@@ -301,29 +301,30 @@ RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV,
301301*
302302* Compute T_{2,2} recursively
303303*
304- CALL DLARFT(DIRECT, STOREV, N- L, K- L, V(L+1 ,L+1 ), LDV,
305- $ TAU(L+1 ), T(L+1 ,L+1 ), LDT)
304+ CALL DLARFT(DIRECT, STOREV, N- L, K- L, V(L+1 , L+1 ), LDV,
305+ $ TAU(L+1 ), T(L+1 , L+1 ), LDT)
306306*
307307* Compute T_{1,2}
308308* T_{1,2} = V_{2,1}'
309309*
310310 DO J = 1 , L
311311 DO I = 1 , K- L
312- T(J,L+ I) = V(L+ I,J)
312+ T(J, L+ I) = V(L+ I, J)
313313 END DO
314314 END DO
315315*
316316* T_{1,2} = T_{1,2}*V_{2,2}
317317*
318318 CALL DTRMM(' Right' , ' Lower' , ' No transpose' , ' Unit' , L,
319- $ K- L, ONE, V(L+1 , L+1 ), LDV, T(1 , L+1 ), LDT)
319+ $ K- L, ONE, V(L+1 , L+1 ), LDV, T(1 , L+1 ), LDT)
320320
321321*
322322* T_{1,2} = V_{3,1}'*V_{3,2} + T_{1,2}
323323* Note: We assume K <= N, and GEMM will do nothing if N=K
324324*
325325 CALL DGEMM(' Transpose' , ' No transpose' , L, K- L, N- K, ONE,
326- $ V(K+1 , 1 ), LDV, V(K+1 ,L+1 ), LDV, ONE, T(1 , L+1 ), LDT)
326+ $ V(K+1 , 1 ), LDV, V(K+1 , L+1 ), LDV, ONE,
327+ $ T(1 , L+1 ), LDT)
327328*
328329* At this point, we have that T_{1,2} = V_1'*V_2
329330* All that is left is to pre and post multiply by -T_{1,1} and T_{2,2}
@@ -332,12 +333,12 @@ RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV,
332333* T_{1,2} = -T_{1,1}*T_{1,2}
333334*
334335 CALL DTRMM(' Left' , ' Upper' , ' No transpose' , ' Non-unit' , L,
335- $ K- L, NEG_ONE, T, LDT, T(1 , L+1 ), LDT)
336+ $ K- L, NEG_ONE, T, LDT, T(1 , L+1 ), LDT)
336337*
337338* T_{1,2} = T_{1,2}*T_{2,2}
338339*
339340 CALL DTRMM(' Right' , ' Upper' , ' No transpose' , ' Non-unit' , L,
340- $ K- L, ONE, T(L+1 ,L+1 ), LDT, T(1 , L+1 ), LDT)
341+ $ K- L, ONE, T(L+1 , L+1 ), LDT, T(1 , L+1 ), LDT)
341342
342343 ELSE IF (LQ) THEN
343344*
@@ -395,26 +396,27 @@ RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV,
395396*
396397* Compute T_{2,2} recursively
397398*
398- CALL DLARFT(DIRECT, STOREV, N- L, K- L, V(L+1 ,L+1 ), LDV,
399- $ TAU(L+1 ), T(L+1 ,L+1 ), LDT)
399+ CALL DLARFT(DIRECT, STOREV, N- L, K- L, V(L+1 , L+1 ), LDV,
400+ $ TAU(L+1 ), T(L+1 , L+1 ), LDT)
400401
401402*
402403* Compute T_{1,2}
403404* T_{1,2} = V_{1,2}
404405*
405- CALL DLACPY(' All' , L, K - L, V(1 ,L+1 ), LDV, T(1 , L+1 ), LDT)
406+ CALL DLACPY(' All' , L, K- L, V(1 , L+1 ), LDV, T(1 , L+1 ), LDT)
406407*
407408* T_{1,2} = T_{1,2}*V_{2,2}'
408409*
409410 CALL DTRMM(' Right' , ' Upper' , ' Transpose' , ' Unit' , L, K- L,
