/* Subroutine */
int zsytf2_rook_(char *uplo, integer *n, doublecomplex *a, integer *lda, integer *ipiv, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
doublecomplex z__1, z__2, z__3, z__4, z__5, z__6;
/* Builtin functions */
double sqrt(doublereal), d_imag(doublecomplex *);
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j, k, p;
doublecomplex t, d11, d12, d21, d22;
integer ii, kk, kp;
doublecomplex wk, wkm1, wkp1;
logical done;
integer imax, jmax;
extern /* Subroutine */
int zsyr_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *);
doublereal alpha;
extern logical lsame_(char *, char *);
doublereal dtemp, sfmin;
extern /* Subroutine */
int zscal_(integer *, doublecomplex *, doublecomplex *, integer *);
integer itemp, kstep;
logical upper;
extern /* Subroutine */
int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *);
extern doublereal dlamch_(char *);
doublereal absakk;
extern /* Subroutine */
int xerbla_(char *, integer *);
doublereal colmax;
extern integer izamax_(integer *, doublecomplex *, integer *);
doublereal rowmax;
/* -- LAPACK computational routine (version 3.5.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2013 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L"))
{
*info = -1;
}
else if (*n < 0)
{
*info = -2;
}
else if (*lda < max(1,*n))
{
*info = -4;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("ZSYTF2_ROOK", &i__1);
return 0;
}
/* Initialize ALPHA for use in choosing pivot block size. */
alpha = (sqrt(17.) + 1.) / 8.;
/* Compute machine safe minimum */
sfmin = dlamch_("S");
if (upper)
{
/* Factorize A as U*D*U**T 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;
L10: /* If K < 1, exit from loop */
if (k < 1)
{
goto L70;
}
kstep = 1;
p = k;
/* Determine rows and columns to be interchanged and whether */
/* a 1-by-1 or 2-by-2 pivot block will be used */
i__1 = k + k * a_dim1;
absakk = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k + k * a_dim1]), abs(d__2));
/* IMAX is the row-index of the largest off-diagonal element in */
/* column K, and COLMAX is its absolute value. */
/* Determine both COLMAX and IMAX. */
if (k > 1)
{
i__1 = k - 1;
imax = izamax_(&i__1, &a[k * a_dim1 + 1], &c__1);
i__1 = imax + k * a_dim1;
colmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[imax + k * a_dim1]), abs(d__2));
}
else
{
colmax = 0.;
}
if (max(absakk,colmax) == 0.)
{
/* Column K is zero or underflow: set INFO and continue */
if (*info == 0)
{
*info = k;
}
kp = k;
}
else
{
/* Test for interchange */
/* Equivalent to testing for (used to handle NaN and Inf) */
/* ABSAKK.GE.ALPHA*COLMAX */
if (! (absakk < alpha * colmax))
{
/* no interchange, */
/* use 1-by-1 pivot block */
kp = k;
}
else
{
done = FALSE_;
/* Loop until pivot found */
L12: /* Begin pivot search loop body */
/* JMAX is the column-index of the largest off-diagonal */
/* element in row IMAX, and ROWMAX is its absolute value. */
/* Determine both ROWMAX and JMAX. */
if (imax != k)
{
i__1 = k - imax;
jmax = imax + izamax_(&i__1, &a[imax + (imax + 1) * a_dim1], lda);
i__1 = imax + jmax * a_dim1;
rowmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(& a[imax + jmax * a_dim1]), abs(d__2));
}
else
{
rowmax = 0.;
}
if (imax > 1)
{
i__1 = imax - 1;
itemp = izamax_(&i__1, &a[imax * a_dim1 + 1], &c__1);
i__1 = itemp + imax * a_dim1;
dtemp = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[ itemp + imax * a_dim1]), abs(d__2));
if (dtemp > rowmax)
{
rowmax = dtemp;
jmax = itemp;
}
}
