razzaline/tahoma2d
1
0
Fork 0
Code Issues Pull requests Projects Releases 1 Packages Wiki Activity
tahoma2d/thirdparty/superlu/SuperLU_4.1/SRC/mc64ad.c
kusano 7d535a97dc Add 3rd party libraries
2016-03-24 01:31:57 +09:00

2641 lines
68 KiB
C
Raw Blame History

/* mc64ad.f -- translated by f2c (version 20100827).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "slu_ddefs.h"
#define abs(a) ((a) >= 0) ? (a) : -(a)
#define min(a,b) ((a) < (b)) ? (a) : (b)
/* Table of constant values */
static int_t c__1 = 1;
static int_t c__2 = 2;
/* CCCC COPYRIGHT (c) 1999 Council for the Central Laboratory of the */
/* CCCC Research Councils. All rights reserved. */
/* CCCC PACKAGE MC64A/AD */
/* CCCC AUTHORS Iain Duff (i.duff@rl.ac.uk) and Jacko Koster (jak@ii.uib.no) */
/* CCCC LAST UPDATE 20/09/99 */
/* CCCC */
/* *** Conditions on external use *** */
/* The user shall acknowledge the contribution of this */
/* package in any publication of material dependent upon the use of */
/* the package. The user shall use reasonable endeavours to notify */
/* the authors of the package of this publication. */
/* The user can modify this code but, at no time */
/* shall the right or title to all or any part of this package pass */
/* to the user. The user shall make available free of charge */
/* to the authors for any purpose all information relating to any */
/* alteration or addition made to this package for the purposes of */
/* extending the capabilities or enhancing the performance of this */
/* package. */
/* The user shall not pass this code directly to a third party without the */
/* express prior consent of the authors. Users wanting to licence their */
/* own copy of these routines should send email to hsl@aeat.co.uk */
/* None of the comments from the Copyright notice up to and including this */
/* one shall be removed or altered in any way. */
/* ********************************************************************** */
/* Subroutine */ int_t mc64id_(int_t *icntl)
{
int_t i__;
/* *** Copyright (c) 1999 Council for the Central Laboratory of the */
/* Research Councils *** */
/* *** Although every effort has been made to ensure robustness and *** */
/* *** reliability of the subroutines in this MC64 suite, we *** */
/* *** disclaim any liability arising through the use or misuse of *** */
/* *** any of the subroutines. *** */
/* *** Any problems? Contact ... */
/* Iain Duff (I.Duff@rl.ac.uk) or Jacko Koster (jak@ii.uib.no) *** */
/* Purpose */
/* ======= */
/* The components of the array ICNTL control the action of MC64A/AD. */
/* Default values for these are set in this subroutine. */
/* Parameters */
/* ========== */
/* Local variables */
/* ICNTL(1) has default value 6. */
/* It is the output stream for error messages. If it */
/* is negative, these messages will be suppressed. */
/* ICNTL(2) has default value 6. */
/* It is the output stream for warning messages. */
/* If it is negative, these messages are suppressed. */
/* ICNTL(3) has default value -1. */
/* It is the output stream for monitoring printing. */
/* If it is negative, these messages are suppressed. */
/* ICNTL(4) has default value 0. */
/* If left at the defaut value, the incoming data is checked for */
/* out-of-range indices and duplicates. Setting ICNTL(4) to any */
/* other will avoid the checks but is likely to cause problems */
/* later if out-of-range indices or duplicates are present. */
/* The user should only set ICNTL(4) non-zero, if the data is */
/* known to avoid these problems. */
/* ICNTL(5) to ICNTL(10) are not used by MC64A/AD but are set to */
/* zero in this routine. */
/* Initialization of the ICNTL array. */
/* Parameter adjustments */
--icntl;
/* Function Body */
icntl[1] = 6;
icntl[2] = 6;
icntl[3] = -1;
for (i__ = 4; i__ <= 10; ++i__) {
icntl[i__] = 0;
/* L10: */
}
return 0;
} /* mc64id_ */
/* ********************************************************************** */
/* Subroutine */ int_t mc64ad_(int_t *job, int_t *n, int_t *ne, int_t *
ip, int_t *irn, double *a, int_t *num, int_t *cperm,
int_t *liw, int_t *iw, int_t *ldw, double *dw, int_t *
icntl, int_t *info)
{
/* System generated locals */
int_t i__1, i__2;
double d__1, d__2;
/* Builtin functions */
double log(double);
/* Local variables */
int_t i__, j, k;
double fact, rinf;
extern /* Subroutine */ int_t mc21ad_(int_t *, int_t *, int_t *,
int_t *, int_t *, int_t *, int_t *, int_t *), mc64bd_(
int_t *, int_t *, int_t *, int_t *, double *, int_t
*, int_t *, int_t *, int_t *, int_t *, int_t *,
double *), mc64rd_(int_t *, int_t *, int_t *, int_t *,
double *), mc64sd_(int_t *, int_t *, int_t *, int_t *
, double *, int_t *, int_t *, int_t *, int_t *,
int_t *, int_t *, int_t *, int_t *, int_t *), mc64wd_(
int_t *, int_t *, int_t *, int_t *, double *, int_t
*, int_t *, int_t *, int_t *, int_t *, int_t *, int_t
*, double *, double *);
/* *** Copyright (c) 1999 Council for the Central Laboratory of the */
/* Research Councils *** */
/* *** Although every effort has been made to ensure robustness and *** */
/* *** reliability of the subroutines in this MC64 suite, we *** */
/* *** disclaim any liability arising through the use or misuse of *** */
/* *** any of the subroutines. *** */
/* *** Any problems? Contact ... */
/* Iain Duff (I.Duff@rl.ac.uk) or Jacko Koster (jak@ii.uib.no) *** */
/* Purpose */
/* ======= */
/* This subroutine attempts to find a column permutation for an NxN */
/* sparse matrix A = {a_ij} that makes the permuted matrix have N */
/* entries on its diagonal. */
/* If the matrix is structurally nonsingular, the subroutine optionally */
/* returns a column permutation that maximizes the smallest element */
/* on the diagonal, maximizes the sum of the diagonal entries, or */
/* maximizes the product of the diagonal entries of the permuted matrix. */
/* For the latter option, the subroutine also finds scaling factors */
/* that may be used to scale the matrix so that the nonzero diagonal */
/* entries of the permuted matrix are one in absolute value and all the */
/* off-diagonal entries are less than or equal to one in absolute value. */
/* The natural logarithms of the scaling factors u(i), i=1..N, for the */
/* rows and v(j), j=1..N, for the columns are returned so that the */
/* scaled matrix B = {b_ij} has entries b_ij = a_ij * EXP(u_i + v_j). */
/* Parameters */
/* ========== */
/* JOB is an INT_T variable which must be set by the user to */
/* control the action. It is not altered by the subroutine. */
/* Possible values for JOB are: */
/* 1 Compute a column permutation of the matrix so that the */
/* permuted matrix has as many entries on its diagonal as possible. */
/* The values on the diagonal are of arbitrary size. HSL subroutine */
/* MC21A/AD is used for this. See [1]. */
/* 2 Compute a column permutation of the matrix so that the smallest */
/* value on the diagonal of the permuted matrix is maximized. */
/* See [3]. */
/* 3 Compute a column permutation of the matrix so that the smallest */
/* value on the diagonal of the permuted matrix is maximized. */
/* The algorithm differs from the one used for JOB = 2 and may */
/* have quite a different performance. See [2]. */
/* 4 Compute a column permutation of the matrix so that the sum */
/* of the diagonal entries of the permuted matrix is maximized. */
/* See [3]. */
/* 5 Compute a column permutation of the matrix so that the product */
/* of the diagonal entries of the permuted matrix is maximized */
/* and vectors to scale the matrix so that the nonzero diagonal */
/* entries of the permuted matrix are one in absolute value and */
/* all the off-diagonal entries are less than or equal to one in */
/* absolute value. See [3]. */
/* Restriction: 1 <= JOB <= 5. */
/* N is an INT_T variable which must be set by the user to the */
