Annotation of rpl/lapack/lapack/zsytf2_rook.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZSYTF2_ROOK computes the factorization of a complex symmetric indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm).
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZSYTF2_ROOK + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytf2_rook.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytf2_rook.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytf2_rook.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZSYTF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, LDA, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * INTEGER IPIV( * )
! 29: * COMPLEX*16 A( LDA, * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> ZSYTF2_ROOK computes the factorization of a complex symmetric matrix A
! 39: *> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:
! 40: *>
! 41: *> A = U*D*U**T or A = L*D*L**T
! 42: *>
! 43: *> where U (or L) is a product of permutation and unit upper (lower)
! 44: *> triangular matrices, U**T is the transpose of U, and D is symmetric and
! 45: *> block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
! 46: *>
! 47: *> This is the unblocked version of the algorithm, calling Level 2 BLAS.
! 48: *> \endverbatim
! 49: *
! 50: * Arguments:
! 51: * ==========
! 52: *
! 53: *> \param[in] UPLO
! 54: *> \verbatim
! 55: *> UPLO is CHARACTER*1
! 56: *> Specifies whether the upper or lower triangular part of the
! 57: *> symmetric matrix A is stored:
! 58: *> = 'U': Upper triangular
! 59: *> = 'L': Lower triangular
! 60: *> \endverbatim
! 61: *>
! 62: *> \param[in] N
! 63: *> \verbatim
! 64: *> N is INTEGER
! 65: *> The order of the matrix A. N >= 0.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in,out] A
! 69: *> \verbatim
! 70: *> A is COMPLEX*16 array, dimension (LDA,N)
! 71: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
! 72: *> n-by-n upper triangular part of A contains the upper
! 73: *> triangular part of the matrix A, and the strictly lower
! 74: *> triangular part of A is not referenced. If UPLO = 'L', the
! 75: *> leading n-by-n lower triangular part of A contains the lower
! 76: *> triangular part of the matrix A, and the strictly upper
! 77: *> triangular part of A is not referenced.
! 78: *>
! 79: *> On exit, the block diagonal matrix D and the multipliers used
! 80: *> to obtain the factor U or L (see below for further details).
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in] LDA
! 84: *> \verbatim
! 85: *> LDA is INTEGER
! 86: *> The leading dimension of the array A. LDA >= max(1,N).
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[out] IPIV
! 90: *> \verbatim
! 91: *> IPIV is INTEGER array, dimension (N)
! 92: *> Details of the interchanges and the block structure of D.
! 93: *>
! 94: *> If UPLO = 'U':
! 95: *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
! 96: *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
! 97: *>
! 98: *> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
! 99: *> columns k and -IPIV(k) were interchanged and rows and
! 100: *> columns k-1 and -IPIV(k-1) were inerchaged,
! 101: *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
! 102: *>
! 103: *> If UPLO = 'L':
! 104: *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
! 105: *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
! 106: *>
! 107: *> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
! 108: *> columns k and -IPIV(k) were interchanged and rows and
! 109: *> columns k+1 and -IPIV(k+1) were inerchaged,
! 110: *> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
! 111: *> \endverbatim
! 112: *>
! 113: *> \param[out] INFO
! 114: *> \verbatim
! 115: *> INFO is INTEGER
! 116: *> = 0: successful exit
! 117: *> < 0: if INFO = -k, the k-th argument had an illegal value
! 118: *> > 0: if INFO = k, D(k,k) is exactly zero. The factorization
! 119: *> has been completed, but the block diagonal matrix D is
! 120: *> exactly singular, and division by zero will occur if it
! 121: *> is used to solve a system of equations.
! 122: *> \endverbatim
! 123: *
! 124: * Authors:
! 125: * ========
! 126: *
! 127: *> \author Univ. of Tennessee
! 128: *> \author Univ. of California Berkeley
! 129: *> \author Univ. of Colorado Denver
! 130: *> \author NAG Ltd.
