223 SUBROUTINE zhpt21( ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP,
224 $ tau, work, rwork, result )
233 INTEGER itype, kband, ldu, n
236 DOUBLE PRECISION d( * ), e( * ), result( 2 ), rwork( * )
237 COMPLEX*16 ap( * ), tau( * ), u( ldu, * ), vp( * ),
244 DOUBLE PRECISION zero, one, ten
245 parameter( zero = 0.0d+0, one = 1.0d+0, ten = 10.0d+0 )
246 DOUBLE PRECISION half
247 parameter( half = 1.0d+0 / 2.0d+0 )
248 COMPLEX*16 czero, cone
249 parameter( czero = ( 0.0d+0, 0.0d+0 ),
250 $ cone = ( 1.0d+0, 0.0d+0 ) )
255 INTEGER iinfo,
j, jp, jp1, jr, lap
256 DOUBLE PRECISION anorm, ulp, unfl, wnorm
257 COMPLEX*16 temp, vsave
270 INTRINSIC dble, dcmplx, max, min
282 lap = ( n*( n+1 ) ) / 2
284 IF(
lsame( uplo,
'U' ) )
THEN
292 unfl =
dlamch(
'Safe minimum' )
297 IF( itype.LT.1 .OR. itype.GT.3 )
THEN
298 result( 1 ) = ten / ulp
306 IF( itype.EQ.3 )
THEN
309 anorm = max(
zlanhp(
'1', cuplo, n, ap, rwork ), unfl )
314 IF( itype.EQ.1 )
THEN
318 CALL
zlaset(
'Full', n, n, czero, czero, work, n )
319 CALL
zcopy( lap, ap, 1, work, 1 )
322 CALL
zhpr( cuplo, n, -d(
j ), u( 1,
j ), 1, work )
325 IF( n.GT.1 .AND. kband.EQ.1 )
THEN
327 CALL
zhpr2( cuplo, n, -dcmplx( e(
j ) ), u( 1,
j ), 1,
328 $ u( 1,
j-1 ), 1, work )
331 wnorm =
zlanhp(
'1', cuplo, n, work, rwork )
333 ELSE IF( itype.EQ.2 )
THEN
337 CALL
zlaset(
'Full', n, n, czero, czero, work, n )
341 DO 40
j = n - 1, 1, -1
342 jp = ( ( 2*n-
j )*(
j-1 ) ) / 2
344 IF( kband.EQ.1 )
THEN
345 work( jp+
j+1 ) = ( cone-tau(
j ) )*e(
j )
347 work( jp+jr ) = -tau(
j )*e(
j )*vp( jp+jr )
351 IF( tau(
j ).NE.czero )
THEN
354 CALL
zhpmv(
'L', n-
j, cone, work( jp1+
j+1 ),
355 $ vp( jp+
j+1 ), 1, czero, work( lap+1 ), 1 )
356 temp = -half*tau(
j )*
zdotc( n-
j, work( lap+1 ), 1,
358 CALL
zaxpy( n-
j, temp, vp( jp+
j+1 ), 1, work( lap+1 ),
360 CALL
zhpr2(
'L', n-
j, -tau(
j ), vp( jp+
j+1 ), 1,
361 $ work( lap+1 ), 1, work( jp1+
j+1 ) )
365 work( jp+
j ) = d(
j )
370 jp = (
j*(
j-1 ) ) / 2
372 IF( kband.EQ.1 )
THEN
373 work( jp1+
j ) = ( cone-tau(
j ) )*e(
j )
375 work( jp1+jr ) = -tau(
j )*e(
j )*vp( jp1+jr )
379 IF( tau(
j ).NE.czero )
THEN
382 CALL
zhpmv(
'U',
j, cone, work, vp( jp1+1 ), 1, czero,
384 temp = -half*tau(
j )*
zdotc(
j, work( lap+1 ), 1,
386 CALL
zaxpy(
j, temp, vp( jp1+1 ), 1, work( lap+1 ),
388 CALL
zhpr2(
'U',
j, -tau(
j ), vp( jp1+1 ), 1,
389 $ work( lap+1 ), 1, work )
392 work( jp1+
j+1 ) = d(
j+1 )
397 work(
j ) = work(
j ) - ap(
j )
399 wnorm =
zlanhp(
'1', cuplo, n, work, rwork )
401 ELSE IF( itype.EQ.3 )
THEN
407 CALL
zlacpy(
' ', n, n, u, ldu, work, n )
408 CALL
zupmtr(
'R', cuplo,
'C', n, n, vp, tau, work, n,
409 $ work( n**2+1 ), iinfo )
410 IF( iinfo.NE.0 )
THEN
411 result( 1 ) = ten / ulp
416 work( ( n+1 )*(
j-1 )+1 ) = work( ( n+1 )*(
j-1 )+1 ) - cone
419 wnorm =
zlange(
'1', n, n, work, n, rwork )
422 IF( anorm.GT.wnorm )
THEN
423 result( 1 ) = ( wnorm / anorm ) / ( n*ulp )
425 IF( anorm.LT.one )
THEN
426 result( 1 ) = ( min( wnorm, n*anorm ) / anorm ) / ( n*ulp )
428 result( 1 ) = min( wnorm / anorm, dble( n ) ) / ( n*ulp )
436 IF( itype.EQ.1 )
THEN
437 CALL
zgemm(
'N',
'C', n, n, n, cone, u, ldu, u, ldu, czero,
441 work( ( n+1 )*(
j-1 )+1 ) = work( ( n+1 )*(
j-1 )+1 ) - cone
444 result( 2 ) = min(
zlange(
'1', n, n, work, n, rwork ),
445 $ dble( n ) ) / ( n*ulp )