Annotation of rpl/lapack/lapack/dgelq.f, revision 1.1
1.1 ! bertrand 1: *
! 2: * Definition:
! 3: * ===========
! 4: *
! 5: * SUBROUTINE DGELQ( M, N, A, LDA, T, TSIZE, WORK, LWORK,
! 6: * INFO )
! 7: *
! 8: * .. Scalar Arguments ..
! 9: * INTEGER INFO, LDA, M, N, TSIZE, LWORK
! 10: * ..
! 11: * .. Array Arguments ..
! 12: * DOUBLE PRECISION A( LDA, * ), T( * ), WORK( * )
! 13: * ..
! 14: *
! 15: *
! 16: *> \par Purpose:
! 17: * =============
! 18: *>
! 19: *> \verbatim
! 20: *> DGELQ computes a LQ factorization of an M-by-N matrix A.
! 21: *> \endverbatim
! 22: *
! 23: * Arguments:
! 24: * ==========
! 25: *
! 26: *> \param[in] M
! 27: *> \verbatim
! 28: *> M is INTEGER
! 29: *> The number of rows of the matrix A. M >= 0.
! 30: *> \endverbatim
! 31: *>
! 32: *> \param[in] N
! 33: *> \verbatim
! 34: *> N is INTEGER
! 35: *> The number of columns of the matrix A. N >= 0.
! 36: *> \endverbatim
! 37: *>
! 38: *> \param[in,out] A
! 39: *> \verbatim
! 40: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 41: *> On entry, the M-by-N matrix A.
! 42: *> On exit, the elements on and below the diagonal of the array
! 43: *> contain the M-by-min(M,N) lower trapezoidal matrix L
! 44: *> (L is lower triangular if M <= N);
! 45: *> the elements above the diagonal are used to store part of the
! 46: *> data structure to represent Q.
! 47: *> \endverbatim
! 48: *>
! 49: *> \param[in] LDA
! 50: *> \verbatim
! 51: *> LDA is INTEGER
! 52: *> The leading dimension of the array A. LDA >= max(1,M).
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[out] T
! 56: *> \verbatim
! 57: *> T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE))
! 58: *> On exit, if INFO = 0, T(1) returns optimal (or either minimal
! 59: *> or optimal, if query is assumed) TSIZE. See TSIZE for details.
! 60: *> Remaining T contains part of the data structure used to represent Q.
! 61: *> If one wants to apply or construct Q, then one needs to keep T
! 62: *> (in addition to A) and pass it to further subroutines.
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] TSIZE
! 66: *> \verbatim
! 67: *> TSIZE is INTEGER
! 68: *> If TSIZE >= 5, the dimension of the array T.
! 69: *> If TSIZE = -1 or -2, then a workspace query is assumed. The routine
! 70: *> only calculates the sizes of the T and WORK arrays, returns these
! 71: *> values as the first entries of the T and WORK arrays, and no error
! 72: *> message related to T or WORK is issued by XERBLA.
! 73: *> If TSIZE = -1, the routine calculates optimal size of T for the
! 74: *> optimum performance and returns this value in T(1).
! 75: *> If TSIZE = -2, the routine calculates minimal size of T and
! 76: *> returns this value in T(1).
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[out] WORK
! 80: *> \verbatim
! 81: *> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 82: *> On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
! 83: *> or optimal, if query was assumed) LWORK.
! 84: *> See LWORK for details.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[in] LWORK
! 88: *> \verbatim
! 89: *> LWORK is INTEGER
! 90: *> The dimension of the array WORK.
! 91: *> If LWORK = -1 or -2, then a workspace query is assumed. The routine
! 92: *> only calculates the sizes of the T and WORK arrays, returns these
! 93: *> values as the first entries of the T and WORK arrays, and no error
! 94: *> message related to T or WORK is issued by XERBLA.
! 95: *> If LWORK = -1, the routine calculates optimal size of WORK for the
! 96: *> optimal performance and returns this value in WORK(1).
! 97: *> If LWORK = -2, the routine calculates minimal size of WORK and
! 98: *> returns this value in WORK(1).
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[out] INFO
! 102: *> \verbatim
! 103: *> INFO is INTEGER
! 104: *> = 0: successful exit
! 105: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 106: *> \endverbatim
! 107: *
! 108: * Authors:
! 109: * ========
! 110: *
! 111: *> \author Univ. of Tennessee
! 112: *> \author Univ. of California Berkeley
! 113: *> \author Univ. of Colorado Denver
! 114: *> \author NAG Ltd.
