Annotation of rpl/lapack/lapack/zung2r.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZUNG2R
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZUNG2R + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zung2r.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zung2r.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zung2r.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, K, LDA, M, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> ZUNG2R generates an m by n complex matrix Q with orthonormal columns,
! 37: *> which is defined as the first n columns of a product of k elementary
! 38: *> reflectors of order m
! 39: *>
! 40: *> Q = H(1) H(2) . . . H(k)
! 41: *>
! 42: *> as returned by ZGEQRF.
! 43: *> \endverbatim
! 44: *
! 45: * Arguments:
! 46: * ==========
! 47: *
! 48: *> \param[in] M
! 49: *> \verbatim
! 50: *> M is INTEGER
! 51: *> The number of rows of the matrix Q. M >= 0.
! 52: *> \endverbatim
! 53: *>
! 54: *> \param[in] N
! 55: *> \verbatim
! 56: *> N is INTEGER
! 57: *> The number of columns of the matrix Q. M >= N >= 0.
! 58: *> \endverbatim
! 59: *>
! 60: *> \param[in] K
! 61: *> \verbatim
! 62: *> K is INTEGER
! 63: *> The number of elementary reflectors whose product defines the
! 64: *> matrix Q. N >= K >= 0.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in,out] A
! 68: *> \verbatim
! 69: *> A is COMPLEX*16 array, dimension (LDA,N)
! 70: *> On entry, the i-th column must contain the vector which
! 71: *> defines the elementary reflector H(i), for i = 1,2,...,k, as
! 72: *> returned by ZGEQRF in the first k columns of its array
! 73: *> argument A.
! 74: *> On exit, the m by n matrix Q.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] LDA
! 78: *> \verbatim
! 79: *> LDA is INTEGER
! 80: *> The first dimension of the array A. LDA >= max(1,M).
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] TAU
! 84: *> \verbatim
! 85: *> TAU is COMPLEX*16 array, dimension (K)
! 86: *> TAU(i) must contain the scalar factor of the elementary
! 87: *> reflector H(i), as returned by ZGEQRF.
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[out] WORK
! 91: *> \verbatim
! 92: *> WORK is COMPLEX*16 array, dimension (N)
! 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 has 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 complex16OTHERcomputational
! 113: *
! 114: * =====================================================================
1.1 bertrand 115: SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, 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: INTEGER INFO, K, LDA, M, N
124: * ..
125: * .. Array Arguments ..
126: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
127: * ..
128: *
129: * =====================================================================
130: *
131: * .. Parameters ..
132: COMPLEX*16 ONE, ZERO
133: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
134: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
135: * ..
136: * .. Local Scalars ..
137: INTEGER I, J, L
138: * ..
139: * .. External Subroutines ..
140: EXTERNAL XERBLA, ZLARF, ZSCAL
141: * ..
142: * .. Intrinsic Functions ..
143: INTRINSIC MAX
144: * ..
145: * .. Executable Statements ..
146: *
147: * Test the input arguments
148: *
149: INFO = 0
150: IF( M.LT.0 ) THEN
151: INFO = -1
152: ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
153: INFO = -2
154: ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
155: INFO = -3
156: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
157: INFO = -5
158: END IF
159: IF( INFO.NE.0 ) THEN
160: CALL XERBLA( 'ZUNG2R', -INFO )
161: RETURN
162: END IF
163: *
164: * Quick return if possible
165: *
166: IF( N.LE.0 )
167: $ RETURN
168: *
169: * Initialise columns k+1:n to columns of the unit matrix
170: *
171: DO 20 J = K + 1, N
172: DO 10 L = 1, M
173: A( L, J ) = ZERO
174: 10 CONTINUE
175: A( J, J ) = ONE
176: 20 CONTINUE
177: *
178: DO 40 I = K, 1, -1
179: *
180: * Apply H(i) to A(i:m,i:n) from the left
181: *
182: IF( I.LT.N ) THEN
183: A( I, I ) = ONE
184: CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
185: $ A( I, I+1 ), LDA, WORK )
186: END IF
187: IF( I.LT.M )
188: $ CALL ZSCAL( M-I, -TAU( I ), A( I+1, I ), 1 )
189: A( I, I ) = ONE - TAU( I )
190: *
191: * Set A(1:i-1,i) to zero
192: *
193: DO 30 L = 1, I - 1
194: A( L, I ) = ZERO
195: 30 CONTINUE
196: 40 CONTINUE
197: RETURN
198: *
199: * End of ZUNG2R
200: *
201: END
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