Annotation of rpl/lapack/lapack/dlaorhr_col_getrfnp.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b DLAORHR_COL_GETRFNP
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLAORHR_COL_GETRFNP + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaorhr_col_getrfnp.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaorhr_col_getrfnp.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaorhr_col_getrfnp.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLAORHR_COL_GETRFNP( M, N, A, LDA, D, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDA, M, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * DOUBLE PRECISION A( LDA, * ), D( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> DLAORHR_COL_GETRFNP computes the modified LU factorization without
! 37: *> pivoting of a real general M-by-N matrix A. The factorization has
! 38: *> the form:
! 39: *>
! 40: *> A - S = L * U,
! 41: *>
! 42: *> where:
! 43: *> S is a m-by-n diagonal sign matrix with the diagonal D, so that
! 44: *> D(i) = S(i,i), 1 <= i <= min(M,N). The diagonal D is constructed
! 45: *> as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing
! 46: *> i-1 steps of Gaussian elimination. This means that the diagonal
! 47: *> element at each step of "modified" Gaussian elimination is
! 48: *> at least one in absolute value (so that division-by-zero not
! 49: *> not possible during the division by the diagonal element);
! 50: *>
! 51: *> L is a M-by-N lower triangular matrix with unit diagonal elements
! 52: *> (lower trapezoidal if M > N);
! 53: *>
! 54: *> and U is a M-by-N upper triangular matrix
! 55: *> (upper trapezoidal if M < N).
! 56: *>
! 57: *> This routine is an auxiliary routine used in the Householder
! 58: *> reconstruction routine DORHR_COL. In DORHR_COL, this routine is
! 59: *> applied to an M-by-N matrix A with orthonormal columns, where each
! 60: *> element is bounded by one in absolute value. With the choice of
! 61: *> the matrix S above, one can show that the diagonal element at each
! 62: *> step of Gaussian elimination is the largest (in absolute value) in
! 63: *> the column on or below the diagonal, so that no pivoting is required
! 64: *> for numerical stability [1].
! 65: *>
! 66: *> For more details on the Householder reconstruction algorithm,
! 67: *> including the modified LU factorization, see [1].
! 68: *>
! 69: *> This is the blocked right-looking version of the algorithm,
! 70: *> calling Level 3 BLAS to update the submatrix. To factorize a block,
! 71: *> this routine calls the recursive routine DLAORHR_COL_GETRFNP2.
! 72: *>
! 73: *> [1] "Reconstructing Householder vectors from tall-skinny QR",
! 74: *> G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen,
! 75: *> E. Solomonik, J. Parallel Distrib. Comput.,
! 76: *> vol. 85, pp. 3-31, 2015.
! 77: *> \endverbatim
! 78: *
! 79: * Arguments:
! 80: * ==========
! 81: *
! 82: *> \param[in] M
! 83: *> \verbatim
! 84: *> M is INTEGER
! 85: *> The number of rows of the matrix A. M >= 0.
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in] N
! 89: *> \verbatim
! 90: *> N is INTEGER
! 91: *> The number of columns of the matrix A. N >= 0.
! 92: *> \endverbatim
! 93: *>
! 94: *> \param[in,out] A
! 95: *> \verbatim
! 96: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 97: *> On entry, the M-by-N matrix to be factored.
! 98: *> On exit, the factors L and U from the factorization
! 99: *> A-S=L*U; the unit diagonal elements of L are not stored.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in] LDA
! 103: *> \verbatim
! 104: *> LDA is INTEGER
! 105: *> The leading dimension of the array A. LDA >= max(1,M).
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[out] D
! 109: *> \verbatim
! 110: *> D is DOUBLE PRECISION array, dimension min(M,N)
! 111: *> The diagonal elements of the diagonal M-by-N sign matrix S,
! 112: *> D(i) = S(i,i), where 1 <= i <= min(M,N). The elements can
! 113: *> be only plus or minus one.
! 114: *> \endverbatim
! 115: *>
! 116: *> \param[out] INFO
! 117: *> \verbatim
! 118: *> INFO is INTEGER
! 119: *> = 0: successful exit
! 120: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 121: *> \endverbatim
! 122: *>
! 123: * Authors:
! 124: * ========
! 125: *
! 126: *> \author Univ. of Tennessee
! 127: *> \author Univ. of California Berkeley
! 128: *> \author Univ. of Colorado Denver
! 129: *> \author NAG Ltd.