! 131: *
! 132: *> \date November 2013
! 133: *
! 134: *> \ingroup complex16SYcomputational
! 135: *
! 136: *> \par Further Details:
! 137: * =====================
! 138: *>
! 139: *> \verbatim
! 140: *>
! 141: *> If UPLO = 'U', then A = U*D*U**T, where
! 142: *> U = P(n)*U(n)* ... *P(k)U(k)* ...,
! 143: *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
! 144: *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
! 145: *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
! 146: *> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
! 147: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 148: *>
! 149: *> ( I v 0 ) k-s
! 150: *> U(k) = ( 0 I 0 ) s
! 151: *> ( 0 0 I ) n-k
! 152: *> k-s s n-k
! 153: *>
! 154: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
! 155: *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
! 156: *> and A(k,k), and v overwrites A(1:k-2,k-1:k).
! 157: *>
! 158: *> If UPLO = 'L', then A = L*D*L**T, where
! 159: *> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
! 160: *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
! 161: *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
! 162: *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
! 163: *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
! 164: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 165: *>
! 166: *> ( I 0 0 ) k-1
! 167: *> L(k) = ( 0 I 0 ) s
! 168: *> ( 0 v I ) n-k-s+1
! 169: *> k-1 s n-k-s+1
! 170: *>
! 171: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
! 172: *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
! 173: *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
! 174: *> \endverbatim
! 175: *
! 176: *> \par Contributors:
! 177: * ==================
! 178: *>
! 179: *> \verbatim
! 180: *>
! 181: *> November 2013, Igor Kozachenko,
! 182: *> Computer Science Division,
! 183: *> University of California, Berkeley
! 184: *>
! 185: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
! 186: *> School of Mathematics,
! 187: *> University of Manchester
! 188: *>
! 189: *> 01-01-96 - Based on modifications by
! 190: *> J. Lewis, Boeing Computer Services Company
! 191: *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville abd , USA
! 192: *> \endverbatim
! 193: *
! 194: * =====================================================================
! 195: SUBROUTINE ZSYTF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
! 196: *
! 197: * -- LAPACK computational routine (version 3.5.0) --
! 198: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 199: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 200: * November 2013
! 201: *
! 202: * .. Scalar Arguments ..
! 203: CHARACTER UPLO
! 204: INTEGER INFO, LDA, N
! 205: * ..
! 206: * .. Array Arguments ..
! 207: INTEGER IPIV( * )
! 208: COMPLEX*16 A( LDA, * )
! 209: * ..
! 210: *
! 211: * =====================================================================
! 212: *
! 213: * .. Parameters ..
! 214: DOUBLE PRECISION ZERO, ONE
! 215: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 216: DOUBLE PRECISION EIGHT, SEVTEN
! 217: PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
! 218: COMPLEX*16 CONE
! 219: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
! 220: * ..
! 221: * .. Local Scalars ..
! 222: LOGICAL UPPER, DONE
! 223: INTEGER I, IMAX, J, JMAX, ITEMP, K, KK, KP, KSTEP,
! 224: $ P, II
! 225: DOUBLE PRECISION ABSAKK, ALPHA, COLMAX, ROWMAX, DTEMP, SFMIN
! 226: COMPLEX*16 D11, D12, D21, D22, T, WK, WKM1, WKP1, Z
! 227: * ..
! 228: * .. External Functions ..
! 229: LOGICAL LSAME
! 230: INTEGER IZAMAX
! 231: DOUBLE PRECISION DLAMCH
! 232: EXTERNAL LSAME, IZAMAX, DLAMCH
! 233: * ..
! 234: * .. External Subroutines ..
! 235: EXTERNAL ZSCAL, ZSWAP, ZSYR, XERBLA
! 236: * ..
! 237: * .. Intrinsic Functions ..
! 238: INTRINSIC ABS, MAX, SQRT, DIMAG, DBLE
! 239: * ..
! 240: * .. Statement Functions ..
! 241: DOUBLE PRECISION CABS1
! 242: * ..
! 243: * .. Statement Function definitions ..
! 244: CABS1( Z ) = ABS( DBLE( Z ) ) + ABS( DIMAG( Z ) )
! 245: * ..
! 246: * .. Executable Statements ..
! 247: *
! 248: * Test the input parameters.
