#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int chptrf_(char *uplo, integer *n, complex *ap, integer *
ipiv, integer *info)
{
/* -- LAPACK 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
=======
CHPTRF computes the factorization of a complex Hermitian packed
matrix A using the Bunch-Kaufman diagonal pivoting method:
A = U*D*U**H or A = L*D*L**H
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is Hermitian and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
On exit, the block diagonal matrix D and the multipliers used
to obtain the factor U or L, stored as a packed triangular
matrix overwriting A (see below for further details).
IPIV (output) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D.
If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.
If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, and division by zero will occur if it
is used to solve a system of equations.
Further Details
===============
5-96 - Based on modifications by J. Lewis, Boeing Computer Services
Company
If UPLO = 'U', then A = U*D*U', where
U = P(n)*U(n)* ... *P(k)U(k)* ...,
i.e., U is a product of terms P(k)*U(k), where k decreases from n to
1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
that if the diagonal block D(k) is of order s (s = 1 or 2), then
( I v 0 ) k-s
U(k) = ( 0 I 0 ) s
( 0 0 I ) n-k
k-s s n-k
If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
and A(k,k), and v overwrites A(1:k-2,k-1:k).
If UPLO = 'L', then A = L*D*L', where
L = P(1)*L(1)* ... *P(k)*L(k)* ...,
i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
that if the diagonal block D(k) is of order s (s = 1 or 2), then
( I 0 0 ) k-1
L(k) = ( 0 I 0 ) s
( 0 v I ) n-k-s+1
k-1 s n-k-s+1
If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5, i__6;
real r__1, r__2, r__3, r__4;
complex q__1, q__2, q__3, q__4, q__5, q__6;
/* Builtin functions */
double sqrt(doublereal), r_imag(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
extern /* Subroutine */ int chpr_(char *, integer *, real *, complex *,
integer *, complex *);
static integer imax, jmax;
static real d__;
static integer i__, j, k;
static complex t;
static real alpha;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int cswap_(integer *, complex *, integer *,
complex *, integer *);
static integer kstep;
static logical upper;
static real r1, d11;
static complex d12;
static real d22;
static complex d21;
extern doublereal slapy2_(real *, real *);
static integer kc, kk, kp;
static real absakk;
static complex wk;
static integer kx;
extern integer icamax_(integer *, complex *, integer *);
static real tt;
extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
*), xerbla_(char *, integer *);
static real colmax, rowmax;
static integer knc, kpc, npp;
