int main()
{
const int N=1000;
double *a;
double *b;
double scale;
int *ipiv, *jpiv;
double maxerr;
int i,j, info;
a=malloc(sizeof(double)*N*N);
if(a==NULL){
perror("");
exit(1);
}
b=malloc(sizeof(double)*N);
if(b==NULL){
perror("");
exit(1);
}
ipiv=malloc(sizeof(int)*N);
if(ipiv==NULL){
perror("");
exit(1);
}
jpiv=malloc(sizeof(int)*N);
if(jpiv==NULL){
perror("");
exit(1);
}
/* matrix from http://www.cs.yale.edu/homes/spielman/BAP/lect6.pdf */
for(i=0; i<N; i++){
for(j=0; j<i; j++){
a[i+j*N]=-1.0;
}
a[i+i*N]=1.0;
for(j=i+1; j<N-1; j++){
a[i+j*N]=0.0;
}
a[i+(N-1)*N]=1.0;
b[i]=0.0;
for(j=0; j<N; j++){
b[i]+=a[i+j*N];
}
ipiv[i]=0;
jpiv[i]=0;
}
/* solve */
mydgetc2_(&N, a, &N, ipiv, jpiv, &info);
dgesc2_(&N, a, &N, b, ipiv, jpiv, &scale);
if(scale!=1.0){
for(i=0; i<N; i++){
b[i]*=scale;
}
}
/* output */
maxerr=0.0;
for(i=0; i<N; i++){
if(!(fabs(b[i]-1.0)<=fabs(maxerr))){
maxerr=b[i]-1.0;
}
}
printf("%g\n",maxerr);
if(!(fabs(maxerr)<=1.0e-8)){
fprintf(stderr, "Large error\n");
exit(1);
}
free(a);
free(b);
free(ipiv);
free(jpiv);
return 0;
}
/* Subroutine */ int dlatdf_(integer *ijob, integer *n, doublereal *z__,
integer *ldz, doublereal *rhs, doublereal *rdsum, doublereal *rdscal,
integer *ipiv, integer *jpiv)
{
/* -- 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
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.
=====================================================================
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static doublereal c_b23 = 1.;
static doublereal c_b37 = -1.;
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
static integer info;
static doublereal temp, work[32];
static integer i__, j, k;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern doublereal dasum_(integer *, doublereal *, integer *);
static doublereal pmone;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), daxpy_(integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *);
static doublereal sminu;
static integer iwork[8];
static doublereal splus;
extern /* Subroutine */ int dgesc2_(integer *, doublereal *, integer *,
doublereal *, integer *, integer *, doublereal *);
static doublereal bm, bp;
extern /* Subroutine */ int dgecon_(char *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, integer *,
integer *);
static doublereal xm[8], xp[8];
extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *,
doublereal *, doublereal *), dlaswp_(integer *, doublereal *,
integer *, integer *, integer *, integer *, integer *);
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--rhs;
--ipiv;
--jpiv;
/* Function Body */
if (*ijob != 2) {
/* Apply permutations IPIV to RHS */
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 = -1.;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
bp = rhs[j] + 1.;
bm = rhs[j] - 1.;
splus = 1.;
/* Look-ahead for L-part RHS(1:N-1) = + or -1, SPLUS and
SMIN computed more efficiently than in BSOLVE [1]. */
i__2 = *n - j;
splus += ddot_(&i__2, &z___ref(j + 1, j), &c__1, &z___ref(j + 1,
j), &c__1);
i__2 = *n - j;
sminu = ddot_(&i__2, &z___ref(j + 1, j), &c__1, &rhs[j + 1], &
c__1);
splus *= rhs[j];
if (splus > sminu) {
rhs[j] = bp;
} else if (sminu > splus) {
rhs[j] = bm;
} 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] += pmone;
pmone = 1.;
}
/* Compute the remaining r.h.s. */
temp = -rhs[j];
i__2 = *n - j;
daxpy_(&i__2, &temp, &z___ref(j + 1, j), &c__1, &rhs[j + 1], &
c__1);
/* 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). */
i__1 = *n - 1;
dcopy_(&i__1, &rhs[1], &c__1, xp, &c__1);
xp[*n - 1] = rhs[*n] + 1.;
rhs[*n] += -1.;
splus = 0.;
sminu = 0.;
for (i__ = *n; i__ >= 1; --i__) {
temp = 1. / z___ref(i__, i__);
xp[i__ - 1] *= temp;
rhs[i__] *= temp;
i__1 = *n;
for (k = i__ + 1; k <= i__1; ++k) {
xp[i__ - 1] -= xp[k - 1] * (z___ref(i__, k) * temp);
rhs[i__] -= rhs[k] * (z___ref(i__, k) * temp);
/* L20: */
}
splus += (d__1 = xp[i__ - 1], abs(d__1));
sminu += (d__1 = rhs[i__], abs(d__1));
/* L30: */
}
if (splus > sminu) {
dcopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Apply the permutations JPIV to the computed solution (RHS) */
i__1 = *n - 1;
dlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);
/* Compute the sum of squares */
dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);
} else {
/* IJOB = 2, Compute approximate nullvector XM of Z */
dgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, &
info);
dcopy_(n, &work[*n], &c__1, xm, &c__1);
/* Compute RHS */
i__1 = *n - 1;
dlaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
temp = 1. / sqrt(ddot_(n, xm, &c__1, xm, &c__1));
dscal_(n, &temp, xm, &c__1);
dcopy_(n, xm, &c__1, xp, &c__1);
daxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1);
daxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1);
dgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &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 */
dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);
}
return 0;
/* End of DLATDF */
} /* dlatdf_ */
/*< >*/
/* 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_ */
