Annotation of rpl/lapack/lapack/zgehd2.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZGEHD2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGEHD2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgehd2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgehd2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgehd2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER IHI, ILO, INFO, LDA, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H
! 37: *> by a unitary similarity transformation: Q**H * A * Q = H .
! 38: *> \endverbatim
! 39: *
! 40: * Arguments:
! 41: * ==========
! 42: *
! 43: *> \param[in] N
! 44: *> \verbatim
! 45: *> N is INTEGER
! 46: *> The order of the matrix A. N >= 0.
! 47: *> \endverbatim
! 48: *>
! 49: *> \param[in] ILO
! 50: *> \verbatim
! 51: *> ILO is INTEGER
! 52: *> \endverbatim
! 53: *>
! 54: *> \param[in] IHI
! 55: *> \verbatim
! 56: *> IHI is INTEGER
! 57: *>
! 58: *> It is assumed that A is already upper triangular in rows
! 59: *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
! 60: *> set by a previous call to ZGEBAL; otherwise they should be
! 61: *> set to 1 and N respectively. See Further Details.
! 62: *> 1 <= ILO <= IHI <= max(1,N).
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in,out] A
! 66: *> \verbatim
! 67: *> A is COMPLEX*16 array, dimension (LDA,N)
! 68: *> On entry, the n by n general matrix to be reduced.
! 69: *> On exit, the upper triangle and the first subdiagonal of A
! 70: *> are overwritten with the upper Hessenberg matrix H, and the
! 71: *> elements below the first subdiagonal, with the array TAU,
! 72: *> represent the unitary matrix Q as a product of elementary
! 73: *> reflectors. See Further Details.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] LDA
! 77: *> \verbatim
! 78: *> LDA is INTEGER
! 79: *> The leading dimension of the array A. LDA >= max(1,N).
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[out] TAU
! 83: *> \verbatim
! 84: *> TAU is COMPLEX*16 array, dimension (N-1)
! 85: *> The scalar factors of the elementary reflectors (see Further
! 86: *> Details).
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[out] WORK
! 90: *> \verbatim
! 91: *> WORK is COMPLEX*16 array, dimension (N)
! 92: *> \endverbatim
! 93: *>
! 94: *> \param[out] INFO
! 95: *> \verbatim
! 96: *> INFO is INTEGER
! 97: *> = 0: successful exit
! 98: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 99: *> \endverbatim
! 100: *
! 101: * Authors:
! 102: * ========
! 103: *
! 104: *> \author Univ. of Tennessee
! 105: *> \author Univ. of California Berkeley
! 106: *> \author Univ. of Colorado Denver
! 107: *> \author NAG Ltd.
! 108: *
! 109: *> \date November 2011
! 110: *
! 111: *> \ingroup complex16GEcomputational
! 112: *
! 113: *> \par Further Details:
! 114: * =====================
! 115: *>
! 116: *> \verbatim
! 117: *>
! 118: *> The matrix Q is represented as a product of (ihi-ilo) elementary
! 119: *> reflectors
! 120: *>
! 121: *> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
! 122: *>
! 123: *> Each H(i) has the form
! 124: *>
! 125: *> H(i) = I - tau * v * v**H
! 126: *>
! 127: *> where tau is a complex scalar, and v is a complex vector with
! 128: *> v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
! 129: *> exit in A(i+2:ihi,i), and tau in TAU(i).
! 130: *>
! 131: *> The contents of A are illustrated by the following example, with
! 132: *> n = 7, ilo = 2 and ihi = 6:
! 133: *>
! 134: *> on entry, on exit,
! 135: *>
! 136: *> ( a a a a a a a ) ( a a h h h h a )
! 137: *> ( a a a a a a ) ( a h h h h a )
! 138: *> ( a a a a a a ) ( h h h h h h )
! 139: *> ( a a a a a a ) ( v2 h h h h h )
! 140: *> ( a a a a a a ) ( v2 v3 h h h h )
! 141: *> ( a a a a a a ) ( v2 v3 v4 h h h )
! 142: *> ( a ) ( a )
! 143: *>
! 144: *> where a denotes an element of the original matrix A, h denotes a
! 145: *> modified element of the upper Hessenberg matrix H, and vi denotes an
! 146: *> element of the vector defining H(i).
! 147: *> \endverbatim
! 148: *>
! 149: * =====================================================================
1.1 bertrand 150: SUBROUTINE ZGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )
151: *
1.9 ! bertrand 152: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 153: * -- LAPACK is a software package provided by Univ. of Tennessee, --
154: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 155: * November 2011
1.1 bertrand 156: *
157: * .. Scalar Arguments ..
158: INTEGER IHI, ILO, INFO, LDA, N
159: * ..
160: * .. Array Arguments ..
161: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
162: * ..
163: *
164: * =====================================================================
165: *
166: * .. Parameters ..
167: COMPLEX*16 ONE
168: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
169: * ..
170: * .. Local Scalars ..
171: INTEGER I
172: COMPLEX*16 ALPHA
173: * ..
174: * .. External Subroutines ..
175: EXTERNAL XERBLA, ZLARF, ZLARFG
176: * ..
177: * .. Intrinsic Functions ..
178: INTRINSIC DCONJG, MAX, MIN
179: * ..
180: * .. Executable Statements ..
181: *
182: * Test the input parameters
183: *
184: INFO = 0
185: IF( N.LT.0 ) THEN
186: INFO = -1
187: ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
188: INFO = -2
189: ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
190: INFO = -3
191: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
192: INFO = -5
193: END IF
194: IF( INFO.NE.0 ) THEN
195: CALL XERBLA( 'ZGEHD2', -INFO )
196: RETURN
197: END IF
198: *
199: DO 10 I = ILO, IHI - 1
200: *
201: * Compute elementary reflector H(i) to annihilate A(i+2:ihi,i)
202: *
203: ALPHA = A( I+1, I )
204: CALL ZLARFG( IHI-I, ALPHA, A( MIN( I+2, N ), I ), 1, TAU( I ) )
205: A( I+1, I ) = ONE
206: *
207: * Apply H(i) to A(1:ihi,i+1:ihi) from the right
208: *
209: CALL ZLARF( 'Right', IHI, IHI-I, A( I+1, I ), 1, TAU( I ),
210: $ A( 1, I+1 ), LDA, WORK )
211: *
1.8 bertrand 212: * Apply H(i)**H to A(i+1:ihi,i+1:n) from the left
1.1 bertrand 213: *
214: CALL ZLARF( 'Left', IHI-I, N-I, A( I+1, I ), 1,
215: $ DCONJG( TAU( I ) ), A( I+1, I+1 ), LDA, WORK )
216: *
217: A( I+1, I ) = ALPHA
218: 10 CONTINUE
219: *
220: RETURN
221: *
222: * End of ZGEHD2
223: *
224: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zgehd2.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack