Annotation of rpl/lapack/lapack/zgeqr2p.f, revision 1.17

1.9       bertrand    1: *> \brief \b ZGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.
1.6       bertrand    2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
1.14      bertrand    5: * Online html documentation available at
                      6: *            http://www.netlib.org/lapack/explore-html/
1.6       bertrand    7: *
                      8: *> \htmlonly
1.14      bertrand    9: *> Download ZGEQR2P + dependencies
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqr2p.f">
                     11: *> [TGZ]</a>
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqr2p.f">
                     13: *> [ZIP]</a>
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqr2p.f">
1.6       bertrand   15: *> [TXT]</a>
1.14      bertrand   16: *> \endhtmlonly
1.6       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE ZGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
1.14      bertrand   22: *
1.6       bertrand   23: *       .. Scalar Arguments ..
                     24: *       INTEGER            INFO, LDA, M, N
                     25: *       ..
                     26: *       .. Array Arguments ..
                     27: *       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
                     28: *       ..
1.14      bertrand   29: *
1.6       bertrand   30: *
                     31: *> \par Purpose:
                     32: *  =============
                     33: *>
                     34: *> \verbatim
                     35: *>
1.17    ! bertrand   36: *> ZGEQR2P computes a QR factorization of a complex m-by-n matrix A:
        !            37: *>
        !            38: *>    A = Q * ( R ),
        !            39: *>            ( 0 )
        !            40: *>
        !            41: *> where:
        !            42: *>
        !            43: *>    Q is a m-by-m orthogonal matrix;
        !            44: *>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
        !            45: *>    entries;
        !            46: *>    0 is a (m-n)-by-n zero matrix, if m > n.
        !            47: *>
1.6       bertrand   48: *> \endverbatim
                     49: *
                     50: *  Arguments:
                     51: *  ==========
                     52: *
                     53: *> \param[in] M
                     54: *> \verbatim
                     55: *>          M is INTEGER
                     56: *>          The number of rows of the matrix A.  M >= 0.
                     57: *> \endverbatim
                     58: *>
                     59: *> \param[in] N
                     60: *> \verbatim
                     61: *>          N is INTEGER
                     62: *>          The number of columns of the matrix A.  N >= 0.
                     63: *> \endverbatim
                     64: *>
                     65: *> \param[in,out] A
                     66: *> \verbatim
                     67: *>          A is COMPLEX*16 array, dimension (LDA,N)
                     68: *>          On entry, the m by n matrix A.
                     69: *>          On exit, the elements on and above the diagonal of the array
                     70: *>          contain the min(m,n) by n upper trapezoidal matrix R (R is
1.14      bertrand   71: *>          upper triangular if m >= n). The diagonal entries of R
1.12      bertrand   72: *>          are real and nonnegative; the elements below the diagonal,
1.6       bertrand   73: *>          with the array TAU, represent the unitary matrix Q as a
                     74: *>          product of elementary reflectors (see Further Details).
                     75: *> \endverbatim
                     76: *>
                     77: *> \param[in] LDA
                     78: *> \verbatim
                     79: *>          LDA is INTEGER
                     80: *>          The leading dimension of the array A.  LDA >= max(1,M).
                     81: *> \endverbatim
                     82: *>
                     83: *> \param[out] TAU
                     84: *> \verbatim
                     85: *>          TAU is COMPLEX*16 array, dimension (min(M,N))
                     86: *>          The scalar factors of the elementary reflectors (see Further
                     87: *>          Details).
                     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 had an illegal value
                    100: *> \endverbatim
                    101: *
                    102: *  Authors:
                    103: *  ========
                    104: *
1.14      bertrand  105: *> \author Univ. of Tennessee
                    106: *> \author Univ. of California Berkeley
                    107: *> \author Univ. of Colorado Denver
                    108: *> \author NAG Ltd.
1.6       bertrand  109: *
1.17    ! bertrand  110: *> \date November 2019
1.6       bertrand  111: *
                    112: *> \ingroup complex16GEcomputational
                    113: *
                    114: *> \par Further Details:
                    115: *  =====================
                    116: *>
                    117: *> \verbatim
                    118: *>
                    119: *>  The matrix Q is represented as a product of elementary reflectors
                    120: *>
                    121: *>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
                    122: *>
                    123: *>  Each H(i) has the form
                    124: *>
                    125: *>     H(i) = I - tau * v * v**H
                    126: *>
                    127: *>  where tau is a complex scalar, and v is a complex vector with
                    128: *>  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
                    129: *>  and tau in TAU(i).
1.12      bertrand  130: *>
                    131: *> See Lapack Working Note 203 for details
1.6       bertrand  132: *> \endverbatim
                    133: *>
                    134: *  =====================================================================
1.1       bertrand  135:       SUBROUTINE ZGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
                    136: *
1.17    ! bertrand  137: *  -- LAPACK computational routine (version 3.9.0) --
1.1       bertrand  138: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    139: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.17    ! bertrand  140: *     November 2019
1.1       bertrand  141: *
                    142: *     .. Scalar Arguments ..
                    143:       INTEGER            INFO, LDA, M, N
                    144: *     ..
                    145: *     .. Array Arguments ..
                    146:       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
                    147: *     ..
                    148: *
                    149: *  =====================================================================
                    150: *
                    151: *     .. Parameters ..
                    152:       COMPLEX*16         ONE
                    153:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
                    154: *     ..
                    155: *     .. Local Scalars ..
                    156:       INTEGER            I, K
                    157:       COMPLEX*16         ALPHA
                    158: *     ..
                    159: *     .. External Subroutines ..
                    160:       EXTERNAL           XERBLA, ZLARF, ZLARFGP
                    161: *     ..
                    162: *     .. Intrinsic Functions ..
                    163:       INTRINSIC          DCONJG, MAX, MIN
                    164: *     ..
                    165: *     .. Executable Statements ..
                    166: *
                    167: *     Test the input arguments
                    168: *
                    169:       INFO = 0
                    170:       IF( M.LT.0 ) THEN
                    171:          INFO = -1
                    172:       ELSE IF( N.LT.0 ) THEN
                    173:          INFO = -2
                    174:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
                    175:          INFO = -4
                    176:       END IF
                    177:       IF( INFO.NE.0 ) THEN
                    178:          CALL XERBLA( 'ZGEQR2P', -INFO )
                    179:          RETURN
                    180:       END IF
                    181: *
                    182:       K = MIN( M, N )
                    183: *
                    184:       DO 10 I = 1, K
                    185: *
                    186: *        Generate elementary reflector H(i) to annihilate A(i+1:m,i)
                    187: *
                    188:          CALL ZLARFGP( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,
                    189:      $                TAU( I ) )
                    190:          IF( I.LT.N ) THEN
                    191: *
1.5       bertrand  192: *           Apply H(i)**H to A(i:m,i+1:n) from the left
1.1       bertrand  193: *
                    194:             ALPHA = A( I, I )
                    195:             A( I, I ) = ONE
                    196:             CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
                    197:      $                  DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
                    198:             A( I, I ) = ALPHA
                    199:          END IF
                    200:    10 CONTINUE
                    201:       RETURN
                    202: *
                    203: *     End of ZGEQR2P
                    204: *
                    205:       END

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