410- $ ONE, V(L+1 , L+1 ), LDV, T(1 , L+1 ), LDT)
411+ $ ONE, V(L+1 , L+1 ), LDV, T(1 , L+1 ), LDT)
411412
412413*
413414* T_{1,2} = V_{1,3}*V_{2,3}' + T_{1,2}
414415* Note: We assume K <= N, and GEMM will do nothing if N=K
415416*
416417 CALL DGEMM(' No transpose' , ' Transpose' , L, K- L, N- K, ONE,
417- $ V(1 , K+1 ), LDV, V(L+1 , K+1 ), LDV, ONE, T(1 , L+1 ), LDT)
418+ $ V(1 , K+1 ), LDV, V(L+1 , K+1 ), LDV, ONE,
419+ $ T(1 , L+1 ), LDT)
418420*
419421* At this point, we have that T_{1,2} = V_1*V_2'
420422* All that is left is to pre and post multiply by -T_{1,1} and T_{2,2}
@@ -423,13 +425,13 @@ RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV,
423425* T_{1,2} = -T_{1,1}*T_{1,2}
424426*
425427 CALL DTRMM(' Left' , ' Upper' , ' No transpose' , ' Non-unit' , L,
426- $ K- L, NEG_ONE, T, LDT, T(1 , L+1 ), LDT)
428+ $ K- L, NEG_ONE, T, LDT, T(1 , L+1 ), LDT)
427429
428430*
429431* T_{1,2} = T_{1,2}*T_{2,2}
430432*
431433 CALL DTRMM(' Right' , ' Upper' , ' No transpose' , ' Non-unit' , L,
432- $ K- L, ONE, T(L+1 ,L+1 ), LDT, T(1 , L+1 ), LDT)
434+ $ K- L, ONE, T(L+1 , L+1 ), LDT, T(1 , L+1 ), LDT)
433435 ELSE IF (QL) THEN
434436*
435437* Break V apart into 6 components
@@ -487,28 +489,29 @@ RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV,
487489* Compute T_{2,2} recursively
488490*
489491 CALL DLARFT(DIRECT, STOREV, N, L, V(1 , K- L+1 ), LDV,
490- $ TAU(K- L+1 ), T(K- L+1 ,K- L+1 ), LDT)
492+ $ TAU(K- L+1 ), T(K- L+1 , K- L+1 ), LDT)
491493*
492494* Compute T_{2,1}
493495* T_{2,1} = V_{2,2}'
494496*
495497 DO J = 1 , K- L
496498 DO I = 1 , L
497- T(K- L+ I,J) = V(N- K+ J, K- L+ I)
499+ T(K- L+ I, J) = V(N- K+ J, K- L+ I)
498500 END DO
499501 END DO
500502*
501503* T_{2,1} = T_{2,1}*V_{2,1}
502504*
503505 CALL DTRMM(' Right' , ' Upper' , ' No transpose' , ' Unit' , L,
504- $ K- L, ONE, V(N- K+1 ,1 ), LDV, T(K- L+1 ,1 ), LDT)
506+ $ K- L, ONE, V(N- K+1 , 1 ), LDV, T(K- L+1 , 1 ), LDT)
505507
506508*
507509* T_{2,1} = V_{2,2}'*V_{2,1} + T_{2,1}
508510* Note: We assume K <= N, and GEMM will do nothing if N=K
509511*
510512 CALL DGEMM(' Transpose' , ' No transpose' , L, K- L, N- K, ONE,
511- $ V(1 ,K- L+1 ), LDV, V, LDV, ONE, T(K- L+1 ,1 ), LDT)
513+ $ V(1 , K- L+1 ), LDV, V, LDV, ONE, T(K- L+1 , 1 ),
514+ $ LDT)
512515*
513516* At this point, we have that T_{2,1} = V_2'*V_1
514517* All that is left is to pre and post multiply by -T_{2,2} and T_{1,1}
