q[i + *j * q_dim1] *= t;
|
|---|
| 2162 | }
|
|---|
| 2163 | L40:
|
|---|
| 2164 | t = s;
|
|---|
| 2165 | if (*jr == 2) {
|
|---|
| 2166 | goto L50;
|
|---|
| 2167 | }
|
|---|
| 2168 | if (*jl != 2) {
|
|---|
| 2169 | goto L70;
|
|---|
| 2170 | }
|
|---|
| 2171 | t = r;
|
|---|
| 2172 | L50:
|
|---|
| 2173 | i__1 = *mp;
|
|---|
| 2174 | for (i = 1; i <= i__1; ++i) {
|
|---|
| 2175 | /* L60: */
|
|---|
| 2176 | p[i + *j * p_dim1] *= t;
|
|---|
| 2177 | }
|
|---|
| 2178 | L70:
|
|---|
| 2179 | l = *j + 1;
|
|---|
| 2180 | h = *j;
|
|---|
| 2181 | i__1 = *k;
|
|---|
| 2182 | for (m = l; m <= i__1; ++m) {
|
|---|
| 2183 | t = e[m];
|
|---|
| 2184 | r__1 = sqrt((fabs(t)));
|
|---|
| 2185 | t = r_sign(&r__1, &t);
|
|---|
| 2186 | e[m] = (double)1.;
|
|---|
| 2187 | s = f[m];
|
|---|
| 2188 | r__1 = sqrt((fabs(s)));
|
|---|
| 2189 | s = r_sign(&r__1, &s);
|
|---|
| 2190 | f[m] = (double)1.;
|
|---|
| 2191 | d[m] = s * d[m] * t;
|
|---|
| 2192 | u[h] = r * u[h] * s;
|
|---|
| 2193 | h = m;
|
|---|
| 2194 | r = t;
|
|---|
| 2195 | v = t;
|
|---|
| 2196 | if (*jl == 1) {
|
|---|
| 2197 | goto L80;
|
|---|
| 2198 | }
|
|---|
| 2199 | if (*jr != 1) {
|
|---|
| 2200 | goto L100;
|
|---|
| 2201 | }
|
|---|
| 2202 | v = s;
|
|---|
| 2203 | L80:
|
|---|
| 2204 | i__2 = *mq;
|
|---|
| 2205 | for (i = 1; i <= i__2; ++i) {
|
|---|
| 2206 | /* L90: */
|
|---|
| 2207 | q[i + m * q_dim1] *= v;
|
|---|
| 2208 | }
|
|---|
| 2209 | L100:
|
|---|
| 2210 | v = s;
|
|---|
| 2211 | if (*jr == 2) {
|
|---|
| 2212 | goto L110;
|
|---|
| 2213 | }
|
|---|
| 2214 | if (*jl != 2) {
|
|---|
| 2215 | goto L130;
|
|---|
| 2216 | }
|
|---|
| 2217 | v = t;
|
|---|
| 2218 | L110:
|
|---|
| 2219 | i__2 = *mp;
|
|---|
| 2220 | for (i = 1; i <= i__2; ++i) {
|
|---|
| 2221 | /* L120: */
|
|---|
| 2222 | p[i + m * p_dim1] *= v;
|
|---|
| 2223 | }
|
|---|
| 2224 | L130:
|
|---|
| 2225 | ;
|
|---|
| 2226 | }
|
|---|
| 2227 | return 0;
|
|---|
| 2228 | } /* scl_ */
|
|---|
| 2229 |
|
|---|
| 2230 | static int
|
|---|
| 2231 | eig3_(double *ea, double *eb, double *a, double *b, double *y, double *z)
|
|---|
| 2232 | {
|
|---|
| 2233 | /* Local variables */
|
|---|
| 2234 | static real c, s, t;
|
|---|
| 2235 |
|
|---|
| 2236 | t = (*b - *a) * (double).5;
|
|---|
| 2237 | c = sqrt((fabs(*y))) * sqrt((fabs(*z)));
|
|---|
| 2238 | if (fabs(t) > fabs(c)) {
|
|---|
| 2239 | goto L30;
|
|---|
| 2240 | }
|
|---|
| 2241 | if (c != (double)0.) {
|
|---|
| 2242 | goto L10;
|
|---|
| 2243 | }
|
|---|
| 2244 | *ea = *a;
|
|---|
| 2245 | *eb = *b;
|
|---|
| 2246 | return 0;
|
|---|
| 2247 | L10:
|
|---|
| 2248 | t /= fabs(c);
|
|---|
| 2249 | s = fabs(c) / (fabs(t) + sqrt(t * t + (double)1.));
|
|---|
| 2250 | if (t < (double)0.) {
|
|---|
| 2251 | goto L20;
|
|---|
| 2252 | }
|
|---|
| 2253 | *ea = *a - s;
|
|---|
| 2254 | *eb = *b + s;
|
|---|
| 2255 | return 0;
|
|---|
| 2256 | L20:
|
|---|
| 2257 | *ea = *a + s;
|
|---|
| 2258 | *eb = *b - s;
|
|---|
| 2259 | return 0;
|
|---|
| 2260 | L30:
|
|---|
| 2261 | t = fabs(c) / t;
|
|---|
| 2262 | s = t * fabs(c) / (sqrt(t * t + (double)1.) + (double)1.);
|
|---|
| 2263 | *ea = *a - s;
|
|---|
| 2264 | *eb = *b + s;
|
|---|
| 2265 | return 0;
|
|---|
| 2266 | } /* eig3_ */
|
|---|
| 2267 |
|
|---|
| 2268 | /* ________________________________________________________ */
|
|---|
| 2269 | /* | | */
|
|---|
| 2270 | /* | SORT AN ARRAY IN INCREASING ORDER | */
|
|---|
| 2271 | /* | | */
|
|---|
| 2272 | /* | INPUT: | */
|
|---|
| 2273 | /* | | */
|
|---|
| 2274 | /* | X --ARRAY OF NUMBERS | */
|
|---|
| 2275 | /* | | */
|
|---|
| 2276 | /* | W --WORKING ARRAY (LENGTH AT LEAST N) | */
|
|---|
| 2277 | /* | | */
|
|---|
| 2278 | /* | N --NUMBER OF ARRAY ELEMENTS TO SORT | */
|
|---|
| 2279 | /* | | */
|
|---|
| 2280 | /* | OUTPUT: | */
|
|---|
| 2281 | /* | | */
|
|---|
| 2282 | /* | X --ORIGINAL ARRAY | */
|
|---|
| 2283 | /* | | */
|
|---|
| 2284 | /* | Y --INDICES OF X GIVING INCREASING ORDER | */
|
|---|
| 2285 | /* |________________________________________________________| */
|
|---|
| 2286 |
|
|---|
| 2287 | static int
|
|---|
| 2288 | sort2_(double *x, double *y, double *w, int *n)
|
|---|
| 2289 | {
|
|---|
| 2290 | static integer i, j, k, l, m, p, q;
|
|---|
| 2291 | static real s, t;
|
|---|
| 2292 |
|
|---|
| 2293 | /* Parameter adjustments */
|
|---|
| 2294 | --w;
|
|---|
| 2295 | --y;
|
|---|
| 2296 | --x;
|
|---|
| 2297 |
|
|---|
| 2298 | /* Function Body */
|
|---|
| 2299 | i = 1;
|
|---|
| 2300 | L10:
|
|---|
| 2301 | k = i;
|
|---|
| 2302 | L20:
|
|---|
| 2303 | j = i;
|
|---|
| 2304 | y[i] = (real) i;
|
|---|
| 2305 | ++i;
|
|---|
| 2306 | if (j == *n) {
|
|---|
| 2307 | goto L30;
|
|---|
| 2308 | }
|
|---|
| 2309 | if (x[i] >= x[j]) {
|
|---|
| 2310 | goto L20;
|
|---|
| 2311 | }
|
|---|
| 2312 | w[k] = (real) i;
|
|---|
| 2313 | goto L10;
|
|---|
| 2314 | L30:
|
|---|
| 2315 | if (k == 1) {
|
|---|
| 2316 | return 0;
|
|---|
| 2317 | }
|
|---|
| 2318 | w[k] = (real) (*n + 1);
|
|---|
| 2319 | L40:
|
|---|
| 2320 | m = 1;
|
|---|
| 2321 | l = 1;
|
|---|
| 2322 | L50:
|
|---|
| 2323 | i = l;
|
|---|
| 2324 | if (i > *n) {
|
|---|
| 2325 | goto L120;
|
|---|
| 2326 | }
|
|---|
| 2327 | p = y[i];
|
|---|
| 2328 | s = x[p];
|
|---|
| 2329 | j = w[i];
|
|---|
| 2330 | k = j;
|
|---|
| 2331 | if (j > *n) {
|
|---|
| 2332 | goto L100;
|
|---|
| 2333 | }
|
|---|
| 2334 | q = y[j];
|
|---|
| 2335 | t = x[q];
|
|---|
| 2336 | l = w[j];
|
|---|
| 2337 | y[i] = (real) l;
|
|---|
| 2338 | L60:
|
|---|
| 2339 | if (s > t) {
|
|---|
| 2340 | goto L70;
|
|---|
| 2341 | }
|
|---|
| 2342 | w[m] = (real) p;
|
|---|
| 2343 | ++m;
|
|---|
| 2344 | ++i;
|
|---|
| 2345 | if (i == k) {
|
|---|
| 2346 | goto L80;
|
|---|
| 2347 | }
|
|---|
| 2348 | p = y[i];
|
|---|
| 2349 | s = x[p];
|
|---|
| 2350 | goto L60;
|
|---|
| 2351 | L70:
|
|---|
| 2352 | w[m] = (real) q;
|
|---|
| 2353 | ++m;
|
|---|
| 2354 | ++j;
|
|---|
| 2355 | if (j == l) {
|
|---|
| 2356 | goto L110;
|
|---|
| 2357 | }
|
|---|
| 2358 | q = y[j];
|
|---|
| 2359 | t = x[q];
|
|---|
| 2360 | goto L60;
|
|---|
| 2361 | L80:
|
|---|
| 2362 | w[m] = (real) q;
|
|---|
| 2363 | k = m + l - j;
|
|---|
| 2364 | i = j - m;
|
|---|
| 2365 | L90:
|
|---|
| 2366 | ++m;
|
|---|
| 2367 | if (m == k) {
|
|---|
| 2368 | goto L50;
|
|---|
| 2369 | }
|
|---|
| 2370 | w[m] = y[m + i];
|
|---|
| 2371 | goto L90;
|
|---|
| 2372 | L100:
|
|---|
| 2373 | y[i] = (real) j;
|
|---|
| 2374 | l = j;
|
|---|
| 2375 | L110:
|
|---|
| 2376 | w[m] = (real) p;
|
|---|
| 2377 | k = m + k - i;
|
|---|
| 2378 | i -= m;
|
|---|
| 2379 | goto L90;
|
|---|
| 2380 | L120:
|
|---|
| 2381 | i = 1;
|
|---|
| 2382 | L130:
|
|---|
| 2383 | k = i;
|
|---|
| 2384 | j = y[i];
|
|---|
| 2385 | L140:
|
|---|
| 2386 | y[i] = w[i];
|
|---|
| 2387 | ++i;
|
|---|
| 2388 | if (i < j) {
|
|---|
| 2389 | goto L140;
|
|---|
| 2390 | }
|
|---|
| 2391 | w[k] = (real) i;
|
|---|
| 2392 | if (i <= *n) {
|
|---|
| 2393 | goto L130;
|
|---|
| 2394 | }
|
|---|
| 2395 | if (k > 1) {
|
|---|
| 2396 | goto L40;
|
|---|
| 2397 | }
|
|---|
| 2398 | return 0;
|
|---|
| 2399 | } /* sort2_ */
|
|---|
| 2400 |
|
|---|
