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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
-*
-* -- LAPACK auxiliary routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- INTEGER K, LDA, LDT, LDY, N, NB
-* ..
-* .. Array Arguments ..
- COMPLEX*16 A( LDA, * ), T( LDT, NB ), TAU( NB ),
- $ Y( LDY, NB )
-* ..
-*
-* Purpose
-* =======
-*
-* ZLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1)
-* matrix A so that elements below the k-th subdiagonal are zero. The
-* reduction is performed by an unitary similarity transformation
-* Q' * A * Q. The routine returns the matrices V and T which determine
-* Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.
-*
-* This is an auxiliary routine called by ZGEHRD.
-*
-* Arguments
-* =========
-*
-* N (input) INTEGER
-* The order of the matrix A.
-*
-* K (input) INTEGER
-* The offset for the reduction. Elements below the k-th
-* subdiagonal in the first NB columns are reduced to zero.
-* K < N.
-*
-* NB (input) INTEGER
-* The number of columns to be reduced.
-*
-* A (input/output) COMPLEX*16 array, dimension (LDA,N-K+1)
-* On entry, the n-by-(n-k+1) general matrix A.
-* On exit, the elements on and above the k-th subdiagonal in
-* the first NB columns are overwritten with the corresponding
-* elements of the reduced matrix; the elements below the k-th
-* subdiagonal, with the array TAU, represent the matrix Q as a
-* product of elementary reflectors. The other columns of A are
-* unchanged. See Further Details.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* TAU (output) COMPLEX*16 array, dimension (NB)
-* The scalar factors of the elementary reflectors. See Further
-* Details.
-*
-* T (output) COMPLEX*16 array, dimension (LDT,NB)
-* The upper triangular matrix T.
-*
-* LDT (input) INTEGER
-* The leading dimension of the array T. LDT >= NB.
-*
-* Y (output) COMPLEX*16 array, dimension (LDY,NB)
-* The n-by-nb matrix Y.
-*
-* LDY (input) INTEGER
-* The leading dimension of the array Y. LDY >= N.
-*
-* Further Details
-* ===============
-*
-* The matrix Q is represented as a product of nb elementary reflectors
-*
-* Q = H(1) H(2) . . . H(nb).
-*
-* Each H(i) has the form
-*
-* H(i) = I - tau * v * v'
-*
-* where tau is a complex scalar, and v is a complex vector with
-* v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
-* A(i+k+1:n,i), and tau in TAU(i).
-*
-* The elements of the vectors v together form the (n-k+1)-by-nb matrix
-* V which is needed, with T and Y, to apply the transformation to the
-* unreduced part of the matrix, using an update of the form:
-* A := (I - V*T*V') * (A - Y*V').
-*
-* The contents of A on exit are illustrated by the following example
-* with n = 7, k = 3 and nb = 2:
-*
-* ( a a a a a )
-* ( a a a a a )
-* ( a a a a a )
-* ( h h a a a )
-* ( v1 h a a a )
-* ( v1 v2 a a a )
-* ( v1 v2 a a a )
-*
-* where a denotes an element of the original matrix A, h denotes a
-* modified element of the upper Hessenberg matrix H, and vi denotes an
-* element of the vector defining H(i).
-*
-* This file is a slight modification of LAPACK-3.0's ZLAHRD
-* incorporating improvements proposed by Quintana-Orti and Van de
-* Gejin. Note that the entries of A(1:K,2:NB) differ from those
-* returned by the original LAPACK routine. This function is
-* not backward compatible with LAPACK3.0.
-*
-* =====================================================================
-*
-* .. Parameters ..
- COMPLEX*16 ZERO, ONE
- PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
- $ ONE = ( 1.0D+0, 0.0D+0 ) )
-* ..
-* .. Local Scalars ..
- INTEGER I
- COMPLEX*16 EI
-* ..
-* .. External Subroutines ..
- EXTERNAL ZAXPY, ZCOPY, ZGEMM, ZGEMV, ZLACPY,
- $ ZLARFG, ZSCAL, ZTRMM, ZTRMV, ZLACGV
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC MIN
-* ..
-* .. Executable Statements ..
