LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zgeqrt2.f
Go to the documentation of this file.
00001 *> \brief \b ZGEQRT2
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZGEQRT2 + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqrt2.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqrt2.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqrt2.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZGEQRT2( M, N, A, LDA, T, LDT, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       INTEGER   INFO, LDA, LDT, M, N
00025 *       ..
00026 *       .. Array Arguments ..
00027 *       COMPLEX*16   A( LDA, * ), T( LDT, * )
00028 *       ..
00029 *  
00030 *
00031 *> \par Purpose:
00032 *  =============
00033 *>
00034 *> \verbatim
00035 *>
00036 *> ZGEQRT2 computes a QR factorization of a complex M-by-N matrix A, 
00037 *> using the compact WY representation of Q. 
00038 *> \endverbatim
00039 *
00040 *  Arguments:
00041 *  ==========
00042 *
00043 *> \param[in] M
00044 *> \verbatim
00045 *>          M is INTEGER
00046 *>          The number of rows of the matrix A.  M >= N.
00047 *> \endverbatim
00048 *>
00049 *> \param[in] N
00050 *> \verbatim
00051 *>          N is INTEGER
00052 *>          The number of columns of the matrix A.  N >= 0.
00053 *> \endverbatim
00054 *>
00055 *> \param[in,out] A
00056 *> \verbatim
00057 *>          A is COMPLEX*16 array, dimension (LDA,N)
00058 *>          On entry, the complex M-by-N matrix A.  On exit, the elements on and
00059 *>          above the diagonal contain the N-by-N upper triangular matrix R; the
00060 *>          elements below the diagonal are the columns of V.  See below for
00061 *>          further details.
00062 *> \endverbatim
00063 *>
00064 *> \param[in] LDA
00065 *> \verbatim
00066 *>          LDA is INTEGER
00067 *>          The leading dimension of the array A.  LDA >= max(1,M).
00068 *> \endverbatim
00069 *>
00070 *> \param[out] T
00071 *> \verbatim
00072 *>          T is COMPLEX*16 array, dimension (LDT,N)
00073 *>          The N-by-N upper triangular factor of the block reflector.
00074 *>          The elements on and above the diagonal contain the block
00075 *>          reflector T; the elements below the diagonal are not used.
00076 *>          See below for further details.
00077 *> \endverbatim
00078 *>
00079 *> \param[in] LDT
00080 *> \verbatim
00081 *>          LDT is INTEGER
00082 *>          The leading dimension of the array T.  LDT >= max(1,N).
00083 *> \endverbatim
00084 *>
00085 *> \param[out] INFO
00086 *> \verbatim
00087 *>          INFO is INTEGER
00088 *>          = 0: successful exit
00089 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00090 *> \endverbatim
00091 *
00092 *  Authors:
00093 *  ========
00094 *
00095 *> \author Univ. of Tennessee 
00096 *> \author Univ. of California Berkeley 
00097 *> \author Univ. of Colorado Denver 
00098 *> \author NAG Ltd. 
00099 *
00100 *> \date November 2011
00101 *
00102 *> \ingroup complex16GEcomputational
00103 *
00104 *> \par Further Details:
00105 *  =====================
00106 *>
00107 *> \verbatim
00108 *>
00109 *>  The matrix V stores the elementary reflectors H(i) in the i-th column
00110 *>  below the diagonal. For example, if M=5 and N=3, the matrix V is
00111 *>
00112 *>               V = (  1       )
00113 *>                   ( v1  1    )
00114 *>                   ( v1 v2  1 )
00115 *>                   ( v1 v2 v3 )
00116 *>                   ( v1 v2 v3 )
00117 *>
00118 *>  where the vi's represent the vectors which define H(i), which are returned
00119 *>  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
00120 *>  block reflector H is then given by
00121 *>
00122 *>               H = I - V * T * V**H
00123 *>
00124 *>  where V**H is the conjugate transpose of V.
