sggqrf.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 236 行 · 第 1/2 页

</span><span class="comment">*</span><span class="comment">          RQ factorization of an N-by-P matrix, and NB3 is the optimal
</span><span class="comment">*</span><span class="comment">          blocksize for a call of <a name="SORMQR.101"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment">          only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment">          this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment">          message related to LWORK is issued by <a name="XERBLA.106"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The matrix Q is represented as a product of elementary reflectors
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Q = H(1) H(2) . . . H(k), where k = min(n,m).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Each H(i) has the form
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     H(i) = I - taua * v * v'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where taua is a real scalar, and v is a real vector with
</span><span class="comment">*</span><span class="comment">  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
</span><span class="comment">*</span><span class="comment">  and taua in TAUA(i).
</span><span class="comment">*</span><span class="comment">  To form Q explicitly, use LAPACK subroutine <a name="SORGQR.126"></a><a href="sorgqr.f.html#SORGQR.1">SORGQR</a>.
</span><span class="comment">*</span><span class="comment">  To use Q to update another matrix, use LAPACK subroutine <a name="SORMQR.127"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The matrix Z is represented as a product of elementary reflectors
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Z = H(1) H(2) . . . H(k), where k = min(n,p).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Each H(i) has the form
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     H(i) = I - taub * v * v'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where taub is a real scalar, and v is a real vector with
</span><span class="comment">*</span><span class="comment">  v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in
</span><span class="comment">*</span><span class="comment">  B(n-k+i,1:p-k+i-1), and taub in TAUB(i).
</span><span class="comment">*</span><span class="comment">  To form Z explicitly, use LAPACK subroutine <a name="SORGRQ.140"></a><a href="sorgrq.f.html#SORGRQ.1">SORGRQ</a>.
</span><span class="comment">*</span><span class="comment">  To use Z to update another matrix, use LAPACK subroutine <a name="SORMRQ.141"></a><a href="sormrq.f.html#SORMRQ.1">SORMRQ</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LQUERY
      INTEGER            LOPT, LWKOPT, NB, NB1, NB2, NB3
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SGEQRF.150"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>, <a name="SGERQF.150"></a><a href="sgerqf.f.html#SGERQF.1">SGERQF</a>, <a name="SORMQR.150"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>, <a name="XERBLA.150"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      INTEGER            <a name="ILAENV.153"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      EXTERNAL           <a name="ILAENV.154"></a><a href="hfy-index.html#ILAENV">ILAENV</a> 
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          INT, MAX, MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      NB1 = <a name="ILAENV.164"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SGEQRF.164"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>'</span>, <span class="string">' '</span>, N, M, -1, -1 )
      NB2 = <a name="ILAENV.165"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SGERQF.165"></a><a href="sgerqf.f.html#SGERQF.1">SGERQF</a>'</span>, <span class="string">' '</span>, N, P, -1, -1 )
      NB3 = <a name="ILAENV.166"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SORMQR.166"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>'</span>, <span class="string">' '</span>, N, M, P, -1 )
      NB = MAX( NB1, NB2, NB3 )
      LWKOPT = MAX( N, M, P )*NB
      WORK( 1 ) = LWKOPT
      LQUERY = ( LWORK.EQ.-1 )
      IF( N.LT.0 ) THEN
         INFO = -1
      ELSE IF( M.LT.0 ) THEN
         INFO = -2
      ELSE IF( P.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -8
      ELSE IF( LWORK.LT.MAX( 1, N, M, P ) .AND. .NOT.LQUERY ) THEN
         INFO = -11
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.185"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SGGQRF.185"></a><a href="sggqrf.f.html#SGGQRF.1">SGGQRF</a>'</span>, -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     QR factorization of N-by-M matrix A: A = Q*R
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="SGEQRF.193"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>( N, M, A, LDA, TAUA, WORK, LWORK, INFO )
      LOPT = WORK( 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Update B := Q'*B.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="SORMQR.198"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>( <span class="string">'Left'</span>, <span class="string">'Transpose'</span>, N, P, MIN( N, M ), A, LDA, TAUA,
     $             B, LDB, WORK, LWORK, INFO )
      LOPT = MAX( LOPT, INT( WORK( 1 ) ) )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     RQ factorization of N-by-P matrix B: B = T*Z.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="SGERQF.204"></a><a href="sgerqf.f.html#SGERQF.1">SGERQF</a>( N, P, B, LDB, TAUB, WORK, LWORK, INFO )
      WORK( 1 ) = MAX( LOPT, INT( WORK( 1 ) ) )
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SGGQRF.209"></a><a href="sggqrf.f.html#SGGQRF.1">SGGQRF</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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