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Add numerical tests for trevc3 #682

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Mar 18, 2023
Merged

Add numerical tests for trevc3 #682

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22d1721
Add missing numerical tests for TREVC3
angsch Jun 19, 2022
9f9295f
standardize style in laqr5
angsch Jul 3, 2022
0a6cd43
Rewrite [ds]hgeqz to use FMA with Householder reflectors
angsch Jul 5, 2022
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25 changes: 14 additions & 11 deletions SRC/claqr5.f
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Original file line number Diff line number Diff line change
Expand Up @@ -533,11 +533,13 @@ SUBROUTINE CLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
* . Mth bulge. Exploit fact that first two elements
* . of row are actually zero. ====
*
REFSUM = V( 1, M )*V( 3, M )*H( K+3, K+2 )
H( K+3, K ) = -REFSUM
H( K+3, K+1 ) = -REFSUM*CONJG( V( 2, M ) )
H( K+3, K+2 ) = H( K+3, K+2 ) -
$ REFSUM*CONJG( V( 3, M ) )
T1 = V( 1, M )
T2 = T1*CONJG( V( 2, M ) )
T3 = T1*CONJG( V( 3, M ) )
REFSUM = V( 3, M )*H( K+3, K+2 )
H( K+3, K ) = -REFSUM*T1
H( K+3, K+1 ) = -REFSUM*T2
H( K+3, K+2 ) = H( K+3, K+2 ) - REFSUM*T3
*
* ==== Calculate reflection to move
* . Mth bulge one step. ====
Expand Down Expand Up @@ -572,12 +574,13 @@ SUBROUTINE CLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
$ S( 2*M ), VT )
ALPHA = VT( 1 )
CALL CLARFG( 3, ALPHA, VT( 2 ), 1, VT( 1 ) )
REFSUM = CONJG( VT( 1 ) )*
$ ( H( K+1, K )+CONJG( VT( 2 ) )*
$ H( K+2, K ) )
T1 = CONJG( VT( 1 ) )
T2 = T1*VT( 2 )
T3 = T1*VT( 3 )
REFSUM = H( K+1, K )+CONJG( VT( 2 ) )*H( K+2, K )
*
IF( CABS1( H( K+2, K )-REFSUM*VT( 2 ) )+
$ CABS1( REFSUM*VT( 3 ) ).GT.ULP*
IF( CABS1( H( K+2, K )-REFSUM*T2 )+
$ CABS1( REFSUM*T3 ).GT.ULP*
$ ( CABS1( H( K, K ) )+CABS1( H( K+1,
$ K+1 ) )+CABS1( H( K+2, K+2 ) ) ) ) THEN
*
Expand All @@ -595,7 +598,7 @@ SUBROUTINE CLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
* . Replace the old reflector with
* . the new one. ====
*
H( K+1, K ) = H( K+1, K ) - REFSUM
H( K+1, K ) = H( K+1, K ) - REFSUM*T1
H( K+2, K ) = ZERO
H( K+3, K ) = ZERO
V( 1, M ) = VT( 1 )
Expand Down
70 changes: 37 additions & 33 deletions SRC/dhgeqz.f
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Original file line number Diff line number Diff line change
Expand Up @@ -337,9 +337,9 @@ SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
$ BTOL, C, C11I, C11R, C12, C21, C22I, C22R, CL,
$ CQ, CR, CZ, ESHIFT, S, S1, S1INV, S2, SAFMAX,
$ SAFMIN, SCALE, SL, SQI, SQR, SR, SZI, SZR, T1,
$ TAU, TEMP, TEMP2, TEMPI, TEMPR, U1, U12, U12L,
$ U2, ULP, VS, W11, W12, W21, W22, WABS, WI, WR,
$ WR2
$ T2, T3, TAU, TEMP, TEMP2, TEMPI, TEMPR, U1,
$ U12, U12L, U2, ULP, VS, W11, W12, W21, W22,
$ WABS, WI, WR, WR2
* ..
* .. Local Arrays ..
