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/* lapack/double/dlatdf.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static doublereal c_b23 = 1.;
static doublereal c_b37 = -1.;
/*< >*/
/* Subroutine */ int dlatdf_(integer *ijob, integer *n, doublereal *z__,
integer *ldz, doublereal *rhs, doublereal *rdsum, doublereal *rdscal,
integer *ipiv, integer *jpiv)
{
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k;
doublereal bm, bp, xm[8], xp[8];
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
integer info;
doublereal temp, work[32];
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern doublereal dasum_(integer *, doublereal *, integer *);
doublereal pmone;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), daxpy_(integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *);
doublereal sminu;
integer iwork[8];
doublereal splus;
extern /* Subroutine */ int dgesc2_(integer *, doublereal *, integer *,
doublereal *, integer *, integer *, doublereal *), dgecon_(char *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *, integer *, ftnlen), dlassq_(integer *,
doublereal *, integer *, doublereal *, doublereal *), dlaswp_(
integer *, doublereal *, integer *, integer *, integer *, integer
*, integer *);
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/*< INTEGER IJOB, LDZ, N >*/
/*< DOUBLE PRECISION RDSCAL, RDSUM >*/
/* .. */
/* .. Array Arguments .. */
/*< INTEGER IPIV( * ), JPIV( * ) >*/
/*< DOUBLE PRECISION RHS( * ), Z( LDZ, * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* DLATDF uses the LU factorization of the n-by-n matrix Z computed by */
/* DGETC2 and computes a contribution to the reciprocal Dif-estimate */
/* by solving Z * x = b for x, and choosing the r.h.s. b such that */
/* the norm of x is as large as possible. On entry RHS = b holds the */
/* contribution from earlier solved sub-systems, and on return RHS = x. */
/* The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q, */
/* where P and Q are permutation matrices. L is lower triangular with */
/* unit diagonal elements and U is upper triangular. */
/* Arguments */
/* ========= */
/* IJOB (input) INTEGER */
/* IJOB = 2: First compute an approximative null-vector e */
/* of Z using DGECON, e is normalized and solve for */
/* Zx = +-e - f with the sign giving the greater value */
/* of 2-norm(x). About 5 times as expensive as Default. */
/* IJOB .ne. 2: Local look ahead strategy where all entries of */
/* the r.h.s. b is choosen as either +1 or -1 (Default). */
/* N (input) INTEGER */
/* The number of columns of the matrix Z. */
/* Z (input) DOUBLE PRECISION array, dimension (LDZ, N) */
/* On entry, the LU part of the factorization of the n-by-n */
/* matrix Z computed by DGETC2: Z = P * L * U * Q */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDA >= max(1, N). */
/* RHS (input/output) DOUBLE PRECISION array, dimension N. */
/* On entry, RHS contains contributions from other subsystems. */
/* On exit, RHS contains the solution of the subsystem with */
/* entries acoording to the value of IJOB (see above). */
/* RDSUM (input/output) DOUBLE PRECISION */
/* On entry, the sum of squares of computed contributions to */
/* the Dif-estimate under computation by DTGSYL, where the */
/* scaling factor RDSCAL (see below) has been factored out. */
/* On exit, the corresponding sum of squares updated with the */
/* contributions from the current sub-system. */
/* If TRANS = 'T' RDSUM is not touched. */
/* NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL. */
/* RDSCAL (input/output) DOUBLE PRECISION */
/* On entry, scaling factor used to prevent overflow in RDSUM. */
