Annotation of rpl/lapack/lapack/dlasyf_rook.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b DLASYF_ROOK *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLASYF_ROOK + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasyf_rook.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasyf_rook.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasyf_rook.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLASYF_ROOK( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARADLATER UPLO
! 25: * INTEGER INFO, KB, LDA, LDW, N, NB
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * INTEGER IPIV( * )
! 29: * DOUBLE PRECISION A( LDA, * ), W( LDW, * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> DLASYF_ROOK computes a partial factorization of a real symmetric
! 39: *> matrix A using the bounded Bunch-Kaufman ("rook") diagonal
! 40: *> pivoting method. The partial factorization has the form:
! 41: *>
! 42: *> A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or:
! 43: *> ( 0 U22 ) ( 0 D ) ( U12**T U22**T )
! 44: *>
! 45: *> A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = 'L'
! 46: *> ( L21 I ) ( 0 A22 ) ( 0 I )
! 47: *>
! 48: *> where the order of D is at most NB. The actual order is returned in
! 49: *> the argument KB, and is either NB or NB-1, or N if N <= NB.
! 50: *>
! 51: *> DLASYF_ROOK is an auxiliary routine called by DSYTRF_ROOK. It uses
! 52: *> blocked code (calling Level 3 BLAS) to update the submatrix
! 53: *> A11 (if UPLO = 'U') or A22 (if UPLO = 'L').
! 54: *> \endverbatim
! 55: *
! 56: * Arguments:
! 57: * ==========
! 58: *
! 59: *> \param[in] UPLO
! 60: *> \verbatim
! 61: *> UPLO is CHARACTER*1
! 62: *> Specifies whether the upper or lower triangular part of the
! 63: *> symmetric matrix A is stored:
! 64: *> = 'U': Upper triangular
! 65: *> = 'L': Lower triangular
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] N
! 69: *> \verbatim
! 70: *> N is INTEGER
! 71: *> The order of the matrix A. N >= 0.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in] NB
! 75: *> \verbatim
! 76: *> NB is INTEGER
! 77: *> The maximum number of columns of the matrix A that should be
! 78: *> factored. NB should be at least 2 to allow for 2-by-2 pivot
! 79: *> blocks.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[out] KB
! 83: *> \verbatim
! 84: *> KB is INTEGER
! 85: *> The number of columns of A that were actually factored.
! 86: *> KB is either NB-1 or NB, or N if N <= NB.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in,out] A
! 90: *> \verbatim
! 91: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 92: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
! 93: *> n-by-n upper triangular part of A contains the upper
! 94: *> triangular part of the matrix A, and the strictly lower
! 95: *> triangular part of A is not referenced. If UPLO = 'L', the
! 96: *> leading n-by-n lower triangular part of A contains the lower
! 97: *> triangular part of the matrix A, and the strictly upper
! 98: *> triangular part of A is not referenced.
! 99: *> On exit, A contains details of the partial factorization.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in] LDA
! 103: *> \verbatim
! 104: *> LDA is INTEGER
! 105: *> The leading dimension of the array A. LDA >= max(1,N).
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[out] IPIV
! 109: *> \verbatim
! 110: *> IPIV is INTEGER array, dimension (N)
! 111: *> Details of the interchanges and the block structure of D.
! 112: *>
! 113: *> If UPLO = 'U':
! 114: *> Only the last KB elements of IPIV are set.
! 115: *>
! 116: *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
! 117: *> interchanged and D(k,k) is a 1-by-1 diagonal block.
! 118: *>
! 119: *> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
! 120: *> columns k and -IPIV(k) were interchanged and rows and
! 121: *> columns k-1 and -IPIV(k-1) were inerchaged,
! 122: *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
! 123: *>
! 124: *> If UPLO = 'L':
! 125: *> Only the first KB elements of IPIV are set.
! 126: *>
! 127: *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
! 128: *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
! 129: *>
! 130: *> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
! 131: *> columns k and -IPIV(k) were interchanged and rows and
! 132: *> columns k+1 and -IPIV(k+1) were inerchaged,
! 133: *> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
! 134: *> \endverbatim
! 135: *>
! 136: *> \param[out] W
! 137: *> \verbatim
! 138: *> W is DOUBLE PRECISION array, dimension (LDW,NB)
! 139: *> \endverbatim
! 140: *>
! 141: *> \param[in] LDW
! 142: *> \verbatim
! 143: *> LDW is INTEGER
! 144: *> The leading dimension of the array W. LDW >= max(1,N).