! 130: *
! 131: *> \date November 2019
! 132: *
! 133: *> \ingroup doubleGEcomputational
! 134: *
! 135: *> \par Contributors:
! 136: * ==================
! 137: *>
! 138: *> \verbatim
! 139: *>
! 140: *> November 2019, Igor Kozachenko,
! 141: *> Computer Science Division,
! 142: *> University of California, Berkeley
! 143: *>
! 144: *> \endverbatim
! 145: *
! 146: * =====================================================================
! 147: SUBROUTINE DLAORHR_COL_GETRFNP( M, N, A, LDA, D, INFO )
! 148: IMPLICIT NONE
! 149: *
! 150: * -- LAPACK computational routine (version 3.9.0) --
! 151: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 152: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 153: * November 2019
! 154: *
! 155: * .. Scalar Arguments ..
! 156: INTEGER INFO, LDA, M, N
! 157: * ..
! 158: * .. Array Arguments ..
! 159: DOUBLE PRECISION A( LDA, * ), D( * )
! 160: * ..
! 161: *
! 162: * =====================================================================
! 163: *
! 164: * .. Parameters ..
! 165: DOUBLE PRECISION ONE
! 166: PARAMETER ( ONE = 1.0D+0 )
! 167: * ..
! 168: * .. Local Scalars ..
! 169: INTEGER IINFO, J, JB, NB
! 170: * ..
! 171: * .. External Subroutines ..
! 172: EXTERNAL DGEMM, DLAORHR_COL_GETRFNP2, DTRSM, XERBLA
! 173: * ..
! 174: * .. External Functions ..
! 175: INTEGER ILAENV
! 176: EXTERNAL ILAENV
! 177: * ..
! 178: * .. Intrinsic Functions ..
! 179: INTRINSIC MAX, MIN
! 180: * ..
! 181: * .. Executable Statements ..
! 182: *
! 183: * Test the input parameters.
! 184: *
! 185: INFO = 0
! 186: IF( M.LT.0 ) THEN
! 187: INFO = -1
! 188: ELSE IF( N.LT.0 ) THEN
! 189: INFO = -2
! 190: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 191: INFO = -4
! 192: END IF
! 193: IF( INFO.NE.0 ) THEN
! 194: CALL XERBLA( 'DLAORHR_COL_GETRFNP', -INFO )
! 195: RETURN
! 196: END IF
! 197: *
! 198: * Quick return if possible
! 199: *
! 200: IF( MIN( M, N ).EQ.0 )
! 201: $ RETURN
! 202: *
! 203: * Determine the block size for this environment.
! 204: *
! 205:
! 206: NB = ILAENV( 1, 'DLAORHR_COL_GETRFNP', ' ', M, N, -1, -1 )
! 207:
! 208: IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
! 209: *
! 210: * Use unblocked code.
! 211: *
! 212: CALL DLAORHR_COL_GETRFNP2( M, N, A, LDA, D, INFO )
! 213: ELSE
! 214: *
! 215: * Use blocked code.
! 216: *
! 217: DO J = 1, MIN( M, N ), NB
! 218: JB = MIN( MIN( M, N )-J+1, NB )
! 219: *
! 220: * Factor diagonal and subdiagonal blocks.
! 221: *
! 222: CALL DLAORHR_COL_GETRFNP2( M-J+1, JB, A( J, J ), LDA,
! 223: $ D( J ), IINFO )
! 224: *
! 225: IF( J+JB.LE.N ) THEN
! 226: *
! 227: * Compute block row of U.
! 228: *
! 229: CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,
! 230: $ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ),
! 231: $ LDA )
! 232: IF( J+JB.LE.M ) THEN
! 233: *
! 234: * Update trailing submatrix.
! 235: *
! 236: CALL DGEMM( 'No transpose', 'No transpose', M-J-JB+1,
! 237: $ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA,
! 238: $ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ),
! 239: $ LDA )
! 240: END IF
! 241: END IF
! 242: END DO
! 243: END IF
! 244: RETURN
! 245: *
! 246: * End of DLAORHR_COL_GETRFNP
! 247: *
! 248: END
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