/* order of the matrix A. It is not altered by the subroutine. */
/* Restriction: N >= 1. */
/* NE is an INT_T variable which must be set by the user to the */
/* number of entries in the matrix. It is not altered by the */
/* subroutine. */
/* Restriction: NE >= 1. */
/* IP is an INT_T array of length N+1. */
/* IP(J), J=1..N, must be set by the user to the position in array IRN */
/* of the first row index of an entry in column J. IP(N+1) must be set */
/* to NE+1. It is not altered by the subroutine. */
/* IRN is an INT_T array of length NE. */
/* IRN(K), K=1..NE, must be set by the user to hold the row indices of */
/* the entries of the matrix. Those belonging to column J must be */
/* stored contiguously in the positions IP(J)..IP(J+1)-1. The ordering */
/* of the row indices within each column is unimportant. Repeated */
/* entries are not allowed. The array IRN is not altered by the */
/* subroutine. */
/* A is a REAL (DOUBLE PRECISION in the D-version) array of length NE. */
/* The user must set A(K), K=1..NE, to the numerical value of the */
/* entry that corresponds to IRN(K). */
/* It is not used by the subroutine when JOB = 1. */
/* It is not altered by the subroutine. */
/* NUM is an INT_T variable that need not be set by the user. */
/* On successful exit, NUM will be the number of entries on the */
/* diagonal of the permuted matrix. */
/* If NUM < N, the matrix is structurally singular. */
/* CPERM is an INT_T array of length N that need not be set by the */
/* user. On successful exit, CPERM contains the column permutation. */
/* Column CPERM(J) of the original matrix is column J in the permuted */
/* matrix, J=1..N. */
/* LIW is an INT_T variable that must be set by the user to */
/* the dimension of array IW. It is not altered by the subroutine. */
/* Restriction: */
/* JOB = 1 : LIW >= 5N */
/* JOB = 2 : LIW >= 4N */
/* JOB = 3 : LIW >= 10N + NE */
/* JOB = 4 : LIW >= 5N */
/* JOB = 5 : LIW >= 5N */
/* IW is an INT_T array of length LIW that is used for workspace. */
/* LDW is an INT_T variable that must be set by the user to the */
/* dimension of array DW. It is not altered by the subroutine. */
/* Restriction: */
/* JOB = 1 : LDW is not used */
/* JOB = 2 : LDW >= N */
/* JOB = 3 : LDW >= NE */
/* JOB = 4 : LDW >= 2N + NE */
/* JOB = 5 : LDW >= 3N + NE */
/* DW is a REAL (DOUBLE PRECISION in the D-version) array of length LDW */
/* that is used for workspace. If JOB = 5, on return, */
/* DW(i) contains u_i, i=1..N, and DW(N+j) contains v_j, j=1..N. */
/* ICNTL is an INT_T array of length 10. Its components control the */
/* output of MC64A/AD and must be set by the user before calling */
/* MC64A/AD. They are not altered by the subroutine. */
/* ICNTL(1) must be set to specify the output stream for */
/* error messages. If ICNTL(1) < 0, messages are suppressed. */
/* The default value set by MC46I/ID is 6. */
/* ICNTL(2) must be set by the user to specify the output stream for */
/* warning messages. If ICNTL(2) < 0, messages are suppressed. */
/* The default value set by MC46I/ID is 6. */
/* ICNTL(3) must be set by the user to specify the output stream for */
/* diagnostic messages. If ICNTL(3) < 0, messages are suppressed. */
/* The default value set by MC46I/ID is -1. */
/* ICNTL(4) must be set by the user to a value other than 0 to avoid */
/* checking of the input data. */
/* The default value set by MC46I/ID is 0. */
/* INFO is an INT_T array of length 10 which need not be set by the */
/* user. INFO(1) is set non-negative to indicate success. A negative */
/* value is returned if an error occurred, a positive value if a */
/* warning occurred. INFO(2) holds further information on the error. */
/* On exit from the subroutine, INFO(1) will take one of the */
/* following values: */
/* 0 : successful entry (for structurally nonsingular matrix). */
/* +1 : successful entry (for structurally singular matrix). */
/* +2 : the returned scaling factors are large and may cause */
/* overflow when used to scale the matrix. */
/* (For JOB = 5 entry only.) */
/* -1 : JOB < 1 or JOB > 5. Value of JOB held in INFO(2). */
/* -2 : N < 1. Value of N held in INFO(2). */
/* -3 : NE < 1. Value of NE held in INFO(2). */
/* -4 : the defined length LIW violates the restriction on LIW. */
/* Value of LIW required given by INFO(2). */
/* -5 : the defined length LDW violates the restriction on LDW. */
/* Value of LDW required given by INFO(2). */
/* -6 : entries are found whose row indices are out of range. INFO(2) */
/* contains the index of a column in which such an entry is found. */
/* -7 : repeated entries are found. INFO(2) contains the index of a */
/* column in which such entries are found. */
/* INFO(3) to INFO(10) are not currently used and are set to zero by */
/* the routine. */
/* References: */
/* [1] I. S. Duff, (1981), */
/* "Algorithm 575. Permutations for a zero-free diagonal", */
/* ACM Trans. Math. Software 7(3), 387-390. */
/* [2] I. S. Duff and J. Koster, (1998), */
/* "The design and use of algorithms for permuting large */
/* entries to the diagonal of sparse matrices", */
/* SIAM J. Matrix Anal. Appl., vol. 20, no. 4, pp. 889-901. */
/* [3] I. S. Duff and J. Koster, (1999), */
/* "On algorithms for permuting large entries to the diagonal */
/* of sparse matrices", */
/* Technical Report RAL-TR-1999-030, RAL, Oxfordshire, England. */
/* Local variables and parameters */
/* External routines and functions */
/* EXTERNAL FD05AD */
/* DOUBLE PRECISION FD05AD */
/* Intrinsic functions */
/* Set RINF to largest positive real number (infinity) */
/* XSL RINF = FD05AD(5) */
/* Parameter adjustments */
--cperm;
--ip;
--a;
--irn;
--iw;
--dw;
--icntl;
--info;
/* Function Body */
rinf = dlamch_("Overflow");
/* Check value of JOB */
if (*job < 1 || *job > 5) {
info[1] = -1;
info[2] = *job;
if (icntl[1] >= 0) {
printf(" ****** Error in MC64A/AD. INFO(1) = %2d", info[1],
" because JOB = %d\n", *job);
}
goto L99;
}
/* Check value of N */
if (*n < 1) {
info[1] = -2;
info[2] = *n;
if (icntl[1] >= 0) {
printf(" ****** Error in MC64A/AD. INFO(1) = %2d", info[1],
" because N = %d\n", *job);
}
goto L99;
}
/* Check value of NE */
if (*ne < 1) {
info[1] = -3;
info[2] = *ne;
if (icntl[1] >= 0) {
printf(" ****** Error in MC64A/AD. INFO(1) = %2d", info[1],
" because NE = %d\n", *job);
}
goto L99;
}
/* Check LIW */
if (*job == 1) {
k = *n * 5;
}
if (*job == 2) {
k = *n << 2;
}
if (*job == 3) {
k = *n * 10 + *ne;
}
if (*job == 4) {
k = *n * 5;
}
if (*job == 5) {
k = *n * 5;
}
if (*liw < k) {
info[1] = -4;
info[2] = k;
if (icntl[1] >= 0) {
printf(" ****** Error in MC64A/AD. INFO(1) = %2d", info[1],
" LIW too small, must be at least %8d\n", k);
}
goto L99;
}
/* Check LDW */
/* If JOB = 1, do not check */
if (*job > 1) {
if (*job == 2) {
k = *n;
}
if (*job == 3) {
k = *ne;
}
if (*job == 4) {
k = (*n << 1) + *ne;
}
if (*job == 5) {
k = *n * 3 + *ne;
}
if (*ldw < k) {
info[1] = -5;
info[2] = k;
if (icntl[1] >= 0) {
printf(" ****** Error in MC64A/AD. INFO(1) = %2d", info[1],
" LDW too small, must be at least %8d\n", k);
}
goto L99;
}
}
if (icntl[4] == 0) {
/* Check row indices. Use IW(1:N) as workspace */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
iw[i__] = 0;
/* L3: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
i__ = irn[k];
/* Check for row indices that are out of range */
if (i__ < 1 || i__ > *n) {
info[1] = -6;
info[2] = j;
if (icntl[1] >= 0) {
printf(" ****** Error in MC64A/AD. INFO(1) = %2d",
info[1], " Column %8d", j,
" contains an entry with invalid row index %8d\n", i__);
}
goto L99;
}
/* Check for repeated row indices within a column */
if (iw[i__] == j) {
info[1] = -7;
info[2] = j;
if (icntl[1] >= 0) {
printf(" ****** Error in MC64A/AD. INFO(1) = %2d", info[1],
" Column %8d", j,