! 115: *
! 116: *> \par Further Details
! 117: * ====================
! 118: *>
! 119: *> \verbatim
! 120: *>
! 121: *> The goal of the interface is to give maximum freedom to the developers for
! 122: *> creating any LQ factorization algorithm they wish. The triangular
! 123: *> (trapezoidal) L has to be stored in the lower part of A. The lower part of A
! 124: *> and the array T can be used to store any relevant information for applying or
! 125: *> constructing the Q factor. The WORK array can safely be discarded after exit.
! 126: *>
! 127: *> Caution: One should not expect the sizes of T and WORK to be the same from one
! 128: *> LAPACK implementation to the other, or even from one execution to the other.
! 129: *> A workspace query (for T and WORK) is needed at each execution. However,
! 130: *> for a given execution, the size of T and WORK are fixed and will not change
! 131: *> from one query to the next.
! 132: *>
! 133: *> \endverbatim
! 134: *>
! 135: *> \par Further Details particular to this LAPACK implementation:
! 136: * ==============================================================
! 137: *>
! 138: *> \verbatim
! 139: *>
! 140: *> These details are particular for this LAPACK implementation. Users should not
! 141: *> take them for granted. These details may change in the future, and are unlikely not
! 142: *> true for another LAPACK implementation. These details are relevant if one wants
! 143: *> to try to understand the code. They are not part of the interface.
! 144: *>
! 145: *> In this version,
! 146: *>
! 147: *> T(2): row block size (MB)
! 148: *> T(3): column block size (NB)
! 149: *> T(6:TSIZE): data structure needed for Q, computed by
! 150: *> DLASWLQ or DGELQT
! 151: *>
! 152: *> Depending on the matrix dimensions M and N, and row and column
! 153: *> block sizes MB and NB returned by ILAENV, DGELQ will use either
! 154: *> DLASWLQ (if the matrix is short-and-wide) or DGELQT to compute
! 155: *> the LQ factorization.
! 156: *> \endverbatim
! 157: *>
! 158: * =====================================================================
! 159: SUBROUTINE DGELQ( M, N, A, LDA, T, TSIZE, WORK, LWORK,
! 160: $ INFO )
! 161: *
! 162: * -- LAPACK computational routine (version 3.7.0) --
! 163: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 164: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
! 165: * December 2016
! 166: *
! 167: * .. Scalar Arguments ..
! 168: INTEGER INFO, LDA, M, N, TSIZE, LWORK
! 169: * ..
! 170: * .. Array Arguments ..
! 171: DOUBLE PRECISION A( LDA, * ), T( * ), WORK( * )
! 172: * ..
! 173: *
! 174: * =====================================================================
! 175: *
! 176: * ..
! 177: * .. Local Scalars ..
! 178: LOGICAL LQUERY, LMINWS, MINT, MINW
! 179: INTEGER MB, NB, MINTSZ, NBLCKS
! 180: * ..
! 181: * .. External Functions ..
! 182: LOGICAL LSAME
! 183: EXTERNAL LSAME
! 184: * ..
! 185: * .. External Subroutines ..
! 186: EXTERNAL DGELQT, DLASWLQ, XERBLA
! 187: * ..
! 188: * .. Intrinsic Functions ..
! 189: INTRINSIC MAX, MIN, MOD
! 190: * ..
! 191: * .. External Functions ..
! 192: INTEGER ILAENV
! 193: EXTERNAL ILAENV
! 194: * ..
! 195: * .. Executable Statements ..
! 196: *
! 197: * Test the input arguments
! 198: *
! 199: INFO = 0
! 200: *
! 201: LQUERY = ( TSIZE.EQ.-1 .OR. TSIZE.EQ.-2 .OR.
! 202: $ LWORK.EQ.-1 .OR. LWORK.EQ.-2 )
! 203: *
! 204: MINT = .FALSE.
! 205: MINW = .FALSE.
! 206: IF( TSIZE.EQ.-2 .OR. LWORK.EQ.-2 ) THEN
! 207: IF( TSIZE.NE.-1 ) MINT = .TRUE.
! 208: IF( LWORK.NE.-1 ) MINW = .TRUE.
