Annotation of rpl/lapack/lapack/zgeqp3.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK,
! 2: $ INFO )
! 3: *
! 4: * -- LAPACK routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: INTEGER INFO, LDA, LWORK, M, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: INTEGER JPVT( * )
! 14: DOUBLE PRECISION RWORK( * )
! 15: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZGEQP3 computes a QR factorization with column pivoting of a
! 22: * matrix A: A*P = Q*R using Level 3 BLAS.
! 23: *
! 24: * Arguments
! 25: * =========
! 26: *
! 27: * M (input) INTEGER
! 28: * The number of rows of the matrix A. M >= 0.
! 29: *
! 30: * N (input) INTEGER
! 31: * The number of columns of the matrix A. N >= 0.
! 32: *
! 33: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 34: * On entry, the M-by-N matrix A.
! 35: * On exit, the upper triangle of the array contains the
! 36: * min(M,N)-by-N upper trapezoidal matrix R; the elements below
! 37: * the diagonal, together with the array TAU, represent the
! 38: * unitary matrix Q as a product of min(M,N) elementary
! 39: * reflectors.
! 40: *
! 41: * LDA (input) INTEGER
! 42: * The leading dimension of the array A. LDA >= max(1,M).
! 43: *
! 44: * JPVT (input/output) INTEGER array, dimension (N)
! 45: * On entry, if JPVT(J).ne.0, the J-th column of A is permuted
! 46: * to the front of A*P (a leading column); if JPVT(J)=0,
! 47: * the J-th column of A is a free column.
! 48: * On exit, if JPVT(J)=K, then the J-th column of A*P was the
! 49: * the K-th column of A.
! 50: *
! 51: * TAU (output) COMPLEX*16 array, dimension (min(M,N))
! 52: * The scalar factors of the elementary reflectors.
! 53: *
! 54: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 55: * On exit, if INFO=0, WORK(1) returns the optimal LWORK.
! 56: *
! 57: * LWORK (input) INTEGER
! 58: * The dimension of the array WORK. LWORK >= N+1.
! 59: * For optimal performance LWORK >= ( N+1 )*NB, where NB
! 60: * is the optimal blocksize.
! 61: *
! 62: * If LWORK = -1, then a workspace query is assumed; the routine
! 63: * only calculates the optimal size of the WORK array, returns
! 64: * this value as the first entry of the WORK array, and no error
! 65: * message related to LWORK is issued by XERBLA.
! 66: *
! 67: * RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
! 68: *
! 69: * INFO (output) INTEGER
! 70: * = 0: successful exit.
! 71: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 72: *
! 73: * Further Details
! 74: * ===============
! 75: *
! 76: * The matrix Q is represented as a product of elementary reflectors
! 77: *
! 78: * Q = H(1) H(2) . . . H(k), where k = min(m,n).
! 79: *
! 80: * Each H(i) has the form
! 81: *
! 82: * H(i) = I - tau * v * v'
! 83: *
! 84: * where tau is a real/complex scalar, and v is a real/complex vector
! 85: * with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
! 86: * A(i+1:m,i), and tau in TAU(i).
! 87: *
! 88: * Based on contributions by
! 89: * G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
! 90: * X. Sun, Computer Science Dept., Duke University, USA
! 91: *
! 92: * =====================================================================
! 93: *
! 94: * .. Parameters ..
! 95: INTEGER INB, INBMIN, IXOVER
! 96: PARAMETER ( INB = 1, INBMIN = 2, IXOVER = 3 )
! 97: * ..
! 98: * .. Local Scalars ..
! 99: LOGICAL LQUERY
! 100: INTEGER FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB,
! 101: $ NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN
! 102: * ..
! 103: * .. External Subroutines ..
! 104: EXTERNAL XERBLA, ZGEQRF, ZLAQP2, ZLAQPS, ZSWAP, ZUNMQR
! 105: * ..
! 106: * .. External Functions ..
! 107: INTEGER ILAENV
! 108: DOUBLE PRECISION DZNRM2
! 109: EXTERNAL ILAENV, DZNRM2
! 110: * ..
! 111: * .. Intrinsic Functions ..
! 112: INTRINSIC INT, MAX, MIN
! 113: * ..
! 114: * .. Executable Statements ..
! 115: *
! 116: * Test input arguments
! 117: * ====================
! 118: *
! 119: INFO = 0
! 120: LQUERY = ( LWORK.EQ.-1 )
! 121: IF( M.LT.0 ) THEN
! 122: INFO = -1
! 123: ELSE IF( N.LT.0 ) THEN
! 124: INFO = -2
! 125: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 126: INFO = -4
! 127: END IF
! 128: *
! 129: IF( INFO.EQ.0 ) THEN
! 130: MINMN = MIN( M, N )
! 131: IF( MINMN.EQ.0 ) THEN
! 132: IWS = 1
! 133: LWKOPT = 1
! 134: ELSE
! 135: IWS = N + 1
! 136: NB = ILAENV( INB, 'ZGEQRF', ' ', M, N, -1, -1 )
! 137: LWKOPT = ( N + 1 )*NB
! 138: END IF
! 139: WORK( 1 ) = LWKOPT
! 140: *
! 141: IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN
! 142: INFO = -8
! 143: END IF
! 144: END IF
! 145: *
! 146: IF( INFO.NE.0 ) THEN
! 147: CALL XERBLA( 'ZGEQP3', -INFO )
! 148: RETURN
! 149: ELSE IF( LQUERY ) THEN
! 150: RETURN
! 151: END IF
! 152: *
! 153: * Quick return if possible.
