149 lines
4.6 KiB
FortranFixed
149 lines
4.6 KiB
FortranFixed
SUBROUTINE ZGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
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*
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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INTEGER IHI, ILO, INFO, LDA, N
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H
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* by a unitary similarity transformation: Q' * A * Q = H .
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*
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* Arguments
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* =========
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0.
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*
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* ILO (input) INTEGER
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* IHI (input) INTEGER
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* It is assumed that A is already upper triangular in rows
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* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
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* set by a previous call to ZGEBAL; otherwise they should be
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* set to 1 and N respectively. See Further Details.
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* 1 <= ILO <= IHI <= max(1,N).
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*
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* A (input/output) COMPLEX*16 array, dimension (LDA,N)
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* On entry, the n by n general matrix to be reduced.
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* On exit, the upper triangle and the first subdiagonal of A
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* are overwritten with the upper Hessenberg matrix H, and the
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* elements below the first subdiagonal, with the array TAU,
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* represent the unitary matrix Q as a product of elementary
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* reflectors. See Further Details.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,N).
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*
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* TAU (output) COMPLEX*16 array, dimension (N-1)
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* The scalar factors of the elementary reflectors (see Further
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* Details).
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*
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* WORK (workspace) COMPLEX*16 array, dimension (N)
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value.
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*
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* Further Details
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* ===============
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*
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* The matrix Q is represented as a product of (ihi-ilo) elementary
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* reflectors
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*
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* Q = H(ilo) H(ilo+1) . . . H(ihi-1).
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*
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* Each H(i) has the form
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*
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* H(i) = I - tau * v * v'
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*
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* where tau is a complex scalar, and v is a complex vector with
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* v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
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* exit in A(i+2:ihi,i), and tau in TAU(i).
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*
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* The contents of A are illustrated by the following example, with
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* n = 7, ilo = 2 and ihi = 6:
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*
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* on entry, on exit,
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*
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* ( a a a a a a a ) ( a a h h h h a )
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* ( a a a a a a ) ( a h h h h a )
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* ( a a a a a a ) ( h h h h h h )
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* ( a a a a a a ) ( v2 h h h h h )
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* ( a a a a a a ) ( v2 v3 h h h h )
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* ( a a a a a a ) ( v2 v3 v4 h h h )
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* ( a ) ( a )
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*
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* where a denotes an element of the original matrix A, h denotes a
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* modified element of the upper Hessenberg matrix H, and vi denotes an
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* element of the vector defining H(i).
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX*16 ONE
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PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I
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COMPLEX*16 ALPHA
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZLARF, ZLARFG
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DCONJG, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters
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*
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INFO = 0
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
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INFO = -2
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ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZGEHD2', -INFO )
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RETURN
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END IF
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*
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DO 10 I = ILO, IHI - 1
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*
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* Compute elementary reflector H(i) to annihilate A(i+2:ihi,i)
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*
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ALPHA = A( I+1, I )
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CALL ZLARFG( IHI-I, ALPHA, A( MIN( I+2, N ), I ), 1, TAU( I ) )
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A( I+1, I ) = ONE
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*
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* Apply H(i) to A(1:ihi,i+1:ihi) from the right
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*
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CALL ZLARF( 'Right', IHI, IHI-I, A( I+1, I ), 1, TAU( I ),
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$ A( 1, I+1 ), LDA, WORK )
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*
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* Apply H(i)' to A(i+1:ihi,i+1:n) from the left
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*
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CALL ZLARF( 'Left', IHI-I, N-I, A( I+1, I ), 1,
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$ DCONJG( TAU( I ) ), A( I+1, I+1 ), LDA, WORK )
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*
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A( I+1, I ) = ALPHA
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10 CONTINUE
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*
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RETURN
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*
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* End of ZGEHD2
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*
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END
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