! 145: *> \endverbatim
! 146: *>
! 147: *> \param[out] INFO
! 148: *> \verbatim
! 149: *> INFO is INTEGER
! 150: *> = 0: successful exit
! 151: *> > 0: if INFO = k, D(k,k) is exactly zero. The factorization
! 152: *> has been completed, but the block diagonal matrix D is
! 153: *> exactly singular.
! 154: *> \endverbatim
! 155: *
! 156: * Authors:
! 157: * ========
! 158: *
! 159: *> \author Univ. of Tennessee
! 160: *> \author Univ. of California Berkeley
! 161: *> \author Univ. of Colorado Denver
! 162: *> \author NAG Ltd.
! 163: *
! 164: *> \date November 2013
! 165: *
! 166: *> \ingroup doubleSYcomputational
! 167: *
! 168: *> \par Contributors:
! 169: * ==================
! 170: *>
! 171: *> \verbatim
! 172: *>
! 173: *> November 2013, Igor Kozachenko,
! 174: *> Computer Science Division,
! 175: *> University of California, Berkeley
! 176: *>
! 177: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
! 178: *> School of Mathematics,
! 179: *> University of Manchester
! 180: *>
! 181: *> \endverbatim
! 182: *
! 183: * =====================================================================
! 184: SUBROUTINE DLASYF_ROOK( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW,
! 185: $ INFO )
! 186: *
! 187: * -- LAPACK computational routine (version 3.5.0) --
! 188: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 189: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 190: * November 2013
! 191: *
! 192: * .. Scalar Arguments ..
! 193: CHARACTER UPLO
! 194: INTEGER INFO, KB, LDA, LDW, N, NB
! 195: * ..
! 196: * .. Array Arguments ..
! 197: INTEGER IPIV( * )
! 198: DOUBLE PRECISION A( LDA, * ), W( LDW, * )
! 199: * ..
! 200: *
! 201: * =====================================================================
! 202: *
! 203: * .. Parameters ..
! 204: DOUBLE PRECISION ZERO, ONE
! 205: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 206: DOUBLE PRECISION EIGHT, SEVTEN
! 207: PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
! 208: * ..
! 209: * .. Local Scalars ..
! 210: LOGICAL DONE
! 211: INTEGER IMAX, ITEMP, J, JB, JJ, JMAX, JP1, JP2, K, KK,
! 212: $ KW, KKW, KP, KSTEP, P, II
! 213:
! 214: DOUBLE PRECISION ABSAKK, ALPHA, COLMAX, D11, D12, D21, D22,
! 215: $ DTEMP, R1, ROWMAX, T, SFMIN
! 216: * ..
! 217: * .. External Functions ..
! 218: LOGICAL LSAME
! 219: INTEGER IDAMAX
! 220: DOUBLE PRECISION DLAMCH
! 221: EXTERNAL LSAME, IDAMAX, DLAMCH
! 222: * ..
! 223: * .. External Subroutines ..
! 224: EXTERNAL DCOPY, DGEMM, DGEMV, DSCAL, DSWAP
! 225: * ..
! 226: * .. Intrinsic Functions ..
! 227: INTRINSIC ABS, MAX, MIN, SQRT
! 228: * ..
! 229: * .. Executable Statements ..
! 230: *
! 231: INFO = 0
! 232: *
! 233: * Initialize ALPHA for use in choosing pivot block size.