/* Equivalent to testing for (used to handle NaN and Inf) */
/* CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX */
i__1 = imax + imax * a_dim1;
if (! ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[imax + imax * a_dim1]), abs(d__2)) < alpha * rowmax))
{
/* interchange rows and columns K and IMAX, */
/* use 1-by-1 pivot block */
kp = imax;
done = TRUE_;
/* Equivalent to testing for ROWMAX .EQ. COLMAX, */
/* used to handle NaN and Inf */
}
else if (p == jmax || rowmax <= colmax)
{
/* interchange rows and columns K+1 and IMAX, */
/* use 2-by-2 pivot block */
kp = imax;
kstep = 2;
done = TRUE_;
}
else
{
/* Pivot NOT found, set variables and repeat */
p = imax;
colmax = rowmax;
imax = jmax;
}
/* End pivot search loop body */
if (! done)
{
goto L12;
}
}
/* Swap TWO rows and TWO columns */
/* First swap */
if (kstep == 2 && p != k)
{
/* Interchange rows and column K and P in the leading */
/* submatrix A(1:k,1:k) if we have a 2-by-2 pivot */
if (p > 1)
{
i__1 = p - 1;
zswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &c__1);
}
if (p < k - 1)
{
i__1 = k - p - 1;
zswap_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p + 1) * a_dim1], lda);
}
i__1 = k + k * a_dim1;
t.r = a[i__1].r;
t.i = a[i__1].i; // , expr subst
i__1 = k + k * a_dim1;
i__2 = p + p * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = p + p * a_dim1;
a[i__1].r = t.r;
a[i__1].i = t.i; // , expr subst
}
/* Second swap */
kk = k - kstep + 1;
if (kp != kk)
{
/* Interchange rows and columns KK and KP in the leading */
/* submatrix A(1:k,1:k) */
if (kp > 1)
{
i__1 = kp - 1;
zswap_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &c__1);
}
if (kk > 1 && kp < kk - 1)
{
i__1 = kk - kp - 1;
zswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + ( kp + 1) * a_dim1], lda);
}
i__1 = kk + kk * a_dim1;
t.r = a[i__1].r;
t.i = a[i__1].i; // , expr subst
i__1 = kk + kk * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + kp * a_dim1;
a[i__1].r = t.r;
a[i__1].i = t.i; // , expr subst
if (kstep == 2)
{
i__1 = k - 1 + k * a_dim1;
t.r = a[i__1].r;
t.i = a[i__1].i; // , expr subst
i__1 = k - 1 + k * a_dim1;
i__2 = kp + k * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + k * a_dim1;
a[i__1].r = t.r;
a[i__1].i = t.i; // , expr subst
}
}
/* 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 */
if (k > 1)
{
/* Perform a rank-1 update of A(1:k-1,1:k-1) and */
/* store U(k) in column k */
i__1 = k + k * a_dim1;
if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k + k * a_dim1]), abs(d__2)) >= sfmin)
{
/* Perform a rank-1 update of A(1:k-1,1:k-1) as */
/* A := A - U(k)*D(k)*U(k)**T */
/* = A - W(k)*1/D(k)*W(k)**T */
z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
d11.r = z__1.r;
d11.i = z__1.i; // , expr subst
i__1 = k - 1;
z__1.r = -d11.r;
z__1.i = -d11.i; // , expr subst
zsyr_(uplo, &i__1, &z__1, &a[k * a_dim1 + 1], &c__1, & a[a_offset], lda);
/* Store U(k) in column k */
i__1 = k - 1;
zscal_(&i__1, &d11, &a[k * a_dim1 + 1], &c__1);
}
else
{
/* Store L(k) in column K */
i__1 = k + k * a_dim1;
d11.r = a[i__1].r;
d11.i = a[i__1].i; // , expr subst
i__1 = k - 1;
for (ii = 1;
ii <= i__1;
++ii)
{
i__2 = ii + k * a_dim1;
z_div(&z__1, &a[ii + k * a_dim1], &d11);
a[i__2].r = z__1.r;
a[i__2].i = z__1.i; // , expr subst
/* L16: */
}
/* Perform a rank-1 update of A(k+1:n,k+1:n) as */
/* A := A - U(k)*D(k)*U(k)**T */
/* = A - W(k)*(1/D(k))*W(k)**T */
/* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T */
i__1 = k - 1;
z__1.r = -d11.r;