00125 *> \endverbatim
00126 *>
00127 *  =====================================================================
00128       SUBROUTINE ZGEQRT2( M, N, A, LDA, T, LDT, INFO )
00129 *
00130 *  -- LAPACK computational routine (version 3.4.0) --
00131 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00132 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00133 *     November 2011
00134 *
00135 *     .. Scalar Arguments ..
00136       INTEGER   INFO, LDA, LDT, M, N
00137 *     ..
00138 *     .. Array Arguments ..
00139       COMPLEX*16   A( LDA, * ), T( LDT, * )
00140 *     ..
00141 *
00142 *  =====================================================================
00143 *
00144 *     .. Parameters ..
00145       COMPLEX*16  ONE, ZERO
00146       PARAMETER( ONE = (1.0D+00,0.0D+00), ZERO = (0.0D+00,0.0D+00) )
00147 *     ..
00148 *     .. Local Scalars ..
00149       INTEGER   I, K
00150       COMPLEX*16   AII, ALPHA
00151 *     ..
00152 *     .. External Subroutines ..
00153       EXTERNAL  ZLARFG, ZGEMV, ZGERC, ZTRMV, XERBLA
00154 *     ..
00155 *     .. Executable Statements ..
00156 *
00157 *     Test the input arguments
00158 *
00159       INFO = 0
00160       IF( M.LT.0 ) THEN
00161          INFO = -1
00162       ELSE IF( N.LT.0 ) THEN
00163          INFO = -2
00164       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00165          INFO = -4
00166       ELSE IF( LDT.LT.MAX( 1, N ) ) THEN
00167          INFO = -6
00168       END IF
00169       IF( INFO.NE.0 ) THEN
00170          CALL XERBLA( 'ZGEQRT2', -INFO )
00171          RETURN
00172       END IF
00173 *      
00174       K = MIN( M, N )
00175 *
00176       DO I = 1, K
00177 *
00178 *        Generate elem. refl. H(i) to annihilate A(i+1:m,i), tau(I) -> T(I,1)
00179 *
00180          CALL ZLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
00181      $                T( I, 1 ) )
00182          IF( I.LT.N ) THEN
00183 *
00184 *           Apply H(i) to A(I:M,I+1:N) from the left
00185 *
00186             AII = A( I, I )
00187             A( I, I ) = ONE
00188 *
00189 *           W(1:N-I) := A(I:M,I+1:N)^H * A(I:M,I) [W = T(:,N)]
00190 *
00191             CALL ZGEMV( 'C',M-I+1, N-I, ONE, A( I, I+1 ), LDA, 
00192      $                  A( I, I ), 1, ZERO, T( 1, N ), 1 )
00193 *
00194 *           A(I:M,I+1:N) = A(I:m,I+1:N) + alpha*A(I:M,I)*W(1:N-1)^H
00195 *
00196             ALPHA = -CONJG(T( I, 1 ))
00197             CALL ZGERC( M-I+1, N-I, ALPHA, A( I, I ), 1, 
00198      $           T( 1, N ), 1, A( I, I+1 ), LDA )
00199             A( I, I ) = AII
00200          END IF
00201       END DO
00202 *
00203       DO I = 2, N
00204          AII = A( I, I )
00205          A( I, I ) = ONE
00206 *
00207 *        T(1:I-1,I) := alpha * A(I:M,1:I-1)**H * A(I:M,I)
00208 *
00209          ALPHA = -T( I, 1 )
00210          CALL ZGEMV( 'C', M-I+1, I-1, ALPHA, A( I, 1 ), LDA, 
00211      $               A( I, I ), 1, ZERO, T( 1, I ), 1 )
00212          A( I, I ) = AII
00213 *
00214 *        T(1:I-1,I) := T(1:I-1,1:I-1) * T(1:I-1,I)
00215 *
00216          CALL ZTRMV( 'U', 'N', 'N', I-1, T, LDT, T( 1, I ), 1 )
00217 *
00218 *           T(I,I) = tau(I)
00219 *
00220             T( I, I ) = T( I, 1 )
00221             T( I, 1) = ZERO
00222       END DO
00223    
00224 *
00225 *     End of ZGEQRT2
00226 *
00227       END
 All Files Functions