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Avoid overflow in the 2x2 pivot inverse of the symmetric-indefinite factorizations (Reference-LAPACK PR 1377) #6175

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martin-frbg merged 5 commits into from
Oct 26, 2026
Merged

Avoid overflow in the 2x2 pivot inverse of the symmetric-indefinite factorizations (Reference-LAPACK PR 1377) #6175

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ce4ece1
Avoid overflow in 2x2 pivot inverse of the symmetric-indefinite facto…
martin-frbg Oct 25, 2026
61d0a5e
Avoid overflow in 2x2 pivot inverse of the symmetric-indefinite facto…
martin-frbg Oct 25, 2026
c52f7a5
Avoid overflow in 2x2 pivot inverse of the symmetric-indefinite facto…
martin-frbg Oct 25, 2026
166625a
fix declaration of xerbla
martin-frbg Oct 25, 2026
6b8e4e5
fix symbol
martin-frbg Oct 25, 2026
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91 changes: 43 additions & 48 deletions lapack-netlib/SRC/chetf2.c
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Original file line number Diff line number Diff line change
Expand Up @@ -249,7 +249,6 @@ typedef struct Namelist Namelist;




/* Table of constant values */

static integer c__1 = 1;
Expand All @@ -262,7 +261,6 @@ thod (unblocked algorithm calling Level 2 BLAS). */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download CHETF2 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetf2.
f"> */
Expand All @@ -273,7 +271,6 @@ f"> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetf2.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/* Definition: */
/* =========== */
Expand Down Expand Up @@ -383,9 +380,7 @@ f"> */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \date December 2016 */

/* > \ingroup complexHEcomputational */
/* > \ingroup hetf2 */

/* > \par Further Details: */
/* ===================== */
Expand Down Expand Up @@ -445,45 +440,43 @@ f"> */
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
real r__1=0., r__2=0., r__3=0., r__4=0.;
complex q__1={0.,0.}, q__2={0.,0.}, q__3={0.,0.}, q__4={0.,0.}, q__5={0.,0.}, q__6={0.,0.};
real r__1, r__2, r__3, r__4;
complex q__1, q__2, q__3, q__4, q__5, q__6;

/* Local variables */
extern /* Subroutine */ void cher_(char *, integer *, real *, complex *,
integer *, complex *, integer *);
integer imax, jmax;
real d__;
integer i__, j, k;
complex t;
real r1, d11;
complex d12;
real d22;
complex d21;
integer kk, kp;
complex wk;
real tt;
complex wkm1, wkp1;
extern /* Subroutine */ void cher_(char *, integer *, real *, complex *,
integer *, complex *, integer *);
integer imax, jmax;
real alpha;
extern logical lsame_(char *, char *);
extern /* Subroutine */ void cswap_(integer *, complex *, integer *,
complex *, integer *);
integer kstep;
logical upper;
real r1, d11;
complex d12;
real d22;
complex d21;
extern real slapy2_(real *, real *);
integer kk, kp;
real absakk;
complex wk;
extern integer icamax_(integer *, complex *, integer *);
real tt;
extern /* Subroutine */ void csscal_(integer *, real *, complex *, integer
*);
extern void xerbla_(char *, integer *, ftnlen);
*), xerbla_(char *, integer *, ftnlen);
real colmax;
extern logical sisnan_(real *);
real rowmax;
complex wkm1, wkp1;


/* -- LAPACK computational routine (version 3.7.0) -- */
/* -- LAPACK computational routine -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* December 2016 */


/* ===================================================================== */
Expand All @@ -493,7 +486,7 @@ f"> */

/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;

