Annotation of rpl/lapack/lapack/dtpqrt.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b DTPQRT
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DTPQRT + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtpqrt.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtpqrt.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtpqrt.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
! 22: * INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DTPQRT computes a blocked QR factorization of a real
! 38: *> "triangular-pentagonal" matrix C, which is composed of a
! 39: *> triangular block A and pentagonal block B, using the compact
! 40: *> WY representation for Q.
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] M
! 47: *> \verbatim
! 48: *> M is INTEGER
! 49: *> The number of rows of the matrix B.
! 50: *> M >= 0.
! 51: *> \endverbatim
! 52: *>
! 53: *> \param[in] N
! 54: *> \verbatim
! 55: *> N is INTEGER
! 56: *> The number of columns of the matrix B, and the order of the
! 57: *> triangular matrix A.
! 58: *> N >= 0.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] L
! 62: *> \verbatim
! 63: *> L is INTEGER
! 64: *> The number of rows of the upper trapezoidal part of B.
! 65: *> MIN(M,N) >= L >= 0. See Further Details.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] NB
! 69: *> \verbatim
! 70: *> NB is INTEGER
! 71: *> The block size to be used in the blocked QR. N >= NB >= 1.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in,out] A
! 75: *> \verbatim
! 76: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 77: *> On entry, the upper triangular N-by-N matrix A.
! 78: *> On exit, the elements on and above the diagonal of the array
! 79: *> contain the upper triangular matrix R.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] LDA
! 83: *> \verbatim
! 84: *> LDA is INTEGER
! 85: *> The leading dimension of the array A. LDA >= max(1,N).
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in,out] B
! 89: *> \verbatim
! 90: *> B is DOUBLE PRECISION array, dimension (LDB,N)
! 91: *> On entry, the pentagonal M-by-N matrix B. The first M-L rows
! 92: *> are rectangular, and the last L rows are upper trapezoidal.
! 93: *> On exit, B contains the pentagonal matrix V. See Further Details.
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] LDB
! 97: *> \verbatim
! 98: *> LDB is INTEGER
! 99: *> The leading dimension of the array B. LDB >= max(1,M).
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[out] T
! 103: *> \verbatim
! 104: *> T is DOUBLE PRECISION array, dimension (LDT,N)
! 105: *> The upper triangular block reflectors stored in compact form
! 106: *> as a sequence of upper triangular blocks. See Further Details.
! 107: *> \endverbatim
! 108: *>
! 109: *> \param[in] LDT
! 110: *> \verbatim
! 111: *> LDT is INTEGER
! 112: *> The leading dimension of the array T. LDT >= NB.
! 113: *> \endverbatim
! 114: *>
! 115: *> \param[out] WORK
! 116: *> \verbatim
! 117: *> WORK is DOUBLE PRECISION array, dimension (NB*N)
! 118: *> \endverbatim
! 119: *>
! 120: *> \param[out] INFO
! 121: *> \verbatim
! 122: *> INFO is INTEGER
! 123: *> = 0: successful exit
! 124: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 125: *> \endverbatim
! 126: *
! 127: * Authors:
! 128: * ========
! 129: *
! 130: *> \author Univ. of Tennessee
! 131: *> \author Univ. of California Berkeley
! 132: *> \author Univ. of Colorado Denver
! 133: *> \author NAG Ltd.
! 134: *
! 135: *> \date April 2012
! 136: *
! 137: *> \ingroup doubleOTHERcomputational
! 138: *
! 139: *> \par Further Details:
! 140: * =====================
! 141: *>
! 142: *> \verbatim
! 143: *>
! 144: *> The input matrix C is a (N+M)-by-N matrix
! 145: *>
! 146: *> C = [ A ]
! 147: *> [ B ]
! 148: *>
! 149: *> where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
! 150: *> matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
! 151: *> upper trapezoidal matrix B2:
! 152: *>
! 153: *> B = [ B1 ] <- (M-L)-by-N rectangular
! 154: *> [ B2 ] <- L-by-N upper trapezoidal.
! 155: *>
! 156: *> The upper trapezoidal matrix B2 consists of the first L rows of a
! 157: *> N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N). If L=0,
! 158: *> B is rectangular M-by-N; if M=L=N, B is upper triangular.