static complex wkm1, wkp1;
--ipiv;
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHPTRF", &i__1);
return 0;
}
/* Initialize ALPHA for use in choosing pivot block size. */
alpha = (sqrt(17.f) + 1.f) / 8.f;
if (upper) {
/* Factorize A as U*D*U' using the upper triangle of A
K is the main loop index, decreasing from N to 1 in steps of
1 or 2 */
k = *n;
kc = (*n - 1) * *n / 2 + 1;
L10:
knc = kc;
/* If K < 1, exit from loop */
if (k < 1) {
goto L110;
}
kstep = 1;
/* Determine rows and columns to be interchanged and whether
a 1-by-1 or 2-by-2 pivot block will be used */
i__1 = kc + k - 1;
absakk = (r__1 = ap[i__1].r, dabs(r__1));
/* IMAX is the row-index of the largest off-diagonal element in
column K, and COLMAX is its absolute value */
if (k > 1) {
i__1 = k - 1;
imax = icamax_(&i__1, &ap[kc], &c__1);
i__1 = kc + imax - 1;
colmax = (r__1 = ap[i__1].r, dabs(r__1)) + (r__2 = r_imag(&ap[kc
+ imax - 1]), dabs(r__2));
} else {
colmax = 0.f;
}
if (dmax(absakk,colmax) == 0.f) {
/* Column K is zero: set INFO and continue */
if (*info == 0) {
*info = k;
}
kp = k;
i__1 = kc + k - 1;
i__2 = kc + k - 1;
r__1 = ap[i__2].r;
ap[i__1].r = r__1, ap[i__1].i = 0.f;
} else {
if (absakk >= alpha * colmax) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else {
/* JMAX is the column-index of the largest off-diagonal
element in row IMAX, and ROWMAX is its absolute value */
rowmax = 0.f;
jmax = imax;
kx = imax * (imax + 1) / 2 + imax;
i__1 = k;
for (j = imax + 1; j <= i__1; ++j) {
i__2 = kx;
if ((r__1 = ap[i__2].r, dabs(r__1)) + (r__2 = r_imag(&ap[
kx]), dabs(r__2)) > rowmax) {
i__2 = kx;
rowmax = (r__1 = ap[i__2].r, dabs(r__1)) + (r__2 =
r_imag(&ap[kx]), dabs(r__2));
jmax = j;
}
kx += j;
/* L20: */
}
kpc = (imax - 1) * imax / 2 + 1;
if (imax > 1) {
i__1 = imax - 1;
jmax = icamax_(&i__1, &ap[kpc], &c__1);
/* Computing MAX */
i__1 = kpc + jmax - 1;
r__3 = rowmax, r__4 = (r__1 = ap[i__1].r, dabs(r__1)) + (
r__2 = r_imag(&ap[kpc + jmax - 1]), dabs(r__2));
rowmax = dmax(r__3,r__4);
}
if (absakk >= alpha * colmax * (colmax / rowmax)) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else /* if(complicated condition) */ {
i__1 = kpc + imax - 1;
if ((r__1 = ap[i__1].r, dabs(r__1)) >= alpha * rowmax) {
/* interchange rows and columns K and IMAX, use 1-by-1
pivot block */
kp = imax;
} else {
/* interchange rows and columns K-1 and IMAX, use 2-by-2
pivot block */
kp = imax;
kstep = 2;
}
}
}
kk = k - kstep + 1;
if (kstep == 2) {
knc = knc - k + 1;
}
if (kp != kk) {
/* Interchange rows and columns KK and KP in the leading
submatrix A(1:k,1:k) */
i__1 = kp - 1;
cswap_(&i__1, &ap[knc], &c__1, &ap[kpc], &c__1);
kx = kpc + kp - 1;
i__1 = kk - 1;
for (j = kp + 1; j <= i__1; ++j) {
kx = kx + j - 1;
r_cnjg(&q__1, &ap[knc + j - 1]);
t.r = q__1.r, t.i = q__1.i;