" contains two or more entries with row index %8d\n", i__);
}
goto L99;
} else {
iw[i__] = j;
}
/* L4: */
}
/* L6: */
}
}
/* Print diagnostics on input */
if (icntl[3] >= 0) {
printf(" ****** Input parameters for MC64A/AD: JOB = %8d,"
" N = %d, NE = %8d\n", *job, *n, *ne);
printf(" IP(1:N+1) = ");
for (j=1; j<=(*n+1); ++j) {
printf("%8d", ip[j]);
if (j%8 == 0) printf("\n");
}
printf("\n IRN(1:NE) = ");
for (j=1; j<=(*ne); ++j) {
printf("%8d", irn[j]);
if (j%8 == 0) printf("\n");
}
printf("\n");
if (*job > 1) {
printf(" A(1:NE) = ");
for (j=1; j<=(*ne); ++j) {
printf("%f14.4", a[j]);
if (j%4 == 0) printf("\n");
}
printf("\n");
}
}
/* Set components of INFO to zero */
for (i__ = 1; i__ <= 10; ++i__) {
info[i__] = 0;
/* L8: */
}
/* Compute maximum matching with MC21A/AD */
if (*job == 1) {
/* Put length of column J in IW(J) */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
iw[j] = ip[j + 1] - ip[j];
/* L10: */
}
/* IW(N+1:5N) is workspace */
#if 0
mc21ad_(n, &irn[1], ne, &ip[1], &iw[1], &cperm[1], num, &iw[*n+1]);
#else
printf(" ****** Warning from MC64A/AD. Need to link mc21ad.\n");
#endif
goto L90;
}
/* Compute bottleneck matching */
if (*job == 2) {
/* IW(1:5N), DW(1:N) are workspaces */
mc64bd_(n, ne, &ip[1], &irn[1], &a[1], &cperm[1], num, &iw[1], &iw[*n
+ 1], &iw[(*n << 1) + 1], &iw[*n * 3 + 1], &dw[1]);
goto L90;
}
/* Compute bottleneck matching */
if (*job == 3) {
/* Copy IRN(K) into IW(K), ABS(A(K)) into DW(K), K=1..NE */
i__1 = *ne;
for (k = 1; k <= i__1; ++k) {
iw[k] = irn[k];
dw[k] = (d__1 = a[k], abs(d__1));
/* L20: */
}
/* Sort entries in each column by decreasing value. */
mc64rd_(n, ne, &ip[1], &iw[1], &dw[1]);
/* IW(NE+1:NE+10N) is workspace */
mc64sd_(n, ne, &ip[1], &iw[1], &dw[1], &cperm[1], num, &iw[*ne + 1], &
iw[*ne + *n + 1], &iw[*ne + (*n << 1) + 1], &iw[*ne + *n * 3
+ 1], &iw[*ne + (*n << 2) + 1], &iw[*ne + *n * 5 + 1], &iw[*
ne + *n * 6 + 1]);
goto L90;
}
if (*job == 4) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
fact = 0.;
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
if ((d__1 = a[k], abs(d__1)) > fact) {
fact = (d__2 = a[k], abs(d__2));
}
/* L30: */
}
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
dw[(*n << 1) + k] = fact - (d__1 = a[k], abs(d__1));
/* L40: */
}
/* L50: */
}
/* B = DW(2N+1:2N+NE); IW(1:5N) and DW(1:2N) are workspaces */
mc64wd_(n, ne, &ip[1], &irn[1], &dw[(*n << 1) + 1], &cperm[1], num, &
iw[1], &iw[*n + 1], &iw[(*n << 1) + 1], &iw[*n * 3 + 1], &iw[(
*n << 2) + 1], &dw[1], &dw[*n + 1]);
goto L90;
}
if (*job == 5) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
fact = 0.;
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
dw[*n * 3 + k] = (d__1 = a[k], abs(d__1));
if (dw[*n * 3 + k] > fact) {
fact = dw[*n * 3 + k];
}
/* L60: */
}
dw[(*n << 1) + j] = fact;
if (fact != 0.) {
fact = log(fact);
} else {
fact = rinf / *n;
}
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
if (dw[*n * 3 + k] != 0.) {
dw[*n * 3 + k] = fact - log(dw[*n * 3 + k]);
} else {
dw[*n * 3 + k] = rinf / *n;
}
/* L70: */
}
/* L75: */
}
/* B = DW(3N+1:3N+NE); IW(1:5N) and DW(1:2N) are workspaces */
mc64wd_(n, ne, &ip[1], &irn[1], &dw[*n * 3 + 1], &cperm[1], num, &iw[
1], &iw[*n + 1], &iw[(*n << 1) + 1], &iw[*n * 3 + 1], &iw[(*n
<< 2) + 1], &dw[1], &dw[*n + 1]);
if (*num == *n) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (dw[(*n << 1) + j] != 0.) {
dw[*n + j] -= log(dw[(*n << 1) + j]);
} else {
dw[*n + j] = 0.;
}
/* L80: */
}
}
/* Check size of scaling factors */
fact = log(rinf) * .5f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (dw[j] < fact && dw[*n + j] < fact) {
goto L86;
}
info[1] = 2;
goto L90;
L86:
;
}
/* GO TO 90 */
}
L90:
if (info[1] == 0 && *num < *n) {
/* Matrix is structurally singular, return with warning */
info[1] = 1;
if (icntl[2] >= 0) {
printf(" ****** Warning from MC64A/AD. INFO(1) = %2d", info[1],
" The matrix is structurally singular.\n");
}
}
if (info[1] == 2) {
/* Scaling factors are large, return with warning */
if (icntl[2] >= 0) {
printf(" ****** Warning from MC64A/AD. INFO(1) = %2d\n", info[1],
" Some scaling factors may be too large.\n");
}
}
/* Print diagnostics on output */
if (icntl[3] >= 0) {
printf(" ****** Output parameters for MC64A/AD: INFO(1:2) = %8d%8d\n",
info[1], info[2]);
printf(" NUM = ", *num);
printf(" CPERM(1:N) = ");
for (j=1; j<=*n; ++j) {
printf("%8d", cperm[j]);
if (j%8 == 0) printf("\n");
}
if (*job == 5) {
printf("\n DW(1:N) = ");
for (j=1; j<=*n; ++j) {
printf("%11.3f", dw[j]);
if (j%5 == 0) printf("\n");
}
printf("\n DW(N+1:2N) = ");
for (j=1; j<=*n; ++j) {
printf("%11.3f", dw[*n+j]);
if (j%5 == 0) printf("\n");
}
printf("\n");
}
}
/* Return from subroutine. */
L99:
return 0;
} /* mc64ad_ */
/* ********************************************************************** */
/* Subroutine */ int_t mc64bd_(int_t *n, int_t *ne, int_t *ip, int_t *
irn, double *a, int_t *iperm, int_t *num, int_t *jperm,
int_t *pr, int_t *q, int_t *l, double *d__)
{
/* System generated locals */
int_t i__1, i__2, i__3;
double d__1, d__2, d__3;
/* Local variables */
int_t i__, j, k;
double a0;
int_t i0, q0;
double ai, di;
int_t ii, jj, kk;
double bv;
int_t up;
double dq0;
int_t kk1, kk2;
double csp;
int_t isp, jsp, low;
double dnew;
int_t jord, qlen, idum, jdum;
double rinf;
extern /* Subroutine */ int_t mc64dd_(int_t *, int_t *, int_t *,
double *, int_t *, int_t *), mc64ed_(int_t *, int_t *,
int_t *, double *, int_t *, int_t *), mc64fd_(int_t *
, int_t *, int_t *, int_t *, double *, int_t *, int_t *);
/* *** Copyright (c) 1999 Council for the Central Laboratory of the */
/* Research Councils *** */
/* *** Although every effort has been made to ensure robustness and *** */
/* *** reliability of the subroutines in this MC64 suite, we *** */
/* *** disclaim any liability arising through the use or misuse of *** */
/* *** any of the subroutines. *** */
/* *** Any problems? Contact ... */
/* Iain Duff (I.Duff@rl.ac.uk) or Jacko Koster (jak@ii.uib.no) *** */
/* N, NE, IP, IRN are described in MC64A/AD. */
/* A is a REAL (DOUBLE PRECISION in the D-version) array of length */
/* NE. A(K), K=1..NE, must be set to the value of the entry */
/* that corresponds to IRN(K). It is not altered. */
/* IPERM is an INT_T array of length N. On exit, it contains the */
/* matching: IPERM(I) = 0 or row I is matched to column IPERM(I). */
/* NUM is INT_T variable. On exit, it contains the cardinality of the */
/* matching stored in IPERM. */
/* IW is an INT_T work array of length 4N. */
/* DW is a REAL (DOUBLE PRECISION in D-version) work array of length N. */
/* Local variables */
/* Local parameters */
/* Intrinsic functions */
/* External subroutines and/or functions */
/* EXTERNAL FD05AD,MC64DD,MC64ED,MC64FD, DLAMCH */
/* DOUBLE PRECISION FD05AD, DLAMCH */
/* Set RINF to largest positive real number */
/* XSL RINF = FD05AD(5) */
/* Parameter adjustments */
--d__;
--l;
--q;
--pr;
--jperm;
--iperm;
--ip;
--a;
--irn;
/* Function Body */
rinf = dlamch_("Overflow");
/* Initialization */
*num = 0;
bv = rinf;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
iperm[k] = 0;
jperm[k] = 0;
pr[k] = ip[k];
d__[k] = 0.;
/* L10: */
}
/* Scan columns of matrix; */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
a0 = -1.;
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
i__ = irn[k];
ai = (d__1 = a[k], abs(d__1));
if (ai > d__[i__]) {
d__[i__] = ai;
}
if (jperm[j] != 0) {
goto L30;
}
if (ai >= bv) {
a0 = bv;
if (iperm[i__] != 0) {
goto L30;
}
jperm[j] = i__;
iperm[i__] = j;
++(*num);
} else {
if (ai <= a0) {
goto L30;
}
a0 = ai;
i0 = i__;
}
L30:
;
}
if (a0 != -1. && a0 < bv) {
bv = a0;
if (iperm[i0] != 0) {
goto L20;
}
iperm[i0] = j;
jperm[j] = i0;
++(*num);
}
L20:
;
}
/* Update BV with smallest of all the largest maximum absolute values */
