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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 DGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, 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, N
-* ..
-* .. Array Arguments ..
- DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
-* ..
-*
-* Purpose
-* =======
-*
-* DGEHD2 reduces a real general matrix A to upper Hessenberg form H by
-* an orthogonal 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 DGEBAL; otherwise they should be
-* set to 1 and N respectively. See Further Details.
-* 1 <= ILO <= IHI <= max(1,N).
-*
-* A (input/output) DOUBLE PRECISION 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 orthogonal 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) DOUBLE PRECISION array, dimension (N-1)
-* The scalar factors of the elementary reflectors (see Further
-* Details).
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (N)
-*
-* 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 real scalar, and v is a real 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).
-*
-* =====================================================================
-*
-* .. Parameters ..
- DOUBLE PRECISION ONE
- PARAMETER ( ONE = 1.0D+0 )
-* ..
-* .. Local Scalars ..
- INTEGER I
- DOUBLE PRECISION AII
-* ..
-* .. External Subroutines ..
- EXTERNAL DLARF, DLARFG, XERBLA
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC MAX, MIN
-* ..
-* .. Executable Statements ..
-*
-* Test the input parameters
-*
- INFO = 0
- 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
- END IF
- IF( INFO.NE.0 ) THEN
- CALL XERBLA( 'DGEHD2', -INFO )
- RETURN
- END IF
-*
- DO 10 I = ILO, IHI - 1
-*
-* Compute elementary reflector H(i) to annihilate A(i+2:ihi,i)
-*
- CALL DLARFG( IHI-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1,
- $ TAU( I ) )
- AII = A( I+1, I )
- A( I+1, I ) = ONE
-*
-* Apply H(i) to A(1:ihi,i+1:ihi) from the right
-*
- CALL DLARF( 'Right', IHI, IHI-I, A( I+1, I ), 1, TAU( I ),
- $ A( 1, I+1 ), LDA, WORK )
-*
-* Apply H(i) to A(i+1:ihi,i+1:n) from the left
-*
- CALL DLARF( 'Left', IHI-I, N-I, A( I+1, I ), 1, TAU( I ),
- $ A( I+1, I+1 ), LDA, WORK )
-*
- A( I+1, I ) = AII
- 10 CONTINUE
-*
- RETURN
-*
-* End of DGEHD2
-*
- END