z__1.i = -d11.i; // , expr subst
zsyr_(uplo, &i__1, &z__1, &a[k * a_dim1 + 1], &c__1, & a[a_offset], lda);
}
}
}
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) )**T */
/* = A - ( ( A(k-1)A(k) )*inv(D(k)) ) * ( A(k-1)A(k) )**T */
/* and store L(k) and L(k+1) in columns k and k+1 */
if (k > 2)
{
i__1 = k - 1 + k * a_dim1;
d12.r = a[i__1].r;
d12.i = a[i__1].i; // , expr subst
z_div(&z__1, &a[k - 1 + (k - 1) * a_dim1], &d12);
d22.r = z__1.r;
d22.i = z__1.i; // , expr subst
z_div(&z__1, &a[k + k * a_dim1], &d12);
d11.r = z__1.r;
d11.i = z__1.i; // , expr subst
z__3.r = d11.r * d22.r - d11.i * d22.i;
z__3.i = d11.r * d22.i + d11.i * d22.r; // , expr subst
z__2.r = z__3.r - 1.;
z__2.i = z__3.i - 0.; // , expr subst
z_div(&z__1, &c_b1, &z__2);
t.r = z__1.r;
t.i = z__1.i; // , expr subst
for (j = k - 2;
j >= 1;
--j)
{
i__1 = j + (k - 1) * a_dim1;
z__3.r = d11.r * a[i__1].r - d11.i * a[i__1].i;
z__3.i = d11.r * a[i__1].i + d11.i * a[i__1] .r; // , expr subst
i__2 = j + k * a_dim1;
z__2.r = z__3.r - a[i__2].r;
z__2.i = z__3.i - a[i__2] .i; // , expr subst
z__1.r = t.r * z__2.r - t.i * z__2.i;
z__1.i = t.r * z__2.i + t.i * z__2.r; // , expr subst
wkm1.r = z__1.r;
wkm1.i = z__1.i; // , expr subst
i__1 = j + k * a_dim1;
z__3.r = d22.r * a[i__1].r - d22.i * a[i__1].i;
z__3.i = d22.r * a[i__1].i + d22.i * a[i__1] .r; // , expr subst
i__2 = j + (k - 1) * a_dim1;
z__2.r = z__3.r - a[i__2].r;
z__2.i = z__3.i - a[i__2] .i; // , expr subst
z__1.r = t.r * z__2.r - t.i * z__2.i;
z__1.i = t.r * z__2.i + t.i * z__2.r; // , expr subst
wk.r = z__1.r;
wk.i = z__1.i; // , expr subst
for (i__ = j;
i__ >= 1;
--i__)
{
i__1 = i__ + j * a_dim1;
i__2 = i__ + j * a_dim1;
z_div(&z__4, &a[i__ + k * a_dim1], &d12);
z__3.r = z__4.r * wk.r - z__4.i * wk.i;
z__3.i = z__4.r * wk.i + z__4.i * wk.r; // , expr subst
z__2.r = a[i__2].r - z__3.r;
z__2.i = a[i__2].i - z__3.i; // , expr subst
z_div(&z__6, &a[i__ + (k - 1) * a_dim1], &d12);
z__5.r = z__6.r * wkm1.r - z__6.i * wkm1.i;
z__5.i = z__6.r * wkm1.i + z__6.i * wkm1.r; // , expr subst
z__1.r = z__2.r - z__5.r;
z__1.i = z__2.i - z__5.i; // , expr subst
a[i__1].r = z__1.r;
a[i__1].i = z__1.i; // , expr subst
/* L20: */
}
/* Store U(k) and U(k-1) in cols k and k-1 for row J */
i__1 = j + k * a_dim1;
z_div(&z__1, &wk, &d12);
a[i__1].r = z__1.r;
a[i__1].i = z__1.i; // , expr subst
i__1 = j + (k - 1) * a_dim1;
z_div(&z__1, &wkm1, &d12);
a[i__1].r = z__1.r;
a[i__1].i = z__1.i; // , expr subst
/* L30: */
}
}
}
}
/* Store details of the interchanges in IPIV */
if (kstep == 1)
{
ipiv[k] = kp;
}
else
{
ipiv[k] = -p;
ipiv[k - 1] = -kp;
}
/* Decrease K and return to the start of the main loop */
k -= kstep;
goto L10;
}
else
{
/* Factorize A as L*D*L**T 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;
L40: /* If K > N, exit from loop */
if (k > *n)
{
goto L70;
}
kstep = 1;
p = k;
/* Determine rows and columns to be interchanged and whether */
/* a 1-by-1 or 2-by-2 pivot block will be used */
i__1 = k + k * a_dim1;
absakk = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k + k * a_dim1]), abs(d__2));
/* IMAX is the row-index of the largest off-diagonal element in */
/* column K, and COLMAX is its absolute value. */
/* Determine both COLMAX and IMAX. */
if (k < *n)
{
i__1 = *n - k;
imax = k + izamax_(&i__1, &a[k + 1 + k * a_dim1], &c__1);
i__1 = imax + k * a_dim1;
colmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[imax + k * a_dim1]), abs(d__2));
}
else
{
colmax = 0.;
}
if (max(absakk,colmax) == 0.)
{
/* Column K is zero or underflow: set INFO and continue */
if (*info == 0)
{
*info = k;
}
kp = k;
}
else
{
/* Test for interchange */
/* Equivalent to testing for (used to handle NaN and Inf) */
/* ABSAKK.GE.ALPHA*COLMAX */
if (! (absakk < alpha * colmax))
{
/* no interchange, use 1-by-1 pivot block */
kp = k;
}
else
{
done = FALSE_;
/* Loop until pivot found */
L42: /* Begin pivot search loop body */
/* JMAX is the column-index of the largest off-diagonal */
/* element in row IMAX, and ROWMAX is its absolute value. */
/* Determine both ROWMAX and JMAX. */
if (imax != k)
{
i__1 = imax - k;
jmax = k - 1 + izamax_(&i__1, &a[imax + k * a_dim1], lda);
i__1 = imax + jmax * a_dim1;
rowmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(& a[imax + jmax * a_dim1]), abs(d__2));
}
else
{
rowmax = 0.;
}
if (imax < *n)
{
i__1 = *n - imax;
itemp = imax + izamax_(&i__1, &a[imax + 1 + imax * a_dim1] , &c__1);
i__1 = itemp + imax * a_dim1;
dtemp = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[ itemp + imax * a_dim1]), abs(d__2));
if (dtemp > rowmax)
{
rowmax = dtemp;
jmax = itemp;
}
}
/* Equivalent to testing for (used to handle NaN and Inf) */
/* CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX */
i__1 = imax + imax * a_dim1;
if (! ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[imax + imax * a_dim1]), abs(d__2)) < alpha * rowmax))
{
/* interchange rows and columns K and IMAX, */
/* use 1-by-1 pivot block */
kp = imax;
done = TRUE_;
/* Equivalent to testing for ROWMAX .EQ. COLMAX, */
/* used to handle NaN and Inf */
}
else if (p == jmax || rowmax <= colmax)
{
/* interchange rows and columns K+1 and IMAX, */
/* use 2-by-2 pivot block */
kp = imax;
kstep = 2;
done = TRUE_;
}
else
{
/* Pivot NOT found, set variables and repeat */
p = imax;
colmax = rowmax;
imax = jmax;
}
/* End pivot search loop body */
if (! done)
{
goto L42;
}
}
/* Swap TWO rows and TWO columns */
/* First swap */
if (kstep == 2 && p != k)
{
/* Interchange rows and column K and P in the trailing */
/* submatrix A(k:n,k:n) if we have a 2-by-2 pivot */
if (p < *n)
{
i__1 = *n - p;
zswap_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + 1 + p * a_dim1], &c__1);
}
if (p > k + 1)
{
i__1 = p - k - 1;
zswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[p + (k + 1) * a_dim1], lda);
}
i__1 = k + k * a_dim1;
t.r = a[i__1].r;
t.i = a[i__1].i; // , expr subst
i__1 = k + k * a_dim1;
i__2 = p + p * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = p + p * a_dim1;
a[i__1].r = t.r;
a[i__1].i = t.i; // , expr subst
}
/* Second swap */
kk = k + kstep - 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;
zswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1 + kp * a_dim1], &c__1);
}
if (kk < *n && kp > kk + 1)
{
i__1 = kp - kk - 1;
zswap_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + ( kk + 1) * a_dim1], lda);
}
i__1 = kk + kk * a_dim1;
t.r = a[i__1].r;
t.i = a[i__1].i; // , expr subst
i__1 = kk + kk * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + kp * a_dim1;
a[i__1].r = t.r;
a[i__1].i = t.i; // , expr subst
if (kstep == 2)
{
i__1 = k + 1 + k * a_dim1;
t.r = a[i__1].r;
t.i = a[i__1].i; // , expr subst
i__1 = k + 1 + k * a_dim1;
i__2 = kp + k * a_dim1;
a[i__1].r = a[i__2].r;
a[i__1].i = a[i__2].i; // , expr subst
i__1 = kp + k * a_dim1;
a[i__1].r = t.r;
a[i__1].i = t.i; // , expr subst
}
}
/* 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) and */
/* store L(k) in column k */
i__1 = k + k * a_dim1;
if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k + k * a_dim1]), abs(d__2)) >= sfmin)
{
/* Perform a rank-1 update of A(k+1:n,k+1:n) as */
/* A := A - L(k)*D(k)*L(k)**T */
/* = A - W(k)*(1/D(k))*W(k)**T */
z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
d11.r = z__1.r;
d11.i = z__1.i; // , expr subst
i__1 = *n - k;
z__1.r = -d11.r;
z__1.i = -d11.i; // , expr subst
zsyr_(uplo, &i__1, &z__1, &a[k + 1 + k * a_dim1], & c__1, &a[k + 1 + (k + 1) * a_dim1], lda);