@@ -517,12 +520,13 @@ RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV,
517520* T_{2,1} = -T_{2,2}*T_{2,1}
518521*
519522 CALL DTRMM(' Left' , ' Lower' , ' No transpose' , ' Non-unit' , L,
520- $ K- L, NEG_ONE, T(K- L+1 ,K- L+1 ), LDT, T(K- L+1 ,1 ), LDT)
523+ $ K- L, NEG_ONE, T(K- L+1 , K- L+1 ), LDT,
524+ $ T(K- L+1 , 1 ), LDT)
521525*
522526* T_{2,1} = T_{2,1}*T_{1,1}
523527*
524528 CALL DTRMM(' Right' , ' Lower' , ' No transpose' , ' Non-unit' , L,
525- $ K- L, ONE, T, LDT, T(K- L+1 ,1 ), LDT)
529+ $ K- L, ONE, T, LDT, T(K- L+1 , 1 ), LDT)
526530 ELSE
527531*
528532* Else means RQ case
@@ -581,27 +585,28 @@ RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV,
581585*
582586* Compute T_{2,2} recursively
583587*
584- CALL DLARFT(DIRECT, STOREV, N, L, V(K- L+1 ,1 ), LDV,
585- $ TAU(K- L+1 ), T(K- L+1 ,K- L+1 ), LDT)
588+ CALL DLARFT(DIRECT, STOREV, N, L, V(K- L+1 , 1 ), LDV,
589+ $ TAU(K- L+1 ), T(K- L+1 , K- L+1 ), LDT)
586590*
587591* Compute T_{2,1}
588592* T_{2,1} = V_{2,2}
589593*
590- CALL DLACPY(' All' , L, K- L, V(K- L+1 ,N- K+1 ), LDV, T(K - L +1 , 1 ) ,
591- $ LDT)
594+ CALL DLACPY(' All' , L, K- L, V(K- L+1 , N- K+1 ), LDV,
595+ $ T(K - L +1 , 1 ), LDT)
592596
593597*
594598* T_{2,1} = T_{2,1}*V_{1,2}'
595599*
596600 CALL DTRMM(' Right' , ' Lower' , ' Transpose' , ' Unit' , L, K- L,
597- $ ONE, V(1 , N- K+1 ), LDV, T(K- L+1 ,1 ), LDT)
601+ $ ONE, V(1 , N- K+1 ), LDV, T(K- L+1 , 1 ), LDT)
598602
599603*
600604* T_{2,1} = V_{2,1}*V_{1,1}' + T_{2,1}
601605* Note: We assume K <= N, and GEMM will do nothing if N=K
602606*
603607 CALL DGEMM(' No transpose' , ' Transpose' , L, K- L, N- K, ONE,
604- $ V(K- L+1 ,1 ), LDV, V, LDV, ONE, T(K- L+1 ,1 ), LDT)
608+ $ V(K- L+1 , 1 ), LDV, V, LDV, ONE, T(K- L+1 , 1 ),
609+ $ LDT)
605610
606611*
607612* At this point, we have that T_{2,1} = V_2*V_1'
@@ -611,12 +616,13 @@ RECURSIVE SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV,
611616* T_{2,1} = -T_{2,2}*T_{2,1}
612617*
613618 CALL DTRMM(' Left' , ' Lower' , ' No tranpose' , ' Non-unit' , L,
614- $ K- L, NEG_ONE, T(K- L+1 ,K- L+1 ), LDT, T(K- L+1 ,1 ), LDT)
619+ $ K- L, NEG_ONE, T(K- L+1 , K- L+1 ), LDT,
620+ $ T(K- L+1 , 1 ), LDT)
615621
616622*
617623* T_{2,1} = T_{2,1}*T_{1,1}
618624*
619625 CALL DTRMM(' Right' , ' Lower' , ' No tranpose' , ' Non-unit' , L,
620- $ K- L, ONE, T, LDT, T(K- L+1 ,1 ), LDT)
626+ $ K- L, ONE, T, LDT, T(K- L+1 , 1 ), LDT)
621627 END IF
622628 END SUBROUTINE
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