DOUBLE PRECISION V( 3 )
Expand Down Expand Up @@ -1132,25 +1132,27 @@ SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
H( J+2, J-1 ) = ZERO
END IF
*
T2 = TAU*V( 2 )
T3 = TAU*V( 3 )
DO 230 JC = J, ILASTM
TEMP = TAU*( H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
$ H( J+2, JC ) )
H( J, JC ) = H( J, JC ) - TEMP
H( J+1, JC ) = H( J+1, JC ) - TEMP*V( 2 )
H( J+2, JC ) = H( J+2, JC ) - TEMP*V( 3 )
TEMP2 = TAU*( T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
$ T( J+2, JC ) )
T( J, JC ) = T( J, JC ) - TEMP2
T( J+1, JC ) = T( J+1, JC ) - TEMP2*V( 2 )
T( J+2, JC ) = T( J+2, JC ) - TEMP2*V( 3 )
TEMP = H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
$ H( J+2, JC )
H( J, JC ) = H( J, JC ) - TEMP*TAU
H( J+1, JC ) = H( J+1, JC ) - TEMP*T2
H( J+2, JC ) = H( J+2, JC ) - TEMP*T3
TEMP2 = T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
$ T( J+2, JC )
T( J, JC ) = T( J, JC ) - TEMP2*TAU
T( J+1, JC ) = T( J+1, JC ) - TEMP2*T2
T( J+2, JC ) = T( J+2, JC ) - TEMP2*T3
230 CONTINUE
IF( ILQ ) THEN
DO 240 JR = 1, N
TEMP = TAU*( Q( JR, J )+V( 2 )*Q( JR, J+1 )+V( 3 )*
$ Q( JR, J+2 ) )
Q( JR, J ) = Q( JR, J ) - TEMP
Q( JR, J+1 ) = Q( JR, J+1 ) - TEMP*V( 2 )
Q( JR, J+2 ) = Q( JR, J+2 ) - TEMP*V( 3 )
TEMP = Q( JR, J )+V( 2 )*Q( JR, J+1 )+V( 3 )*
$ Q( JR, J+2 )
Q( JR, J ) = Q( JR, J ) - TEMP*TAU
Q( JR, J+1 ) = Q( JR, J+1 ) - TEMP*T2
Q( JR, J+2 ) = Q( JR, J+2 ) - TEMP*T3
240 CONTINUE
END IF
*
Expand Down Expand Up @@ -1238,27 +1240,29 @@ SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
*
* Apply transformations from the right.
*
T2 = TAU*V(2)
T3 = TAU*V(3)
DO 260 JR = IFRSTM, MIN( J+3, ILAST )
TEMP = TAU*( H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
$ H( JR, J+2 ) )
H( JR, J ) = H( JR, J ) - TEMP
H( JR, J+1 ) = H( JR, J+1 ) - TEMP*V( 2 )
H( JR, J+2 ) = H( JR, J+2 ) - TEMP*V( 3 )
TEMP = H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
$ H( JR, J+2 )
H( JR, J ) = H( JR, J ) - TEMP*TAU
H( JR, J+1 ) = H( JR, J+1 ) - TEMP*T2
H( JR, J+2 ) = H( JR, J+2 ) - TEMP*T3
260 CONTINUE
DO 270 JR = IFRSTM, J + 2
TEMP = TAU*( T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
$ T( JR, J+2 ) )
T( JR, J ) = T( JR, J ) - TEMP
T( JR, J+1 ) = T( JR, J+1 ) - TEMP*V( 2 )
T( JR, J+2 ) = T( JR, J+2 ) - TEMP*V( 3 )
TEMP = T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
$ T( JR, J+2 )
T( JR, J ) = T( JR, J ) - TEMP*TAU
T( JR, J+1 ) = T( JR, J+1 ) - TEMP*T2
T( JR, J+2 ) = T( JR, J+2 ) - TEMP*T3
270 CONTINUE
IF( ILZ ) THEN
DO 280 JR = 1, N
TEMP = TAU*( Z( JR, J )+V( 2 )*Z( JR, J+1 )+V( 3 )*
