--- SuperLU_5.2.1/SRC/mc64ad.c 2016-05-22 17:58:44.000000000 +0200 +++ mc64ad.c 2018-04-13 17:13:23.571981656 +0200 @@ -1,2645 +1,16 @@ -/* 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., +#include +#include - 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) - -#if 0 -/* Table of constant values */ -static int_t c__1 = 1; -static int_t c__2 = 2; -#endif - -/* 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@stfc.ac.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 = dmach("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" - " because JOB = %d\n", info[1], *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" - " because N = %d\n", info[1], *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" - " because NE = %d\n", info[1], *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" - " LIW too small, must be at least %8d\n", info[1], 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" - " LDW too small, must be at least %8d\n", info[1], 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 Column %8d" - " contains an entry with invalid row index %8d\n", - info[1], j, 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" - " Column %8d" - " contains two or more entries with row index %8d\n", - info[1], j, 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" - " The matrix is structurally singular.\n", info[1]); - } - } - if (info[1] == 2) { -/* Scaling factors are large, return with warning */ - if (icntl[2] >= 0) { - printf(" ****** Warning from MC64A/AD. INFO(1) = %2d\n" - " Some scaling factors may be too large.\n", info[1]); - } - } -/* 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 = %8d", *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; - int_t c__1 = 1; - - /* 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, DMACH */ -/* DOUBLE PRECISION FD05AD, DMACH */ -/* 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 = dmach("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; - int_t c__1 = 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) +void mc64id_(int *a) { - /* 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 = dmach("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, c__2 = 2; - - /* 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 = dmach("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_ */ - - + fprintf(stderr, "SuperLU: MC64 functionality not available (it uses non-free code). Aborting.\n"); + abort(); +} + +void mc64ad_(int *a, int *b, int *c, int d[], int e[], double f[], + int *g, int h[], int *i, int j[], int *k, double l[], + int m[], int n[]) +{ + fprintf(stderr, "SuperLU: MC64 functionality not available (it uses non-free code). Aborting.\n"); + abort(); +}