i__2 = knc + j - 1;
r_cnjg(&q__1, &ap[kx]);
ap[i__2].r = q__1.r, ap[i__2].i = q__1.i;
i__2 = kx;
ap[i__2].r = t.r, ap[i__2].i = t.i;
/* L30: */
}
i__1 = kx + kk - 1;
r_cnjg(&q__1, &ap[kx + kk - 1]);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = knc + kk - 1;
r1 = ap[i__1].r;
i__1 = knc + kk - 1;
i__2 = kpc + kp - 1;
r__1 = ap[i__2].r;
ap[i__1].r = r__1, ap[i__1].i = 0.f;
i__1 = kpc + kp - 1;
ap[i__1].r = r1, ap[i__1].i = 0.f;
if (kstep == 2) {
i__1 = kc + k - 1;
i__2 = kc + k - 1;
r__1 = ap[i__2].r;
ap[i__1].r = r__1, ap[i__1].i = 0.f;
i__1 = kc + k - 2;
t.r = ap[i__1].r, t.i = ap[i__1].i;
i__1 = kc + k - 2;
i__2 = kc + kp - 1;
ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
i__1 = kc + kp - 1;
ap[i__1].r = t.r, ap[i__1].i = t.i;
}
} else {
i__1 = kc + k - 1;
i__2 = kc + k - 1;
r__1 = ap[i__2].r;
ap[i__1].r = r__1, ap[i__1].i = 0.f;
if (kstep == 2) {
i__1 = kc - 1;
i__2 = kc - 1;
r__1 = ap[i__2].r;
ap[i__1].r = r__1, ap[i__1].i = 0.f;
}
}
/* Update the leading submatrix */
if (kstep == 1) {
/* 1-by-1 pivot block D(k): column k now holds
W(k) = U(k)*D(k)
where U(k) is the k-th column of U
Perform a rank-1 update of A(1:k-1,1:k-1) as
A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)' */
i__1 = kc + k - 1;
r1 = 1.f / ap[i__1].r;
i__1 = k - 1;
r__1 = -r1;
chpr_(uplo, &i__1, &r__1, &ap[kc], &c__1, &ap[1]);
/* Store U(k) in column k */
i__1 = k - 1;
csscal_(&i__1, &r1, &ap[kc], &c__1);
} else {
/* 2-by-2 pivot block D(k): columns k and k-1 now hold
( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
where U(k) and U(k-1) are the k-th and (k-1)-th columns
of U
Perform a rank-2 update of A(1:k-2,1:k-2) as
A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
= A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )' */
if (k > 2) {
i__1 = k - 1 + (k - 1) * k / 2;
r__1 = ap[i__1].r;
r__2 = r_imag(&ap[k - 1 + (k - 1) * k / 2]);
d__ = slapy2_(&r__1, &r__2);
i__1 = k - 1 + (k - 2) * (k - 1) / 2;
d22 = ap[i__1].r / d__;
i__1 = k + (k - 1) * k / 2;
d11 = ap[i__1].r / d__;
tt = 1.f / (d11 * d22 - 1.f);
i__1 = k - 1 + (k - 1) * k / 2;
q__1.r = ap[i__1].r / d__, q__1.i = ap[i__1].i / d__;
d12.r = q__1.r, d12.i = q__1.i;
d__ = tt / d__;
for (j = k - 2; j >= 1; --j) {
i__1 = j + (k - 2) * (k - 1) / 2;
q__3.r = d11 * ap[i__1].r, q__3.i = d11 * ap[i__1].i;
r_cnjg(&q__5, &d12);
i__2 = j + (k - 1) * k / 2;
q__4.r = q__5.r * ap[i__2].r - q__5.i * ap[i__2].i,
q__4.i = q__5.r * ap[i__2].i + q__5.i * ap[
i__2].r;
q__2.r = q__3.r - q__4.r, q__2.i = q__3.i - q__4.i;
q__1.r = d__ * q__2.r, q__1.i = d__ * q__2.i;
wkm1.r = q__1.r, wkm1.i = q__1.i;
i__1 = j + (k - 1) * k / 2;
q__3.r = d22 * ap[i__1].r, q__3.i = d22 * ap[i__1].i;
i__2 = j + (k - 2) * (k - 1) / 2;
q__4.r = d12.r * ap[i__2].r - d12.i * ap[i__2].i,