! 209: END IF
! 210: *
! 211: * Determine the block size
! 212: *
! 213: IF( MIN( M, N ).GT.0 ) THEN
! 214: MB = ILAENV( 1, 'DGELQ ', ' ', M, N, 1, -1 )
! 215: NB = ILAENV( 1, 'DGELQ ', ' ', M, N, 2, -1 )
! 216: ELSE
! 217: MB = 1
! 218: NB = N
! 219: END IF
! 220: IF( MB.GT.MIN( M, N ) .OR. MB.LT.1 ) MB = 1
! 221: IF( NB.GT.N .OR. NB.LE.M ) NB = N
! 222: MINTSZ = M + 5
! 223: IF ( NB.GT.M .AND. N.GT.M ) THEN
! 224: IF( MOD( N - M, NB - M ).EQ.0 ) THEN
! 225: NBLCKS = ( N - M ) / ( NB - M )
! 226: ELSE
! 227: NBLCKS = ( N - M ) / ( NB - M ) + 1
! 228: END IF
! 229: ELSE
! 230: NBLCKS = 1
! 231: END IF
! 232: *
! 233: * Determine if the workspace size satisfies minimal size
! 234: *
! 235: LMINWS = .FALSE.
! 236: IF( ( TSIZE.LT.MAX( 1, MB*M*NBLCKS + 5 ) .OR. LWORK.LT.MB*M )
! 237: $ .AND. ( LWORK.GE.M ) .AND. ( TSIZE.GE.MINTSZ )
! 238: $ .AND. ( .NOT.LQUERY ) ) THEN
! 239: IF( TSIZE.LT.MAX( 1, MB*M*NBLCKS + 5 ) ) THEN
! 240: LMINWS = .TRUE.
! 241: MB = 1
! 242: NB = N
! 243: END IF
! 244: IF( LWORK.LT.MB*M ) THEN
! 245: LMINWS = .TRUE.
! 246: MB = 1
! 247: END IF
! 248: END IF
! 249: *
! 250: IF( M.LT.0 ) THEN
! 251: INFO = -1
! 252: ELSE IF( N.LT.0 ) THEN
! 253: INFO = -2
! 254: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 255: INFO = -4
! 256: ELSE IF( TSIZE.LT.MAX( 1, MB*M*NBLCKS + 5 )
! 257: $ .AND. ( .NOT.LQUERY ) .AND. ( .NOT.LMINWS ) ) THEN
! 258: INFO = -6
! 259: ELSE IF( ( LWORK.LT.MAX( 1, M*MB ) ) .AND .( .NOT.LQUERY )
! 260: $ .AND. ( .NOT.LMINWS ) ) THEN
! 261: INFO = -8
! 262: END IF
! 263: *
! 264: IF( INFO.EQ.0 ) THEN
! 265: IF( MINT ) THEN
! 266: T( 1 ) = MINTSZ
! 267: ELSE
! 268: T( 1 ) = MB*M*NBLCKS + 5
! 269: END IF
! 270: T( 2 ) = MB
! 271: T( 3 ) = NB
! 272: IF( MINW ) THEN
! 273: WORK( 1 ) = MAX( 1, N )
! 274: ELSE
! 275: WORK( 1 ) = MAX( 1, MB*M )
! 276: END IF
! 277: END IF
! 278: IF( INFO.NE.0 ) THEN
! 279: CALL XERBLA( 'DGELQ', -INFO )
! 280: RETURN
! 281: ELSE IF( LQUERY ) THEN
! 282: RETURN
! 283: END IF
! 284: *
! 285: * Quick return if possible
! 286: *
! 287: IF( MIN( M, N ).EQ.0 ) THEN
! 288: RETURN
! 289: END IF
! 290: *
! 291: * The LQ Decomposition
! 292: *
! 293: IF( ( N.LE.M ) .OR. ( NB.LE.M ) .OR. ( NB.GE.N ) ) THEN
! 294: CALL DGELQT( M, N, MB, A, LDA, T( 6 ), MB, WORK, INFO )
! 295: ELSE
! 296: CALL DLASWLQ( M, N, MB, NB, A, LDA, T( 6 ), MB, WORK,
! 297: $ LWORK, INFO )
! 298: END IF
! 299: *
! 300: WORK( 1 ) = MAX( 1, MB*M )
! 301: *
! 302: RETURN
! 303: *
! 304: * End of DGELQ
! 305: *
! 306: END
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