/* Store L(k) in column k */
i__1 = *n - k;
zscal_(&i__1, &d11, &a[k + 1 + k * a_dim1], &c__1);
}
else
{
/* Store L(k) in column k */
i__1 = k + k * a_dim1;
d11.r = a[i__1].r;
d11.i = a[i__1].i; // , expr subst
i__1 = *n;
for (ii = k + 1;
ii <= i__1;
++ii)
{
i__2 = ii + k * a_dim1;
z_div(&z__1, &a[ii + k * a_dim1], &d11);
a[i__2].r = z__1.r;
a[i__2].i = z__1.i; // , expr subst
/* L46: */
}
/* Perform a rank-1 update of A(k+1:n,k+1:n) as */
/* A := A - L(k)*D(k)*L(k)**T */
/* = A - W(k)*(1/D(k))*W(k)**T */
/* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T */
i__1 = *n - k;
z__1.r = -d11.r;
z__1.i = -d11.i; // , expr subst
zsyr_(uplo, &i__1, &z__1, &a[k + 1 + k * a_dim1], & c__1, &a[k + 1 + (k + 1) * a_dim1], lda);
}
}
}
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 */
/* 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) )**T */
/* = A - ( ( A(k)A(k+1) )*inv(D(k) ) * ( A(k)A(k+1) )**T */
/* and store L(k) and L(k+1) in columns k and k+1 */
if (k < *n - 1)
{
i__1 = k + 1 + k * a_dim1;
d21.r = a[i__1].r;
d21.i = a[i__1].i; // , expr subst
z_div(&z__1, &a[k + 1 + (k + 1) * a_dim1], &d21);
d11.r = z__1.r;
d11.i = z__1.i; // , expr subst
z_div(&z__1, &a[k + k * a_dim1], &d21);
d22.r = z__1.r;
d22.i = z__1.i; // , expr subst
z__3.r = d11.r * d22.r - d11.i * d22.i;
z__3.i = d11.r * d22.i + d11.i * d22.r; // , expr subst
z__2.r = z__3.r - 1.;
z__2.i = z__3.i - 0.; // , expr subst
z_div(&z__1, &c_b1, &z__2);
t.r = z__1.r;
t.i = z__1.i; // , expr subst
i__1 = *n;
for (j = k + 2;
j <= i__1;
++j)
{
/* Compute D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J */
i__2 = j + k * a_dim1;
z__3.r = d11.r * a[i__2].r - d11.i * a[i__2].i;
z__3.i = d11.r * a[i__2].i + d11.i * a[i__2] .r; // , expr subst
i__3 = j + (k + 1) * a_dim1;
z__2.r = z__3.r - a[i__3].r;
z__2.i = z__3.i - a[i__3] .i; // , expr subst
z__1.r = t.r * z__2.r - t.i * z__2.i;
z__1.i = t.r * z__2.i + t.i * z__2.r; // , expr subst
wk.r = z__1.r;
wk.i = z__1.i; // , expr subst
i__2 = j + (k + 1) * a_dim1;
z__3.r = d22.r * a[i__2].r - d22.i * a[i__2].i;
z__3.i = d22.r * a[i__2].i + d22.i * a[i__2] .r; // , expr subst
i__3 = j + k * a_dim1;
z__2.r = z__3.r - a[i__3].r;
z__2.i = z__3.i - a[i__3] .i; // , expr subst
z__1.r = t.r * z__2.r - t.i * z__2.i;
z__1.i = t.r * z__2.i + t.i * z__2.r; // , expr subst
wkp1.r = z__1.r;
wkp1.i = z__1.i; // , expr subst
/* Perform a rank-2 update of A(k+2:n,k+2:n) */
i__2 = *n;
for (i__ = j;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
z_div(&z__4, &a[i__ + k * a_dim1], &d21);
z__3.r = z__4.r * wk.r - z__4.i * wk.i;
z__3.i = z__4.r * wk.i + z__4.i * wk.r; // , expr subst
z__2.r = a[i__4].r - z__3.r;
z__2.i = a[i__4].i - z__3.i; // , expr subst
z_div(&z__6, &a[i__ + (k + 1) * a_dim1], &d21);
z__5.r = z__6.r * wkp1.r - z__6.i * wkp1.i;
z__5.i = z__6.r * wkp1.i + z__6.i * wkp1.r; // , expr subst
z__1.r = z__2.r - z__5.r;
z__1.i = z__2.i - z__5.i; // , expr subst
a[i__3].r = z__1.r;
a[i__3].i = z__1.i; // , expr subst
/* L50: */
}
/* Store L(k) and L(k+1) in cols k and k+1 for row J */
i__2 = j + k * a_dim1;
z_div(&z__1, &wk, &d21);
a[i__2].r = z__1.r;
a[i__2].i = z__1.i; // , expr subst
i__2 = j + (k + 1) * a_dim1;
z_div(&z__1, &wkp1, &d21);
a[i__2].r = z__1.r;
a[i__2].i = z__1.i; // , expr subst
/* L60: */
}
}
}
}
/* Store details of the interchanges in IPIV */
if (kstep == 1)
{
ipiv[k] = kp;
}
else
{
ipiv[k] = -p;
ipiv[k + 1] = -kp;
}
/* Increase K and return to the start of the main loop */
k += kstep;
goto L40;
}
L70:
return 0;
/* End of ZSYTF2_ROOK */
}
int zsytf2_(char *uplo, int *n, doublecomplex *a,
int *lda, int *ipiv, int *info)
{
/* System generated locals */
int a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
double d__1, d__2, d__3, d__4;
doublecomplex z__1, z__2, z__3, z__4;
/* Builtin functions */
double sqrt(double), d_imag(doublecomplex *);
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
int i__, j, k;