/* of the rows. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MIN */
d__1 = bv, d__2 = d__[i__];
bv = min(d__1,d__2);
/* L25: */
}
if (*num == *n) {
goto L1000;
}
/* Rescan unassigned columns; improve initial assignment */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (jperm[j] != 0) {
goto L95;
}
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
i__ = irn[k];
ai = (d__1 = a[k], abs(d__1));
if (ai < bv) {
goto L50;
}
if (iperm[i__] == 0) {
goto L90;
}
jj = iperm[i__];
kk1 = pr[jj];
kk2 = ip[jj + 1] - 1;
if (kk1 > kk2) {
goto L50;
}
i__3 = kk2;
for (kk = kk1; kk <= i__3; ++kk) {
ii = irn[kk];
if (iperm[ii] != 0) {
goto L70;
}
if ((d__1 = a[kk], abs(d__1)) >= bv) {
goto L80;
}
L70:
;
}
pr[jj] = kk2 + 1;
L50:
;
}
goto L95;
L80:
jperm[jj] = ii;
iperm[ii] = jj;
pr[jj] = kk + 1;
L90:
++(*num);
jperm[j] = i__;
iperm[i__] = j;
pr[j] = k + 1;
L95:
;
}
if (*num == *n) {
goto L1000;
}
/* Prepare for main loop */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = -1.;
l[i__] = 0;
/* L99: */
}
/* Main loop ... each pass round this loop is similar to Dijkstra's */
/* algorithm for solving the single source shortest path problem */
i__1 = *n;
for (jord = 1; jord <= i__1; ++jord) {
if (jperm[jord] != 0) {
goto L100;
}
qlen = 0;
low = *n + 1;
up = *n + 1;
/* CSP is cost of shortest path to any unassigned row */
/* ISP is matrix position of unassigned row element in shortest path */
/* JSP is column index of unassigned row element in shortest path */
csp = -1.;
/* Build shortest path tree starting from unassigned column JORD */
j = jord;
pr[j] = -1;
/* Scan column J */
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
i__ = irn[k];
dnew = (d__1 = a[k], abs(d__1));
if (csp >= dnew) {
goto L115;
}
if (iperm[i__] == 0) {
/* Row I is unassigned; update shortest path info */
csp = dnew;
isp = i__;
jsp = j;
if (csp >= bv) {
goto L160;
}
} else {
d__[i__] = dnew;
if (dnew >= bv) {
/* Add row I to Q2 */
--low;
q[low] = i__;
} else {
/* Add row I to Q, and push it */
++qlen;
l[i__] = qlen;
mc64dd_(&i__, n, &q[1], &d__[1], &l[1], &c__1);
}
jj = iperm[i__];
pr[jj] = j;
}
L115:
;
}
i__2 = *num;
for (jdum = 1; jdum <= i__2; ++jdum) {
/* If Q2 is empty, extract new rows from Q */
if (low == up) {
if (qlen == 0) {
goto L160;
}
i__ = q[1];
if (csp >= d__[i__]) {
goto L160;
}
bv = d__[i__];
i__3 = *n;
for (idum = 1; idum <= i__3; ++idum) {
mc64ed_(&qlen, n, &q[1], &d__[1], &l[1], &c__1);
l[i__] = 0;
--low;
q[low] = i__;
if (qlen == 0) {
goto L153;
}
i__ = q[1];
if (d__[i__] != bv) {
goto L153;
}
/* L152: */
}
/* End of dummy loop; this point is never reached */
}
/* Move row Q0 */
L153:
--up;
q0 = q[up];
dq0 = d__[q0];
l[q0] = up;
/* Scan column that matches with row Q0 */
j = iperm[q0];
i__3 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__3; ++k) {
i__ = irn[k];
/* Update D(I) */
if (l[i__] >= up) {
goto L155;
}
/* Computing MIN */
d__2 = dq0, d__3 = (d__1 = a[k], abs(d__1));
dnew = min(d__2,d__3);
if (csp >= dnew) {
goto L155;
}
if (iperm[i__] == 0) {
/* Row I is unassigned; update shortest path info */
csp = dnew;
isp = i__;
jsp = j;
if (csp >= bv) {
goto L160;
}
} else {
di = d__[i__];
if (di >= bv || di >= dnew) {
goto L155;
}
d__[i__] = dnew;
if (dnew >= bv) {
/* Delete row I from Q (if necessary); add row I to Q2 */
if (di != -1.) {
mc64fd_(&l[i__], &qlen, n, &q[1], &d__[1], &l[1],
&c__1);
}
l[i__] = 0;
--low;
q[low] = i__;
} else {
/* Add row I to Q (if necessary); push row I up Q */
if (di == -1.) {
++qlen;
l[i__] = qlen;
}
mc64dd_(&i__, n, &q[1], &d__[1], &l[1], &c__1);
}
/* Update tree */
jj = iperm[i__];
pr[jj] = j;
}
L155:
;
}
/* L150: */
}
/* If CSP = MINONE, no augmenting path is found */
L160:
if (csp == -1.) {
goto L190;
}
/* Update bottleneck value */
bv = min(bv,csp);
/* Find augmenting path by tracing backward in PR; update IPERM,JPERM */
++(*num);
i__ = isp;
j = jsp;
i__2 = *num + 1;
for (jdum = 1; jdum <= i__2; ++jdum) {
i0 = jperm[j];
jperm[j] = i__;
iperm[i__] = j;
j = pr[j];
if (j == -1) {
goto L190;
}
i__ = i0;
/* L170: */
}
/* End of dummy loop; this point is never reached */
L190:
i__2 = *n;
for (kk = up; kk <= i__2; ++kk) {
i__ = q[kk];
d__[i__] = -1.;
l[i__] = 0;
/* L191: */
}
i__2 = up - 1;
for (kk = low; kk <= i__2; ++kk) {
i__ = q[kk];
d__[i__] = -1.;
/* L192: */
}
i__2 = qlen;
for (kk = 1; kk <= i__2; ++kk) {
i__ = q[kk];
d__[i__] = -1.;
l[i__] = 0;
/* L193: */
}
L100:
;
}
/* End of main loop */
/* BV is bottleneck value of final matching */
if (*num == *n) {
goto L1000;
}
/* Matrix is structurally singular, complete IPERM. */
/* JPERM, PR are work arrays */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jperm[j] = 0;
/* L300: */
}
k = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (iperm[i__] == 0) {
++k;
pr[k] = i__;
} else {
j = iperm[i__];
jperm[j] = i__;
}
/* L310: */
}
k = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (jperm[i__] != 0) {
goto L320;
}
++k;
jdum = pr[k];
iperm[jdum] = i__;
L320:
;
}
L1000:
return 0;
} /* mc64bd_ */
/* ********************************************************************** */
/* Subroutine */ int_t mc64dd_(int_t *i__, int_t *n, int_t *q, double
*d__, int_t *l, int_t *iway)
{
/* System generated locals */
int_t i__1;
/* Local variables */
double di;
int_t qk, pos, idum, posk;
/* *** Copyright (c) 1999 Council for the Central Laboratory of the */
/* Research Councils *** */
/* *** Although every effort has been made to ensure robustness and *** */
/* *** reliability of the subroutines in this MC64 suite, we *** */
/* *** disclaim any liability arising through the use or misuse of *** */
/* *** any of the subroutines. *** */
/* *** Any problems? Contact ... */
/* Iain Duff (I.Duff@rl.ac.uk) or Jacko Koster (jak@ii.uib.no) *** */
/* Variables N,Q,D,L are described in MC64B/BD */
/* IF IWAY is equal to 1, then */
/* node I is pushed from its current position upwards */
/* IF IWAY is not equal to 1, then */
/* node I is pushed from its current position downwards */
/* Local variables and parameters */
/* Parameter adjustments */
--l;
--d__;
--q;
/* Function Body */
di = d__[*i__];
pos = l[*i__];
/* POS is index of current position of I in the tree */
if (*iway == 1) {
i__1 = *n;
for (idum = 1; idum <= i__1; ++idum) {
if (pos <= 1) {
goto L20;
}
posk = pos / 2;
qk = q[posk];
if (di <= d__[qk]) {
goto L20;
}
q[pos] = qk;
l[qk] = pos;
pos = posk;
/* L10: */
}
/* End of dummy loop; this point is never reached */
} else {
i__1 = *n;
for (idum = 1; idum <= i__1; ++idum) {
if (pos <= 1) {
goto L20;
}
posk = pos / 2;
qk = q[posk];
if (di >= d__[qk]) {
goto L20;
}
q[pos] = qk;
l[qk] = pos;
pos = posk;
/* L15: */
}
/* End of dummy loop; this point is never reached */
}
/* End of dummy if; this point is never reached */
L20:
q[pos] = *i__;
l[*i__] = pos;
return 0;
} /* mc64dd_ */
/* ********************************************************************** */
/* Subroutine */ int_t mc64ed_(int_t *qlen, int_t *n, int_t *q,
double *d__, int_t *l, int_t *iway)
{
/* System generated locals */
int_t i__1;
/* Local variables */
int_t i__;
double di, dk, dr;
int_t pos, idum, posk;
/* *** Copyright (c) 1999 Council for the Central Laboratory of the */
/* Research Councils *** */
/* *** Although every effort has been made to ensure robustness and *** */
/* *** reliability of the subroutines in this MC64 suite, we *** */
/* *** disclaim any liability arising through the use or misuse of *** */
/* *** any of the subroutines. *** */
/* *** Any problems? Contact ... */
/* Iain Duff (I.Duff@rl.ac.uk) or Jacko Koster (jak@ii.uib.no) *** */
/* Variables QLEN,N,Q,D,L are described in MC64B/BD (IWAY = 1) or */
/* MC64W/WD (IWAY = 2) */
/* The root node is deleted from the binary heap. */
/* Local variables and parameters */
/* Move last element to begin of Q */
/* Parameter adjustments */
--l;
--d__;
--q;