/* On exit, RDSCAL is updated w.r.t. the current contributions */
/* in RDSUM. */
/* If TRANS = 'T', RDSCAL is not touched. */
/* NOTE: RDSCAL only makes sense when DTGSY2 is called by */
/* DTGSYL. */
/* IPIV (input) INTEGER array, dimension (N). */
/* The pivot indices; for 1 <= i <= N, row i of the */
/* matrix has been interchanged with row IPIV(i). */
/* JPIV (input) INTEGER array, dimension (N). */
/* The pivot indices; for 1 <= j <= N, column j of the */
/* matrix has been interchanged with column JPIV(j). */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* Umea University, S-901 87 Umea, Sweden. */
/* This routine is a further developed implementation of algorithm */
/* BSOLVE in [1] using complete pivoting in the LU factorization. */
/* [1] Bo Kagstrom and Lars Westin, */
/* Generalized Schur Methods with Condition Estimators for */
/* Solving the Generalized Sylvester Equation, IEEE Transactions */
/* on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. */
/* [2] Peter Poromaa, */
/* On Efficient and Robust Estimators for the Separation */
/* between two Regular Matrix Pairs with Applications in */
/* Condition Estimation. Report IMINF-95.05, Departement of */
/* Computing Science, Umea University, S-901 87 Umea, Sweden, 1995. */
/* ===================================================================== */
/* .. Parameters .. */
/*< INTEGER MAXDIM >*/
/*< PARAMETER ( MAXDIM = 8 ) >*/
/*< DOUBLE PRECISION ZERO, ONE >*/
/*< PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER I, INFO, J, K >*/
/*< DOUBLE PRECISION BM, BP, PMONE, SMINU, SPLUS, TEMP >*/
/* .. */
/* .. Local Arrays .. */
/*< INTEGER IWORK( MAXDIM ) >*/
/*< DOUBLE PRECISION WORK( 4*MAXDIM ), XM( MAXDIM ), XP( MAXDIM ) >*/
/* .. */
/* .. External Subroutines .. */
/*< >*/
/* .. */
/* .. External Functions .. */
/*< DOUBLE PRECISION DASUM, DDOT >*/
/*< EXTERNAL DASUM, DDOT >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, SQRT >*/
/* .. */
/* .. Executable Statements .. */
/*< IF( IJOB.NE.2 ) THEN >*/
/* Parameter adjustments */
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--rhs;
--ipiv;
--jpiv;
/* Function Body */
if (*ijob != 2) {
/* Apply permutations IPIV to RHS */
/*< CALL DLASWP( 1, RHS, LDZ, 1, N-1, IPIV, 1 ) >*/
i__1 = *n - 1;
dlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &ipiv[1], &c__1);
/* Solve for L-part choosing RHS either to +1 or -1. */
/*< PMONE = -ONE >*/
pmone = -1.;
/*< DO 10 J = 1, N - 1 >*/
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
/*< BP = RHS( J ) + ONE >*/
bp = rhs[j] + 1.;
/*< BM = RHS( J ) - ONE >*/
bm = rhs[j] - 1.;
/*< SPLUS = ONE >*/
splus = 1.;
/* Look-ahead for L-part RHS(1:N-1) = + or -1, SPLUS and */
/* SMIN computed more efficiently than in BSOLVE [1]. */
/*< SPLUS = SPLUS + DDOT( N-J, Z( J+1, J ), 1, Z( J+1, J ), 1 ) >*/
i__2 = *n - j;
splus += ddot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &z__[j + 1
+ j * z_dim1], &c__1);
/*< SMINU = DDOT( N-J, Z( J+1, J ), 1, RHS( J+1 ), 1 ) >*/
i__2 = *n - j;
sminu = ddot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
&c__1);
/*< SPLUS = SPLUS*RHS( J ) >*/
splus *= rhs[j];
/*< IF( SPLUS.GT.SMINU ) THEN >*/
if (splus > sminu) {
/*< RHS( J ) = BP >*/
rhs[j] = bp;
/*< ELSE IF( SMINU.GT.SPLUS ) THEN >*/
} else if (sminu > splus) {
/*< RHS( J ) = BM >*/
rhs[j] = bm;
/*< ELSE >*/
} else {
/* In this case the updating sums are equal and we can */
/* choose RHS(J) +1 or -1. The first time this happens */
/* we choose -1, thereafter +1. This is a simple way to */
/* get good estimates of matrices like Byers well-known */