$ Z( JR, J+2 ) )
Z( JR, J ) = Z( JR, J ) - TEMP
Z( JR, J+1 ) = Z( JR, J+1 ) - TEMP*V( 2 )
Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*V( 3 )
TEMP = Z( JR, J )+V( 2 )*Z( JR, J+1 )+V( 3 )*
$ Z( JR, J+2 )
Z( JR, J ) = Z( JR, J ) - TEMP*TAU
Z( JR, J+1 ) = Z( JR, J+1 ) - TEMP*T2
Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*T3
280 CONTINUE
END IF
T( J+1, J ) = ZERO
Expand Down
23 changes: 14 additions & 9 deletions SRC/dlaqr5.f
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Original file line number Diff line number Diff line change
Expand Up @@ -558,10 +558,13 @@ SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
* . Mth bulge. Exploit fact that first two elements
* . of row are actually zero. ====
*
REFSUM = V( 1, M )*V( 3, M )*H( K+3, K+2 )
H( K+3, K ) = -REFSUM
H( K+3, K+1 ) = -REFSUM*V( 2, M )
H( K+3, K+2 ) = H( K+3, K+2 ) - REFSUM*V( 3, M )
T1 = V( 1, M )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
REFSUM = V( 3, M )*H( K+3, K+2 )
H( K+3, K ) = -REFSUM*T1
H( K+3, K+1 ) = -REFSUM*T2
H( K+3, K+2 ) = H( K+3, K+2 ) - REFSUM*T3
*
* ==== Calculate reflection to move
* . Mth bulge one step. ====
Expand Down Expand Up @@ -597,11 +600,13 @@ SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
$ VT )
ALPHA = VT( 1 )
CALL DLARFG( 3, ALPHA, VT( 2 ), 1, VT( 1 ) )
REFSUM = VT( 1 )*( H( K+1, K )+VT( 2 )*
$ H( K+2, K ) )
T1 = VT( 1 )
T2 = T1*VT( 2 )
T3 = T1*VT( 3 )
REFSUM = H( K+1, K ) + VT( 2 )*H( K+2, K )
*
IF( ABS( H( K+2, K )-REFSUM*VT( 2 ) )+
$ ABS( REFSUM*VT( 3 ) ).GT.ULP*
IF( ABS( H( K+2, K )-REFSUM*T2 )+
$ ABS( REFSUM*T3 ).GT.ULP*
$ ( ABS( H( K, K ) )+ABS( H( K+1,
$ K+1 ) )+ABS( H( K+2, K+2 ) ) ) ) THEN
*
Expand All @@ -619,7 +624,7 @@ SUBROUTINE DLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
* . Replace the old reflector with
* . the new one. ====
*
H( K+1, K ) = H( K+1, K ) - REFSUM
H( K+1, K ) = H( K+1, K ) - REFSUM*T1
H( K+2, K ) = ZERO
H( K+3, K ) = ZERO
V( 1, M ) = VT( 1 )
Expand Down
70 changes: 37 additions & 33 deletions SRC/shgeqz.f
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -337,9 +337,9 @@ SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
$ BTOL, C, C11I, C11R, C12, C21, C22I, C22R, CL,
$ CQ, CR, CZ, ESHIFT, S, S1, S1INV, S2, SAFMAX,
$ SAFMIN, SCALE, SL, SQI, SQR, SR, SZI, SZR, T1,
$ TAU, TEMP, TEMP2, TEMPI, TEMPR, U1, U12, U12L,
$ U2, ULP, VS, W11, W12, W21, W22, WABS, WI, WR,
$ WR2
$ T2, T3, TAU, TEMP, TEMP2, TEMPI, TEMPR, U1,
$ U12, U12L, U2, ULP, VS, W11, W12, W21, W22,
$ WABS, WI, WR, WR2
* ..
* .. Local Arrays ..
