Merge pull request #4309 from martin-frbg/lapack926

Change ?GECON to return INFO=1 if RCOND is NaN (Reference-LAPACK PR 926)

lapack-netlib/SRC/cgecon.f

@@ -105,8 +105,15 @@
 *> \verbatim
 *>          INFO is INTEGER
 *>          = 0:  successful exit
-*>          < 0:  if INFO = -i, the i-th argument had an illegal value
-*>          =-5:  if ANORM is NAN or negative.
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
+*>                NaNs are illegal values for ANORM, and they propagate to
+*>                the output parameter RCOND.
+*>                Infinity is illegal for ANORM, and it propagates to the output
+*>                parameter RCOND as 0.
+*>          = 1:  if RCOND = NaN, or
+*>                   RCOND = Inf, or
+*>                   the computed norm of the inverse of A is 0.
+*>                In the latter, RCOND = 0 is returned.
 *> \endverbatim
 *
 *  Authors:
@@ -117,7 +124,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complexGEcomputational
+*> \ingroup gecon
 *
 *  =====================================================================
       SUBROUTINE CGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,
@@ -147,7 +154,7 @@
       LOGICAL            ONENRM
       CHARACTER          NORMIN
       INTEGER            IX, KASE, KASE1
-      REAL               AINVNM, SCALE, SL, SMLNUM, SU
+      REAL               AINVNM, SCALE, SL, SMLNUM, SU, HUGEVAL
       COMPLEX            ZDUM
 *     ..
 *     .. Local Arrays ..
@@ -172,6 +179,8 @@
       CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
 *     ..
 *     .. Executable Statements ..
+*
+      HUGEVAL = SLAMCH( 'Overflow' )
 *
 *     Test the input parameters.
 *
@@ -183,7 +192,7 @@
          INFO = -2
       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
          INFO = -4
-      ELSE IF( ANORM.LT.ZERO .OR. SISNAN( ANORM ) ) THEN
+      ELSE IF( ANORM.LT.ZERO ) THEN
          INFO = -5
       END IF
       IF( INFO.NE.0 ) THEN
@@ -199,6 +208,13 @@
          RETURN
       ELSE IF( ANORM.EQ.ZERO ) THEN
          RETURN
+      ELSE IF( SISNAN( ANORM ) ) THEN
+         RCOND = ANORM
+         INFO = -5
+         RETURN
+      ELSE IF( ANORM.GT.HUGEVAL ) THEN
+         INFO = -5
+         RETURN
       END IF
 *
       SMLNUM = SLAMCH( 'Safe minimum' )
@@ -256,8 +272,17 @@
 *
 *     Compute the estimate of the reciprocal condition number.
 *
-      IF( AINVNM.NE.ZERO )
-     $   RCOND = ( ONE / AINVNM ) / ANORM
+      IF( AINVNM.NE.ZERO ) THEN
+         RCOND = ( ONE / AINVNM ) / ANORM
+      ELSE
+         INFO = 1
+         RETURN
+      END IF
+*
+*     Check for NaNs and Infs
+*
+      IF( SISNAN( RCOND ) .OR. RCOND.GT.HUGEVAL )
+     $   INFO = 1
 *
    20 CONTINUE
       RETURN