Expand Down Expand Up @@ -729,27 +722,28 @@ f"> */
i__1 = k - 1 + k * a_dim1;
q__1.r = a[i__1].r / d__, q__1.i = a[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 - 1) * a_dim1;
q__3.r = d11 * a[i__1].r, q__3.i = d11 * a[i__1].i;
r_cnjg(&q__5, &d12);
q__4.r = d11 * a[i__1].r, q__4.i = d11 * a[i__1].i;
r_cnjg(&q__6, &d12);
i__2 = j + k * a_dim1;
q__4.r = q__5.r * a[i__2].r - q__5.i * a[i__2].i,
q__4.i = q__5.r * a[i__2].i + q__5.i * a[i__2]
q__5.r = q__6.r * a[i__2].r - q__6.i * a[i__2].i,
q__5.i = q__6.r * a[i__2].i + q__6.i * a[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;
q__3.r = q__4.r - q__5.r, q__3.i = q__4.i - q__5.i;
q__2.r = q__3.r / d__, q__2.i = q__3.i / d__;
q__1.r = tt * q__2.r, q__1.i = tt * q__2.i;
wkm1.r = q__1.r, wkm1.i = q__1.i;
i__1 = j + k * a_dim1;
q__3.r = d22 * a[i__1].r, q__3.i = d22 * a[i__1].i;
q__4.r = d22 * a[i__1].r, q__4.i = d22 * a[i__1].i;
i__2 = j + (k - 1) * a_dim1;
q__4.r = d12.r * a[i__2].r - d12.i * a[i__2].i,
q__4.i = d12.r * a[i__2].i + d12.i * a[i__2]
q__5.r = d12.r * a[i__2].r - d12.i * a[i__2].i,
q__5.i = d12.r * a[i__2].i + d12.i * a[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;
q__3.r = q__4.r - q__5.r, q__3.i = q__4.i - q__5.i;
q__2.r = q__3.r / d__, q__2.i = q__3.i / d__;
q__1.r = tt * q__2.r, q__1.i = tt * q__2.i;
wk.r = q__1.r, wk.i = q__1.i;
for (i__ = j; i__ >= 1; --i__) {
i__1 = i__ + j * a_dim1;
Expand Down Expand Up @@ -1017,28 +1011,29 @@ f"> */
i__1 = k + 1 + k * a_dim1;
q__1.r = a[i__1].r / d__, q__1.i = a[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 * a_dim1;
q__3.r = d11 * a[i__2].r, q__3.i = d11 * a[i__2].i;
q__4.r = d11 * a[i__2].r, q__4.i = d11 * a[i__2].i;
i__3 = j + (k + 1) * a_dim1;
q__4.r = d21.r * a[i__3].r - d21.i * a[i__3].i,
q__4.i = d21.r * a[i__3].i + d21.i * a[i__3]
q__5.r = d21.r * a[i__3].r - d21.i * a[i__3].i,
q__5.i = d21.r * a[i__3].i + d21.i * a[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;
q__3.r = q__4.r - q__5.r, q__3.i = q__4.i - q__5.i;
q__2.r = q__3.r / d__, q__2.i = q__3.i / d__;
q__1.r = tt * q__2.r, q__1.i = tt * q__2.i;
wk.r = q__1.r, wk.i = q__1.i;
i__2 = j + (k + 1) * a_dim1;
q__3.r = d22 * a[i__2].r, q__3.i = d22 * a[i__2].i;
r_cnjg(&q__5, &d21);
q__4.r = d22 * a[i__2].r, q__4.i = d22 * a[i__2].i;
r_cnjg(&q__6, &d21);
i__3 = j + k * a_dim1;
q__4.r = q__5.r * a[i__3].r - q__5.i * a[i__3].i,
q__4.i = q__5.r * a[i__3].i + q__5.i * a[i__3]
q__5.r = q__6.r * a[i__3].r - q__6.i * a[i__3].i,
q__5.i = q__6.r * a[i__3].i + q__6.i * a[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;
q__3.r = q__4.r - q__5.r, q__3.i = q__4.i - q__5.i;
q__2.r = q__3.r / d__, q__2.i = q__3.i / d__;
q__1.r = tt * q__2.r, q__1.i = tt * q__2.i;
wkp1.r = q__1.r, wkp1.i = q__1.i;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
Expand Down
29 changes: 16 additions & 13 deletions lapack-netlib/SRC/chetf2.f
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -5,15 +5,13 @@