REAL V( 3 )
Expand Down Expand Up @@ -1132,25 +1132,27 @@ SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
H( J+2, J-1 ) = ZERO
END IF
*
T2 = TAU * V( 2 )
T3 = TAU * V( 3 )
DO 230 JC = J, ILASTM
TEMP = TAU*( H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
$ H( J+2, JC ) )
H( J, JC ) = H( J, JC ) - TEMP
H( J+1, JC ) = H( J+1, JC ) - TEMP*V( 2 )
H( J+2, JC ) = H( J+2, JC ) - TEMP*V( 3 )
TEMP2 = TAU*( T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
$ T( J+2, JC ) )
T( J, JC ) = T( J, JC ) - TEMP2
T( J+1, JC ) = T( J+1, JC ) - TEMP2*V( 2 )
T( J+2, JC ) = T( J+2, JC ) - TEMP2*V( 3 )
TEMP = H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
$ H( J+2, JC )
H( J, JC ) = H( J, JC ) - TEMP*TAU
H( J+1, JC ) = H( J+1, JC ) - TEMP*T2
H( J+2, JC ) = H( J+2, JC ) - TEMP*T3
TEMP2 = T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
$ T( J+2, JC )
T( J, JC ) = T( J, JC ) - TEMP2*TAU
T( J+1, JC ) = T( J+1, JC ) - TEMP2*T2
T( J+2, JC ) = T( J+2, JC ) - TEMP2*T3
230 CONTINUE
IF( ILQ ) THEN
DO 240 JR = 1, N
TEMP = TAU*( Q( JR, J )+V( 2 )*Q( JR, J+1 )+V( 3 )*
$ Q( JR, J+2 ) )
Q( JR, J ) = Q( JR, J ) - TEMP
Q( JR, J+1 ) = Q( JR, J+1 ) - TEMP*V( 2 )
Q( JR, J+2 ) = Q( JR, J+2 ) - TEMP*V( 3 )
TEMP = Q( JR, J )+V( 2 )*Q( JR, J+1 )+V( 3 )*
$ Q( JR, J+2 )
Q( JR, J ) = Q( JR, J ) - TEMP*TAU
Q( JR, J+1 ) = Q( JR, J+1 ) - TEMP*T2
Q( JR, J+2 ) = Q( JR, J+2 ) - TEMP*T3
240 CONTINUE
END IF
*
Expand Down Expand Up @@ -1238,27 +1240,29 @@ SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
*
* Apply transformations from the right.
*
T2 = TAU*V( 2 )
T3 = TAU*V( 3 )
DO 260 JR = IFRSTM, MIN( J+3, ILAST )
TEMP = TAU*( H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
$ H( JR, J+2 ) )
H( JR, J ) = H( JR, J ) - TEMP
H( JR, J+1 ) = H( JR, J+1 ) - TEMP*V( 2 )
H( JR, J+2 ) = H( JR, J+2 ) - TEMP*V( 3 )
TEMP = H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
$ H( JR, J+2 )
H( JR, J ) = H( JR, J ) - TEMP*TAU
H( JR, J+1 ) = H( JR, J+1 ) - TEMP*T2
H( JR, J+2 ) = H( JR, J+2 ) - TEMP*T3
260 CONTINUE
DO 270 JR = IFRSTM, J + 2
TEMP = TAU*( T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
$ T( JR, J+2 ) )
T( JR, J ) = T( JR, J ) - TEMP
T( JR, J+1 ) = T( JR, J+1 ) - TEMP*V( 2 )
T( JR, J+2 ) = T( JR, J+2 ) - TEMP*V( 3 )
TEMP = T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
$ T( JR, J+2 )
T( JR, J ) = T( JR, J ) - TEMP*TAU
T( JR, J+1 ) = T( JR, J+1 ) - TEMP*T2
T( JR, J+2 ) = T( JR, J+2 ) - TEMP*T3
270 CONTINUE
IF( ILZ ) THEN
DO 280 JR = 1, N
TEMP = TAU*( Z( JR, J )+V( 2 )*Z( JR, J+1 )+V( 3 )*
$ Z( JR, J+2 ) )
Z( JR, J ) = Z( JR, J ) - TEMP
Z( JR, J+1 ) = Z( JR, J+1 ) - TEMP*V( 2 )
Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*V( 3 )
TEMP = Z( JR, J )+V( 2 )*Z( JR, J+1 )+V( 3 )*
$ Z( JR, J+2 )
Z( JR, J ) = Z( JR, J ) - TEMP*TAU
Z( JR, J+1 ) = Z( JR, J+1 ) - TEMP*T2
Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*T3
280 CONTINUE
END IF
T( J+1, J ) = ZERO
Expand Down
23 changes: 14 additions & 9 deletions SRC/slaqr5.f