/* Function Body */
i__ = q[*qlen];
di = d__[i__];
--(*qlen);
pos = 1;
if (*iway == 1) {
i__1 = *n;
for (idum = 1; idum <= i__1; ++idum) {
posk = pos << 1;
if (posk > *qlen) {
goto L20;
}
dk = d__[q[posk]];
if (posk < *qlen) {
dr = d__[q[posk + 1]];
if (dk < dr) {
++posk;
dk = dr;
}
}
if (di >= dk) {
goto L20;
}
/* Exchange old last element with larger priority child */
q[pos] = q[posk];
l[q[pos]] = pos;
pos = posk;
/* L10: */
}
/* End of dummy loop; this point is never reached */
} else {
i__1 = *n;
for (idum = 1; idum <= i__1; ++idum) {
posk = pos << 1;
if (posk > *qlen) {
goto L20;
}
dk = d__[q[posk]];
if (posk < *qlen) {
dr = d__[q[posk + 1]];
if (dk > dr) {
++posk;
dk = dr;
}
}
if (di <= dk) {
goto L20;
}
/* Exchange old last element with smaller child */
q[pos] = q[posk];
l[q[pos]] = pos;
pos = posk;
/* L15: */
}
/* End of dummy loop; this point is never reached */
}
/* End of dummy if; this point is never reached */
L20:
q[pos] = i__;
l[i__] = pos;
return 0;
} /* mc64ed_ */
/* ********************************************************************** */
/* Subroutine */ int_t mc64fd_(int_t *pos0, int_t *qlen, int_t *n,
int_t *q, double *d__, int_t *l, int_t *iway)
{
/* System generated locals */
int_t i__1;
/* Local variables */
int_t i__;
double di, dk, dr;
int_t qk, pos, idum, posk;
/* *** Copyright (c) 1999 Council for the Central Laboratory of the */
/* Research Councils *** */
/* *** Although every effort has been made to ensure robustness and *** */
/* *** reliability of the subroutines in this MC64 suite, we *** */
/* *** disclaim any liability arising through the use or misuse of *** */
/* *** any of the subroutines. *** */
/* *** Any problems? Contact ... */
/* Iain Duff (I.Duff@rl.ac.uk) or Jacko Koster (jak@ii.uib.no) *** */
/* Variables QLEN,N,Q,D,L are described in MC64B/BD (IWAY = 1) or */
/* MC64WD (IWAY = 2). */
/* Move last element in the heap */
/* Quick return, if possible */
/* Parameter adjustments */
--l;
--d__;
--q;
/* Function Body */
if (*qlen == *pos0) {
--(*qlen);
return 0;
}
/* Move last element from queue Q to position POS0 */
/* POS is current position of node I in the tree */
i__ = q[*qlen];
di = d__[i__];
--(*qlen);
pos = *pos0;
if (*iway == 1) {
i__1 = *n;
for (idum = 1; idum <= i__1; ++idum) {
if (pos <= 1) {
goto L20;
}
posk = pos / 2;
qk = q[posk];
if (di <= d__[qk]) {
goto L20;
}
q[pos] = qk;
l[qk] = pos;
pos = posk;
/* L10: */
}
/* End of dummy loop; this point is never reached */
L20:
q[pos] = i__;
l[i__] = pos;
i__1 = *n;
for (idum = 1; idum <= i__1; ++idum) {
posk = pos << 1;
if (posk > *qlen) {
goto L40;
}
dk = d__[q[posk]];
if (posk < *qlen) {
dr = d__[q[posk + 1]];
if (dk < dr) {
++posk;
dk = dr;
}
}
if (di >= dk) {
goto L40;
}
qk = q[posk];
q[pos] = qk;
l[qk] = pos;
pos = posk;
/* L30: */
}
/* End of dummy loop; this point is never reached */
} else {
i__1 = *n;
for (idum = 1; idum <= i__1; ++idum) {
if (pos <= 1) {
goto L34;
}
posk = pos / 2;
qk = q[posk];
if (di >= d__[qk]) {
goto L34;
}
q[pos] = qk;
l[qk] = pos;
pos = posk;
/* L32: */
}
/* End of dummy loop; this point is never reached */
L34:
q[pos] = i__;
l[i__] = pos;
i__1 = *n;
for (idum = 1; idum <= i__1; ++idum) {
posk = pos << 1;
if (posk > *qlen) {
goto L40;
}
dk = d__[q[posk]];
if (posk < *qlen) {
dr = d__[q[posk + 1]];
if (dk > dr) {
++posk;
dk = dr;
}
}
if (di <= dk) {
goto L40;
}
qk = q[posk];
q[pos] = qk;
l[qk] = pos;
pos = posk;
/* L36: */
}
/* End of dummy loop; this point is never reached */
}
/* End of dummy if; this point is never reached */
L40:
q[pos] = i__;
l[i__] = pos;
return 0;
} /* mc64fd_ */
/* ********************************************************************** */
/* Subroutine */ int_t mc64rd_(int_t *n, int_t *ne, int_t *ip, int_t *
irn, double *a)
{
/* System generated locals */
int_t i__1, i__2, i__3;
/* Local variables */
int_t j, k, r__, s;
double ha;
int_t hi, td, mid, len, ipj;
double key;
int_t last, todo[50], first;
/* *** Copyright (c) 1999 Council for the Central Laboratory of the */
/* Research Councils *** */
/* *** Although every effort has been made to ensure robustness and *** */
/* *** reliability of the subroutines in this MC64 suite, we *** */
/* *** disclaim any liability arising through the use or misuse of *** */
/* *** any of the subroutines. *** */
/* *** Any problems? Contact ... */
/* Iain Duff (I.Duff@rl.ac.uk) or Jacko Koster (jak@ii.uib.no) *** */
/* This subroutine sorts the entries in each column of the */
/* sparse matrix (defined by N,NE,IP,IRN,A) by decreasing */
/* numerical value. */
/* Local constants */
/* Local variables */
/* Local arrays */
/* Parameter adjustments */
--ip;
--a;
--irn;
/* Function Body */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
len = ip[j + 1] - ip[j];
if (len <= 1) {
goto L100;
}
ipj = ip[j];
/* Sort array roughly with partial quicksort */
if (len < 15) {
goto L400;
}
todo[0] = ipj;
todo[1] = ipj + len;
td = 2;
L500:
first = todo[td - 2];
last = todo[td - 1];
/* KEY is the smallest of two values present in interval [FIRST,LAST) */
key = a[(first + last) / 2];
i__2 = last - 1;
for (k = first; k <= i__2; ++k) {
ha = a[k];
if (ha == key) {
goto L475;
}
if (ha > key) {
goto L470;
}
key = ha;
goto L470;
L475:
;
}
/* Only one value found in interval, so it is already sorted */
td += -2;
goto L425;
/* Reorder interval [FIRST,LAST) such that entries before MID are gt KEY */
L470:
mid = first;
i__2 = last - 1;
for (k = first; k <= i__2; ++k) {
if (a[k] <= key) {
goto L450;
}
ha = a[mid];
a[mid] = a[k];
a[k] = ha;
hi = irn[mid];
irn[mid] = irn[k];
irn[k] = hi;
++mid;
L450:
;
}
/* Both subintervals [FIRST,MID), [MID,LAST) are nonempty */
/* Stack the longest of the two subintervals first */
if (mid - first >= last - mid) {
todo[td + 1] = last;
todo[td] = mid;
todo[td - 1] = mid;
/* TODO(TD-1) = FIRST */
} else {
todo[td + 1] = mid;
todo[td] = first;
todo[td - 1] = last;
todo[td - 2] = mid;
}
td += 2;
L425:
if (td == 0) {
goto L400;
}
/* There is still work to be done */
if (todo[td - 1] - todo[td - 2] >= 15) {
goto L500;
}
/* Next interval is already short enough for straightforward insertion */
td += -2;
goto L425;
/* Complete sorting with straightforward insertion */
L400:
i__2 = ipj + len - 1;
for (r__ = ipj + 1; r__ <= i__2; ++r__) {
if (a[r__ - 1] < a[r__]) {
ha = a[r__];
hi = irn[r__];
a[r__] = a[r__ - 1];
irn[r__] = irn[r__ - 1];
i__3 = ipj + 1;
for (s = r__ - 1; s >= i__3; --s) {
if (a[s - 1] < ha) {
a[s] = a[s - 1];
irn[s] = irn[s - 1];
} else {
a[s] = ha;
irn[s] = hi;
goto L200;
}
/* L300: */
}
a[ipj] = ha;
irn[ipj] = hi;
}
L200:
;
}
L100:
;
}
return 0;
} /* mc64rd_ */
/* ********************************************************************** */
/* Subroutine */ int_t mc64sd_(int_t *n, int_t *ne, int_t *ip, int_t *
irn, double *a, int_t *iperm, int_t *numx, int_t *w,
int_t *len, int_t *lenl, int_t *lenh, int_t *fc, int_t *iw,
int_t *iw4)
{
/* System generated locals */
int_t i__1, i__2, i__3, i__4;
/* Local variables */
int_t i__, j, k, l, ii, mod, cnt, num;
double bval, bmin, bmax, rinf;
int_t nval, wlen, idum1, idum2, idum3;
extern /* Subroutine */ int_t mc64qd_(int_t *, int_t *, int_t *,
int_t *, int_t *, double *, int_t *, double *),
mc64ud_(int_t *, int_t *, int_t *, int_t *, int_t *,
int_t *, int_t *, int_t *, int_t *, int_t *, int_t *,
int_t *, int_t *, int_t *, int_t *);
/* *** Copyright (c) 1999 Council for the Central Laboratory of the */
/* Research Councils *** */
/* *** Although every effort has been made to ensure robustness and *** */
/* *** reliability of the subroutines in this MC64 suite, we *** */
/* *** disclaim any liability arising through the use or misuse of *** */
/* *** any of the subroutines. *** */
/* *** Any problems? Contact ... */
/* Iain Duff (I.Duff@rl.ac.uk) or Jacko Koster (jak@ii.uib.no) *** */