! 234: *
! 235: ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
! 236: *
! 237: * Compute machine safe minimum
! 238: *
! 239: SFMIN = DLAMCH( 'S' )
! 240: *
! 241: IF( LSAME( UPLO, 'U' ) ) THEN
! 242: *
! 243: * Factorize the trailing columns of A using the upper triangle
! 244: * of A and working backwards, and compute the matrix W = U12*D
! 245: * for use in updating A11
! 246: *
! 247: * K is the main loop index, decreasing from N in steps of 1 or 2
! 248: *
! 249: K = N
! 250: 10 CONTINUE
! 251: *
! 252: * KW is the column of W which corresponds to column K of A
! 253: *
! 254: KW = NB + K - N
! 255: *
! 256: * Exit from loop
! 257: *
! 258: IF( ( K.LE.N-NB+1 .AND. NB.LT.N ) .OR. K.LT.1 )
! 259: $ GO TO 30
! 260: *
! 261: KSTEP = 1
! 262: P = K
! 263: *
! 264: * Copy column K of A to column KW of W and update it
! 265: *
! 266: CALL DCOPY( K, A( 1, K ), 1, W( 1, KW ), 1 )
! 267: IF( K.LT.N )
! 268: $ CALL DGEMV( 'No transpose', K, N-K, -ONE, A( 1, K+1 ),
! 269: $ LDA, W( K, KW+1 ), LDW, ONE, W( 1, KW ), 1 )
! 270: *
! 271: * Determine rows and columns to be interchanged and whether
! 272: * a 1-by-1 or 2-by-2 pivot block will be used
! 273: *
! 274: ABSAKK = ABS( W( K, KW ) )
! 275: *
! 276: * IMAX is the row-index of the largest off-diagonal element in
! 277: * column K, and COLMAX is its absolute value.
! 278: * Determine both COLMAX and IMAX.
! 279: *
! 280: IF( K.GT.1 ) THEN
! 281: IMAX = IDAMAX( K-1, W( 1, KW ), 1 )
! 282: COLMAX = ABS( W( IMAX, KW ) )
! 283: ELSE
! 284: COLMAX = ZERO
! 285: END IF
! 286: *
! 287: IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
! 288: *
! 289: * Column K is zero or underflow: set INFO and continue
! 290: *
! 291: IF( INFO.EQ.0 )
! 292: $ INFO = K
! 293: KP = K
! 294: CALL DCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
! 295: ELSE
! 296: *
! 297: * ============================================================
! 298: *
! 299: * Test for interchange
! 300: *
! 301: * Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
! 302: * (used to handle NaN and Inf)
! 303: *
! 304: IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
! 305: *
! 306: * no interchange, use 1-by-1 pivot block
! 307: *
! 308: KP = K
! 309: *
! 310: ELSE
! 311: *
! 312: DONE = .FALSE.
! 313: *
! 314: * Loop until pivot found
! 315: *
! 316: 12 CONTINUE
! 317: *
! 318: * Begin pivot search loop body
! 319: *
! 320: *
! 321: * Copy column IMAX to column KW-1 of W and update it
! 322: *
! 323: CALL DCOPY( IMAX, A( 1, IMAX ), 1, W( 1, KW-1 ), 1 )
! 324: CALL DCOPY( K-IMAX, A( IMAX, IMAX+1 ), LDA,
! 325: $ W( IMAX+1, KW-1 ), 1 )
! 326: *
! 327: IF( K.LT.N )
! 328: $ CALL DGEMV( 'No transpose', K, N-K, -ONE,
! 329: $ A( 1, K+1 ), LDA, W( IMAX, KW+1 ), LDW,
! 330: $ ONE, W( 1, KW-1 ), 1 )
! 331: *
! 332: * JMAX is the column-index of the largest off-diagonal
! 333: * element in row IMAX, and ROWMAX is its absolute value.
! 334: * Determine both ROWMAX and JMAX.
! 335: *
! 336: IF( IMAX.NE.K ) THEN
! 337: JMAX = IMAX + IDAMAX( K-IMAX, W( IMAX+1, KW-1 ),
! 338: $ 1 )
! 339: ROWMAX = ABS( W( JMAX, KW-1 ) )
! 340: ELSE
! 341: ROWMAX = ZERO
! 342: END IF
! 343: *
! 344: IF( IMAX.GT.1 ) THEN
! 345: ITEMP = IDAMAX( IMAX-1, W( 1, KW-1 ), 1 )
! 346: DTEMP = ABS( W( ITEMP, KW-1 ) )
! 347: IF( DTEMP.GT.ROWMAX ) THEN
! 348: ROWMAX = DTEMP
! 349: JMAX = ITEMP
! 350: END IF
! 351: END IF
! 352: *
! 353: * Equivalent to testing for
! 354: * ABS( W( IMAX, KW-1 ) ).GE.ALPHA*ROWMAX
! 355: * (used to handle NaN and Inf)
! 356: *
! 357: IF( .NOT.(ABS( W( IMAX, KW-1 ) ).LT.ALPHA*ROWMAX ) )
! 358: $ THEN
! 359: *
! 360: * interchange rows and columns K and IMAX,
! 361: * use 1-by-1 pivot block
! 362: *
! 363: KP = IMAX
! 364: *
! 365: * copy column KW-1 of W to column KW of W
! 366: *
! 367: CALL DCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 )
! 368: *
! 369: DONE = .TRUE.