lapack-netlib/SRC/dgecon.f

@@ -105,8 +105,15 @@
 *> \verbatim
 *>          INFO is INTEGER
 *>          = 0:  successful exit
-*>          < 0:  if INFO = -i, the i-th argument had an illegal value
-*>          =-5:  if ANORM is NAN or negative.
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
+*>                NaNs are illegal values for ANORM, and they propagate to
+*>                the output parameter RCOND.
+*>                Infinity is illegal for ANORM, and it propagates to the output
+*>                parameter RCOND as 0.
+*>          = 1:  if RCOND = NaN, or
+*>                   RCOND = Inf, or
+*>                   the computed norm of the inverse of A is 0.
+*>                In the latter, RCOND = 0 is returned.
 *> \endverbatim
 *
 *  Authors:
@@ -117,7 +124,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup doubleGEcomputational
+*> \ingroup gecon
 *
 *  =====================================================================
       SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK,
@@ -147,7 +154,7 @@
       LOGICAL            ONENRM
       CHARACTER          NORMIN
       INTEGER            IX, KASE, KASE1
-      DOUBLE PRECISION   AINVNM, SCALE, SL, SMLNUM, SU
+      DOUBLE PRECISION   AINVNM, SCALE, SL, SMLNUM, SU, HUGEVAL
 *     ..
 *     .. Local Arrays ..
       INTEGER            ISAVE( 3 )
@@ -165,6 +172,8 @@
       INTRINSIC          ABS, MAX
 *     ..
 *     .. Executable Statements ..
+*
+      HUGEVAL = DLAMCH( 'Overflow' )
 *
 *     Test the input parameters.
 *
@@ -176,7 +185,7 @@
          INFO = -2
       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
          INFO = -4
-      ELSE IF( ANORM.LT.ZERO .OR. DISNAN( ANORM ) ) THEN
+      ELSE IF( ANORM.LT.ZERO ) THEN
          INFO = -5
       END IF
       IF( INFO.NE.0 ) THEN
@@ -192,6 +201,13 @@
          RETURN
       ELSE IF( ANORM.EQ.ZERO ) THEN
          RETURN
+      ELSE IF( DISNAN( ANORM ) ) THEN
+         RCOND = ANORM
+         INFO = -5
+         RETURN
+      ELSE IF( ANORM.GT.HUGEVAL ) THEN
+         INFO = -5
+         RETURN
       END IF
 *
       SMLNUM = DLAMCH( 'Safe minimum' )
@@ -248,8 +264,17 @@
 *
 *     Compute the estimate of the reciprocal condition number.
 *
-      IF( AINVNM.NE.ZERO )
-     $   RCOND = ( ONE / AINVNM ) / ANORM
+      IF( AINVNM.NE.ZERO ) THEN
+         RCOND = ( ONE / AINVNM ) / ANORM
+      ELSE
+         INFO = 1
+         RETURN
+      END IF
+*
+*     Check for NaNs and Infs
+*
+      IF( DISNAN( RCOND ) .OR. RCOND.GT.HUGEVAL )
+     $   INFO = 1
 *
    20 CONTINUE
       RETURN

lapack-netlib/SRC/sgecon.f

@@ -105,8 +105,15 @@
 *> \verbatim
 *>          INFO is INTEGER
 *>          = 0:  successful exit
-*>          < 0:  if INFO = -i, the i-th argument had an illegal value
-*>          =-5:  if ANORM is NAN or negative.
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
+*>                NaNs are illegal values for ANORM, and they propagate to
+*>                the output parameter RCOND.
+*>                Infinity is illegal for ANORM, and it propagates to the output
+*>                parameter RCOND as 0.
+*>          = 1:  if RCOND = NaN, or
+*>                   RCOND = Inf, or
+*>                   the computed norm of the inverse of A is 0.
+*>                In the latter, RCOND = 0 is returned.
 *> \endverbatim
 *
 *  Authors:
@@ -117,7 +124,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup realGEcomputational
+*> \ingroup gecon
 *
 *  =====================================================================
       SUBROUTINE SGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK,
@@ -147,7 +154,7 @@
       LOGICAL            ONENRM
       CHARACTER          NORMIN
       INTEGER            IX, KASE, KASE1
-      REAL               AINVNM, SCALE, SL, SMLNUM, SU
+      REAL               AINVNM, SCALE, SL, SMLNUM, SU, HUGEVAL
 *     ..
 *     .. Local Arrays ..
       INTEGER            ISAVE( 3 )
@@ -165,6 +172,8 @@
       INTRINSIC          ABS, MAX
 *     ..
 *     .. Executable Statements ..
+*
+      HUGEVAL = SLAMCH( 'Overflow' )
 *
 *     Test the input parameters.
 *
@@ -176,7 +185,7 @@
          INFO = -2
       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
          INFO = -4
-      ELSE IF( ANORM.LT.ZERO .OR. SISNAN( ANORM ) ) THEN
+      ELSE IF( ANORM.LT.ZERO ) THEN
          INFO = -5
       END IF
       IF( INFO.NE.0 ) THEN
@@ -192,6 +201,13 @@
          RETURN
       ELSE IF( ANORM.EQ.ZERO ) THEN
          RETURN
+      ELSE IF( SISNAN( ANORM ) ) THEN
+         RCOND = ANORM
+         INFO = -5
+         RETURN
+      ELSE IF( ANORM.GT.HUGEVAL ) THEN
+         INFO = -5
+         RETURN
       END IF
 *
       SMLNUM = SLAMCH( 'Safe minimum' )
@@ -248,8 +264,17 @@
 *
 *     Compute the estimate of the reciprocal condition number.
 *
-      IF( AINVNM.NE.ZERO )
-     $   RCOND = ( ONE / AINVNM ) / ANORM
+      IF( AINVNM.NE.ZERO ) THEN
+         RCOND = ( ONE / AINVNM ) / ANORM
+      ELSE
+         INFO = 1
+         RETURN
+      END IF
+*
+*     Check for NaNs and Infs
+*
+      IF( SISNAN( RCOND ) .OR. RCOND.GT.HUGEVAL )
+     $   INFO = 1
 *
    20 CONTINUE
       RETURN

