--- rpl/lapack/lapack/zlarft.f 2011/11/21 20:43:17 1.9
+++ rpl/lapack/lapack/zlarft.f 2023/08/07 08:39:31 1.22
@@ -1,25 +1,25 @@
-*> \brief \b ZLARFT
+*> \brief \b ZLARFT forms the triangular factor T of a block reflector H = I - vtvH
*
* =========== DOCUMENTATION ===========
*
-* Online html documentation available at
-* http://www.netlib.org/lapack/explore-html/
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
-*> Download ZLARFT + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download ZLARFT + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
-*
+*
* .. Scalar Arguments ..
* CHARACTER DIRECT, STOREV
* INTEGER K, LDT, LDV, N
@@ -27,7 +27,7 @@
* .. Array Arguments ..
* COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * )
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -86,7 +86,7 @@
*> elementary reflectors). K >= 1.
*> \endverbatim
*>
-*> \param[in,out] V
+*> \param[in] V
*> \verbatim
*> V is COMPLEX*16 array, dimension
*> (LDV,K) if STOREV = 'C'
@@ -125,12 +125,10 @@
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
-*
-*> \date November 2011
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
*> \ingroup complex16OTHERauxiliary
*
@@ -141,9 +139,7 @@
*>
*> The shape of the matrix V and the storage of the vectors which define
*> the H(i) is best illustrated by the following example with n = 5 and
-*> k = 3. The elements equal to 1 are not stored; the corresponding
-*> array elements are modified but restored on exit. The rest of the
-*> array is not used.
+*> k = 3. The elements equal to 1 are not stored.
*>
*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
*>
@@ -165,10 +161,9 @@
* =====================================================================
SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
*
-* -- LAPACK auxiliary routine (version 3.4.0) --
+* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2011
*
* .. Scalar Arguments ..
CHARACTER DIRECT, STOREV
@@ -187,10 +182,9 @@
* ..
* .. Local Scalars ..
INTEGER I, J, PREVLASTV, LASTV
- COMPLEX*16 VII
* ..
* .. External Subroutines ..
- EXTERNAL ZGEMV, ZLACGV, ZTRMV
+ EXTERNAL ZGEMV, ZTRMV, ZGEMM
* ..
* .. External Functions ..
LOGICAL LSAME
@@ -205,51 +199,50 @@
*
IF( LSAME( DIRECT, 'F' ) ) THEN
PREVLASTV = N
- DO 20 I = 1, K
+ DO I = 1, K
PREVLASTV = MAX( PREVLASTV, I )
IF( TAU( I ).EQ.ZERO ) THEN
*
* H(i) = I
*
- DO 10 J = 1, I
+ DO J = 1, I
T( J, I ) = ZERO
- 10 CONTINUE
+ END DO
ELSE
*
* general case
*
- VII = V( I, I )
- V( I, I ) = ONE
IF( LSAME( STOREV, 'C' ) ) THEN
-! Skip any trailing zeros.
+* Skip any trailing zeros.
DO LASTV = N, I+1, -1
IF( V( LASTV, I ).NE.ZERO ) EXIT
END DO
+ DO J = 1, I-1
+ T( J, I ) = -TAU( I ) * CONJG( V( I , J ) )
+ END DO
J = MIN( LASTV, PREVLASTV )
*
* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i)
*
- CALL ZGEMV( 'Conjugate transpose', J-I+1, I-1,
- $ -TAU( I ), V( I, 1 ), LDV, V( I, I ), 1,
- $ ZERO, T( 1, I ), 1 )
+ CALL ZGEMV( 'Conjugate transpose', J-I, I-1,
+ $ -TAU( I ), V( I+1, 1 ), LDV,
+ $ V( I+1, I ), 1, ONE, T( 1, I ), 1 )
ELSE
-! Skip any trailing zeros.
+* Skip any trailing zeros.
DO LASTV = N, I+1, -1
IF( V( I, LASTV ).NE.ZERO ) EXIT
END DO
+ DO J = 1, I-1
+ T( J, I ) = -TAU( I ) * V( J , I )
+ END DO
J = MIN( LASTV, PREVLASTV )
*
* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H
*
- IF( I.LT.J )
- $ CALL ZLACGV( J-I, V( I, I+1 ), LDV )
- CALL ZGEMV( 'No transpose', I-1, J-I+1, -TAU( I ),
- $ V( 1, I ), LDV, V( I, I ), LDV, ZERO,
- $ T( 1, I ), 1 )
- IF( I.LT.J )
- $ CALL ZLACGV( J-I, V( I, I+1 ), LDV )
+ CALL ZGEMM( 'N', 'C', I-1, 1, J-I, -TAU( I ),
+ $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV,
+ $ ONE, T( 1, I ), LDT )
END IF
- V( I, I ) = VII
*
* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i)
*
@@ -262,56 +255,52 @@
PREVLASTV = LASTV
END IF
END IF
- 20 CONTINUE
+ END DO
ELSE
PREVLASTV = 1
- DO 40 I = K, 1, -1
+ DO I = K, 1, -1
IF( TAU( I ).EQ.ZERO ) THEN
*
* H(i) = I
*
- DO 30 J = I, K
+ DO J = I, K
T( J, I ) = ZERO
- 30 CONTINUE
+ END DO
ELSE
*
* general case
*
IF( I.LT.K ) THEN
IF( LSAME( STOREV, 'C' ) ) THEN
- VII = V( N-K+I, I )
- V( N-K+I, I ) = ONE
-! Skip any leading zeros.
+* Skip any leading zeros.
DO LASTV = 1, I-1
IF( V( LASTV, I ).NE.ZERO ) EXIT
END DO
+ DO J = I+1, K
+ T( J, I ) = -TAU( I ) * CONJG( V( N-K+I , J ) )
+ END DO
J = MAX( LASTV, PREVLASTV )
*
-* T(i+1:k,i) :=
-* - tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i)
+* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i)
*
- CALL ZGEMV( 'Conjugate transpose', N-K+I-J+1, K-I,
+ CALL ZGEMV( 'Conjugate transpose', N-K+I-J, K-I,
$ -TAU( I ), V( J, I+1 ), LDV, V( J, I ),
- $ 1, ZERO, T( I+1, I ), 1 )
- V( N-K+I, I ) = VII
+ $ 1, ONE, T( I+1, I ), 1 )
ELSE
- VII = V( I, N-K+I )
- V( I, N-K+I ) = ONE
-! Skip any leading zeros.
+* Skip any leading zeros.
DO LASTV = 1, I-1
IF( V( I, LASTV ).NE.ZERO ) EXIT
END DO
+ DO J = I+1, K
+ T( J, I ) = -TAU( I ) * V( J, N-K+I )
+ END DO
J = MAX( LASTV, PREVLASTV )
*
-* T(i+1:k,i) :=
-* - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H
+* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H
*
- CALL ZLACGV( N-K+I-1-J+1, V( I, J ), LDV )
- CALL ZGEMV( 'No transpose', K-I, N-K+I-J+1,
- $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV,
- $ ZERO, T( I+1, I ), 1 )
- CALL ZLACGV( N-K+I-1-J+1, V( I, J ), LDV )
- V( I, N-K+I ) = VII
+ CALL ZGEMM( 'N', 'C', K-I, 1, N-K+I-J, -TAU( I ),
+ $ V( I+1, J ), LDV, V( I, J ), LDV,
+ $ ONE, T( I+1, I ), LDT )
END IF
*
* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i)
@@ -326,7 +315,7 @@
END IF
T( I, I ) = TAU( I )
END IF
- 40 CONTINUE
+ END DO
END IF
RETURN
*