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dlaqge.c

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00001 /* DLAQGE.F -- translated by f2c (version 19941215).
00002    You must link the resulting object file with the libraries:
00003         -lf2c -lm   (in that order)
00004 */
00005 
00006 #include "f2c.h"
00007 
00008 /* Subroutine */ int dlaqge_(m, n, a, lda, r, c, rowcnd, colcnd, amax, equed, 
00009         equed_len)
00010 integer *m, *n;
00011 doublereal *a;
00012 integer *lda;
00013 doublereal *r, *c, *rowcnd, *colcnd, *amax;
00014 char *equed;
00015 ftnlen equed_len;
00016 {
00017     /* System generated locals */
00018     integer a_dim1, a_offset, i__1, i__2;
00019 
00020     /* Local variables */
00021     static integer i, j;
00022     static doublereal large, small, cj;
00023     extern doublereal dlamch_();
00024 
00025 
00026 /*  -- LAPACK auxiliary routine (version 1.1) -- */
00027 /*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
00028 /*     Courant Institute, Argonne National Lab, and Rice University */
00029 /*     February 29, 1992 */
00030 
00031 /*     .. Scalar Arguments .. */
00032 /*     .. */
00033 /*     .. Array Arguments .. */
00034 /*     .. */
00035 
00036 /*  Purpose */
00037 /*  ======= */
00038 
00039 /*  DLAQGE equilibrates a general M by N matrix A using the row and */
00040 /*  scaling factors in the vectors R and C. */
00041 
00042 /*  Arguments */
00043 /*  ========= */
00044 
00045 /*  M       (input) INTEGER */
00046 /*          The number of rows of the matrix A.  M >= 0. */
00047 
00048 /*  N       (input) INTEGER */
00049 /*          The number of columns of the matrix A.  N >= 0. */
00050 
00051 /*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
00052 /*          On entry, the M by N matrix A. */
00053 /*          On exit, the equilibrated matrix.  See EQUED for the form of 
00054 */
00055 /*          the equilibrated matrix. */
00056 
00057 /*  LDA     (input) INTEGER */
00058 /*          The leading dimension of the array A.  LDA >= max(M,1). */
00059 
00060 /*  R       (input) DOUBLE PRECISION array, dimension (M) */
00061 /*          The row scale factors for A. */
00062 
00063 /*  C       (input) DOUBLE PRECISION array, dimension (N) */
00064 /*          The column scale factors for A. */
00065 
00066 /*  ROWCND  (input) DOUBLE PRECISION */
00067 /*          Ratio of the smallest R(i) to the largest R(i). */
00068 
00069 /*  COLCND  (input) DOUBLE PRECISION */
00070 /*          Ratio of the smallest C(i) to the largest C(i). */
00071 
00072 /*  AMAX    (input) DOUBLE PRECISION */
00073 /*          Absolute value of largest matrix entry. */
00074 
00075 /*  EQUED   (output) CHARACTER*1 */
00076 /*          Specifies the form of equilibration that was done. */
00077 /*          = 'N':  No equilibration */
00078 /*          = 'R':  Row equilibration, i.e., A has been premultiplied by 
00079 */
00080 /*                  diag(R). */
00081 /*          = 'C':  Column equilibration, i.e., A has been postmultiplied 
00082 */
00083 /*                  by diag(C). */
00084 /*          = 'B':  Both row and column equilibration, i.e., A has been */
00085 /*                  replaced by diag(R) * A * diag(C). */
00086 
00087 /*  Internal Parameters */
00088 /*  =================== */
00089 
00090 /*  THRESH is a threshold value used to decide if row or column scaling */
00091 /*  should be done based on the ratio of the row or column scaling */
00092 /*  factors.  If ROWCND < THRESH, row scaling is done, and if */
00093 /*  COLCND < THRESH, column scaling is done. */
00094 
00095 /*  LARGE and SMALL are threshold values used to decide if row scaling */
00096 /*  should be done based on the absolute size of the largest matrix */
00097 /*  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done. */
00098 
00099 /*  ===================================================================== 
00100 */
00101 
00102 /*     .. Parameters .. */
00103 /*     .. */
00104 /*     .. Local Scalars .. */
00105 /*     .. */
00106 /*     .. External Functions .. */
00107 /*     .. */
00108 /*     .. Executable Statements .. */
00109 
00110 /*     Quick return if possible */
00111 
00112     /* Parameter adjustments */
00113     a_dim1 = *lda;
00114     a_offset = a_dim1 + 1;
00115     a -= a_offset;
00116     --r;
00117     --c;
00118 
00119     /* Function Body */
00120     if (*m <= 0 || *n <= 0) {
00121         *(unsigned char *)equed = 'N';
00122         return 0;
00123     }
00124 
00125 /*     Initialize LARGE and SMALL. */
00126 
00127     small = dlamch_("Safe minimum", 12L) / dlamch_("Precision", 9L);
00128     large = 1. / small;
00129 
00130     if (*rowcnd >= .1 && *amax >= small && *amax <= large) {
00131 
00132 /*        No row scaling */
00133 
00134         if (*colcnd >= .1) {
00135 
00136 /*           No column scaling */
00137 
00138             *(unsigned char *)equed = 'N';
00139         } else {
00140 
00141 /*           Column scaling */
00142 
00143             i__1 = *n;
00144             for (j = 1; j <= i__1; ++j) {
00145                 cj = c[j];
00146                 i__2 = *m;
00147                 for (i = 1; i <= i__2; ++i) {
00148                     a[i + j * a_dim1] = cj * a[i + j * a_dim1];
00149 /* L10: */
00150                 }
00151 /* L20: */
00152             }
00153             *(unsigned char *)equed = 'C';
00154         }
00155     } else if (*colcnd >= .1) {
00156 
00157 /*        Row scaling, no column scaling */
00158 
00159         i__1 = *n;
00160         for (j = 1; j <= i__1; ++j) {
00161             i__2 = *m;
00162             for (i = 1; i <= i__2; ++i) {
00163                 a[i + j * a_dim1] = r[i] * a[i + j * a_dim1];
00164 /* L30: */
00165             }
00166 /* L40: */
00167         }
00168         *(unsigned char *)equed = 'R';
00169     } else {
00170 
00171 /*        Row and column scaling */
00172 
00173         i__1 = *n;
00174         for (j = 1; j <= i__1; ++j) {
00175             cj = c[j];
00176             i__2 = *m;
00177             for (i = 1; i <= i__2; ++i) {
00178                 a[i + j * a_dim1] = cj * r[i] * a[i + j * a_dim1];
00179 /* L50: */
00180             }
00181 /* L60: */
00182         }
00183         *(unsigned char *)equed = 'B';
00184     }
00185 
00186     return 0;
00187 
00188 /*     End of DLAQGE */
00189 
00190 } /* dlaqge_ */
00191 

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