/* N, NE, IP, IRN, are described in MC64A/AD. */
/* A is a REAL (DOUBLE PRECISION in the D-version) array of length NE. */
/* A(K), K=1..NE, must be set to the value of the entry that */
/* corresponds to IRN(k). The entries in each column must be */
/* non-negative and ordered by decreasing value. */
/* IPERM is an INT_T array of length N. On exit, it contains the */
/* bottleneck matching: IPERM(I) - 0 or row I is matched to column */
/* IPERM(I). */
/* NUMX is an INT_T variable. On exit, it contains the cardinality */
/* of the matching stored in IPERM. */
/* IW is an INT_T work array of length 10N. */
/* FC is an int_t array of length N that contains the list of */
/* unmatched columns. */
/* LEN(J), LENL(J), LENH(J) are int_t arrays of length N that point */
/* to entries in matrix column J. */
/* In the matrix defined by the column parts IP(J)+LENL(J) we know */
/* a matching does not exist; in the matrix defined by the column */
/* parts IP(J)+LENH(J) we know one exists. */
/* LEN(J) lies between LENL(J) and LENH(J) and determines the matrix */
/* that is tested for a maximum matching. */
/* W is an int_t array of length N and contains the indices of the */
/* columns for which LENL ne LENH. */
/* WLEN is number of indices stored in array W. */
/* IW is int_t work array of length N. */
/* IW4 is int_t work array of length 4N used by MC64U/UD. */
/* EXTERNAL FD05AD,MC64QD,MC64UD */
/* DOUBLE PRECISION FD05AD */
/* BMIN and BMAX are such that a maximum matching exists for the input */
/* matrix in which all entries smaller than BMIN are dropped. */
/* For BMAX, a maximum matching does not exist. */
/* BVAL is a value between BMIN and BMAX. */
/* CNT is the number of calls made to MC64U/UD so far. */
/* NUM is the cardinality of last matching found. */
/* Set RINF to largest positive real number */
/* XSL RINF = FD05AD(5) */
/* Parameter adjustments */
--iw4;
--iw;
--fc;
--lenh;
--lenl;
--len;
--w;
--iperm;
--ip;
--a;
--irn;
/* Function Body */
rinf = dlamch_("Overflow");
/* Compute a first maximum matching from scratch on whole matrix. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
fc[j] = j;
iw[j] = 0;
len[j] = ip[j + 1] - ip[j];
/* L20: */
}
/* The first call to MC64U/UD */
cnt = 1;
mod = 1;
*numx = 0;
mc64ud_(&cnt, &mod, n, &irn[1], ne, &ip[1], &len[1], &fc[1], &iw[1], numx,
n, &iw4[1], &iw4[*n + 1], &iw4[(*n << 1) + 1], &iw4[*n * 3 + 1]);
/* IW contains a maximum matching of length NUMX. */
num = *numx;
if (num != *n) {
/* Matrix is structurally singular */
bmax = rinf;
} else {
/* Matrix is structurally nonsingular, NUM=NUMX=N; */
/* Set BMAX just above the smallest of all the maximum absolute */
/* values of the columns */
bmax = rinf;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
bval = 0.f;
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
if (a[k] > bval) {
bval = a[k];
}
/* L25: */
}
if (bval < bmax) {
bmax = bval;
}
/* L30: */
}
bmax *= 1.001f;
}
/* Initialize BVAL,BMIN */
bval = 0.f;
bmin = 0.f;
/* Initialize LENL,LEN,LENH,W,WLEN according to BMAX. */
/* Set LEN(J), LENH(J) just after last entry in column J. */
/* Set LENL(J) just after last entry in column J with value ge BMAX. */
wlen = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = ip[j + 1] - ip[j];
lenh[j] = l;
len[j] = l;
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
if (a[k] < bmax) {
goto L46;
}
/* L45: */
}
/* Column J is empty or all entries are ge BMAX */
k = ip[j + 1];
L46:
lenl[j] = k - ip[j];
/* Add J to W if LENL(J) ne LENH(J) */
if (lenl[j] == l) {
goto L48;
}
++wlen;
w[wlen] = j;
L48:
;
}
/* Main loop */
i__1 = *ne;
for (idum1 = 1; idum1 <= i__1; ++idum1) {
if (num == *numx) {
/* We have a maximum matching in IW; store IW in IPERM */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
iperm[i__] = iw[i__];
/* L50: */
}
/* Keep going round this loop until matching IW is no longer maximum. */
i__2 = *ne;
for (idum2 = 1; idum2 <= i__2; ++idum2) {
bmin = bval;
if (bmax == bmin) {
goto L99;
}
/* Find splitting value BVAL */
mc64qd_(&ip[1], &lenl[1], &len[1], &w[1], &wlen, &a[1], &nval,
&bval);
if (nval <= 1) {
goto L99;
}
/* Set LEN such that all matrix entries with value lt BVAL are */
/* discarded. Store old LEN in LENH. Do this for all columns W(K). */
/* Each step, either K is incremented or WLEN is decremented. */
k = 1;
i__3 = *n;
for (idum3 = 1; idum3 <= i__3; ++idum3) {
if (k > wlen) {
goto L71;
}
j = w[k];
i__4 = ip[j] + lenl[j];
for (ii = ip[j] + len[j] - 1; ii >= i__4; --ii) {
if (a[ii] >= bval) {
goto L60;
}
i__ = irn[ii];
if (iw[i__] != j) {
goto L55;
}
/* Remove entry from matching */
iw[i__] = 0;
--num;
fc[*n - num] = j;
L55:
;
}
L60:
lenh[j] = len[j];
/* IP(J)+LEN(J)-1 is last entry in column ge BVAL */
len[j] = ii - ip[j] + 1;
/* If LENH(J) = LENL(J), remove J from W */
if (lenl[j] == lenh[j]) {
w[k] = w[wlen];
--wlen;
} else {
++k;
}
/* L70: */
}
L71:
if (num < *numx) {
goto L81;
}
/* L80: */
}
/* End of dummy loop; this point is never reached */
/* Set mode for next call to MC64U/UD */
L81:
mod = 1;
} else {
/* We do not have a maximum matching in IW. */
bmax = bval;
/* BMIN is the bottleneck value of a maximum matching; */
/* for BMAX the matching is not maximum, so BMAX>BMIN */
/* IF (BMAX .EQ. BMIN) GO TO 99 */
/* Find splitting value BVAL */
mc64qd_(&ip[1], &len[1], &lenh[1], &w[1], &wlen, &a[1], &nval, &
bval);
if (nval == 0 || bval == bmin) {
goto L99;
}
/* Set LEN such that all matrix entries with value ge BVAL are */
/* inside matrix. Store old LEN in LENL. Do this for all columns W(K). */
/* Each step, either K is incremented or WLEN is decremented. */
k = 1;
i__2 = *n;
for (idum3 = 1; idum3 <= i__2; ++idum3) {
if (k > wlen) {
goto L88;
}
j = w[k];
i__3 = ip[j] + lenh[j] - 1;
for (ii = ip[j] + len[j]; ii <= i__3; ++ii) {
if (a[ii] < bval) {
goto L86;
}
/* L85: */
}
L86:
lenl[j] = len[j];
len[j] = ii - ip[j];
if (lenl[j] == lenh[j]) {
w[k] = w[wlen];
--wlen;
} else {
++k;
}
/* L87: */
}
/* End of dummy loop; this point is never reached */
/* Set mode for next call to MC64U/UD */
L88:
mod = 0;
}
++cnt;
mc64ud_(&cnt, &mod, n, &irn[1], ne, &ip[1], &len[1], &fc[1], &iw[1], &
num, numx, &iw4[1], &iw4[*n + 1], &iw4[(*n << 1) + 1], &iw4[*
n * 3 + 1]);
/* IW contains maximum matching of length NUM */
/* L90: */
}
/* End of dummy loop; this point is never reached */
/* BMIN is bottleneck value of final matching */
L99:
if (*numx == *n) {
goto L1000;
}
/* The matrix is structurally singular, complete IPERM */
/* W, IW are work arrays */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
w[j] = 0;
/* L300: */
}
k = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (iperm[i__] == 0) {
++k;
iw[k] = i__;
} else {
j = iperm[i__];
w[j] = i__;
}
/* L310: */
}
k = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (w[j] != 0) {
goto L320;
}
++k;
idum1 = iw[k];
iperm[idum1] = j;
L320:
;
}
L1000:
return 0;
} /* mc64sd_ */
/* ********************************************************************** */
/* Subroutine */ int_t mc64qd_(int_t *ip, int_t *lenl, int_t *lenh,
int_t *w, int_t *wlen, double *a, int_t *nval, double *
val)
{
/* System generated locals */
int_t i__1, i__2, i__3;
/* Local variables */
int_t j, k, s;
double ha;
int_t ii, pos;
double split[10];
/* *** Copyright (c) 1999 Council for the Central Laboratory of the */
/* Research Councils *** */
/* *** Although every effort has been made to ensure robustness and *** */
/* *** reliability of the subroutines in this MC64 suite, we *** */
/* *** disclaim any liability arising through the use or misuse of *** */
/* *** any of the subroutines. *** */
/* *** Any problems? Contact ... */
/* Iain Duff (I.Duff@rl.ac.uk) or Jacko Koster (jak@ii.uib.no) *** */
/* This routine searches for at most XX different numerical values */
/* in the columns W(1:WLEN). XX>=2. */
