Rewrite to use FMA with Householder reflectors
This commit is contained in:
Martin Kroeker
GitHub
parent
e1c3c34178
commit
2a83ec1f79
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@ -337,9 +337,9 @@
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$ BTOL, C, C11I, C11R, C12, C21, C22I, C22R, CL,
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$ CQ, CR, CZ, ESHIFT, S, S1, S1INV, S2, SAFMAX,
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$ SAFMIN, SCALE, SL, SQI, SQR, SR, SZI, SZR, T1,
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$ TAU, TEMP, TEMP2, TEMPI, TEMPR, U1, U12, U12L,
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$ U2, ULP, VS, W11, W12, W21, W22, WABS, WI, WR,
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$ WR2
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$ T2, T3, TAU, TEMP, TEMP2, TEMPI, TEMPR, U1,
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$ U12, U12L, U2, ULP, VS, W11, W12, W21, W22,
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$ WABS, WI, WR, WR2
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* ..
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* .. Local Arrays ..
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DOUBLE PRECISION V( 3 )
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@ -1127,25 +1127,27 @@
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H( J+2, J-1 ) = ZERO
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END IF
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*
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T2 = TAU*V( 2 )
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T3 = TAU*V( 3 )
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DO 230 JC = J, ILASTM
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TEMP = TAU*( H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
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$ H( J+2, JC ) )
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H( J, JC ) = H( J, JC ) - TEMP
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H( J+1, JC ) = H( J+1, JC ) - TEMP*V( 2 )
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H( J+2, JC ) = H( J+2, JC ) - TEMP*V( 3 )
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TEMP2 = TAU*( T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
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$ T( J+2, JC ) )
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T( J, JC ) = T( J, JC ) - TEMP2
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T( J+1, JC ) = T( J+1, JC ) - TEMP2*V( 2 )
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T( J+2, JC ) = T( J+2, JC ) - TEMP2*V( 3 )
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TEMP = H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
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$ H( J+2, JC )
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H( J, JC ) = H( J, JC ) - TEMP*TAU
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H( J+1, JC ) = H( J+1, JC ) - TEMP*T2
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H( J+2, JC ) = H( J+2, JC ) - TEMP*T3
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TEMP2 = T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
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$ T( J+2, JC )
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T( J, JC ) = T( J, JC ) - TEMP2*TAU
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T( J+1, JC ) = T( J+1, JC ) - TEMP2*T2
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T( J+2, JC ) = T( J+2, JC ) - TEMP2*T3
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230 CONTINUE
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IF( ILQ ) THEN
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DO 240 JR = 1, N
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TEMP = TAU*( Q( JR, J )+V( 2 )*Q( JR, J+1 )+V( 3 )*
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$ Q( JR, J+2 ) )
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Q( JR, J ) = Q( JR, J ) - TEMP
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Q( JR, J+1 ) = Q( JR, J+1 ) - TEMP*V( 2 )
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Q( JR, J+2 ) = Q( JR, J+2 ) - TEMP*V( 3 )
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TEMP = Q( JR, J )+V( 2 )*Q( JR, J+1 )+V( 3 )*
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$ Q( JR, J+2 )
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Q( JR, J ) = Q( JR, J ) - TEMP*TAU
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Q( JR, J+1 ) = Q( JR, J+1 ) - TEMP*T2
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Q( JR, J+2 ) = Q( JR, J+2 ) - TEMP*T3
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240 CONTINUE
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END IF
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*
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@ -1233,27 +1235,29 @@
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*
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* Apply transformations from the right.
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*
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T2 = TAU*V(2)
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T3 = TAU*V(3)
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DO 260 JR = IFRSTM, MIN( J+3, ILAST )
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TEMP = TAU*( H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
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$ H( JR, J+2 ) )
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H( JR, J ) = H( JR, J ) - TEMP
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H( JR, J+1 ) = H( JR, J+1 ) - TEMP*V( 2 )
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H( JR, J+2 ) = H( JR, J+2 ) - TEMP*V( 3 )
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TEMP = H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
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$ H( JR, J+2 )
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H( JR, J ) = H( JR, J ) - TEMP*TAU
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H( JR, J+1 ) = H( JR, J+1 ) - TEMP*T2
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H( JR, J+2 ) = H( JR, J+2 ) - TEMP*T3
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260 CONTINUE
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DO 270 JR = IFRSTM, J + 2
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TEMP = TAU*( T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
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$ T( JR, J+2 ) )
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T( JR, J ) = T( JR, J ) - TEMP
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T( JR, J+1 ) = T( JR, J+1 ) - TEMP*V( 2 )
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T( JR, J+2 ) = T( JR, J+2 ) - TEMP*V( 3 )
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TEMP = T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
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$ T( JR, J+2 )
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T( JR, J ) = T( JR, J ) - TEMP*TAU
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T( JR, J+1 ) = T( JR, J+1 ) - TEMP*T2
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T( JR, J+2 ) = T( JR, J+2 ) - TEMP*T3
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270 CONTINUE
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IF( ILZ ) THEN
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DO 280 JR = 1, N
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TEMP = TAU*( Z( JR, J )+V( 2 )*Z( JR, J+1 )+V( 3 )*
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$ Z( JR, J+2 ) )
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Z( JR, J ) = Z( JR, J ) - TEMP
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Z( JR, J+1 ) = Z( JR, J+1 ) - TEMP*V( 2 )
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Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*V( 3 )
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TEMP = Z( JR, J )+V( 2 )*Z( JR, J+1 )+V( 3 )*
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$ Z( JR, J+2 )
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Z( JR, J ) = Z( JR, J ) - TEMP*TAU
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Z( JR, J+1 ) = Z( JR, J+1 ) - TEMP*T2
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Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*T3
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280 CONTINUE
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END IF
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T( J+1, J ) = ZERO
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@ -337,9 +337,9 @@
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$ BTOL, C, C11I, C11R, C12, C21, C22I, C22R, CL,
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$ CQ, CR, CZ, ESHIFT, S, S1, S1INV, S2, SAFMAX,
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$ SAFMIN, SCALE, SL, SQI, SQR, SR, SZI, SZR, T1,
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$ TAU, TEMP, TEMP2, TEMPI, TEMPR, U1, U12, U12L,
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$ U2, ULP, VS, W11, W12, W21, W22, WABS, WI, WR,
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$ WR2
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$ T2, T3, TAU, TEMP, TEMP2, TEMPI, TEMPR, U1,
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$ U12, U12L, U2, ULP, VS, W11, W12, W21, W22,
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$ WABS, WI, WR, WR2
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* ..