! 154: *
! 155: IF( MINMN.EQ.0 ) THEN
! 156: RETURN
! 157: END IF
! 158: *
! 159: * Move initial columns up front.
! 160: *
! 161: NFXD = 1
! 162: DO 10 J = 1, N
! 163: IF( JPVT( J ).NE.0 ) THEN
! 164: IF( J.NE.NFXD ) THEN
! 165: CALL ZSWAP( M, A( 1, J ), 1, A( 1, NFXD ), 1 )
! 166: JPVT( J ) = JPVT( NFXD )
! 167: JPVT( NFXD ) = J
! 168: ELSE
! 169: JPVT( J ) = J
! 170: END IF
! 171: NFXD = NFXD + 1
! 172: ELSE
! 173: JPVT( J ) = J
! 174: END IF
! 175: 10 CONTINUE
! 176: NFXD = NFXD - 1
! 177: *
! 178: * Factorize fixed columns
! 179: * =======================
! 180: *
! 181: * Compute the QR factorization of fixed columns and update
! 182: * remaining columns.
! 183: *
! 184: IF( NFXD.GT.0 ) THEN
! 185: NA = MIN( M, NFXD )
! 186: *CC CALL ZGEQR2( M, NA, A, LDA, TAU, WORK, INFO )
! 187: CALL ZGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO )
! 188: IWS = MAX( IWS, INT( WORK( 1 ) ) )
! 189: IF( NA.LT.N ) THEN
! 190: *CC CALL ZUNM2R( 'Left', 'Conjugate Transpose', M, N-NA,
! 191: *CC $ NA, A, LDA, TAU, A( 1, NA+1 ), LDA, WORK,
! 192: *CC $ INFO )
! 193: CALL ZUNMQR( 'Left', 'Conjugate Transpose', M, N-NA, NA, A,
! 194: $ LDA, TAU, A( 1, NA+1 ), LDA, WORK, LWORK,
! 195: $ INFO )
! 196: IWS = MAX( IWS, INT( WORK( 1 ) ) )
! 197: END IF
! 198: END IF
! 199: *
! 200: * Factorize free columns
! 201: * ======================
! 202: *
! 203: IF( NFXD.LT.MINMN ) THEN
! 204: *
! 205: SM = M - NFXD
! 206: SN = N - NFXD
! 207: SMINMN = MINMN - NFXD
! 208: *
! 209: * Determine the block size.
! 210: *
! 211: NB = ILAENV( INB, 'ZGEQRF', ' ', SM, SN, -1, -1 )
! 212: NBMIN = 2
! 213: NX = 0
! 214: *
! 215: IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN
! 216: *
! 217: * Determine when to cross over from blocked to unblocked code.
! 218: *
! 219: NX = MAX( 0, ILAENV( IXOVER, 'ZGEQRF', ' ', SM, SN, -1,
! 220: $ -1 ) )
! 221: *
! 222: *
! 223: IF( NX.LT.SMINMN ) THEN
! 224: *
! 225: * Determine if workspace is large enough for blocked code.
! 226: *
! 227: MINWS = ( SN+1 )*NB
! 228: IWS = MAX( IWS, MINWS )
! 229: IF( LWORK.LT.MINWS ) THEN
! 230: *
! 231: * Not enough workspace to use optimal NB: Reduce NB and
! 232: * determine the minimum value of NB.
! 233: *
! 234: NB = LWORK / ( SN+1 )
! 235: NBMIN = MAX( 2, ILAENV( INBMIN, 'ZGEQRF', ' ', SM, SN,
! 236: $ -1, -1 ) )
! 237: *
! 238: *
! 239: END IF
! 240: END IF
! 241: END IF
! 242: *
! 243: * Initialize partial column norms. The first N elements of work
! 244: * store the exact column norms.
! 245: *
! 246: DO 20 J = NFXD + 1, N
! 247: RWORK( J ) = DZNRM2( SM, A( NFXD+1, J ), 1 )
! 248: RWORK( N+J ) = RWORK( J )
! 249: 20 CONTINUE
! 250: *
! 251: IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND.
! 252: $ ( NX.LT.SMINMN ) ) THEN
! 253: *
! 254: * Use blocked code initially.
! 255: *
! 256: J = NFXD + 1
! 257: *
! 258: * Compute factorization: while loop.
! 259: *
! 260: *
! 261: TOPBMN = MINMN - NX
! 262: 30 CONTINUE
! 263: IF( J.LE.TOPBMN ) THEN
! 264: JB = MIN( NB, TOPBMN-J+1 )
! 265: *
! 266: * Factorize JB columns among columns J:N.
! 267: *
! 268: CALL ZLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA,
! 269: $ JPVT( J ), TAU( J ), RWORK( J ),
! 270: $ RWORK( N+J ), WORK( 1 ), WORK( JB+1 ),
! 271: $ N-J+1 )
! 272: *
! 273: J = J + FJB
! 274: GO TO 30
! 275: END IF
! 276: ELSE
! 277: J = NFXD + 1
! 278: END IF
! 279: *
! 280: * Use unblocked code to factor the last or only block.
! 281: *
! 282: *
! 283: IF( J.LE.MINMN )
! 284: $ CALL ZLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ),
! 285: $ TAU( J ), RWORK( J ), RWORK( N+J ), WORK( 1 ) )
! 286: *
! 287: END IF
! 288: *
! 289: WORK( 1 ) = IWS
! 290: RETURN
! 291: *
! 292: * End of ZGEQP3
! 293: *
! 294: END
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