/* example (see [1]). (Not done in BSOLVE.) */
/*< RHS( J ) = RHS( J ) + PMONE >*/
rhs[j] += pmone;
/*< PMONE = ONE >*/
pmone = 1.;
/*< END IF >*/
}
/* Compute the remaining r.h.s. */
/*< TEMP = -RHS( J ) >*/
temp = -rhs[j];
/*< CALL DAXPY( N-J, TEMP, Z( J+1, J ), 1, RHS( J+1 ), 1 ) >*/
i__2 = *n - j;
daxpy_(&i__2, &temp, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
&c__1);
/*< 10 CONTINUE >*/
/* L10: */
}
/* Solve for U-part, look-ahead for RHS(N) = +-1. This is not done */
/* in BSOLVE and will hopefully give us a better estimate because */
/* any ill-conditioning of the original matrix is transfered to U */
/* and not to L. U(N, N) is an approximation to sigma_min(LU). */
/*< CALL DCOPY( N-1, RHS, 1, XP, 1 ) >*/
i__1 = *n - 1;
dcopy_(&i__1, &rhs[1], &c__1, xp, &c__1);
/*< XP( N ) = RHS( N ) + ONE >*/
xp[*n - 1] = rhs[*n] + 1.;
/*< RHS( N ) = RHS( N ) - ONE >*/
rhs[*n] += -1.;
/*< SPLUS = ZERO >*/
splus = 0.;
/*< SMINU = ZERO >*/
sminu = 0.;
/*< DO 30 I = N, 1, -1 >*/
for (i__ = *n; i__ >= 1; --i__) {
/*< TEMP = ONE / Z( I, I ) >*/
temp = 1. / z__[i__ + i__ * z_dim1];
/*< XP( I ) = XP( I )*TEMP >*/
xp[i__ - 1] *= temp;
/*< RHS( I ) = RHS( I )*TEMP >*/
rhs[i__] *= temp;
/*< DO 20 K = I + 1, N >*/
i__1 = *n;
for (k = i__ + 1; k <= i__1; ++k) {
/*< XP( I ) = XP( I ) - XP( K )*( Z( I, K )*TEMP ) >*/
xp[i__ - 1] -= xp[k - 1] * (z__[i__ + k * z_dim1] * temp);
/*< RHS( I ) = RHS( I ) - RHS( K )*( Z( I, K )*TEMP ) >*/
rhs[i__] -= rhs[k] * (z__[i__ + k * z_dim1] * temp);
/*< 20 CONTINUE >*/
/* L20: */
}
/*< SPLUS = SPLUS + ABS( XP( I ) ) >*/
splus += (d__1 = xp[i__ - 1], abs(d__1));
/*< SMINU = SMINU + ABS( RHS( I ) ) >*/
sminu += (d__1 = rhs[i__], abs(d__1));
/*< 30 CONTINUE >*/
/* L30: */
}
/*< >*/
if (splus > sminu) {
dcopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Apply the permutations JPIV to the computed solution (RHS) */
/*< CALL DLASWP( 1, RHS, LDZ, 1, N-1, JPIV, -1 ) >*/
i__1 = *n - 1;
dlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);
/* Compute the sum of squares */
/*< CALL DLASSQ( N, RHS, 1, RDSCAL, RDSUM ) >*/
dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);
/*< ELSE >*/
} else {
/* IJOB = 2, Compute approximate nullvector XM of Z */
/*< CALL DGECON( 'I', N, Z, LDZ, ONE, TEMP, WORK, IWORK, INFO ) >*/
dgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, &
info, (ftnlen)1);
/*< CALL DCOPY( N, WORK( N+1 ), 1, XM, 1 ) >*/
dcopy_(n, &work[*n], &c__1, xm, &c__1);
/* Compute RHS */
/*< CALL DLASWP( 1, XM, LDZ, 1, N-1, IPIV, -1 ) >*/
i__1 = *n - 1;
dlaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
/*< TEMP = ONE / SQRT( DDOT( N, XM, 1, XM, 1 ) ) >*/
temp = 1. / sqrt(ddot_(n, xm, &c__1, xm, &c__1));
/*< CALL DSCAL( N, TEMP, XM, 1 ) >*/
dscal_(n, &temp, xm, &c__1);
/*< CALL DCOPY( N, XM, 1, XP, 1 ) >*/
dcopy_(n, xm, &c__1, xp, &c__1);
/*< CALL DAXPY( N, ONE, RHS, 1, XP, 1 ) >*/
daxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1);
/*< CALL DAXPY( N, -ONE, XM, 1, RHS, 1 ) >*/
daxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1);
/*< CALL DGESC2( N, Z, LDZ, RHS, IPIV, JPIV, TEMP ) >*/
dgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &temp);
/*< CALL DGESC2( N, Z, LDZ, XP, IPIV, JPIV, TEMP ) >*/
dgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &temp);
/*< >*/
if (dasum_(n, xp, &c__1) > dasum_(n, &rhs[1], &c__1)) {
dcopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Compute the sum of squares */
/*< CALL DLASSQ( N, RHS, 1, RDSCAL, RDSUM ) >*/
dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of DLATDF */
/*< END >*/
} /* dlatdf_ */
#ifdef __cplusplus
}
#endif
|