! 249: *
! 250: INFO = 0
! 251: UPPER = LSAME( UPLO, 'U' )
! 252: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 253: INFO = -1
! 254: ELSE IF( N.LT.0 ) THEN
! 255: INFO = -2
! 256: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 257: INFO = -4
! 258: END IF
! 259: IF( INFO.NE.0 ) THEN
! 260: CALL XERBLA( 'ZSYTF2_ROOK', -INFO )
! 261: RETURN
! 262: END IF
! 263: *
! 264: * Initialize ALPHA for use in choosing pivot block size.
! 265: *
! 266: ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
! 267: *
! 268: * Compute machine safe minimum
! 269: *
! 270: SFMIN = DLAMCH( 'S' )
! 271: *
! 272: IF( UPPER ) THEN
! 273: *
! 274: * Factorize A as U*D*U**T using the upper triangle of A
! 275: *
! 276: * K is the main loop index, decreasing from N to 1 in steps of
! 277: * 1 or 2
! 278: *
! 279: K = N
! 280: 10 CONTINUE
! 281: *
! 282: * If K < 1, exit from loop
! 283: *
! 284: IF( K.LT.1 )
! 285: $ GO TO 70
! 286: KSTEP = 1
! 287: P = K
! 288: *
! 289: * Determine rows and columns to be interchanged and whether
! 290: * a 1-by-1 or 2-by-2 pivot block will be used
! 291: *
! 292: ABSAKK = CABS1( A( K, K ) )
! 293: *
! 294: * IMAX is the row-index of the largest off-diagonal element in
! 295: * column K, and COLMAX is its absolute value.
! 296: * Determine both COLMAX and IMAX.
! 297: *
! 298: IF( K.GT.1 ) THEN
! 299: IMAX = IZAMAX( K-1, A( 1, K ), 1 )
! 300: COLMAX = CABS1( A( IMAX, K ) )
! 301: ELSE
! 302: COLMAX = ZERO
! 303: END IF
! 304: *
! 305: IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) ) THEN
! 306: *
! 307: * Column K is zero or underflow: set INFO and continue
! 308: *
! 309: IF( INFO.EQ.0 )
! 310: $ INFO = K
! 311: KP = K
! 312: ELSE
! 313: *
! 314: * Test for interchange
! 315: *
! 316: * Equivalent to testing for (used to handle NaN and Inf)
! 317: * ABSAKK.GE.ALPHA*COLMAX
! 318: *
! 319: IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
! 320: *
! 321: * no interchange,
! 322: * use 1-by-1 pivot block
! 323: *
! 324: KP = K
! 325: ELSE
! 326: *
! 327: DONE = .FALSE.
! 328: *
! 329: * Loop until pivot found
! 330: *
! 331: 12 CONTINUE
! 332: *
! 333: * Begin pivot search loop body
! 334: *
! 335: * JMAX is the column-index of the largest off-diagonal
! 336: * element in row IMAX, and ROWMAX is its absolute value.
! 337: * Determine both ROWMAX and JMAX.
! 338: *
! 339: IF( IMAX.NE.K ) THEN
! 340: JMAX = IMAX + IZAMAX( K-IMAX, A( IMAX, IMAX+1 ),
! 341: $ LDA )
! 342: ROWMAX = CABS1( A( IMAX, JMAX ) )
! 343: ELSE
! 344: ROWMAX = ZERO
! 345: END IF
! 346: *
! 347: IF( IMAX.GT.1 ) THEN
! 348: ITEMP = IZAMAX( IMAX-1, A( 1, IMAX ), 1 )
! 349: DTEMP = CABS1( A( ITEMP, IMAX ) )
! 350: IF( DTEMP.GT.ROWMAX ) THEN
! 351: ROWMAX = DTEMP
! 352: JMAX = ITEMP
! 353: END IF
! 354: END IF
! 355: *
! 356: * Equivalent to testing for (used to handle NaN and Inf)
! 357: * CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX
! 358: *
! 359: IF( .NOT.( CABS1(A( IMAX, IMAX )).LT.ALPHA*ROWMAX ) )
! 360: $ THEN
! 361: *
! 362: * interchange rows and columns K and IMAX,
! 363: * use 1-by-1 pivot block
! 364: *
! 365: KP = IMAX
! 366: DONE = .TRUE.