! 370: *
! 371: * Equivalent to testing for ROWMAX.EQ.COLMAX,
! 372: * (used to handle NaN and Inf)
! 373: *
! 374: ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
! 375: $ THEN
! 376: *
! 377: * interchange rows and columns K-1 and IMAX,
! 378: * use 2-by-2 pivot block
! 379: *
! 380: KP = IMAX
! 381: KSTEP = 2
! 382: DONE = .TRUE.
! 383: ELSE
! 384: *
! 385: * Pivot not found: set params and repeat
! 386: *
! 387: P = IMAX
! 388: COLMAX = ROWMAX
! 389: IMAX = JMAX
! 390: *
! 391: * Copy updated JMAXth (next IMAXth) column to Kth of W
! 392: *
! 393: CALL DCOPY( K, W( 1, KW-1 ), 1, W( 1, KW ), 1 )
! 394: *
! 395: END IF
! 396: *
! 397: * End pivot search loop body
! 398: *
! 399: IF( .NOT. DONE ) GOTO 12
! 400: *
! 401: END IF
! 402: *
! 403: * ============================================================
! 404: *
! 405: KK = K - KSTEP + 1
! 406: *
! 407: * KKW is the column of W which corresponds to column KK of A
! 408: *
! 409: KKW = NB + KK - N
! 410: *
! 411: IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
! 412: *
! 413: * Copy non-updated column K to column P
! 414: *
! 415: CALL DCOPY( K-P, A( P+1, K ), 1, A( P, P+1 ), LDA )
! 416: CALL DCOPY( P, A( 1, K ), 1, A( 1, P ), 1 )
! 417: *
! 418: * Interchange rows K and P in last N-K+1 columns of A
! 419: * and last N-K+2 columns of W
! 420: *
! 421: CALL DSWAP( N-K+1, A( K, K ), LDA, A( P, K ), LDA )
! 422: CALL DSWAP( N-KK+1, W( K, KKW ), LDW, W( P, KKW ), LDW )
! 423: END IF
! 424: *
! 425: * Updated column KP is already stored in column KKW of W
! 426: *
! 427: IF( KP.NE.KK ) THEN
! 428: *
! 429: * Copy non-updated column KK to column KP
! 430: *
! 431: A( KP, K ) = A( KK, K )
! 432: CALL DCOPY( K-1-KP, A( KP+1, KK ), 1, A( KP, KP+1 ),
! 433: $ LDA )
! 434: CALL DCOPY( KP, A( 1, KK ), 1, A( 1, KP ), 1 )
! 435: *
! 436: * Interchange rows KK and KP in last N-KK+1 columns
! 437: * of A and W
! 438: *
! 439: CALL DSWAP( N-KK+1, A( KK, KK ), LDA, A( KP, KK ), LDA )
! 440: CALL DSWAP( N-KK+1, W( KK, KKW ), LDW, W( KP, KKW ),
! 441: $ LDW )
! 442: END IF
! 443: *
! 444: IF( KSTEP.EQ.1 ) THEN
! 445: *
! 446: * 1-by-1 pivot block D(k): column KW of W now holds
! 447: *
! 448: * W(k) = U(k)*D(k)
! 449: *
! 450: * where U(k) is the k-th column of U
! 451: *
! 452: * Store U(k) in column k of A
! 453: *
! 454: CALL DCOPY( K, W( 1, KW ), 1, A( 1, K ), 1 )
! 455: IF( K.GT.1 ) THEN
! 456: IF( ABS( A( K, K ) ).GE.SFMIN ) THEN
! 457: R1 = ONE / A( K, K )
! 458: CALL DSCAL( K-1, R1, A( 1, K ), 1 )
! 459: ELSE IF( A( K, K ).NE.ZERO ) THEN
! 460: DO 14 II = 1, K - 1
! 461: A( II, K ) = A( II, K ) / A( K, K )
! 462: 14 CONTINUE
! 463: END IF
! 464: END IF
! 465: *
! 466: ELSE
! 467: *
! 468: * 2-by-2 pivot block D(k): columns KW and KW-1 of W now
! 469: * hold
! 470: *
! 471: * ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
! 472: *
! 473: * where U(k) and U(k-1) are the k-th and (k-1)-th columns
! 474: * of U
! 475: *
! 476: IF( K.GT.2 ) THEN
! 477: *