/* Each column J is scanned between IP(J)+LENL(J) and IP(J)+LENH(J)-1 */
/* until XX values are found or all columns have been considered. */
/* On output, NVAL is the number of different values that is found */
/* and SPLIT(1:NVAL) contains the values in decreasing order. */
/* If NVAL > 0, the routine returns VAL = SPLIT((NVAL+1)/2). */
/* Scan columns in W(1:WLEN). For each encountered value, if value not */
/* already present in SPLIT(1:NVAL), insert value such that SPLIT */
/* remains sorted by decreasing value. */
/* The sorting is done by straightforward insertion; therefore the use */
/* of this routine should be avoided for large XX (XX < 20). */
/* Parameter adjustments */
--a;
--w;
--lenh;
--lenl;
--ip;
/* Function Body */
*nval = 0;
i__1 = *wlen;
for (k = 1; k <= i__1; ++k) {
j = w[k];
i__2 = ip[j] + lenh[j] - 1;
for (ii = ip[j] + lenl[j]; ii <= i__2; ++ii) {
ha = a[ii];
if (*nval == 0) {
split[0] = ha;
*nval = 1;
} else {
/* Check presence of HA in SPLIT */
for (s = *nval; s >= 1; --s) {
if (split[s - 1] == ha) {
goto L15;
}
if (split[s - 1] > ha) {
pos = s + 1;
goto L21;
}
/* L20: */
}
pos = 1;
/* The insertion */
L21:
i__3 = pos;
for (s = *nval; s >= i__3; --s) {
split[s] = split[s - 1];
/* L22: */
}
split[pos - 1] = ha;
++(*nval);
}
/* Exit loop if XX values are found */
if (*nval == 10) {
goto L11;
}
L15:
;
}
/* L10: */
}
/* Determine VAL */
L11:
if (*nval > 0) {
*val = split[(*nval + 1) / 2 - 1];
}
return 0;
} /* mc64qd_ */
/* ********************************************************************** */
/* Subroutine */ int_t mc64ud_(int_t *id, int_t *mod, int_t *n, int_t *
irn, int_t *lirn, int_t *ip, int_t *lenc, int_t *fc, int_t *
iperm, int_t *num, int_t *numx, int_t *pr, int_t *arp,
int_t *cv, int_t *out)
{
/* System generated locals */
int_t i__1, i__2, i__3, i__4;
/* Local variables */
int_t i__, j, k, j1, ii, kk, id0, id1, in1, in2, nfc, num0, num1, num2,
jord, last;
/* *** Copyright (c) 1999 Council for the Central Laboratory of the */
/* Research Councils *** */
/* *** Although every effort has been made to ensure robustness and *** */
/* *** reliability of the subroutines in this MC64 suite, we *** */
/* *** disclaim any liability arising through the use or misuse of *** */
/* *** any of the subroutines. *** */
/* *** Any problems? Contact ... */
/* Iain Duff (I.Duff@rl.ac.uk) or Jacko Koster (jak@ii.uib.no) *** */
/* PR(J) is the previous column to J in the depth first search. */
/* Array PR is used as workspace in the sorting algorithm. */
/* Elements (I,IPERM(I)) I=1,..,N are entries at the end of the */
/* algorithm unless N assignments have not been made in which case */
/* N-NUM pairs (I,IPERM(I)) will not be entries in the matrix. */
/* CV(I) is the most recent loop number (ID+JORD) at which row I */
/* was visited. */
/* ARP(J) is the number of entries in column J which have been scanned */
/* when looking for a cheap assignment. */
/* OUT(J) is one less than the number of entries in column J which have */
/* not been scanned during one pass through the main loop. */
/* NUMX is maximum possible size of matching. */
/* Parameter adjustments */
--out;
--cv;
--arp;
--pr;
--iperm;
--fc;
--lenc;
--ip;
--irn;
/* Function Body */
if (*id == 1) {
/* The first call to MC64U/UD. */
/* Initialize CV and ARP; parameters MOD, NUMX are not accessed */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
cv[i__] = 0;
arp[i__] = 0;
/* L5: */
}
num1 = *n;
num2 = *n;
} else {
/* Not the first call to MC64U/UD. */
/* Re-initialize ARP if entries were deleted since last call to MC64U/UD */
if (*mod == 1) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
arp[i__] = 0;
/* L8: */
}
}
num1 = *numx;
num2 = *n - *numx;
}
num0 = *num;
/* NUM0 is size of input matching */
/* NUM1 is maximum possible size of matching */
/* NUM2 is maximum allowed number of unassigned rows/columns */
/* NUM is size of current matching */
/* Quick return if possible */
/* IF (NUM.EQ.N) GO TO 199 */
/* NFC is number of rows/columns that could not be assigned */
nfc = 0;
/* Integers ID0+1 to ID0+N are unique numbers for call ID to MC64U/UD, */
/* so 1st call uses 1..N, 2nd call uses N+1..2N, etc */
id0 = (*id - 1) * *n;
/* Main loop. Each pass round this loop either results in a new */
/* assignment or gives a column with no assignment */
i__1 = *n;
for (jord = num0 + 1; jord <= i__1; ++jord) {
/* Each pass uses unique number ID1 */
id1 = id0 + jord;
/* J is unmatched column */
j = fc[jord - num0];
pr[j] = -1;
i__2 = jord;
for (k = 1; k <= i__2; ++k) {
/* Look for a cheap assignment */
if (arp[j] >= lenc[j]) {
goto L30;
}
in1 = ip[j] + arp[j];
in2 = ip[j] + lenc[j] - 1;
i__3 = in2;
for (ii = in1; ii <= i__3; ++ii) {
i__ = irn[ii];
if (iperm[i__] == 0) {
goto L80;
}
/* L20: */
}
/* No cheap assignment in row */
arp[j] = lenc[j];
/* Begin looking for assignment chain starting with row J */
L30:
out[j] = lenc[j] - 1;
/* Inner loop. Extends chain by one or backtracks */
i__3 = jord;
for (kk = 1; kk <= i__3; ++kk) {
in1 = out[j];
if (in1 < 0) {
goto L50;
}
in2 = ip[j] + lenc[j] - 1;
in1 = in2 - in1;
/* Forward scan */
i__4 = in2;
for (ii = in1; ii <= i__4; ++ii) {
i__ = irn[ii];
if (cv[i__] == id1) {
goto L40;
}
/* Column J has not yet been accessed during this pass */
j1 = j;
j = iperm[i__];
cv[i__] = id1;
pr[j] = j1;
out[j1] = in2 - ii - 1;
goto L70;
L40:
;
}
/* Backtracking step. */
L50:
j1 = pr[j];
if (j1 == -1) {
/* No augmenting path exists for column J. */
++nfc;
fc[nfc] = j;
if (nfc > num2) {
/* A matching of maximum size NUM1 is not possible */
last = jord;
goto L101;
}
goto L100;
}
j = j1;
/* L60: */
}
/* End of dummy loop; this point is never reached */
L70:
;
}
/* End of dummy loop; this point is never reached */
/* New assignment is made. */
L80:
iperm[i__] = j;
arp[j] = ii - ip[j] + 1;
++(*num);
i__2 = jord;
for (k = 1; k <= i__2; ++k) {
j = pr[j];
if (j == -1) {
goto L95;
}
ii = ip[j] + lenc[j] - out[j] - 2;
i__ = irn[ii];
iperm[i__] = j;
/* L90: */
}
/* End of dummy loop; this point is never reached */
L95:
if (*num == num1) {
/* A matching of maximum size NUM1 is found */
last = jord;
goto L101;
}
L100:
;
}
/* All unassigned columns have been considered */
last = *n;
/* Now, a transversal is computed or is not possible. */
/* Complete FC before returning. */
L101:
i__1 = *n;
for (jord = last + 1; jord <= i__1; ++jord) {
++nfc;
fc[nfc] = fc[jord - num0];
/* L110: */
}
/* 199 RETURN */
return 0;
} /* mc64ud_ */
/* ********************************************************************** */
/* Subroutine */ int_t mc64wd_(int_t *n, int_t *ne, int_t *ip, int_t *
irn, double *a, int_t *iperm, int_t *num, int_t *jperm,
int_t *out, int_t *pr, int_t *q, int_t *l, double *u,
double *d__)
{
/* System generated locals */
int_t i__1, i__2, i__3;
/* Local variables */
int_t i__, j, k, i0, k0, k1, k2, q0;
double di;
int_t ii, jj, kk;
double vj;
int_t up;
double dq0;
int_t kk1, kk2;
double csp;
int_t isp, jsp, low;
double dmin__, dnew;
int_t jord, qlen, jdum;
double rinf;
extern /* Subroutine */ int_t mc64dd_(int_t *, int_t *, int_t *,
double *, int_t *, int_t *), mc64ed_(int_t *, int_t *,
int_t *, double *, int_t *, int_t *), mc64fd_(int_t *
, int_t *, int_t *, int_t *, double *, int_t *,
int_t *);
/* *** Copyright (c) 1999 Council for the Central Laboratory of the */
/* Research Councils *** */
/* *** Although every effort has been made to ensure robustness and *** */
/* *** reliability of the subroutines in this MC64 suite, we *** */
/* *** disclaim any liability arising through the use or misuse of *** */
/* *** any of the subroutines. *** */
/* *** Any problems? Contact ... */
/* Iain Duff (I.Duff@rl.ac.uk) or Jacko Koster (jak@ii.uib.no) *** */
/* N, NE, IP, IRN are described in MC64A/AD. */