-*
-* Quick return if possible
-*
- IF( N.LE.1 )
- $ RETURN
-*
- DO 10 I = 1, NB
- IF( I.GT.1 ) THEN
-*
-* Update A(K+1:N,I)
-*
-* Update I-th column of A - Y * V'
-*
- CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA )
- CALL ZGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, Y(K+1,1), LDY,
- $ A( K+I-1, 1 ), LDA, ONE, A( K+1, I ), 1 )
- CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA )
-*
-* Apply I - V * T' * V' to this column (call it b) from the
-* left, using the last column of T as workspace
-*
-* Let V = ( V1 ) and b = ( b1 ) (first I-1 rows)
-* ( V2 ) ( b2 )
-*
-* where V1 is unit lower triangular
-*
-* w := V1' * b1
-*
- CALL ZCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 )
- CALL ZTRMV( 'Lower', 'Conjugate transpose', 'UNIT',
- $ I-1, A( K+1, 1 ),
- $ LDA, T( 1, NB ), 1 )
-*
-* w := w + V2'*b2
-*
- CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1,
- $ ONE, A( K+I, 1 ),
- $ LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 )
-*
-* w := T'*w
-*
- CALL ZTRMV( 'Upper', 'Conjugate transpose', 'NON-UNIT',
- $ I-1, T, LDT,
- $ T( 1, NB ), 1 )
-*
-* b2 := b2 - V2*w
-*
- CALL ZGEMV( 'NO TRANSPOSE', N-K-I+1, I-1, -ONE,
- $ A( K+I, 1 ),
- $ LDA, T( 1, NB ), 1, ONE, A( K+I, I ), 1 )
-*
-* b1 := b1 - V1*w
-*
- CALL ZTRMV( 'Lower', 'NO TRANSPOSE',
- $ 'UNIT', I-1,
- $ A( K+1, 1 ), LDA, T( 1, NB ), 1 )
- CALL ZAXPY( I-1, -ONE, T( 1, NB ), 1, A( K+1, I ), 1 )
-*
- A( K+I-1, I-1 ) = EI
- END IF
-*
-* Generate the elementary reflector H(I) to annihilate
-* A(K+I+1:N,I)
-*
- CALL ZLARFG( N-K-I+1, A( K+I, I ), A( MIN( K+I+1, N ), I ), 1,
- $ TAU( I ) )
- EI = A( K+I, I )
- A( K+I, I ) = ONE
-*
-* Compute Y(K+1:N,I)
-*
- CALL ZGEMV( 'NO TRANSPOSE', N-K, N-K-I+1,
- $ ONE, A( K+1, I+1 ),
- $ LDA, A( K+I, I ), 1, ZERO, Y( K+1, I ), 1 )
- CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1,
- $ ONE, A( K+I, 1 ), LDA,
- $ A( K+I, I ), 1, ZERO, T( 1, I ), 1 )
- CALL ZGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE,
- $ Y( K+1, 1 ), LDY,
- $ T( 1, I ), 1, ONE, Y( K+1, I ), 1 )
- CALL ZSCAL( N-K, TAU( I ), Y( K+1, I ), 1 )
-*
-* Compute T(1:I,I)
-*
- CALL ZSCAL( I-1, -TAU( I ), T( 1, I ), 1 )
- CALL ZTRMV( 'Upper', 'No Transpose', 'NON-UNIT',
- $ I-1, T, LDT,
- $ T( 1, I ), 1 )
- T( I, I ) = TAU( I )
-*
- 10 CONTINUE
- A( K+NB, NB ) = EI
-*
-* Compute Y(1:K,1:NB)
-*
- CALL ZLACPY( 'ALL', K, NB, A( 1, 2 ), LDA, Y, LDY )
- CALL ZTRMM( 'RIGHT', 'Lower', 'NO TRANSPOSE',
- $ 'UNIT', K, NB,
- $ ONE, A( K+1, 1 ), LDA, Y, LDY )
- IF( N.GT.K+NB )
- $ CALL ZGEMM( 'NO TRANSPOSE', 'NO TRANSPOSE', K,
- $ NB, N-K-NB, ONE,
- $ A( 1, 2+NB ), LDA, A( K+1+NB, 1 ), LDA, ONE, Y,
- $ LDY )
- CALL ZTRMM( 'RIGHT', 'Upper', 'NO TRANSPOSE',
- $ 'NON-UNIT', K, NB,
- $ ONE, T, LDT, Y, LDY )
-*
- RETURN
-*
-* End of ZLAHR2
-*
- END