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CHETF2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetf2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetf2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetf2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
Expand Down Expand Up @@ -127,7 +125,7 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexHEcomputational
*> \ingroup hetf2
*
*> \par Further Details:
* =====================
Expand Down Expand Up @@ -183,6 +181,7 @@
*>
* =====================================================================
SUBROUTINE CHETF2( UPLO, N, A, LDA, IPIV, INFO )
IMPLICIT NONE
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
Expand Down Expand Up @@ -284,7 +283,8 @@ SUBROUTINE CHETF2( UPLO, N, A, LDA, IPIV, INFO )
COLMAX = ZERO
END IF
*
IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR.
$ SISNAN(ABSAKK) ) THEN
*
* Column K is or underflow, or contains a NaN:
* set INFO and continue
Expand Down Expand Up @@ -403,11 +403,11 @@ SUBROUTINE CHETF2( UPLO, N, A, LDA, IPIV, INFO )
D11 = REAL( A( K, K ) ) / D
TT = ONE / ( D11*D22-ONE )
D12 = A( K-1, K ) / D
D = TT / D
*
DO 40 J = K - 2, 1, -1
WKM1 = D*( D11*A( J, K-1 )-CONJG( D12 )*A( J, K ) )
WK = D*( D22*A( J, K )-D12*A( J, K-1 ) )
WKM1 = TT*( ( D11*A( J, K-1 )-CONJG( D12 )*
$ A( J, K ) ) / D )
WK = TT*( ( D22*A( J, K )-D12*A( J, K-1 ) ) / D )
DO 30 I = J, 1, -1
A( I, J ) = A( I, J ) - A( I, K )*CONJG( WK ) -
$ A( I, K-1 )*CONJG( WKM1 )
Expand Down Expand Up @@ -468,7 +468,8 @@ SUBROUTINE CHETF2( UPLO, N, A, LDA, IPIV, INFO )
COLMAX = ZERO
END IF
*
IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. SISNAN(ABSAKK) ) THEN
IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR.
$ SISNAN(ABSAKK) ) THEN
*
* Column K is zero or underflow, contains a NaN:
* set INFO and continue
Expand All @@ -491,7 +492,8 @@ SUBROUTINE CHETF2( UPLO, N, A, LDA, IPIV, INFO )
JMAX = K - 1 + ICAMAX( IMAX-K, A( IMAX, K ), LDA )
ROWMAX = CABS1( A( IMAX, JMAX ) )
IF( IMAX.LT.N ) THEN
JMAX = IMAX + ICAMAX( N-IMAX, A( IMAX+1, IMAX ), 1 )
JMAX = IMAX + ICAMAX( N-IMAX, A( IMAX+1, IMAX ),
$ 1 )
ROWMAX = MAX( ROWMAX, CABS1( A( JMAX, IMAX ) ) )
END IF
*
Expand Down Expand Up @@ -524,7 +526,8 @@ SUBROUTINE CHETF2( UPLO, N, A, LDA, IPIV, INFO )
* submatrix A(k:n,k:n)
*
IF( KP.LT.N )
$ CALL CSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
$ CALL CSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ),
$ 1 )
DO 60 J = KK + 1, KP - 1
T = CONJG( A( J, KK ) )
A( J, KK ) = CONJG( A( KP, J ) )
Expand Down Expand Up @@ -590,11 +593,11 @@ SUBROUTINE CHETF2( UPLO, N, A, LDA, IPIV, INFO )
D22 = REAL( A( K, K ) ) / D
TT = ONE / ( D11*D22-ONE )
D21 = A( K+1, K ) / D
D = TT / D
*
DO 80 J = K + 2, N
WK = D*( D11*A( J, K )-D21*A( J, K+1 ) )
WKP1 = D*( D22*A( J, K+1 )-CONJG( D21 )*A( J, K ) )
WK = TT*( ( D11*A( J, K )-D21*A( J, K+1 ) ) / D )
WKP1 = TT*( ( D22*A( J, K+1 )-CONJG( D21 )*
$ A( J, K ) ) / D )
DO 70 I = J, N
A( I, J ) = A( I, J ) - A( I, K )*CONJG( WK ) -
$ A( I, K+1 )*CONJG( WKP1 )
Expand Down
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