lapack-netlib/SRC/zgecon.f

@@ -105,8 +105,15 @@
 *> \verbatim
 *>          INFO is INTEGER
 *>          = 0:  successful exit
-*>          < 0:  if INFO = -i, the i-th argument had an illegal value
-*>          =-5:  if ANORM is NAN or negative.
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
+*>                NaNs are illegal values for ANORM, and they propagate to
+*>                the output parameter RCOND.
+*>                Infinity is illegal for ANORM, and it propagates to the output
+*>                parameter RCOND as 0.
+*>          = 1:  if RCOND = NaN, or
+*>                   RCOND = Inf, or
+*>                   the computed norm of the inverse of A is 0.
+*>                In the latter, RCOND = 0 is returned.
 *> \endverbatim
 *
 *  Authors:
@@ -117,7 +124,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \ingroup complex16GEcomputational
+*> \ingroup gecon
 *
 *  =====================================================================
       SUBROUTINE ZGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK,
@@ -147,7 +154,7 @@
       LOGICAL            ONENRM
       CHARACTER          NORMIN
       INTEGER            IX, KASE, KASE1
-      DOUBLE PRECISION   AINVNM, SCALE, SL, SMLNUM, SU
+      DOUBLE PRECISION   AINVNM, SCALE, SL, SMLNUM, SU, HUGEVAL
       COMPLEX*16         ZDUM
 *     ..
 *     .. Local Arrays ..
@@ -172,6 +179,8 @@
       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
 *     ..
 *     .. Executable Statements ..
+*
+      HUGEVAL = DLAMCH( 'Overflow' )
 *
 *     Test the input parameters.
 *
@@ -183,7 +192,7 @@
          INFO = -2
       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
          INFO = -4
-      ELSE IF( ANORM.LT.ZERO .OR. DISNAN( ANORM ) ) THEN
+      ELSE IF( ANORM.LT.ZERO ) THEN
          INFO = -5
       END IF
       IF( INFO.NE.0 ) THEN
@@ -199,6 +208,13 @@
          RETURN
       ELSE IF( ANORM.EQ.ZERO ) THEN
          RETURN
+      ELSE IF( DISNAN( ANORM ) ) THEN
+         RCOND = ANORM
+         INFO = -5
+         RETURN
+      ELSE IF( ANORM.GT.HUGEVAL ) THEN
+         INFO = -5
+         RETURN
       END IF
 *
       SMLNUM = DLAMCH( 'Safe minimum' )
@@ -256,8 +272,17 @@
 *
 *     Compute the estimate of the reciprocal condition number.
 *
-      IF( AINVNM.NE.ZERO )
-     $   RCOND = ( ONE / AINVNM ) / ANORM
+      IF( AINVNM.NE.ZERO ) THEN
+         RCOND = ( ONE / AINVNM ) / ANORM
+      ELSE
+         INFO = 1
+         RETURN
+      END IF
+*
+*     Check for NaNs and Infs
+*
+      IF( DISNAN( RCOND ) .OR. RCOND.GT.HUGEVAL )
+     $   INFO = 1
 *
    20 CONTINUE
       RETURN