! 478: * Store U(k) and U(k-1) in columns k and k-1 of A
! 479: *
! 480: D12 = W( K-1, KW )
! 481: D11 = W( K, KW ) / D12
! 482: D22 = W( K-1, KW-1 ) / D12
! 483: T = ONE / ( D11*D22-ONE )
! 484: DO 20 J = 1, K - 2
! 485: A( J, K-1 ) = T*( (D11*W( J, KW-1 )-W( J, KW ) ) /
! 486: $ D12 )
! 487: A( J, K ) = T*( ( D22*W( J, KW )-W( J, KW-1 ) ) /
! 488: $ D12 )
! 489: 20 CONTINUE
! 490: END IF
! 491: *
! 492: * Copy D(k) to A
! 493: *
! 494: A( K-1, K-1 ) = W( K-1, KW-1 )
! 495: A( K-1, K ) = W( K-1, KW )
! 496: A( K, K ) = W( K, KW )
! 497: END IF
! 498: END IF
! 499: *
! 500: * Store details of the interchanges in IPIV
! 501: *
! 502: IF( KSTEP.EQ.1 ) THEN
! 503: IPIV( K ) = KP
! 504: ELSE
! 505: IPIV( K ) = -P
! 506: IPIV( K-1 ) = -KP
! 507: END IF
! 508: *
! 509: * Decrease K and return to the start of the main loop
! 510: *
! 511: K = K - KSTEP
! 512: GO TO 10
! 513: *
! 514: 30 CONTINUE
! 515: *
! 516: * Update the upper triangle of A11 (= A(1:k,1:k)) as
! 517: *
! 518: * A11 := A11 - U12*D*U12**T = A11 - U12*W**T
! 519: *
! 520: * computing blocks of NB columns at a time
! 521: *
! 522: DO 50 J = ( ( K-1 ) / NB )*NB + 1, 1, -NB
! 523: JB = MIN( NB, K-J+1 )
! 524: *
! 525: * Update the upper triangle of the diagonal block
! 526: *
! 527: DO 40 JJ = J, J + JB - 1
! 528: CALL DGEMV( 'No transpose', JJ-J+1, N-K, -ONE,
! 529: $ A( J, K+1 ), LDA, W( JJ, KW+1 ), LDW, ONE,
! 530: $ A( J, JJ ), 1 )
! 531: 40 CONTINUE
! 532: *
! 533: * Update the rectangular superdiagonal block
! 534: *
! 535: IF( J.GE.2 )
! 536: $ CALL DGEMM( 'No transpose', 'Transpose', J-1, JB,
! 537: $ N-K, -ONE, A( 1, K+1 ), LDA, W( J, KW+1 ), LDW,
! 538: $ ONE, A( 1, J ), LDA )
! 539: 50 CONTINUE
! 540: *
! 541: * Put U12 in standard form by partially undoing the interchanges
! 542: * in columns k+1:n
! 543: *
! 544: J = K + 1
! 545: 60 CONTINUE
! 546: *
! 547: KSTEP = 1
! 548: JP1 = 1
! 549: JJ = J
! 550: JP2 = IPIV( J )
! 551: IF( JP2.LT.0 ) THEN
! 552: JP2 = -JP2
! 553: J = J + 1
! 554: JP1 = -IPIV( J )
! 555: KSTEP = 2
! 556: END IF
! 557: *
! 558: J = J + 1
! 559: IF( JP2.NE.JJ .AND. J.LE.N )
! 560: $ CALL DSWAP( N-J+1, A( JP2, J ), LDA, A( JJ, J ), LDA )
! 561: JJ = J - 1
! 562: IF( JP1.NE.JJ .AND. KSTEP.EQ.2 )
! 563: $ CALL DSWAP( N-J+1, A( JP1, J ), LDA, A( JJ, J ), LDA )
! 564: IF( J.LE.N )
! 565: $ GO TO 60
! 566: *
! 567: * Set KB to the number of columns factorized
! 568: *
! 569: KB = N - K
! 570: *
! 571: ELSE
! 572: *
! 573: * Factorize the leading columns of A using the lower triangle
! 574: * of A and working forwards, and compute the matrix W = L21*D
! 575: * for use in updating A22
! 576: *
! 577: * K is the main loop index, increasing from 1 in steps of 1 or 2
! 578: *
! 579: K = 1
! 580: 70 CONTINUE
! 581: *
! 582: * Exit from loop
! 583: *
! 584: IF( ( K.GE.NB .AND. NB.LT.N ) .OR. K.GT.N )
! 585: $ GO TO 90
! 586: *
! 587: KSTEP = 1
! 588: P = K
! 589: *
! 590: * Copy column K of A to column K of W and update it
! 591: *
