1
2 /*! @file slaqgs.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 SLAQGE
12 * </pre>
13 */
14 /*
15 * File name: slaqgs.c
16 * History: Modified from LAPACK routine SLAQGE
17 */
18 #include <math.h>
19 #include "slu_sdefs.h"
20
21 /*! \brief
22 *
23 * <pre>
24 * Purpose
25 * =======
26 *
27 * SLAQGS 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_S; Mtype = GE.
39 *
40 * R (input) float*, dimension (A->nrow)
41 * The row scale factors for A.
42 *
43 * C (input) float*, dimension (A->ncol)
44 * The column scale factors for A.
45 *
46 * ROWCND (input) float
47 * Ratio of the smallest R(i) to the largest R(i).
48 *
49 * COLCND (input) float
50 * Ratio of the smallest C(i) to the largest C(i).
51 *
52 * AMAX (input) float
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
slaqgs(SuperMatrix * A,float * r,float * c,float rowcnd,float colcnd,float amax,char * equed)82 slaqgs(SuperMatrix *A, float *r, float *c,
83 float rowcnd, float colcnd, float amax, char *equed)
84 {
85
86
87 #define THRESH (0.1)
88
89 /* Local variables */
90 NCformat *Astore;
91 float *Aval;
92 int i, j, irow;
93 float large, small, cj;
94
95
96 /* Quick return if possible */
97 if (A->nrow <= 0 || A->ncol <= 0) {
98 *(unsigned char *)equed = 'N';
99 return;
100 }
101
102 Astore = A->Store;
103 Aval = Astore->nzval;
104
105 /* Initialize LARGE and SMALL. */
106 small = slamch_("Safe minimum") / slamch_("Precision");
107 large = 1. / small;
108
109 if (rowcnd >= THRESH && amax >= small && amax <= large) {
110 if (colcnd >= THRESH)
111 *(unsigned char *)equed = 'N';
112 else {
113 /* Column scaling */
114 for (j = 0; j < A->ncol; ++j) {
115 cj = c[j];
116 for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
117 Aval[i] *= cj;
118 }
119 }
120 *(unsigned char *)equed = 'C';
121 }
122 } else if (colcnd >= THRESH) {
123 /* Row scaling, no column scaling */
124 for (j = 0; j < A->ncol; ++j)
125 for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
126 irow = Astore->rowind[i];
127 Aval[i] *= r[irow];
128 }
129 *(unsigned char *)equed = 'R';
130 } else {
131 /* Row and column scaling */
132 for (j = 0; j < A->ncol; ++j) {
133 cj = c[j];
134 for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
135 irow = Astore->rowind[i];
136 Aval[i] *= cj * r[irow];
137 }
138 }
139 *(unsigned char *)equed = 'B';
140 }
141
142 return;
143
144 } /* slaqgs */
145
146