q__4.i = d12.r * ap[i__2].i + d12.i * ap[i__2]
.r;
q__2.r = q__3.r - q__4.r, q__2.i = q__3.i - q__4.i;
q__1.r = d__ * q__2.r, q__1.i = d__ * q__2.i;
wk.r = q__1.r, wk.i = q__1.i;
for (i__ = j; i__ >= 1; --i__) {
i__1 = i__ + (j - 1) * j / 2;
i__2 = i__ + (j - 1) * j / 2;
i__3 = i__ + (k - 1) * k / 2;
r_cnjg(&q__4, &wk);
q__3.r = ap[i__3].r * q__4.r - ap[i__3].i *
q__4.i, q__3.i = ap[i__3].r * q__4.i + ap[
i__3].i * q__4.r;
q__2.r = ap[i__2].r - q__3.r, q__2.i = ap[i__2].i
- q__3.i;
i__4 = i__ + (k - 2) * (k - 1) / 2;
r_cnjg(&q__6, &wkm1);
q__5.r = ap[i__4].r * q__6.r - ap[i__4].i *
q__6.i, q__5.i = ap[i__4].r * q__6.i + ap[
i__4].i * q__6.r;
q__1.r = q__2.r - q__5.r, q__1.i = q__2.i -
q__5.i;
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
/* L40: */
}
i__1 = j + (k - 1) * k / 2;
ap[i__1].r = wk.r, ap[i__1].i = wk.i;
i__1 = j + (k - 2) * (k - 1) / 2;
ap[i__1].r = wkm1.r, ap[i__1].i = wkm1.i;
i__1 = j + (j - 1) * j / 2;
i__2 = j + (j - 1) * j / 2;
r__1 = ap[i__2].r;
q__1.r = r__1, q__1.i = 0.f;
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
/* L50: */
}
}
}
}
/* Store details of the interchanges in IPIV */
if (kstep == 1) {
ipiv[k] = kp;
} else {
ipiv[k] = -kp;
ipiv[k - 1] = -kp;
}
/* Decrease K and return to the start of the main loop */
k -= kstep;
kc = knc - k;
goto L10;
} else {
/* Factorize A as L*D*L' using the lower triangle of A
K is the main loop index, increasing from 1 to N in steps of
1 or 2 */
k = 1;
kc = 1;
npp = *n * (*n + 1) / 2;
L60:
knc = kc;
/* If K > N, exit from loop */
if (k > *n) {
goto L110;
}
kstep = 1;
/* Determine rows and columns to be interchanged and whether
a 1-by-1 or 2-by-2 pivot block will be used */
i__1 = kc;
absakk = (r__1 = ap[i__1].r, dabs(r__1));
/* IMAX is the row-index of the largest off-diagonal element in
column K, and COLMAX is its absolute value */
if (k < *n) {
i__1 = *n - k;
imax = k + icamax_(&i__1, &ap[kc + 1], &c__1);
i__1 = kc + imax - k;
colmax = (r__1 = ap[i__1].r, dabs(r__1)) + (r__2 = r_imag(&ap[kc
+ imax - k]), dabs(r__2));
} else {
colmax = 0.f;
}
if (dmax(absakk,colmax) == 0.f) {
/* Column K is zero: set INFO and continue */
if (*info == 0) {
*info = k;
}
kp = k;
i__1 = kc;
i__2 = kc;
r__1 = ap[i__2].r;
ap[i__1].r = r__1, ap[i__1].i = 0.f;
} else {
if (absakk >= alpha * colmax) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else {
/* JMAX is the column-index of the largest off-diagonal
element in row IMAX, and ROWMAX is its absolute value */
rowmax = 0.f;
kx = kc + imax - k;
i__1 = imax - 1;
for (j = k; j <= i__1; ++j) {
i__2 = kx;
if ((r__1 = ap[i__2].r, dabs(r__1)) + (r__2 = r_imag(&ap[
kx]), dabs(r__2)) > rowmax) {
i__2 = kx;
rowmax = (r__1 = ap[i__2].r, dabs(r__1)) + (r__2 =
r_imag(&ap[kx]), dabs(r__2));
jmax = j;
}
kx = kx + *n - j;