! 592: CALL DCOPY( N-K+1, A( K, K ), 1, W( K, K ), 1 )
! 593: IF( K.GT.1 )
! 594: $ CALL DGEMV( 'No transpose', N-K+1, K-1, -ONE, A( K, 1 ),
! 595: $ LDA, W( K, 1 ), LDW, ONE, W( K, K ), 1 )
! 596: *
! 597: * Determine rows and columns to be interchanged and whether
! 598: * a 1-by-1 or 2-by-2 pivot block will be used
! 599: *
! 600: ABSAKK = ABS( W( K, K ) )
! 601: *
! 602: * IMAX is the row-index of the largest off-diagonal element in
! 603: * column K, and COLMAX is its absolute value.
! 604: * Determine both COLMAX and IMAX.
! 605: *
! 606: IF( K.LT.N ) THEN
! 607: IMAX = K + IDAMAX( N-K, W( K+1, K ), 1 )
! 608: COLMAX = ABS( W( IMAX, K ) )
! 609: ELSE
! 610: COLMAX = ZERO
! 611: END IF
! 612: *
! 613: IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
! 614: *
! 615: * Column K is zero or underflow: set INFO and continue
! 616: *
! 617: IF( INFO.EQ.0 )
! 618: $ INFO = K
! 619: KP = K
! 620: CALL DCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
! 621: ELSE
! 622: *
! 623: * ============================================================
! 624: *
! 625: * Test for interchange
! 626: *
! 627: * Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
! 628: * (used to handle NaN and Inf)
! 629: *
! 630: IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
! 631: *
! 632: * no interchange, use 1-by-1 pivot block
! 633: *
! 634: KP = K
! 635: *
! 636: ELSE
! 637: *
! 638: DONE = .FALSE.
! 639: *
! 640: * Loop until pivot found
! 641: *
! 642: 72 CONTINUE
! 643: *
! 644: * Begin pivot search loop body
! 645: *
! 646: *
! 647: * Copy column IMAX to column K+1 of W and update it
! 648: *
! 649: CALL DCOPY( IMAX-K, A( IMAX, K ), LDA, W( K, K+1 ), 1)
! 650: CALL DCOPY( N-IMAX+1, A( IMAX, IMAX ), 1,
! 651: $ W( IMAX, K+1 ), 1 )
! 652: IF( K.GT.1 )
! 653: $ CALL DGEMV( 'No transpose', N-K+1, K-1, -ONE,
! 654: $ A( K, 1 ), LDA, W( IMAX, 1 ), LDW,
! 655: $ ONE, W( K, K+1 ), 1 )
! 656: *
! 657: * JMAX is the column-index of the largest off-diagonal
! 658: * element in row IMAX, and ROWMAX is its absolute value.
! 659: * Determine both ROWMAX and JMAX.
! 660: *
! 661: IF( IMAX.NE.K ) THEN
! 662: JMAX = K - 1 + IDAMAX( IMAX-K, W( K, K+1 ), 1 )
! 663: ROWMAX = ABS( W( JMAX, K+1 ) )
! 664: ELSE
! 665: ROWMAX = ZERO
! 666: END IF
! 667: *
! 668: IF( IMAX.LT.N ) THEN
! 669: ITEMP = IMAX + IDAMAX( N-IMAX, W( IMAX+1, K+1 ), 1)
! 670: DTEMP = ABS( W( ITEMP, K+1 ) )
! 671: IF( DTEMP.GT.ROWMAX ) THEN
! 672: ROWMAX = DTEMP
! 673: JMAX = ITEMP
! 674: END IF
! 675: END IF
! 676: *
! 677: * Equivalent to testing for
! 678: * ABS( W( IMAX, K+1 ) ).GE.ALPHA*ROWMAX
! 679: * (used to handle NaN and Inf)
! 680: *
! 681: IF( .NOT.( ABS( W( IMAX, K+1 ) ).LT.ALPHA*ROWMAX ) )
! 682: $ THEN
! 683: *
! 684: * interchange rows and columns K and IMAX,
! 685: * use 1-by-1 pivot block
! 686: *
! 687: KP = IMAX
! 688: *
! 689: * copy column K+1 of W to column K of W
! 690: *
! 691: CALL DCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
! 692: *
! 693: DONE = .TRUE.