! 159: *>
! 160: *> The matrix W stores the elementary reflectors H(i) in the i-th column
! 161: *> below the diagonal (of A) in the (N+M)-by-N input matrix C
! 162: *>
! 163: *> C = [ A ] <- upper triangular N-by-N
! 164: *> [ B ] <- M-by-N pentagonal
! 165: *>
! 166: *> so that W can be represented as
! 167: *>
! 168: *> W = [ I ] <- identity, N-by-N
! 169: *> [ V ] <- M-by-N, same form as B.
! 170: *>
! 171: *> Thus, all of information needed for W is contained on exit in B, which
! 172: *> we call V above. Note that V has the same form as B; that is,
! 173: *>
! 174: *> V = [ V1 ] <- (M-L)-by-N rectangular
! 175: *> [ V2 ] <- L-by-N upper trapezoidal.
! 176: *>
! 177: *> The columns of V represent the vectors which define the H(i)'s.
! 178: *>
! 179: *> The number of blocks is B = ceiling(N/NB), where each
! 180: *> block is of order NB except for the last block, which is of order
! 181: *> IB = N - (B-1)*NB. For each of the B blocks, a upper triangular block
! 182: *> reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB
! 183: *> for the last block) T's are stored in the NB-by-N matrix T as
! 184: *>
! 185: *> T = [T1 T2 ... TB].
! 186: *> \endverbatim
! 187: *>
! 188: * =====================================================================
! 189: SUBROUTINE DTPQRT( M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK,
! 190: $ INFO )
! 191: *
! 192: * -- LAPACK computational routine (version 3.4.1) --
! 193: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 194: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 195: * April 2012
! 196: *
! 197: * .. Scalar Arguments ..
! 198: INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
! 199: * ..
! 200: * .. Array Arguments ..
! 201: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
! 202: * ..
! 203: *
! 204: * =====================================================================
! 205: *
! 206: * ..
! 207: * .. Local Scalars ..
! 208: INTEGER I, IB, LB, MB, IINFO
! 209: * ..
! 210: * .. External Subroutines ..
! 211: EXTERNAL DTPQRT2, DTPRFB, XERBLA
! 212: * ..
! 213: * .. Executable Statements ..
! 214: *
! 215: * Test the input arguments
! 216: *
! 217: INFO = 0
! 218: IF( M.LT.0 ) THEN
! 219: INFO = -1
! 220: ELSE IF( N.LT.0 ) THEN
! 221: INFO = -2
! 222: ELSE IF( L.LT.0 .OR. L.GT.MIN(M,N) ) THEN
! 223: INFO = -3
! 224: ELSE IF( NB.LT.1 .OR. NB.GT.N ) THEN
! 225: INFO = -4
! 226: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 227: INFO = -6
! 228: ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
! 229: INFO = -8
! 230: ELSE IF( LDT.LT.NB ) THEN
! 231: INFO = -10
! 232: END IF
! 233: IF( INFO.NE.0 ) THEN
! 234: CALL XERBLA( 'DTPQRT', -INFO )
! 235: RETURN
! 236: END IF
! 237: *
! 238: * Quick return if possible
! 239: *
! 240: IF( M.EQ.0 .OR. N.EQ.0 ) RETURN
! 241: *
! 242: DO I = 1, N, NB
! 243: *
! 244: * Compute the QR factorization of the current block
! 245: *
! 246: IB = MIN( N-I+1, NB )
! 247: MB = MIN( M-L+I+IB-1, M )
! 248: IF( I.GE.L ) THEN
! 249: LB = 0
! 250: ELSE
! 251: LB = MB-M+L-I+1
! 252: END IF
! 253: *
! 254: CALL DTPQRT2( MB, IB, LB, A(I,I), LDA, B( 1, I ), LDB,
! 255: $ T(1, I ), LDT, IINFO )
! 256: *
! 257: * Update by applying H**T to B(:,I+IB:N) from the left
! 258: *
! 259: IF( I+IB.LE.N ) THEN
! 260: CALL DTPRFB( 'L', 'T', 'F', 'C', MB, N-I-IB+1, IB, LB,
! 261: $ B( 1, I ), LDB, T( 1, I ), LDT,
! 262: $ A( I, I+IB ), LDA, B( 1, I+IB ), LDB,
! 263: $ WORK, IB )
! 264: END IF
! 265: END DO
! 266: RETURN
! 267: *
! 268: * End of DTPQRT
! 269: *
! 270: END
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