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author | jofret | 2009-04-28 07:17:00 +0000 |
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committer | jofret | 2009-04-28 07:17:00 +0000 |
commit | 8c8d2f518968ce7057eec6aa5cd5aec8faab861a (patch) | |
tree | 3dd1788b71d6a3ce2b73d2d475a3133580e17530 /src/lib/lapack/zgehrd.f | |
parent | 9f652ffc16a310ac6641a9766c5b9e2671e0e9cb (diff) | |
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Moving lapack to right place
Diffstat (limited to 'src/lib/lapack/zgehrd.f')
-rw-r--r-- | src/lib/lapack/zgehrd.f | 273 |
1 files changed, 0 insertions, 273 deletions
diff --git a/src/lib/lapack/zgehrd.f b/src/lib/lapack/zgehrd.f deleted file mode 100644 index 83c1aa32..00000000 --- a/src/lib/lapack/zgehrd.f +++ /dev/null @@ -1,273 +0,0 @@ - SUBROUTINE ZGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER IHI, ILO, INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* Purpose -* ======= -* -* ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by -* an unitary similarity transformation: Q' * A * Q = H . -* -* Arguments -* ========= -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* ILO (input) INTEGER -* IHI (input) INTEGER -* It is assumed that A is already upper triangular in rows -* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally -* set by a previous call to ZGEBAL; otherwise they should be -* set to 1 and N respectively. See Further Details. -* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. -* -* A (input/output) COMPLEX*16 array, dimension (LDA,N) -* On entry, the N-by-N general matrix to be reduced. -* On exit, the upper triangle and the first subdiagonal of A -* are overwritten with the upper Hessenberg matrix H, and the -* elements below the first subdiagonal, with the array TAU, -* represent the unitary matrix Q as a product of elementary -* reflectors. See Further Details. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,N). -* -* TAU (output) COMPLEX*16 array, dimension (N-1) -* The scalar factors of the elementary reflectors (see Further -* Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to -* zero. -* -* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) -* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -* -* LWORK (input) INTEGER -* The length of the array WORK. LWORK >= max(1,N). -* For optimum performance LWORK >= N*NB, where NB is the -* optimal blocksize. -* -* If LWORK = -1, then a workspace query is assumed; the routine -* only calculates the optimal size of the WORK array, returns -* this value as the first entry of the WORK array, and no error -* message related to LWORK is issued by XERBLA. -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value. -* -* Further Details -* =============== -* -* The matrix Q is represented as a product of (ihi-ilo) elementary -* reflectors -* -* Q = H(ilo) H(ilo+1) . . . H(ihi-1). -* -* 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) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on -* exit in A(i+2:ihi,i), and tau in TAU(i). -* -* The contents of A are illustrated by the following example, with -* n = 7, ilo = 2 and ihi = 6: -* -* on entry, on exit, -* -* ( a a a a a a a ) ( a a h h h h a ) -* ( a a a a a a ) ( a h h h h a ) -* ( a a a a a a ) ( h h h h h h ) -* ( a a a a a a ) ( v2 h h h h h ) -* ( a a a a a a ) ( v2 v3 h h h h ) -* ( a a a a a a ) ( v2 v3 v4 h h h ) -* ( 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 ZGEHRD -* subroutine incorporating improvements proposed by Quintana-Orti and -* Van de Geijn (2005). -* -* ===================================================================== -* -* .. Parameters .. - INTEGER NBMAX, LDT - PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) - COMPLEX*16 ZERO, ONE - PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), - $ ONE = ( 1.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, IB, IINFO, IWS, J, LDWORK, LWKOPT, NB, - $ NBMIN, NH, NX - COMPLEX*16 EI -* .. -* .. Local Arrays .. - COMPLEX*16 T( LDT, NBMAX ) -* .. -* .. External Subroutines .. - EXTERNAL ZAXPY, ZGEHD2, ZGEMM, ZLAHR2, ZLARFB, ZTRMM, - $ XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) - LWKOPT = N*NB - WORK( 1 ) = LWKOPT - LQUERY = ( LWORK.EQ.-1 ) - IF( N.LT.0 ) THEN - INFO = -1 - ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN - INFO = -2 - ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN - INFO = -8 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZGEHRD', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero -* - DO 10 I = 1, ILO - 1 - TAU( I ) = ZERO - 10 CONTINUE - DO 20 I = MAX( 1, IHI ), N - 1 - TAU( I ) = ZERO - 20 CONTINUE -* -* Quick return if possible -* - NH = IHI - ILO + 1 - IF( NH.LE.1 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* -* Determine the block size -* - NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) - NBMIN = 2 - IWS = 1 - IF( NB.GT.1 .AND. NB.LT.NH ) THEN -* -* Determine when to cross over from blocked to unblocked code -* (last block is always handled by unblocked code) -* - NX = MAX( NB, ILAENV( 3, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) - IF( NX.LT.NH ) THEN -* -* Determine if workspace is large enough for blocked code -* - IWS = N*NB - IF( LWORK.LT.IWS ) THEN -* -* Not enough workspace to use optimal NB: determine the -* minimum value of NB, and reduce NB or force use of -* unblocked code -* - NBMIN = MAX( 2, ILAENV( 2, 'ZGEHRD', ' ', N, ILO, IHI, - $ -1 ) ) - IF( LWORK.GE.N*NBMIN ) THEN - NB = LWORK / N - ELSE - NB = 1 - END IF - END IF - END IF - END IF - LDWORK = N -* - IF( NB.LT.NBMIN .OR. NB.GE.NH ) THEN -* -* Use unblocked code below -* - I = ILO -* - ELSE -* -* Use blocked code -* - DO 40 I = ILO, IHI - 1 - NX, NB - IB = MIN( NB, IHI-I ) -* -* Reduce columns i:i+ib-1 to Hessenberg form, returning the -* matrices V and T of the block reflector H = I - V*T*V' -* which performs the reduction, and also the matrix Y = A*V*T -* - CALL ZLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT, - $ WORK, LDWORK ) -* -* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the -* right, computing A := A - Y * V'. V(i+ib,ib-1) must be set -* to 1 -* - EI = A( I+IB, I+IB-1 ) - A( I+IB, I+IB-1 ) = ONE - CALL ZGEMM( 'No transpose', 'Conjugate transpose', - $ IHI, IHI-I-IB+1, - $ IB, -ONE, WORK, LDWORK, A( I+IB, I ), LDA, ONE, - $ A( 1, I+IB ), LDA ) - A( I+IB, I+IB-1 ) = EI -* -* Apply the block reflector H to A(1:i,i+1:i+ib-1) from the -* right -* - CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', - $ 'Unit', I, IB-1, - $ ONE, A( I+1, I ), LDA, WORK, LDWORK ) - DO 30 J = 0, IB-2 - CALL ZAXPY( I, -ONE, WORK( LDWORK*J+1 ), 1, - $ A( 1, I+J+1 ), 1 ) - 30 CONTINUE -* -* Apply the block reflector H to A(i+1:ihi,i+ib:n) from the -* left -* - CALL ZLARFB( 'Left', 'Conjugate transpose', 'Forward', - $ 'Columnwise', - $ IHI-I, N-I-IB+1, IB, A( I+1, I ), LDA, T, LDT, - $ A( I+1, I+IB ), LDA, WORK, LDWORK ) - 40 CONTINUE - END IF -* -* Use unblocked code to reduce the rest of the matrix -* - CALL ZGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO ) - WORK( 1 ) = IWS -* - RETURN -* -* End of ZGEHRD -* - END |