! 694: *
! 695: * Equivalent to testing for ROWMAX.EQ.COLMAX,
! 696: * (used to handle NaN and Inf)
! 697: *
! 698: ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
! 699: $ THEN
! 700: *
! 701: * interchange rows and columns K+1 and IMAX,
! 702: * use 2-by-2 pivot block
! 703: *
! 704: KP = IMAX
! 705: KSTEP = 2
! 706: DONE = .TRUE.
! 707: ELSE
! 708: *
! 709: * Pivot not found: set params and repeat
! 710: *
! 711: P = IMAX
! 712: COLMAX = ROWMAX
! 713: IMAX = JMAX
! 714: *
! 715: * Copy updated JMAXth (next IMAXth) column to Kth of W
! 716: *
! 717: CALL DCOPY( N-K+1, W( K, K+1 ), 1, W( K, K ), 1 )
! 718: *
! 719: END IF
! 720: *
! 721: * End pivot search loop body
! 722: *
! 723: IF( .NOT. DONE ) GOTO 72
! 724: *
! 725: END IF
! 726: *
! 727: * ============================================================
! 728: *
! 729: KK = K + KSTEP - 1
! 730: *
! 731: IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
! 732: *
! 733: * Copy non-updated column K to column P
! 734: *
! 735: CALL DCOPY( P-K, A( K, K ), 1, A( P, K ), LDA )
! 736: CALL DCOPY( N-P+1, A( P, K ), 1, A( P, P ), 1 )
! 737: *
! 738: * Interchange rows K and P in first K columns of A
! 739: * and first K+1 columns of W
! 740: *
! 741: CALL DSWAP( K, A( K, 1 ), LDA, A( P, 1 ), LDA )
! 742: CALL DSWAP( KK, W( K, 1 ), LDW, W( P, 1 ), LDW )
! 743: END IF
! 744: *
! 745: * Updated column KP is already stored in column KK of W
! 746: *
! 747: IF( KP.NE.KK ) THEN
! 748: *
! 749: * Copy non-updated column KK to column KP
! 750: *
! 751: A( KP, K ) = A( KK, K )
! 752: CALL DCOPY( KP-K-1, A( K+1, KK ), 1, A( KP, K+1 ), LDA )
! 753: CALL DCOPY( N-KP+1, A( KP, KK ), 1, A( KP, KP ), 1 )
! 754: *
! 755: * Interchange rows KK and KP in first KK columns of A and W
! 756: *
! 757: CALL DSWAP( KK, A( KK, 1 ), LDA, A( KP, 1 ), LDA )
! 758: CALL DSWAP( KK, W( KK, 1 ), LDW, W( KP, 1 ), LDW )
! 759: END IF
! 760: *
! 761: IF( KSTEP.EQ.1 ) THEN
! 762: *
! 763: * 1-by-1 pivot block D(k): column k of W now holds
! 764: *
! 765: * W(k) = L(k)*D(k)
! 766: *
! 767: * where L(k) is the k-th column of L
! 768: *
! 769: * Store L(k) in column k of A
! 770: *
! 771: CALL DCOPY( N-K+1, W( K, K ), 1, A( K, K ), 1 )
! 772: IF( K.LT.N ) THEN
! 773: IF( ABS( A( K, K ) ).GE.SFMIN ) THEN
! 774: R1 = ONE / A( K, K )
! 775: CALL DSCAL( N-K, R1, A( K+1, K ), 1 )
! 776: ELSE IF( A( K, K ).NE.ZERO ) THEN
! 777: DO 74 II = K + 1, N
! 778: A( II, K ) = A( II, K ) / A( K, K )
! 779: 74 CONTINUE
! 780: END IF
! 781: END IF
! 782: *
! 783: ELSE
! 784: *
! 785: * 2-by-2 pivot block D(k): columns k and k+1 of W now hold
! 786: *
! 787: * ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
! 788: *