! 367: *
! 368: * Equivalent to testing for ROWMAX .EQ. COLMAX,
! 369: * used to handle NaN and Inf
! 370: *
! 371: ELSE IF( ( P.EQ.JMAX ).OR.( ROWMAX.LE.COLMAX ) ) THEN
! 372: *
! 373: * interchange rows and columns K+1 and IMAX,
! 374: * use 2-by-2 pivot block
! 375: *
! 376: KP = IMAX
! 377: KSTEP = 2
! 378: DONE = .TRUE.
! 379: ELSE
! 380: *
! 381: * Pivot NOT found, set variables and repeat
! 382: *
! 383: P = IMAX
! 384: COLMAX = ROWMAX
! 385: IMAX = JMAX
! 386: END IF
! 387: *
! 388: * End pivot search loop body
! 389: *
! 390: IF( .NOT. DONE ) GOTO 12
! 391: *
! 392: END IF
! 393: *
! 394: * Swap TWO rows and TWO columns
! 395: *
! 396: * First swap
! 397: *
! 398: IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
! 399: *
! 400: * Interchange rows and column K and P in the leading
! 401: * submatrix A(1:k,1:k) if we have a 2-by-2 pivot
! 402: *
! 403: IF( P.GT.1 )
! 404: $ CALL ZSWAP( P-1, A( 1, K ), 1, A( 1, P ), 1 )
! 405: IF( P.LT.(K-1) )
! 406: $ CALL ZSWAP( K-P-1, A( P+1, K ), 1, A( P, P+1 ),
! 407: $ LDA )
! 408: T = A( K, K )
! 409: A( K, K ) = A( P, P )
! 410: A( P, P ) = T
! 411: END IF
! 412: *
! 413: * Second swap
! 414: *
! 415: KK = K - KSTEP + 1
! 416: IF( KP.NE.KK ) THEN
! 417: *
! 418: * Interchange rows and columns KK and KP in the leading
! 419: * submatrix A(1:k,1:k)
! 420: *
! 421: IF( KP.GT.1 )
! 422: $ CALL ZSWAP( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
! 423: IF( ( KK.GT.1 ) .AND. ( KP.LT.(KK-1) ) )
! 424: $ CALL ZSWAP( KK-KP-1, A( KP+1, KK ), 1, A( KP, KP+1 ),
! 425: $ LDA )
! 426: T = A( KK, KK )
! 427: A( KK, KK ) = A( KP, KP )
! 428: A( KP, KP ) = T
! 429: IF( KSTEP.EQ.2 ) THEN
! 430: T = A( K-1, K )
! 431: A( K-1, K ) = A( KP, K )
! 432: A( KP, K ) = T
! 433: END IF
! 434: END IF
! 435: *
! 436: * Update the leading submatrix
! 437: *
! 438: IF( KSTEP.EQ.1 ) THEN
! 439: *
! 440: * 1-by-1 pivot block D(k): column k now holds
! 441: *
! 442: * W(k) = U(k)*D(k)
! 443: *
! 444: * where U(k) is the k-th column of U
! 445: *
! 446: IF( K.GT.1 ) THEN
! 447: *
! 448: * Perform a rank-1 update of A(1:k-1,1:k-1) and
! 449: * store U(k) in column k
! 450: *
! 451: IF( CABS1( A( K, K ) ).GE.SFMIN ) THEN
! 452: *
! 453: * Perform a rank-1 update of A(1:k-1,1:k-1) as
! 454: * A := A - U(k)*D(k)*U(k)**T
! 455: * = A - W(k)*1/D(k)*W(k)**T
! 456: *
! 457: D11 = CONE / A( K, K )
! 458: CALL ZSYR( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
! 459: *
! 460: * Store U(k) in column k
! 461: *
! 462: CALL ZSCAL( K-1, D11, A( 1, K ), 1 )
! 463: ELSE
! 464: *
! 465: * Store L(k) in column K
! 466: *
! 467: D11 = A( K, K )
! 468: DO 16 II = 1, K - 1
! 469: A( II, K ) = A( II, K ) / D11
! 470: 16 CONTINUE
! 471: *
! 472: * Perform a rank-1 update of A(k+1:n,k+1:n) as
! 473: * A := A - U(k)*D(k)*U(k)**T
! 474: * = A - W(k)*(1/D(k))*W(k)**T
! 475: * = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
! 476: *
! 477: CALL ZSYR( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