doublecomplex t, r1, d11, d12, d21, d22;
int kk, kp;
doublecomplex wk, wkm1, wkp1;
int imax, jmax;
extern int zsyr_(char *, int *, doublecomplex *,
doublecomplex *, int *, doublecomplex *, int *);
double alpha;
extern int lsame_(char *, char *);
extern int zscal_(int *, doublecomplex *,
doublecomplex *, int *);
int kstep;
int upper;
extern int zswap_(int *, doublecomplex *, int *,
doublecomplex *, int *);
double absakk;
extern int disnan_(double *);
extern int xerbla_(char *, int *);
double colmax;
extern int izamax_(int *, doublecomplex *, int *);
double rowmax;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZSYTF2 computes the factorization of a complex symmetric matrix A */
/* using the Bunch-Kaufman diagonal pivoting method: */
/* A = U*D*U' or A = L*D*L' */
/* where U (or L) is a product of permutation and unit upper (lower) */
/* triangular matrices, U' is the transpose of U, and D is symmetric and */
/* block diagonal with 1-by-1 and 2-by-2 diagonal blocks. */
/* This is the unblocked version of the algorithm, calling Level 2 BLAS. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the upper or lower triangular part of the */
/* symmetric matrix A is stored: */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the symmetric matrix A. If UPLO = 'U', the leading */
/* n-by-n upper triangular part of A contains the upper */
/* triangular part of the matrix A, and the strictly lower */
/* triangular part of A is not referenced. If UPLO = 'L', the */
/* leading n-by-n lower triangular part of A contains the lower */
/* triangular part of the matrix A, and the strictly upper */
/* triangular part of A is not referenced. */
/* On exit, the block diagonal matrix D and the multipliers used */
/* to obtain the factor U or L (see below for further details). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,N). */
/* 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 = -k, the k-th argument had an illegal value */
/* > 0: if INFO = k, D(k,k) 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 */
/* =============== */
/* 09-29-06 - patch from */
/* Bobby Cheng, MathWorks */
/* Replace l.209 and l.377 */
/* IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN */
/* by */
/* IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN */
/* 1-96 - 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). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < MAX(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZSYTF2", &i__1);
return 0;
}
/* Initialize ALPHA for use in choosing pivot block size. */
alpha = (sqrt(17.) + 1.) / 8.;
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;
L10:
/* If K < 1, exit from loop */
if (k < 1) {
goto L70;
}
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 = k + k * a_dim1;
absakk = (d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[k + k *
a_dim1]), ABS(d__2));
/* 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 = izamax_(&i__1, &a[k * a_dim1 + 1], &c__1);
i__1 = imax + k * a_dim1;
colmax = (d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[imax +
k * a_dim1]), ABS(d__2));
} else {
colmax = 0.;
}
if (MAX(absakk,colmax) == 0. || disnan_(&absakk)) {
/* Column K is zero or contains a NaN: set INFO and continue */
if (*info == 0) {
*info = k;
}
kp = k;
} 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 */
i__1 = k - imax;
jmax = imax + izamax_(&i__1, &a[imax + (imax + 1) * a_dim1],
lda);
i__1 = imax + jmax * a_dim1;
rowmax = (d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[
imax + jmax * a_dim1]), ABS(d__2));
if (imax > 1) {
i__1 = imax - 1;
jmax = izamax_(&i__1, &a[imax * a_dim1 + 1], &c__1);
/* Computing MAX */
i__1 = jmax + imax * a_dim1;
d__3 = rowmax, d__4 = (d__1 = a[i__1].r, ABS(d__1)) + (
d__2 = d_imag(&a[jmax + imax * a_dim1]), ABS(d__2)
);
rowmax = MAX(d__3,d__4);
}
if (absakk >= alpha * colmax * (colmax / rowmax)) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else /* if(complicated condition) */ {