! 789: * where L(k) and L(k+1) are the k-th and (k+1)-th columns
! 790: * of L
! 791: *
! 792: IF( K.LT.N-1 ) THEN
! 793: *
! 794: * Store L(k) and L(k+1) in columns k and k+1 of A
! 795: *
! 796: D21 = W( K+1, K )
! 797: D11 = W( K+1, K+1 ) / D21
! 798: D22 = W( K, K ) / D21
! 799: T = ONE / ( D11*D22-ONE )
! 800: DO 80 J = K + 2, N
! 801: A( J, K ) = T*( ( D11*W( J, K )-W( J, K+1 ) ) /
! 802: $ D21 )
! 803: A( J, K+1 ) = T*( ( D22*W( J, K+1 )-W( J, K ) ) /
! 804: $ D21 )
! 805: 80 CONTINUE
! 806: END IF
! 807: *
! 808: * Copy D(k) to A
! 809: *
! 810: A( K, K ) = W( K, K )
! 811: A( K+1, K ) = W( K+1, K )
! 812: A( K+1, K+1 ) = W( K+1, K+1 )
! 813: END IF
! 814: END IF
! 815: *
! 816: * Store details of the interchanges in IPIV
! 817: *
! 818: IF( KSTEP.EQ.1 ) THEN
! 819: IPIV( K ) = KP
! 820: ELSE
! 821: IPIV( K ) = -P
! 822: IPIV( K+1 ) = -KP
! 823: END IF
! 824: *
! 825: * Increase K and return to the start of the main loop
! 826: *
! 827: K = K + KSTEP
! 828: GO TO 70
! 829: *
! 830: 90 CONTINUE
! 831: *
! 832: * Update the lower triangle of A22 (= A(k:n,k:n)) as
! 833: *
! 834: * A22 := A22 - L21*D*L21**T = A22 - L21*W**T
! 835: *
! 836: * computing blocks of NB columns at a time
! 837: *
! 838: DO 110 J = K, N, NB
! 839: JB = MIN( NB, N-J+1 )
! 840: *
! 841: * Update the lower triangle of the diagonal block
! 842: *
! 843: DO 100 JJ = J, J + JB - 1
! 844: CALL DGEMV( 'No transpose', J+JB-JJ, K-1, -ONE,
! 845: $ A( JJ, 1 ), LDA, W( JJ, 1 ), LDW, ONE,
! 846: $ A( JJ, JJ ), 1 )
! 847: 100 CONTINUE
! 848: *
! 849: * Update the rectangular subdiagonal block
! 850: *
! 851: IF( J+JB.LE.N )
! 852: $ CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB,
! 853: $ K-1, -ONE, A( J+JB, 1 ), LDA, W( J, 1 ), LDW,
! 854: $ ONE, A( J+JB, J ), LDA )
! 855: 110 CONTINUE
! 856: *
! 857: * Put L21 in standard form by partially undoing the interchanges
! 858: * in columns 1:k-1
! 859: *
! 860: J = K - 1
! 861: 120 CONTINUE
! 862: *
! 863: KSTEP = 1
! 864: JP1 = 1
! 865: JJ = J
! 866: JP2 = IPIV( J )
! 867: IF( JP2.LT.0 ) THEN
! 868: JP2 = -JP2
! 869: J = J - 1
! 870: JP1 = -IPIV( J )
! 871: KSTEP = 2
! 872: END IF
! 873: *
! 874: J = J - 1
! 875: IF( JP2.NE.JJ .AND. J.GE.1 )
! 876: $ CALL DSWAP( J, A( JP2, 1 ), LDA, A( JJ, 1 ), LDA )
! 877: JJ = J + 1
! 878: IF( JP1.NE.JJ .AND. KSTEP.EQ.2 )
! 879: $ CALL DSWAP( J, A( JP1, 1 ), LDA, A( JJ, 1 ), LDA )
! 880: IF( J.GE.1 )
! 881: $ GO TO 120
! 882: *
! 883: * Set KB to the number of columns factorized
! 884: *
! 885: KB = K - 1
! 886: *
! 887: END IF
! 888: RETURN
! 889: *
! 890: * End of DLASYF_ROOK
! 891: *
! 892: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dlasyf_rook.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack