1
2 /*! @file zlaqgs.c
3 * \brief Equlibrates a general sprase matrix
4 *
5 * <pre>
6 * -- SuperLU routine (version 2.0) --
7 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
8 * and Lawrence Berkeley National Lab.
9 * November 15, 1997
10 *
11 * Modified from LAPACK routine ZLAQGE
12 * </pre>
13 */
14 /*
15 * File name: zlaqgs.c
16 * History: Modified from LAPACK routine ZLAQGE
17 */
18 #include <math.h>
19 #include "slu_zdefs.h"
20
21 /*! \brief
22 *
23 * <pre>
24 * Purpose
25 * =======
26 *
27 * ZLAQGS equilibrates a general sparse M by N matrix A using the row and
28 * scaling factors in the vectors R and C.
29 *
30 * See supermatrix.h for the definition of 'SuperMatrix' structure.
31 *
32 * Arguments
33 * =========
34 *
35 * A (input/output) SuperMatrix*
36 * On exit, the equilibrated matrix. See EQUED for the form of
37 * the equilibrated matrix. The type of A can be:
38 * Stype = NC; Dtype = SLU_Z; Mtype = GE.
39 *
40 * R (input) double*, dimension (A->nrow)
41 * The row scale factors for A.
42 *
43 * C (input) double*, dimension (A->ncol)
44 * The column scale factors for A.
45 *
46 * ROWCND (input) double
47 * Ratio of the smallest R(i) to the largest R(i).
48 *
49 * COLCND (input) double
50 * Ratio of the smallest C(i) to the largest C(i).
51 *
52 * AMAX (input) double
53 * Absolute value of largest matrix entry.
54 *
55 * EQUED (output) char*
56 * Specifies the form of equilibration that was done.
57 * = 'N': No equilibration
58 * = 'R': Row equilibration, i.e., A has been premultiplied by
59 * diag(R).
60 * = 'C': Column equilibration, i.e., A has been postmultiplied
61 * by diag(C).
62 * = 'B': Both row and column equilibration, i.e., A has been
63 * replaced by diag(R) * A * diag(C).
64 *
65 * Internal Parameters
66 * ===================
67 *
68 * THRESH is a threshold value used to decide if row or column scaling
69 * should be done based on the ratio of the row or column scaling
70 * factors. If ROWCND < THRESH, row scaling is done, and if
71 * COLCND < THRESH, column scaling is done.
72 *
73 * LARGE and SMALL are threshold values used to decide if row scaling
74 * should be done based on the absolute size of the largest matrix
75 * element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
76 *
77 * =====================================================================
78 * </pre>
79 */
80
81 void
zlaqgs(SuperMatrix * A,double * r,double * c,double rowcnd,double colcnd,double amax,char * equed)82 zlaqgs(SuperMatrix *A, double *r, double *c,
83 double rowcnd, double colcnd, double amax, char *equed)
84 {
85
86
87 #define THRESH (0.1)
88
89 /* Local variables */
90 NCformat *Astore;
91 doublecomplex *Aval;
92 int i, j, irow;
93 double large, small, cj;
94 double temp;
95
96
97 /* Quick return if possible */
98 if (A->nrow <= 0 || A->ncol <= 0) {
99 *(unsigned char *)equed = 'N';
100 return;
101 }
102
103 Astore = A->Store;
104 Aval = Astore->nzval;
105
106 /* Initialize LARGE and SMALL. */
107 small = dlamch_("Safe minimum") / dlamch_("Precision");
108 large = 1. / small;
109
110 if (rowcnd >= THRESH && amax >= small && amax <= large) {
111 if (colcnd >= THRESH)
112 *(unsigned char *)equed = 'N';
113 else {
114 /* Column scaling */
115 for (j = 0; j < A->ncol; ++j) {
116 cj = c[j];
117 for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
118 zd_mult(&Aval[i], &Aval[i], cj);
119 }
120 }
121 *(unsigned char *)equed = 'C';
122 }
123 } else if (colcnd >= THRESH) {
124 /* Row scaling, no column scaling */
125 for (j = 0; j < A->ncol; ++j)
126 for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
127 irow = Astore->rowind[i];
128 zd_mult(&Aval[i], &Aval[i], r[irow]);
129 }
130 *(unsigned char *)equed = 'R';
131 } else {
132 /* Row and column scaling */
133 for (j = 0; j < A->ncol; ++j) {
134 cj = c[j];
135 for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
136 irow = Astore->rowind[i];
137 temp = cj * r[irow];
138 zd_mult(&Aval[i], &Aval[i], temp);
139 }
140 }
141 *(unsigned char *)equed = 'B';
142 }
143
144 return;
145
146 } /* zlaqgs */
147
148