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -558,10 +558,13 @@ SUBROUTINE SLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
* . Mth bulge. Exploit fact that first two elements
* . of row are actually zero. ====
*
REFSUM = V( 1, M )*V( 3, M )*H( K+3, K+2 )
H( K+3, K ) = -REFSUM
H( K+3, K+1 ) = -REFSUM*V( 2, M )
H( K+3, K+2 ) = H( K+3, K+2 ) - REFSUM*V( 3, M )
T1 = V( 1, M )
T2 = T1*V( 2, M )
T3 = T1*V( 3, M )
REFSUM = V( 3, M )*H( K+3, K+2 )
H( K+3, K ) = -REFSUM*T1
H( K+3, K+1 ) = -REFSUM*T2
H( K+3, K+2 ) = H( K+3, K+2 ) - REFSUM*T3
*
* ==== Calculate reflection to move
* . Mth bulge one step. ====
Expand Down Expand Up @@ -597,11 +600,13 @@ SUBROUTINE SLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
$ VT )
ALPHA = VT( 1 )
CALL SLARFG( 3, ALPHA, VT( 2 ), 1, VT( 1 ) )
REFSUM = VT( 1 )*( H( K+1, K )+VT( 2 )*
$ H( K+2, K ) )
T1 = VT( 1 )
T2 = T1*VT( 2 )
T3 = T2*VT( 3 )
REFSUM = H( K+1, K )+VT( 2 )*H( K+2, K )
*
IF( ABS( H( K+2, K )-REFSUM*VT( 2 ) )+
$ ABS( REFSUM*VT( 3 ) ).GT.ULP*
IF( ABS( H( K+2, K )-REFSUM*T2 )+
$ ABS( REFSUM*T3 ).GT.ULP*
$ ( ABS( H( K, K ) )+ABS( H( K+1,
$ K+1 ) )+ABS( H( K+2, K+2 ) ) ) ) THEN
*
Expand All @@ -619,7 +624,7 @@ SUBROUTINE SLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS,
* . Replace the old reflector with
* . the new one. ====
*
H( K+1, K ) = H( K+1, K ) - REFSUM
H( K+1, K ) = H( K+1, K ) - REFSUM*T1
H( K+2, K ) = ZERO
H( K+3, K ) = ZERO
V( 1, M ) = VT( 1 )
Expand Down
25 changes: 14 additions & 11 deletions SRC/zlaqr5.f
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -533,11 +533,13 @@ SUBROUTINE ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
* . Mth bulge. Exploit fact that first two elements
* . of row are actually zero. ====
*
REFSUM = V( 1, M )*V( 3, M )*H( K+3, K+2 )
H( K+3, K ) = -REFSUM
H( K+3, K+1 ) = -REFSUM*DCONJG( V( 2, M ) )
H( K+3, K+2 ) = H( K+3, K+2 ) -
$ REFSUM*DCONJG( V( 3, M ) )
T1 = V( 1, M )
T2 = T1*DCONJG( V( 2, M ) )
T3 = T1*DCONJG( V( 3, M ) )
REFSUM = V( 3, M )*H( K+3, K+2 )
H( K+3, K ) = -REFSUM*T1
H( K+3, K+1 ) = -REFSUM*T2
H( K+3, K+2 ) = H( K+3, K+2 ) - REFSUM*T3
*
* ==== Calculate reflection to move
* . Mth bulge one step. ====
Expand Down Expand Up @@ -572,12 +574,13 @@ SUBROUTINE ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
$ S( 2*M ), VT )
ALPHA = VT( 1 )
CALL ZLARFG( 3, ALPHA, VT( 2 ), 1, VT( 1 ) )
REFSUM = DCONJG( VT( 1 ) )*
$ ( H( K+1, K )+DCONJG( VT( 2 ) )*
$ H( K+2, K ) )
T1 = DCONJG( VT( 1 ) )
T2 = T1*VT( 2 )
T3 = T1*VT( 3 )
REFSUM = H( K+1, K )+DCONJG( VT( 2 ) )*H( K+2, K )
*
IF( CABS1( H( K+2, K )-REFSUM*VT( 2 ) )+
$ CABS1( REFSUM*VT( 3 ) ).GT.ULP*
IF( CABS1( H( K+2, K )-REFSUM*T2 )+
$ CABS1( REFSUM*T3 ).GT.ULP*
$ ( CABS1( H( K, K ) )+CABS1( H( K+1,
$ K+1 ) )+CABS1( H( K+2, K+2 ) ) ) ) THEN
*
Expand All @@ -595,7 +598,7 @@ SUBROUTINE ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S,
* . Replace the old reflector with
* . the new one. ====
*
H( K+1, K ) = H( K+1, K ) - REFSUM
H( K+1, K ) = H( K+1, K ) - REFSUM*T1
H( K+2, K ) = ZERO
H( K+3, K ) = ZERO
V( 1, M ) = VT( 1 )
Expand Down
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