Annotation of rpl/lapack/lapack/dopgtr.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DOPGTR
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DOPGTR + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dopgtr.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dopgtr.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dopgtr.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, LDQ, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DOPGTR generates a real orthogonal matrix Q which is defined as the
! 38: *> product of n-1 elementary reflectors H(i) of order n, as returned by
! 39: *> DSPTRD using packed storage:
! 40: *>
! 41: *> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
! 42: *>
! 43: *> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
! 44: *> \endverbatim
! 45: *
! 46: * Arguments:
! 47: * ==========
! 48: *
! 49: *> \param[in] UPLO
! 50: *> \verbatim
! 51: *> UPLO is CHARACTER*1
! 52: *> = 'U': Upper triangular packed storage used in previous
! 53: *> call to DSPTRD;
! 54: *> = 'L': Lower triangular packed storage used in previous
! 55: *> call to DSPTRD.
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] N
! 59: *> \verbatim
! 60: *> N is INTEGER
! 61: *> The order of the matrix Q. N >= 0.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] AP
! 65: *> \verbatim
! 66: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
! 67: *> The vectors which define the elementary reflectors, as
! 68: *> returned by DSPTRD.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] TAU
! 72: *> \verbatim
! 73: *> TAU is DOUBLE PRECISION array, dimension (N-1)
! 74: *> TAU(i) must contain the scalar factor of the elementary
! 75: *> reflector H(i), as returned by DSPTRD.
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[out] Q
! 79: *> \verbatim
! 80: *> Q is DOUBLE PRECISION array, dimension (LDQ,N)
! 81: *> The N-by-N orthogonal matrix Q.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[in] LDQ
! 85: *> \verbatim
! 86: *> LDQ is INTEGER
! 87: *> The leading dimension of the array Q. LDQ >= max(1,N).
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[out] WORK
! 91: *> \verbatim
! 92: *> WORK is DOUBLE PRECISION array, dimension (N-1)
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[out] INFO
! 96: *> \verbatim
! 97: *> INFO is INTEGER
! 98: *> = 0: successful exit
! 99: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 100: *> \endverbatim
! 101: *
! 102: * Authors:
! 103: * ========
! 104: *
! 105: *> \author Univ. of Tennessee
! 106: *> \author Univ. of California Berkeley
! 107: *> \author Univ. of Colorado Denver
! 108: *> \author NAG Ltd.
! 109: *
! 110: *> \date November 2011
! 111: *
! 112: *> \ingroup doubleOTHERcomputational
! 113: *
! 114: * =====================================================================
1.1 bertrand 115: SUBROUTINE DOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
116: *
1.8 ! bertrand 117: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 118: * -- LAPACK is a software package provided by Univ. of Tennessee, --
119: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 120: * November 2011
1.1 bertrand 121: *
122: * .. Scalar Arguments ..
123: CHARACTER UPLO
124: INTEGER INFO, LDQ, N
125: * ..
126: * .. Array Arguments ..
127: DOUBLE PRECISION AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
128: * ..
129: *
130: * =====================================================================
131: *
132: * .. Parameters ..
133: DOUBLE PRECISION ZERO, ONE
134: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
135: * ..
136: * .. Local Scalars ..
137: LOGICAL UPPER
138: INTEGER I, IINFO, IJ, J
139: * ..
140: * .. External Functions ..
141: LOGICAL LSAME
142: EXTERNAL LSAME
143: * ..
144: * .. External Subroutines ..
145: EXTERNAL DORG2L, DORG2R, XERBLA
146: * ..
147: * .. Intrinsic Functions ..
148: INTRINSIC MAX
149: * ..
150: * .. Executable Statements ..
151: *
152: * Test the input arguments
153: *
154: INFO = 0
155: UPPER = LSAME( UPLO, 'U' )
156: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
157: INFO = -1
158: ELSE IF( N.LT.0 ) THEN
159: INFO = -2
160: ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
161: INFO = -6
162: END IF
163: IF( INFO.NE.0 ) THEN
164: CALL XERBLA( 'DOPGTR', -INFO )
165: RETURN
166: END IF
167: *
168: * Quick return if possible
169: *
170: IF( N.EQ.0 )
171: $ RETURN
172: *
173: IF( UPPER ) THEN
174: *
175: * Q was determined by a call to DSPTRD with UPLO = 'U'
176: *
177: * Unpack the vectors which define the elementary reflectors and
178: * set the last row and column of Q equal to those of the unit
179: * matrix
180: *
181: IJ = 2
182: DO 20 J = 1, N - 1
183: DO 10 I = 1, J - 1
184: Q( I, J ) = AP( IJ )
185: IJ = IJ + 1
186: 10 CONTINUE
187: IJ = IJ + 2
188: Q( N, J ) = ZERO
189: 20 CONTINUE
190: DO 30 I = 1, N - 1
191: Q( I, N ) = ZERO
192: 30 CONTINUE
193: Q( N, N ) = ONE
194: *
195: * Generate Q(1:n-1,1:n-1)
196: *
197: CALL DORG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO )
198: *
199: ELSE
200: *
201: * Q was determined by a call to DSPTRD with UPLO = 'L'.
202: *
203: * Unpack the vectors which define the elementary reflectors and
204: * set the first row and column of Q equal to those of the unit
205: * matrix
206: *
207: Q( 1, 1 ) = ONE
208: DO 40 I = 2, N
209: Q( I, 1 ) = ZERO
210: 40 CONTINUE
211: IJ = 3
212: DO 60 J = 2, N
213: Q( 1, J ) = ZERO
214: DO 50 I = J + 1, N
215: Q( I, J ) = AP( IJ )
216: IJ = IJ + 1
217: 50 CONTINUE
218: IJ = IJ + 2
219: 60 CONTINUE
220: IF( N.GT.1 ) THEN
221: *
222: * Generate Q(2:n,2:n)
223: *
224: CALL DORG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK,
225: $ IINFO )
226: END IF
227: END IF
228: RETURN
229: *
230: * End of DOPGTR
231: *
232: END
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