LAPACK 3.3.1
Linear Algebra PACKage

sgerqs.f

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00001       SUBROUTINE SGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
00002      $                   INFO )
00003 *
00004 *  -- LAPACK routine (version 3.1) --
00005 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS
00010 *     ..
00011 *     .. Array Arguments ..
00012       REAL               A( LDA, * ), B( LDB, * ), TAU( * ),
00013      $                   WORK( LWORK )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  Compute a minimum-norm solution
00020 *      min || A*X - B ||
00021 *  using the RQ factorization
00022 *      A = R*Q
00023 *  computed by SGERQF.
00024 *
00025 *  Arguments
00026 *  =========
00027 *
00028 *  M       (input) INTEGER
00029 *          The number of rows of the matrix A.  M >= 0.
00030 *
00031 *  N       (input) INTEGER
00032 *          The number of columns of the matrix A.  N >= M >= 0.
00033 *
00034 *  NRHS    (input) INTEGER
00035 *          The number of columns of B.  NRHS >= 0.
00036 *
00037 *  A       (input) REAL array, dimension (LDA,N)
00038 *          Details of the RQ factorization of the original matrix A as
00039 *          returned by SGERQF.
00040 *
00041 *  LDA     (input) INTEGER
00042 *          The leading dimension of the array A.  LDA >= M.
00043 *
00044 *  TAU     (input) REAL array, dimension (M)
00045 *          Details of the orthogonal matrix Q.
00046 *
00047 *  B       (input/output) REAL array, dimension (LDB,NRHS)
00048 *          On entry, the right hand side vectors for the linear system.
00049 *          On exit, the solution vectors X.  Each solution vector
00050 *          is contained in rows 1:N of a column of B.
00051 *
00052 *  LDB     (input) INTEGER
00053 *          The leading dimension of the array B. LDB >= max(1,N).
00054 *
00055 *  WORK    (workspace) REAL array, dimension (LWORK)
00056 *
00057 *  LWORK   (input) INTEGER
00058 *          The length of the array WORK.  LWORK must be at least NRHS,
00059 *          and should be at least NRHS*NB, where NB is the block size
00060 *          for this environment.
00061 *
00062 *  INFO    (output) INTEGER
00063 *          = 0: successful exit
00064 *          < 0: if INFO = -i, the i-th argument had an illegal value
00065 *
00066 *  =====================================================================
00067 *
00068 *     .. Parameters ..
00069       REAL               ZERO, ONE
00070       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00071 *     ..
00072 *     .. External Subroutines ..
00073       EXTERNAL           SLASET, SORMRQ, STRSM, XERBLA
00074 *     ..
00075 *     .. Intrinsic Functions ..
00076       INTRINSIC          MAX
00077 *     ..
00078 *     .. Executable Statements ..
00079 *
00080 *     Test the input parameters.
00081 *
00082       INFO = 0
00083       IF( M.LT.0 ) THEN
00084          INFO = -1
00085       ELSE IF( N.LT.0 .OR. M.GT.N ) THEN
00086          INFO = -2
00087       ELSE IF( NRHS.LT.0 ) THEN
00088          INFO = -3
00089       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00090          INFO = -5
00091       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00092          INFO = -8
00093       ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
00094      $          THEN
00095          INFO = -10
00096       END IF
00097       IF( INFO.NE.0 ) THEN
00098          CALL XERBLA( 'SGERQS', -INFO )
00099          RETURN
00100       END IF
00101 *
00102 *     Quick return if possible
00103 *
00104       IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
00105      $   RETURN
00106 *
00107 *     Solve R*X = B(n-m+1:n,:)
00108 *
00109       CALL STRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', M, NRHS,
00110      $            ONE, A( 1, N-M+1 ), LDA, B( N-M+1, 1 ), LDB )
00111 *
00112 *     Set B(1:n-m,:) to zero
00113 *
00114       CALL SLASET( 'Full', N-M, NRHS, ZERO, ZERO, B, LDB )
00115 *
00116 *     B := Q' * B
00117 *
00118       CALL SORMRQ( 'Left', 'Transpose', N, NRHS, M, A, LDA, TAU, B, LDB,
00119      $             WORK, LWORK, INFO )
00120 *
00121       RETURN
00122 *
00123 *     End of SGERQS
00124 *
00125       END
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