/* L70: */
}
kpc = npp - (*n - imax + 1) * (*n - imax + 2) / 2 + 1;
if (imax < *n) {
i__1 = *n - imax;
jmax = imax + icamax_(&i__1, &ap[kpc + 1], &c__1);
/* Computing MAX */
i__1 = kpc + jmax - imax;
r__3 = rowmax, r__4 = (r__1 = ap[i__1].r, dabs(r__1)) + (
r__2 = r_imag(&ap[kpc + jmax - imax]), dabs(r__2))
;
rowmax = dmax(r__3,r__4);
}
if (absakk >= alpha * colmax * (colmax / rowmax)) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else /* if(complicated condition) */ {
i__1 = kpc;
if ((r__1 = ap[i__1].r, dabs(r__1)) >= alpha * rowmax) {
/* interchange rows and columns K and IMAX, use 1-by-1
pivot block */
kp = imax;
} else {
/* interchange rows and columns K+1 and IMAX, use 2-by-2
pivot block */
kp = imax;
kstep = 2;
}
}
}
kk = k + kstep - 1;
if (kstep == 2) {
knc = knc + *n - k + 1;
}
if (kp != kk) {
/* Interchange rows and columns KK and KP in the trailing
submatrix A(k:n,k:n) */
if (kp < *n) {
i__1 = *n - kp;
cswap_(&i__1, &ap[knc + kp - kk + 1], &c__1, &ap[kpc + 1],
&c__1);
}
kx = knc + kp - kk;
i__1 = kp - 1;
for (j = kk + 1; j <= i__1; ++j) {
kx = kx + *n - j + 1;
r_cnjg(&q__1, &ap[knc + j - kk]);
t.r = q__1.r, t.i = q__1.i;
i__2 = knc + j - kk;
r_cnjg(&q__1, &ap[kx]);
ap[i__2].r = q__1.r, ap[i__2].i = q__1.i;
i__2 = kx;
ap[i__2].r = t.r, ap[i__2].i = t.i;
/* L80: */
}
i__1 = knc + kp - kk;
r_cnjg(&q__1, &ap[knc + kp - kk]);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = knc;
r1 = ap[i__1].r;
i__1 = knc;
i__2 = kpc;
r__1 = ap[i__2].r;
ap[i__1].r = r__1, ap[i__1].i = 0.f;
i__1 = kpc;
ap[i__1].r = r1, ap[i__1].i = 0.f;
if (kstep == 2) {
i__1 = kc;
i__2 = kc;
r__1 = ap[i__2].r;
ap[i__1].r = r__1, ap[i__1].i = 0.f;
i__1 = kc + 1;
t.r = ap[i__1].r, t.i = ap[i__1].i;
i__1 = kc + 1;
i__2 = kc + kp - k;
ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
i__1 = kc + kp - k;
ap[i__1].r = t.r, ap[i__1].i = t.i;
}
} else {
i__1 = kc;
i__2 = kc;
r__1 = ap[i__2].r;
ap[i__1].r = r__1, ap[i__1].i = 0.f;
if (kstep == 2) {
i__1 = knc;
i__2 = knc;
r__1 = ap[i__2].r;
ap[i__1].r = r__1, ap[i__1].i = 0.f;
}
}
/* Update the trailing submatrix */
if (kstep == 1) {
/* 1-by-1 pivot block D(k): column k now holds
W(k) = L(k)*D(k)
where L(k) is the k-th column of L */
if (k < *n) {
/* Perform a rank-1 update of A(k+1:n,k+1:n) as
A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)' */
i__1 = kc;
r1 = 1.f / ap[i__1].r;
i__1 = *n - k;
r__1 = -r1;
chpr_(uplo, &i__1, &r__1, &ap[kc + 1], &c__1, &ap[kc + *n
- k + 1]);
/* Store L(k) in column K */
i__1 = *n - k;
csscal_(&i__1, &r1, &ap[kc + 1], &c__1);
}
} else {
/* 2-by-2 pivot block D(k): columns K and K+1 now hold
( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
where L(k) and L(k+1) are the k-th and (k+1)-th columns
of L */
if (k < *n - 1) {