i__1 = imax + imax * a_dim1;
if ((d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[
imax + imax * a_dim1]), ABS(d__2)) >= 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 (kp != kk) {
/* Interchange rows and columns KK and KP in the leading */
/* submatrix A(1:k,1:k) */
i__1 = kp - 1;
zswap_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1],
&c__1);
i__1 = kk - kp - 1;
zswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
1) * a_dim1], lda);
i__1 = kk + kk * a_dim1;
t.r = a[i__1].r, t.i = a[i__1].i;
i__1 = kk + kk * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = kp + kp * a_dim1;
a[i__1].r = t.r, a[i__1].i = t.i;
if (kstep == 2) {
i__1 = k - 1 + k * a_dim1;
t.r = a[i__1].r, t.i = a[i__1].i;
i__1 = k - 1 + k * a_dim1;
i__2 = kp + k * a_dim1;
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = kp + k * a_dim1;
a[i__1].r = t.r, a[i__1].i = t.i;
}
}
/* 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)' */
z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
r1.r = z__1.r, r1.i = z__1.i;
i__1 = k - 1;
z__1.r = -r1.r, z__1.i = -r1.i;
zsyr_(uplo, &i__1, &z__1, &a[k * a_dim1 + 1], &c__1, &a[
a_offset], lda);
/* Store U(k) in column k */
i__1 = k - 1;
zscal_(&i__1, &r1, &a[k * a_dim1 + 1], &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 * a_dim1;
d12.r = a[i__1].r, d12.i = a[i__1].i;
z_div(&z__1, &a[k - 1 + (k - 1) * a_dim1], &d12);
d22.r = z__1.r, d22.i = z__1.i;
z_div(&z__1, &a[k + k * a_dim1], &d12);
d11.r = z__1.r, d11.i = z__1.i;
z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
d22.i + d11.i * d22.r;
z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.;
z_div(&z__1, &c_b1, &z__2);
t.r = z__1.r, t.i = z__1.i;
z_div(&z__1, &t, &d12);
d12.r = z__1.r, d12.i = z__1.i;
for (j = k - 2; j >= 1; --j) {
i__1 = j + (k - 1) * a_dim1;
z__3.r = d11.r * a[i__1].r - d11.i * a[i__1].i,
z__3.i = d11.r * a[i__1].i + d11.i * a[i__1]
.r;
i__2 = j + k * a_dim1;
z__2.r = z__3.r - a[i__2].r, z__2.i = z__3.i - a[i__2]
.i;
z__1.r = d12.r * z__2.r - d12.i * z__2.i, z__1.i =
d12.r * z__2.i + d12.i * z__2.r;
wkm1.r = z__1.r, wkm1.i = z__1.i;
i__1 = j + k * a_dim1;
z__3.r = d22.r * a[i__1].r - d22.i * a[i__1].i,
z__3.i = d22.r * a[i__1].i + d22.i * a[i__1]
.r;
i__2 = j + (k - 1) * a_dim1;
z__2.r = z__3.r - a[i__2].r, z__2.i = z__3.i - a[i__2]
.i;
z__1.r = d12.r * z__2.r - d12.i * z__2.i, z__1.i =
d12.r * z__2.i + d12.i * z__2.r;
wk.r = z__1.r, wk.i = z__1.i;
for (i__ = j; i__ >= 1; --i__) {
i__1 = i__ + j * a_dim1;
i__2 = i__ + j * a_dim1;
i__3 = i__ + k * a_dim1;
z__3.r = a[i__3].r * wk.r - a[i__3].i * wk.i,
z__3.i = a[i__3].r * wk.i + a[i__3].i *
wk.r;
z__2.r = a[i__2].r - z__3.r, z__2.i = a[i__2].i -
z__3.i;
i__4 = i__ + (k - 1) * a_dim1;
z__4.r = a[i__4].r * wkm1.r - a[i__4].i * wkm1.i,
z__4.i = a[i__4].r * wkm1.i + a[i__4].i *
wkm1.r;
z__1.r = z__2.r - z__4.r, z__1.i = z__2.i -
z__4.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
/* L20: */
}
i__1 = j + k * a_dim1;
a[i__1].r = wk.r, a[i__1].i = wk.i;
i__1 = j + (k - 1) * a_dim1;
a[i__1].r = wkm1.r, a[i__1].i = wkm1.i;
/* L30: */
}
}
}
}
/* 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;
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;
L40:
/* If K > N, exit from loop */
if (k > *n) {
goto L70;
}
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 = k + k * a_dim1;
absakk = (d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[k + k *
a_dim1]), ABS(d__2));
/* 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 + izamax_(&i__1, &a[k + 1 + k * a_dim1], &c__1);
i__1 = imax + k * a_dim1;
colmax = (d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[imax +
k * a_dim1]), ABS(d__2));
} else {
colmax = 0.;
}
if (MAX(absakk,colmax) == 0. || disnan_(&absakk)) {
/* Column K is zero or contains a NaN: set INFO and continue */
if (*info == 0) {
*info = k;
}
kp = k;
} 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 */
