Annotation of rpl/lapack/lapack/dgeqp3.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: INTEGER INFO, LDA, LWORK, M, N
! 10: * ..
! 11: * .. Array Arguments ..
! 12: INTEGER JPVT( * )
! 13: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DGEQP3 computes a QR factorization with column pivoting of a
! 20: * matrix A: A*P = Q*R using Level 3 BLAS.
! 21: *
! 22: * Arguments
! 23: * =========
! 24: *
! 25: * M (input) INTEGER
! 26: * The number of rows of the matrix A. M >= 0.
! 27: *
! 28: * N (input) INTEGER
! 29: * The number of columns of the matrix A. N >= 0.
! 30: *
! 31: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
! 32: * On entry, the M-by-N matrix A.
! 33: * On exit, the upper triangle of the array contains the
! 34: * min(M,N)-by-N upper trapezoidal matrix R; the elements below
! 35: * the diagonal, together with the array TAU, represent the
! 36: * orthogonal matrix Q as a product of min(M,N) elementary
! 37: * reflectors.
! 38: *
! 39: * LDA (input) INTEGER
! 40: * The leading dimension of the array A. LDA >= max(1,M).
! 41: *
! 42: * JPVT (input/output) INTEGER array, dimension (N)
! 43: * On entry, if JPVT(J).ne.0, the J-th column of A is permuted
! 44: * to the front of A*P (a leading column); if JPVT(J)=0,
! 45: * the J-th column of A is a free column.
! 46: * On exit, if JPVT(J)=K, then the J-th column of A*P was the
! 47: * the K-th column of A.
! 48: *
! 49: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
! 50: * The scalar factors of the elementary reflectors.
! 51: *
! 52: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 53: * On exit, if INFO=0, WORK(1) returns the optimal LWORK.
! 54: *
! 55: * LWORK (input) INTEGER
! 56: * The dimension of the array WORK. LWORK >= 3*N+1.
! 57: * For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
! 58: * is the optimal blocksize.
! 59: *
! 60: * If LWORK = -1, then a workspace query is assumed; the routine
! 61: * only calculates the optimal size of the WORK array, returns
! 62: * this value as the first entry of the WORK array, and no error
! 63: * message related to LWORK is issued by XERBLA.
! 64: *
! 65: * INFO (output) INTEGER
! 66: * = 0: successful exit.
! 67: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 68: *
! 69: * Further Details
! 70: * ===============
! 71: *
! 72: * The matrix Q is represented as a product of elementary reflectors
! 73: *
! 74: * Q = H(1) H(2) . . . H(k), where k = min(m,n).
! 75: *
! 76: * Each H(i) has the form
! 77: *
! 78: * H(i) = I - tau * v * v'
! 79: *
! 80: * where tau is a real/complex scalar, and v is a real/complex vector
! 81: * with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
! 82: * A(i+1:m,i), and tau in TAU(i).
! 83: *
! 84: * Based on contributions by
! 85: * G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
! 86: * X. Sun, Computer Science Dept., Duke University, USA
! 87: *
! 88: * =====================================================================
! 89: *
! 90: * .. Parameters ..
! 91: INTEGER INB, INBMIN, IXOVER
! 92: PARAMETER ( INB = 1, INBMIN = 2, IXOVER = 3 )
! 93: * ..
! 94: * .. Local Scalars ..
! 95: LOGICAL LQUERY
! 96: INTEGER FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB,
! 97: $ NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN
! 98: * ..
! 99: * .. External Subroutines ..
! 100: EXTERNAL DGEQRF, DLAQP2, DLAQPS, DORMQR, DSWAP, XERBLA
! 101: * ..
! 102: * .. External Functions ..
! 103: INTEGER ILAENV
! 104: DOUBLE PRECISION DNRM2
! 105: EXTERNAL ILAENV, DNRM2
! 106: * ..
! 107: * .. Intrinsic Functions ..
! 108: INTRINSIC INT, MAX, MIN
! 109: * ..
! 110: * .. Executable Statements ..
! 111: *
! 112: * Test input arguments
! 113: * ====================
! 114: *
! 115: INFO = 0
! 116: LQUERY = ( LWORK.EQ.-1 )
! 117: IF( M.LT.0 ) THEN
! 118: INFO = -1
! 119: ELSE IF( N.LT.0 ) THEN
! 120: INFO = -2
! 121: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 122: INFO = -4
! 123: END IF
! 124: *
! 125: IF( INFO.EQ.0 ) THEN
! 126: MINMN = MIN( M, N )
! 127: IF( MINMN.EQ.0 ) THEN
! 128: IWS = 1
! 129: LWKOPT = 1
! 130: ELSE
! 131: IWS = 3*N + 1
! 132: NB = ILAENV( INB, 'DGEQRF', ' ', M, N, -1, -1 )
! 133: LWKOPT = 2*N + ( N + 1 )*NB
! 134: END IF
! 135: WORK( 1 ) = LWKOPT
! 136: *
! 137: IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN
! 138: INFO = -8
! 139: END IF
! 140: END IF
! 141: *
! 142: IF( INFO.NE.0 ) THEN
! 143: CALL XERBLA( 'DGEQP3', -INFO )
! 144: RETURN
! 145: ELSE IF( LQUERY ) THEN
! 146: RETURN
! 147: END IF
! 148: *
! 149: * Quick return if possible.