/* A is a REAL (DOUBLE PRECISION in the D-version) array of length NE. */
/* A(K), K=1..NE, must be set to the value of the entry that */
/* corresponds to IRN(K). It is not altered. */
/* All values A(K) must be non-negative. */
/* IPERM is an INT_T array of length N. On exit, it contains the */
/* weighted matching: IPERM(I) = 0 or row I is matched to column */
/* IPERM(I). */
/* NUM is an INT_T variable. On exit, it contains the cardinality of */
/* the matching stored in IPERM. */
/* IW is an INT_T work array of length 5N. */
/* DW is a REAL (DOUBLE PRECISION in the D-version) array of length 2N. */
/* On exit, U = D(1:N) contains the dual row variable and */
/* V = D(N+1:2N) contains the dual column variable. If the matrix */
/* is structurally nonsingular (NUM = N), the following holds: */
/* U(I)+V(J) <= A(I,J) if IPERM(I) |= J */
/* U(I)+V(J) = A(I,J) if IPERM(I) = J */
/* U(I) = 0 if IPERM(I) = 0 */
/* V(J) = 0 if there is no I for which IPERM(I) = J */
/* Local variables */
/* Local parameters */
/* External subroutines and/or functions */
/* EXTERNAL FD05AD,MC64DD,MC64ED,MC64FD */
/* DOUBLE PRECISION FD05AD */
/* Set RINF to largest positive real number */
/* XSL RINF = FD05AD(5) */
/* Parameter adjustments */
--d__;
--u;
--l;
--q;
--pr;
--out;
--jperm;
--iperm;
--ip;
--a;
--irn;
/* Function Body */
rinf = dlamch_("Overflow");
/* Initialization */
*num = 0;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
u[k] = rinf;
d__[k] = 0.;
iperm[k] = 0;
jperm[k] = 0;
pr[k] = ip[k];
l[k] = 0;
/* L10: */
}
/* Initialize U(I) */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
i__ = irn[k];
if (a[k] > u[i__]) {
goto L20;
}
u[i__] = a[k];
iperm[i__] = j;
l[i__] = k;
L20:
;
}
/* L30: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
j = iperm[i__];
if (j == 0) {
goto L40;
}
/* Row I is not empty */
iperm[i__] = 0;
if (jperm[j] != 0) {
goto L40;
}
/* Assignment of column J to row I */
++(*num);
iperm[i__] = j;
jperm[j] = l[i__];
L40:
;
}
if (*num == *n) {
goto L1000;
}
/* Scan unassigned columns; improve assignment */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* JPERM(J) ne 0 iff column J is already assigned */
if (jperm[j] != 0) {
goto L95;
}
k1 = ip[j];
k2 = ip[j + 1] - 1;
/* Continue only if column J is not empty */
if (k1 > k2) {
goto L95;
}
vj = rinf;
i__2 = k2;
for (k = k1; k <= i__2; ++k) {
i__ = irn[k];
di = a[k] - u[i__];
if (di > vj) {
goto L50;
}
if (di < vj || di == rinf) {
goto L55;
}
if (iperm[i__] != 0 || iperm[i0] == 0) {
goto L50;
}
L55:
vj = di;
i0 = i__;
k0 = k;
L50:
;
}
d__[j] = vj;
k = k0;
i__ = i0;
if (iperm[i__] == 0) {
goto L90;
}
i__2 = k2;
for (k = k0; k <= i__2; ++k) {
i__ = irn[k];
if (a[k] - u[i__] > vj) {
goto L60;
}
jj = iperm[i__];
/* Scan remaining part of assigned column JJ */
kk1 = pr[jj];
kk2 = ip[jj + 1] - 1;
if (kk1 > kk2) {
goto L60;
}
i__3 = kk2;
for (kk = kk1; kk <= i__3; ++kk) {
ii = irn[kk];
if (iperm[ii] > 0) {
goto L70;
}
if (a[kk] - u[ii] <= d__[jj]) {
goto L80;
}
L70:
;
}
pr[jj] = kk2 + 1;
L60:
;
}
goto L95;
L80:
jperm[jj] = kk;
iperm[ii] = jj;
pr[jj] = kk + 1;
L90:
++(*num);
jperm[j] = k;
iperm[i__] = j;
pr[j] = k + 1;
L95:
;
}
if (*num == *n) {
goto L1000;
}
/* Prepare for main loop */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = rinf;
l[i__] = 0;
/* L99: */
}
/* Main loop ... each pass round this loop is similar to Dijkstra's */
/* algorithm for solving the single source shortest path problem */
i__1 = *n;
for (jord = 1; jord <= i__1; ++jord) {
if (jperm[jord] != 0) {
goto L100;
}
/* JORD is next unmatched column */
/* DMIN is the length of shortest path in the tree */
dmin__ = rinf;
qlen = 0;
low = *n + 1;
up = *n + 1;
/* CSP is the cost of the shortest augmenting path to unassigned row */
/* IRN(ISP). The corresponding column index is JSP. */
csp = rinf;
/* Build shortest path tree starting from unassigned column (root) JORD */
j = jord;
pr[j] = -1;
/* Scan column J */
i__2 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__2; ++k) {
i__ = irn[k];
dnew = a[k] - u[i__];
if (dnew >= csp) {
goto L115;
}
if (iperm[i__] == 0) {
csp = dnew;
isp = k;
jsp = j;
} else {
if (dnew < dmin__) {
dmin__ = dnew;
}
d__[i__] = dnew;
++qlen;
q[qlen] = k;
}
L115:
;
}
/* Initialize heap Q and Q2 with rows held in Q(1:QLEN) */
q0 = qlen;
qlen = 0;
i__2 = q0;
for (kk = 1; kk <= i__2; ++kk) {
k = q[kk];
i__ = irn[k];
if (csp <= d__[i__]) {
d__[i__] = rinf;
goto L120;
}
if (d__[i__] <= dmin__) {
--low;
q[low] = i__;
l[i__] = low;
} else {
++qlen;
l[i__] = qlen;
mc64dd_(&i__, n, &q[1], &d__[1], &l[1], &c__2);
}
/* Update tree */
jj = iperm[i__];
out[jj] = k;
pr[jj] = j;
L120:
;
}
i__2 = *num;
for (jdum = 1; jdum <= i__2; ++jdum) {
/* If Q2 is empty, extract rows from Q */
if (low == up) {
if (qlen == 0) {
goto L160;
}
i__ = q[1];
if (d__[i__] >= csp) {
goto L160;
}
dmin__ = d__[i__];
L152:
mc64ed_(&qlen, n, &q[1], &d__[1], &l[1], &c__2);
--low;
q[low] = i__;
l[i__] = low;
if (qlen == 0) {
goto L153;
}
i__ = q[1];
if (d__[i__] > dmin__) {
goto L153;
}
goto L152;
}
/* Q0 is row whose distance D(Q0) to the root is smallest */
L153:
q0 = q[up - 1];
dq0 = d__[q0];
/* Exit loop if path to Q0 is longer than the shortest augmenting path */
if (dq0 >= csp) {
goto L160;
}
--up;
/* Scan column that matches with row Q0 */
j = iperm[q0];
vj = dq0 - a[jperm[j]] + u[q0];
i__3 = ip[j + 1] - 1;
for (k = ip[j]; k <= i__3; ++k) {
i__ = irn[k];
if (l[i__] >= up) {
goto L155;
}
/* DNEW is new cost */
dnew = vj + a[k] - u[i__];
/* Do not update D(I) if DNEW ge cost of shortest path */
if (dnew >= csp) {
goto L155;
}
if (iperm[i__] == 0) {
/* Row I is unmatched; update shortest path info */
csp = dnew;
isp = k;
jsp = j;
} else {
/* Row I is matched; do not update D(I) if DNEW is larger */
di = d__[i__];
if (di <= dnew) {
goto L155;
}
if (l[i__] >= low) {
goto L155;
}
d__[i__] = dnew;
if (dnew <= dmin__) {
if (l[i__] != 0) {
mc64fd_(&l[i__], &qlen, n, &q[1], &d__[1], &l[1],
&c__2);
}
--low;
q[low] = i__;
l[i__] = low;
} else {
if (l[i__] == 0) {
++qlen;
l[i__] = qlen;
}
mc64dd_(&i__, n, &q[1], &d__[1], &l[1], &c__2);
}
/* Update tree */
jj = iperm[i__];
out[jj] = k;
pr[jj] = j;
}
L155:
;
}
/* L150: */
}
/* If CSP = RINF, no augmenting path is found */
L160:
if (csp == rinf) {
goto L190;
}
/* Find augmenting path by tracing backward in PR; update IPERM,JPERM */
++(*num);
i__ = irn[isp];
iperm[i__] = jsp;
jperm[jsp] = isp;
j = jsp;
i__2 = *num;
for (jdum = 1; jdum <= i__2; ++jdum) {
jj = pr[j];
if (jj == -1) {
goto L180;
}
k = out[j];
i__ = irn[k];
iperm[i__] = jj;
jperm[jj] = k;
j = jj;
/* L170: */
}
/* End of dummy loop; this point is never reached */
/* Update U for rows in Q(UP:N) */
L180:
i__2 = *n;
for (kk = up; kk <= i__2; ++kk) {
i__ = q[kk];
u[i__] = u[i__] + d__[i__] - csp;
/* L185: */
}
L190:
i__2 = *n;
for (kk = low; kk <= i__2; ++kk) {
i__ = q[kk];
d__[i__] = rinf;
l[i__] = 0;
/* L191: */
}
i__2 = qlen;
for (kk = 1; kk <= i__2; ++kk) {
i__ = q[kk];
d__[i__] = rinf;
l[i__] = 0;
/* L193: */
}
L100:
;
}
/* End of main loop */
/* Set dual column variable in D(1:N) */
L1000:
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
k = jperm[j];
if (k != 0) {
d__[j] = a[k] - u[irn[k]];
} else {
d__[j] = 0.;
}
if (iperm[j] == 0) {
u[j] = 0.;
}
/* L200: */
}
if (*num == *n) {
goto L1100;
}
/* The matrix is structurally singular, complete IPERM. */
/* JPERM, OUT are work arrays */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jperm[j] = 0;
/* L300: */
}
k = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (iperm[i__] == 0) {
++k;
out[k] = i__;
} else {
j = iperm[i__];
jperm[j] = i__;
}
/* L310: */
}
k = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (jperm[j] != 0) {
goto L320;
}
++k;
jdum = out[k];
iperm[jdum] = j;
L320:
;
}
L1100:
return 0;
} /* mc64wd_ */
Reference in a new issue View git blame Copy permalink