i__1 = imax - k;
jmax = k - 1 + izamax_(&i__1, &a[imax + k * a_dim1], lda);
i__1 = imax + jmax * a_dim1;
rowmax = (d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[
imax + jmax * a_dim1]), ABS(d__2));
if (imax < *n) {
i__1 = *n - imax;
jmax = imax + izamax_(&i__1, &a[imax + 1 + imax * a_dim1],
&c__1);
/* Computing MAX */
i__1 = jmax + imax * a_dim1;
d__3 = rowmax, d__4 = (d__1 = a[i__1].r, ABS(d__1)) + (
d__2 = d_imag(&a[jmax + imax * a_dim1]), ABS(d__2)
);
rowmax = MAX(d__3,d__4);
}
if (absakk >= alpha * colmax * (colmax / rowmax)) {
/* no interchange, use 1-by-1 pivot block */
kp = k;
} else /* if(complicated condition) */ {
i__1 = imax + imax * a_dim1;
if ((d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[
imax + imax * a_dim1]), ABS(d__2)) >= 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 (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;
zswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
+ kp * a_dim1], &c__1);
}
i__1 = kp - kk - 1;
zswap_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
1) * a_dim1], lda);
i__1 = kk + kk * a_dim1;
t.r = a[i__1].r, t.i = a[i__1].i;
i__1 = kk + kk * a_dim1;
i__2 = kp + kp * a_dim1;
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = kp + kp * a_dim1;
a[i__1].r = t.r, a[i__1].i = t.i;
if (kstep == 2) {
i__1 = k + 1 + k * a_dim1;
t.r = a[i__1].r, t.i = a[i__1].i;
i__1 = k + 1 + k * a_dim1;
i__2 = kp + k * a_dim1;
a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
i__1 = kp + k * a_dim1;
a[i__1].r = t.r, a[i__1].i = t.i;
}
}
/* 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)' */
z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
r1.r = z__1.r, r1.i = z__1.i;
i__1 = *n - k;
z__1.r = -r1.r, z__1.i = -r1.i;
zsyr_(uplo, &i__1, &z__1, &a[k + 1 + k * a_dim1], &c__1, &
a[k + 1 + (k + 1) * a_dim1], lda);
/* Store L(k) in column K */
i__1 = *n - k;
zscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
}
} else {
/* 2-by-2 pivot block D(k) */
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 * a_dim1;
d21.r = a[i__1].r, d21.i = a[i__1].i;
z_div(&z__1, &a[k + 1 + (k + 1) * a_dim1], &d21);
d11.r = z__1.r, d11.i = z__1.i;
z_div(&z__1, &a[k + k * a_dim1], &d21);
d22.r = z__1.r, d22.i = z__1.i;
z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
d22.i + d11.i * d22.r;
z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.;
z_div(&z__1, &c_b1, &z__2);
t.r = z__1.r, t.i = z__1.i;
z_div(&z__1, &t, &d21);
d21.r = z__1.r, d21.i = z__1.i;
i__1 = *n;
for (j = k + 2; j <= i__1; ++j) {
i__2 = j + k * a_dim1;
z__3.r = d11.r * a[i__2].r - d11.i * a[i__2].i,
z__3.i = d11.r * a[i__2].i + d11.i * a[i__2]
.r;
i__3 = j + (k + 1) * a_dim1;
z__2.r = z__3.r - a[i__3].r, z__2.i = z__3.i - a[i__3]
.i;
z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
d21.r * z__2.i + d21.i * z__2.r;
wk.r = z__1.r, wk.i = z__1.i;
i__2 = j + (k + 1) * a_dim1;
z__3.r = d22.r * a[i__2].r - d22.i * a[i__2].i,
z__3.i = d22.r * a[i__2].i + d22.i * a[i__2]
.r;
i__3 = j + k * a_dim1;
z__2.r = z__3.r - a[i__3].r, z__2.i = z__3.i - a[i__3]
.i;
z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
d21.r * z__2.i + d21.i * z__2.r;
wkp1.r = z__1.r, wkp1.i = z__1.i;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = i__ + j * a_dim1;
i__5 = i__ + k * a_dim1;
z__3.r = a[i__5].r * wk.r - a[i__5].i * wk.i,
z__3.i = a[i__5].r * wk.i + a[i__5].i *
wk.r;
z__2.r = a[i__4].r - z__3.r, z__2.i = a[i__4].i -
z__3.i;
i__6 = i__ + (k + 1) * a_dim1;
z__4.r = a[i__6].r * wkp1.r - a[i__6].i * wkp1.i,
z__4.i = a[i__6].r * wkp1.i + a[i__6].i *
wkp1.r;
z__1.r = z__2.r - z__4.r, z__1.i = z__2.i -
z__4.i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L50: */
}
i__2 = j + k * a_dim1;
a[i__2].r = wk.r, a[i__2].i = wk.i;
i__2 = j + (k + 1) * a_dim1;
a[i__2].r = wkp1.r, a[i__2].i = wkp1.i;
/* L60: */
}
}
}
}
/* 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;
goto L40;
}
L70:
return 0;
/* End of ZSYTF2 */
} /* zsytf2_ */