Use normwise criterion for inf eigenvalues in QZ

thijssteel · thijssteel · commit c6994068c3a7 · 2022-08-08T10:28:18.000+02:00
diff --git a/SRC/chgeqz.f b/SRC/chgeqz.f
@@ -523,9 +523,7 @@ SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
-     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
-     $          ) ) ) ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
             T( ILAST, ILAST ) = CZERO
             GO TO 50
          END IF
@@ -551,10 +549,7 @@ SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
 *
 *           Test 2: for T(j,j)=0
 *
-            TEMP = ABS ( T( J, J + 1 ) )
-            IF ( J .GT. ILO )
-     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
-            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
                T( J, J ) = CZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A
diff --git a/SRC/dhgeqz.f b/SRC/dhgeqz.f
@@ -536,9 +536,7 @@ SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
-     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
-     $          ) ) ) ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
             T( ILAST, ILAST ) = ZERO
             GO TO 70
          END IF
@@ -564,10 +562,7 @@ SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
 *
 *           Test 2: for T(j,j)=0
 *
-            TEMP = ABS ( T( J, J + 1 ) )
-            IF ( J .GT. ILO )
-     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
-            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
                T( J, J ) = ZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A
diff --git a/SRC/shgeqz.f b/SRC/shgeqz.f
@@ -536,9 +536,7 @@ SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
-     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
-     $          ) ) ) ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
             T( ILAST, ILAST ) = ZERO
             GO TO 70
          END IF
@@ -564,10 +562,7 @@ SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
 *
 *           Test 2: for T(j,j)=0
 *
-            TEMP = ABS ( T( J, J + 1 ) )
-            IF ( J .GT. ILO )
-     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
-            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
                T( J, J ) = ZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A
diff --git a/SRC/zhgeqz.f b/SRC/zhgeqz.f
@@ -524,9 +524,7 @@ SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
-     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
-     $          ) ) ) ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
             T( ILAST, ILAST ) = CZERO
             GO TO 50
          END IF
@@ -552,10 +550,7 @@ SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
 *
 *           Test 2: for T(j,j)=0
 *
-            TEMP = ABS ( T( J, J + 1 ) )
-            IF ( J .GT. ILO )
-     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
-            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
                T( J, J ) = CZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A

Original file line number	Diff line number	Diff line change
`@@ -523,9 +523,7 @@ SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,`
`523`	`523`	`END IF`
`524`	`524`	`END IF`
`525`	`525`	`*`
`526`		`- IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*(`
`527`		`- $ ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )`
`528`		`- $ ) ) ) ) THEN`
	`526`	`+ IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN`
`529`	`527`	`T( ILAST, ILAST ) = CZERO`
`530`	`528`	`GO TO 50`
`531`	`529`	`END IF`
`@@ -551,10 +549,7 @@ SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,`
`551`	`549`	`*`
`552`	`550`	`* Test 2: for T(j,j)=0`
`553`	`551`	`*`
`554`		`- TEMP = ABS ( T( J, J + 1 ) )`
`555`		`- IF ( J .GT. ILO )`
`556`		`- $ TEMP = TEMP + ABS ( T( J - 1, J ) )`
`557`		`- IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN`
	`552`	`+ IF( ABS( T( J, J ) ).LT.BTOL ) THEN`
`558`	`553`	`T( J, J ) = CZERO`
`559`	`554`	`*`
`560`	`555`	`* Test 1a: Check for 2 consecutive small subdiagonals in A`
Original file line number	Diff line number	Diff line change
`@@ -536,9 +536,7 @@ SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,`
`536`	`536`	`END IF`
`537`	`537`	`END IF`
`538`	`538`	`*`
`539`		`- IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*(`
`540`		`- $ ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )`
`541`		`- $ ) ) ) ) THEN`
	`539`	`+ IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN`
`542`	`540`	`T( ILAST, ILAST ) = ZERO`
`543`	`541`	`GO TO 70`
`544`	`542`	`END IF`
`@@ -564,10 +562,7 @@ SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,`
`564`	`562`	`*`
`565`	`563`	`* Test 2: for T(j,j)=0`
`566`	`564`	`*`
`567`		`- TEMP = ABS ( T( J, J + 1 ) )`
`568`		`- IF ( J .GT. ILO )`
`569`		`- $ TEMP = TEMP + ABS ( T( J - 1, J ) )`
`570`		`- IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN`
	`565`	`+ IF( ABS( T( J, J ) ).LT.BTOL ) THEN`
`571`	`566`	`T( J, J ) = ZERO`
`572`	`567`	`*`
`573`	`568`	`* Test 1a: Check for 2 consecutive small subdiagonals in A`
Original file line number	Diff line number	Diff line change
`@@ -536,9 +536,7 @@ SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,`
`536`	`536`	`END IF`
`537`	`537`	`END IF`
`538`	`538`	`*`
`539`		`- IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*(`
`540`		`- $ ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )`
`541`		`- $ ) ) ) ) THEN`
	`539`	`+ IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN`
`542`	`540`	`T( ILAST, ILAST ) = ZERO`
`543`	`541`	`GO TO 70`
`544`	`542`	`END IF`
`@@ -564,10 +562,7 @@ SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,`
`564`	`562`	`*`
`565`	`563`	`* Test 2: for T(j,j)=0`
`566`	`564`	`*`
`567`		`- TEMP = ABS ( T( J, J + 1 ) )`
`568`		`- IF ( J .GT. ILO )`
`569`		`- $ TEMP = TEMP + ABS ( T( J - 1, J ) )`
`570`		`- IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN`
	`565`	`+ IF( ABS( T( J, J ) ).LT.BTOL ) THEN`
`571`	`566`	`T( J, J ) = ZERO`
`572`	`567`	`*`
`573`	`568`	`* Test 1a: Check for 2 consecutive small subdiagonals in A`
Original file line number	Diff line number	Diff line change
`@@ -524,9 +524,7 @@ SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,`
`524`	`524`	`END IF`
`525`	`525`	`END IF`
`526`	`526`	`*`
`527`		`- IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*(`
`528`		`- $ ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )`
`529`		`- $ ) ) ) ) THEN`
	`527`	`+ IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN`
`530`	`528`	`T( ILAST, ILAST ) = CZERO`
`531`	`529`	`GO TO 50`
`532`	`530`	`END IF`
`@@ -552,10 +550,7 @@ SUBROUTINE ZHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,`
`552`	`550`	`*`
`553`	`551`	`* Test 2: for T(j,j)=0`
`554`	`552`	`*`
`555`		`- TEMP = ABS ( T( J, J + 1 ) )`
`556`		`- IF ( J .GT. ILO )`
`557`		`- $ TEMP = TEMP + ABS ( T( J - 1, J ) )`
`558`		`- IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN`
	`553`	`+ IF( ABS( T( J, J ) ).LT.BTOL ) THEN`
`559`	`554`	`T( J, J ) = CZERO`
`560`	`555`	`*`
`561`	`556`	`* Test 1a: Check for 2 consecutive small subdiagonals in A`