! 478: END IF
! 479: END IF
! 480: *
! 481: ELSE
! 482: *
! 483: * 2-by-2 pivot block D(k): columns k and k-1 now hold
! 484: *
! 485: * ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
! 486: *
! 487: * where U(k) and U(k-1) are the k-th and (k-1)-th columns
! 488: * of U
! 489: *
! 490: * Perform a rank-2 update of A(1:k-2,1:k-2) as
! 491: *
! 492: * A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
! 493: * = A - ( ( A(k-1)A(k) )*inv(D(k)) ) * ( A(k-1)A(k) )**T
! 494: *
! 495: * and store L(k) and L(k+1) in columns k and k+1
! 496: *
! 497: IF( K.GT.2 ) THEN
! 498: *
! 499: D12 = A( K-1, K )
! 500: D22 = A( K-1, K-1 ) / D12
! 501: D11 = A( K, K ) / D12
! 502: T = CONE / ( D11*D22-CONE )
! 503: *
! 504: DO 30 J = K - 2, 1, -1
! 505: *
! 506: WKM1 = T*( D11*A( J, K-1 )-A( J, K ) )
! 507: WK = T*( D22*A( J, K )-A( J, K-1 ) )
! 508: *
! 509: DO 20 I = J, 1, -1
! 510: A( I, J ) = A( I, J ) - (A( I, K ) / D12 )*WK -
! 511: $ ( A( I, K-1 ) / D12 )*WKM1
! 512: 20 CONTINUE
! 513: *
! 514: * Store U(k) and U(k-1) in cols k and k-1 for row J
! 515: *
! 516: A( J, K ) = WK / D12
! 517: A( J, K-1 ) = WKM1 / D12
! 518: *
! 519: 30 CONTINUE
! 520: *
! 521: END IF
! 522: *
! 523: END IF
! 524: END IF
! 525: *
! 526: * Store details of the interchanges in IPIV
! 527: *
! 528: IF( KSTEP.EQ.1 ) THEN
! 529: IPIV( K ) = KP
! 530: ELSE
! 531: IPIV( K ) = -P
! 532: IPIV( K-1 ) = -KP
! 533: END IF
! 534: *
! 535: * Decrease K and return to the start of the main loop
! 536: *
! 537: K = K - KSTEP
! 538: GO TO 10
! 539: *
! 540: ELSE
! 541: *
! 542: * Factorize A as L*D*L**T using the lower triangle of A
! 543: *
! 544: * K is the main loop index, increasing from 1 to N in steps of
! 545: * 1 or 2
! 546: *
! 547: K = 1
! 548: 40 CONTINUE
! 549: *
! 550: * If K > N, exit from loop
! 551: *
! 552: IF( K.GT.N )
! 553: $ GO TO 70
! 554: KSTEP = 1
! 555: P = K
! 556: *
! 557: * Determine rows and columns to be interchanged and whether
! 558: * a 1-by-1 or 2-by-2 pivot block will be used
! 559: *
! 560: ABSAKK = CABS1( A( K, K ) )
! 561: *
! 562: * IMAX is the row-index of the largest off-diagonal element in
! 563: * column K, and COLMAX is its absolute value.
! 564: * Determine both COLMAX and IMAX.
! 565: *
! 566: IF( K.LT.N ) THEN
! 567: IMAX = K + IZAMAX( N-K, A( K+1, K ), 1 )
! 568: COLMAX = CABS1( A( IMAX, K ) )
! 569: ELSE
! 570: COLMAX = ZERO
! 571: END IF
! 572: *
! 573: IF( ( MAX( ABSAKK, COLMAX ).EQ.ZERO ) ) THEN
! 574: *
! 575: * Column K is zero or underflow: set INFO and continue
! 576: *
! 577: IF( INFO.EQ.0 )
! 578: $ INFO = K
! 579: KP = K
! 580: ELSE
! 581: *
! 582: * Test for interchange
! 583: *
! 584: * Equivalent to testing for (used to handle NaN and Inf)
! 585: * ABSAKK.GE.ALPHA*COLMAX
! 586: *
! 587: IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
! 588: *
! 589: * no interchange, use 1-by-1 pivot block
! 590: *
! 591: KP = K
! 592: ELSE
! 593: *
! 594: DONE = .FALSE.