! 150: *
! 151: IF( MINMN.EQ.0 ) THEN
! 152: RETURN
! 153: END IF
! 154: *
! 155: * Move initial columns up front.
! 156: *
! 157: NFXD = 1
! 158: DO 10 J = 1, N
! 159: IF( JPVT( J ).NE.0 ) THEN
! 160: IF( J.NE.NFXD ) THEN
! 161: CALL DSWAP( M, A( 1, J ), 1, A( 1, NFXD ), 1 )
! 162: JPVT( J ) = JPVT( NFXD )
! 163: JPVT( NFXD ) = J
! 164: ELSE
! 165: JPVT( J ) = J
! 166: END IF
! 167: NFXD = NFXD + 1
! 168: ELSE
! 169: JPVT( J ) = J
! 170: END IF
! 171: 10 CONTINUE
! 172: NFXD = NFXD - 1
! 173: *
! 174: * Factorize fixed columns
! 175: * =======================
! 176: *
! 177: * Compute the QR factorization of fixed columns and update
! 178: * remaining columns.
! 179: *
! 180: IF( NFXD.GT.0 ) THEN
! 181: NA = MIN( M, NFXD )
! 182: *CC CALL DGEQR2( M, NA, A, LDA, TAU, WORK, INFO )
! 183: CALL DGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO )
! 184: IWS = MAX( IWS, INT( WORK( 1 ) ) )
! 185: IF( NA.LT.N ) THEN
! 186: *CC CALL DORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA,
! 187: *CC $ TAU, A( 1, NA+1 ), LDA, WORK, INFO )
! 188: CALL DORMQR( 'Left', 'Transpose', M, N-NA, NA, A, LDA, TAU,
! 189: $ A( 1, NA+1 ), LDA, WORK, LWORK, INFO )
! 190: IWS = MAX( IWS, INT( WORK( 1 ) ) )
! 191: END IF
! 192: END IF
! 193: *
! 194: * Factorize free columns
! 195: * ======================
! 196: *
! 197: IF( NFXD.LT.MINMN ) THEN
! 198: *
! 199: SM = M - NFXD
! 200: SN = N - NFXD
! 201: SMINMN = MINMN - NFXD
! 202: *
! 203: * Determine the block size.
! 204: *
! 205: NB = ILAENV( INB, 'DGEQRF', ' ', SM, SN, -1, -1 )
! 206: NBMIN = 2
! 207: NX = 0
! 208: *
! 209: IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN
! 210: *
! 211: * Determine when to cross over from blocked to unblocked code.
! 212: *
! 213: NX = MAX( 0, ILAENV( IXOVER, 'DGEQRF', ' ', SM, SN, -1,
! 214: $ -1 ) )
! 215: *
! 216: *
! 217: IF( NX.LT.SMINMN ) THEN
! 218: *
! 219: * Determine if workspace is large enough for blocked code.
! 220: *
! 221: MINWS = 2*SN + ( SN+1 )*NB
! 222: IWS = MAX( IWS, MINWS )
! 223: IF( LWORK.LT.MINWS ) THEN
! 224: *
! 225: * Not enough workspace to use optimal NB: Reduce NB and
! 226: * determine the minimum value of NB.
! 227: *
! 228: NB = ( LWORK-2*SN ) / ( SN+1 )
! 229: NBMIN = MAX( 2, ILAENV( INBMIN, 'DGEQRF', ' ', SM, SN,
! 230: $ -1, -1 ) )
! 231: *
! 232: *
! 233: END IF
! 234: END IF
! 235: END IF
! 236: *
! 237: * Initialize partial column norms. The first N elements of work
! 238: * store the exact column norms.
! 239: *
! 240: DO 20 J = NFXD + 1, N
! 241: WORK( J ) = DNRM2( SM, A( NFXD+1, J ), 1 )
! 242: WORK( N+J ) = WORK( J )
! 243: 20 CONTINUE
! 244: *
! 245: IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND.
! 246: $ ( NX.LT.SMINMN ) ) THEN
! 247: *
! 248: * Use blocked code initially.
! 249: *
! 250: J = NFXD + 1
! 251: *
! 252: * Compute factorization: while loop.
! 253: *
! 254: *
! 255: TOPBMN = MINMN - NX
! 256: 30 CONTINUE
! 257: IF( J.LE.TOPBMN ) THEN
! 258: JB = MIN( NB, TOPBMN-J+1 )
! 259: *
! 260: * Factorize JB columns among columns J:N.
! 261: *
! 262: CALL DLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA,
! 263: $ JPVT( J ), TAU( J ), WORK( J ), WORK( N+J ),
! 264: $ WORK( 2*N+1 ), WORK( 2*N+JB+1 ), N-J+1 )
! 265: *
! 266: J = J + FJB
! 267: GO TO 30
! 268: END IF
! 269: ELSE
! 270: J = NFXD + 1
! 271: END IF
! 272: *
! 273: * Use unblocked code to factor the last or only block.
! 274: *
! 275: *
! 276: IF( J.LE.MINMN )
! 277: $ CALL DLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ),
! 278: $ TAU( J ), WORK( J ), WORK( N+J ),
! 279: $ WORK( 2*N+1 ) )
! 280: *
! 281: END IF
! 282: *
! 283: WORK( 1 ) = IWS
! 284: RETURN
! 285: *
! 286: * End of DGEQP3
! 287: *
! 288: END
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