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* .. Local Arrays ..
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REAL V( 3 )
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@ -1127,25 +1127,27 @@
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H( J+2, J-1 ) = ZERO
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END IF
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*
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T2 = TAU * V( 2 )
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T3 = TAU * V( 3 )
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DO 230 JC = J, ILASTM
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TEMP = TAU*( H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
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$ H( J+2, JC ) )
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H( J, JC ) = H( J, JC ) - TEMP
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H( J+1, JC ) = H( J+1, JC ) - TEMP*V( 2 )
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H( J+2, JC ) = H( J+2, JC ) - TEMP*V( 3 )
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TEMP2 = TAU*( T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
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$ T( J+2, JC ) )
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T( J, JC ) = T( J, JC ) - TEMP2
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T( J+1, JC ) = T( J+1, JC ) - TEMP2*V( 2 )
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T( J+2, JC ) = T( J+2, JC ) - TEMP2*V( 3 )
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TEMP = H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
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$ H( J+2, JC )
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H( J, JC ) = H( J, JC ) - TEMP*TAU
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H( J+1, JC ) = H( J+1, JC ) - TEMP*T2
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H( J+2, JC ) = H( J+2, JC ) - TEMP*T3
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TEMP2 = T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
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$ T( J+2, JC )
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T( J, JC ) = T( J, JC ) - TEMP2*TAU
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T( J+1, JC ) = T( J+1, JC ) - TEMP2*T2
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T( J+2, JC ) = T( J+2, JC ) - TEMP2*T3
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230 CONTINUE
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IF( ILQ ) THEN
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DO 240 JR = 1, N
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TEMP = TAU*( Q( JR, J )+V( 2 )*Q( JR, J+1 )+V( 3 )*
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$ Q( JR, J+2 ) )
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Q( JR, J ) = Q( JR, J ) - TEMP
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Q( JR, J+1 ) = Q( JR, J+1 ) - TEMP*V( 2 )
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Q( JR, J+2 ) = Q( JR, J+2 ) - TEMP*V( 3 )
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TEMP = Q( JR, J )+V( 2 )*Q( JR, J+1 )+V( 3 )*
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$ Q( JR, J+2 )
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Q( JR, J ) = Q( JR, J ) - TEMP*TAU
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Q( JR, J+1 ) = Q( JR, J+1 ) - TEMP*T2
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Q( JR, J+2 ) = Q( JR, J+2 ) - TEMP*T3
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240 CONTINUE
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END IF
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*
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@ -1233,27 +1235,29 @@
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*
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* Apply transformations from the right.
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*
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T2 = TAU*V( 2 )
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T3 = TAU*V( 3 )
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DO 260 JR = IFRSTM, MIN( J+3, ILAST )
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TEMP = TAU*( H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
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$ H( JR, J+2 ) )
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H( JR, J ) = H( JR, J ) - TEMP
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H( JR, J+1 ) = H( JR, J+1 ) - TEMP*V( 2 )
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H( JR, J+2 ) = H( JR, J+2 ) - TEMP*V( 3 )
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TEMP = H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
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$ H( JR, J+2 )
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H( JR, J ) = H( JR, J ) - TEMP*TAU
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H( JR, J+1 ) = H( JR, J+1 ) - TEMP*T2
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H( JR, J+2 ) = H( JR, J+2 ) - TEMP*T3
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260 CONTINUE
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DO 270 JR = IFRSTM, J + 2
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TEMP = TAU*( T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
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$ T( JR, J+2 ) )
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T( JR, J ) = T( JR, J ) - TEMP
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T( JR, J+1 ) = T( JR, J+1 ) - TEMP*V( 2 )
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T( JR, J+2 ) = T( JR, J+2 ) - TEMP*V( 3 )
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TEMP = T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
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$ T( JR, J+2 )
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T( JR, J ) = T( JR, J ) - TEMP*TAU
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T( JR, J+1 ) = T( JR, J+1 ) - TEMP*T2
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T( JR, J+2 ) = T( JR, J+2 ) - TEMP*T3
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270 CONTINUE
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IF( ILZ ) THEN
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DO 280 JR = 1, N
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TEMP = TAU*( Z( JR, J )+V( 2 )*Z( JR, J+1 )+V( 3 )*
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$ Z( JR, J+2 ) )
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Z( JR, J ) = Z( JR, J ) - TEMP
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Z( JR, J+1 ) = Z( JR, J+1 ) - TEMP*V( 2 )
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Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*V( 3 )
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TEMP = Z( JR, J )+V( 2 )*Z( JR, J+1 )+V( 3 )*
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$ Z( JR, J+2 )
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Z( JR, J ) = Z( JR, J ) - TEMP*TAU
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Z( JR, J+1 ) = Z( JR, J+1 ) - TEMP*T2
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Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*T3
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280 CONTINUE
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END IF
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T( J+1, J ) = ZERO
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