/* Perform a rank-2 update of A(k+2:n,k+2:n) as
A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
= A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
where L(k) and L(k+1) are the k-th and (k+1)-th
columns of L */
i__1 = k + 1 + (k - 1) * ((*n << 1) - k) / 2;
r__1 = ap[i__1].r;
r__2 = r_imag(&ap[k + 1 + (k - 1) * ((*n << 1) - k) / 2]);
d__ = slapy2_(&r__1, &r__2);
i__1 = k + 1 + k * ((*n << 1) - k - 1) / 2;
d11 = ap[i__1].r / d__;
i__1 = k + (k - 1) * ((*n << 1) - k) / 2;
d22 = ap[i__1].r / d__;
tt = 1.f / (d11 * d22 - 1.f);
i__1 = k + 1 + (k - 1) * ((*n << 1) - k) / 2;
q__1.r = ap[i__1].r / d__, q__1.i = ap[i__1].i / d__;
d21.r = q__1.r, d21.i = q__1.i;
d__ = tt / d__;
i__1 = *n;
for (j = k + 2; j <= i__1; ++j) {
i__2 = j + (k - 1) * ((*n << 1) - k) / 2;
q__3.r = d11 * ap[i__2].r, q__3.i = d11 * ap[i__2].i;
i__3 = j + k * ((*n << 1) - k - 1) / 2;
q__4.r = d21.r * ap[i__3].r - d21.i * ap[i__3].i,
q__4.i = d21.r * ap[i__3].i + d21.i * ap[i__3]
.r;
q__2.r = q__3.r - q__4.r, q__2.i = q__3.i - q__4.i;
q__1.r = d__ * q__2.r, q__1.i = d__ * q__2.i;
wk.r = q__1.r, wk.i = q__1.i;
i__2 = j + k * ((*n << 1) - k - 1) / 2;
q__3.r = d22 * ap[i__2].r, q__3.i = d22 * ap[i__2].i;
r_cnjg(&q__5, &d21);
i__3 = j + (k - 1) * ((*n << 1) - k) / 2;
q__4.r = q__5.r * ap[i__3].r - q__5.i * ap[i__3].i,
q__4.i = q__5.r * ap[i__3].i + q__5.i * ap[
i__3].r;
q__2.r = q__3.r - q__4.r, q__2.i = q__3.i - q__4.i;
q__1.r = d__ * q__2.r, q__1.i = d__ * q__2.i;
wkp1.r = q__1.r, wkp1.i = q__1.i;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + (j - 1) * ((*n << 1) - j) / 2;
i__4 = i__ + (j - 1) * ((*n << 1) - j) / 2;
i__5 = i__ + (k - 1) * ((*n << 1) - k) / 2;
r_cnjg(&q__4, &wk);
q__3.r = ap[i__5].r * q__4.r - ap[i__5].i *
q__4.i, q__3.i = ap[i__5].r * q__4.i + ap[
i__5].i * q__4.r;
q__2.r = ap[i__4].r - q__3.r, q__2.i = ap[i__4].i
- q__3.i;
i__6 = i__ + k * ((*n << 1) - k - 1) / 2;
r_cnjg(&q__6, &wkp1);
q__5.r = ap[i__6].r * q__6.r - ap[i__6].i *
q__6.i, q__5.i = ap[i__6].r * q__6.i + ap[
i__6].i * q__6.r;
q__1.r = q__2.r - q__5.r, q__1.i = q__2.i -
q__5.i;
ap[i__3].r = q__1.r, ap[i__3].i = q__1.i;
/* L90: */
}
i__2 = j + (k - 1) * ((*n << 1) - k) / 2;
ap[i__2].r = wk.r, ap[i__2].i = wk.i;
i__2 = j + k * ((*n << 1) - k - 1) / 2;
ap[i__2].r = wkp1.r, ap[i__2].i = wkp1.i;
i__2 = j + (j - 1) * ((*n << 1) - j) / 2;
i__3 = j + (j - 1) * ((*n << 1) - j) / 2;
r__1 = ap[i__3].r;
q__1.r = r__1, q__1.i = 0.f;
ap[i__2].r = q__1.r, ap[i__2].i = q__1.i;
/* L100: */
}
}
}
}
/* Store details of the interchanges in IPIV */
if (kstep == 1) {
ipiv[k] = kp;
} else {
ipiv[k] = -kp;
ipiv[k + 1] = -kp;
}
/* Increase K and return to the start of the main loop */
k += kstep;
kc = knc + *n - k + 2;
goto L60;
}
L110:
return 0;
/* End of CHPTRF */
} /* chptrf_ */