! 595: *
! 596: * Loop until pivot found
! 597: *
! 598: 42 CONTINUE
! 599: *
! 600: * Begin pivot search loop body
! 601: *
! 602: * JMAX is the column-index of the largest off-diagonal
! 603: * element in row IMAX, and ROWMAX is its absolute value.
! 604: * Determine both ROWMAX and JMAX.
! 605: *
! 606: IF( IMAX.NE.K ) THEN
! 607: JMAX = K - 1 + IZAMAX( IMAX-K, A( IMAX, K ), LDA )
! 608: ROWMAX = CABS1( A( IMAX, JMAX ) )
! 609: ELSE
! 610: ROWMAX = ZERO
! 611: END IF
! 612: *
! 613: IF( IMAX.LT.N ) THEN
! 614: ITEMP = IMAX + IZAMAX( N-IMAX, A( IMAX+1, IMAX ),
! 615: $ 1 )
! 616: DTEMP = CABS1( A( ITEMP, IMAX ) )
! 617: IF( DTEMP.GT.ROWMAX ) THEN
! 618: ROWMAX = DTEMP
! 619: JMAX = ITEMP
! 620: END IF
! 621: END IF
! 622: *
! 623: * Equivalent to testing for (used to handle NaN and Inf)
! 624: * CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX
! 625: *
! 626: IF( .NOT.( CABS1(A( IMAX, IMAX )).LT.ALPHA*ROWMAX ) )
! 627: $ THEN
! 628: *
! 629: * interchange rows and columns K and IMAX,
! 630: * use 1-by-1 pivot block
! 631: *
! 632: KP = IMAX
! 633: DONE = .TRUE.
! 634: *
! 635: * Equivalent to testing for ROWMAX .EQ. COLMAX,
! 636: * used to handle NaN and Inf
! 637: *
! 638: ELSE IF( ( P.EQ.JMAX ).OR.( ROWMAX.LE.COLMAX ) ) THEN
! 639: *
! 640: * interchange rows and columns K+1 and IMAX,
! 641: * use 2-by-2 pivot block
! 642: *
! 643: KP = IMAX
! 644: KSTEP = 2
! 645: DONE = .TRUE.
! 646: ELSE
! 647: *
! 648: * Pivot NOT found, set variables and repeat
! 649: *
! 650: P = IMAX
! 651: COLMAX = ROWMAX
! 652: IMAX = JMAX
! 653: END IF
! 654: *
! 655: * End pivot search loop body
! 656: *
! 657: IF( .NOT. DONE ) GOTO 42
! 658: *
! 659: END IF
! 660: *
! 661: * Swap TWO rows and TWO columns
! 662: *
! 663: * First swap
! 664: *
! 665: IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
! 666: *
! 667: * Interchange rows and column K and P in the trailing
! 668: * submatrix A(k:n,k:n) if we have a 2-by-2 pivot
! 669: *
! 670: IF( P.LT.N )
! 671: $ CALL ZSWAP( N-P, A( P+1, K ), 1, A( P+1, P ), 1 )
! 672: IF( P.GT.(K+1) )
! 673: $ CALL ZSWAP( P-K-1, A( K+1, K ), 1, A( P, K+1 ), LDA )
! 674: T = A( K, K )
! 675: A( K, K ) = A( P, P )
! 676: A( P, P ) = T
! 677: END IF
! 678: *
! 679: * Second swap
! 680: *
! 681: KK = K + KSTEP - 1
! 682: IF( KP.NE.KK ) THEN
! 683: *
! 684: * Interchange rows and columns KK and KP in the trailing
! 685: * submatrix A(k:n,k:n)
! 686: *
! 687: IF( KP.LT.N )
! 688: $ CALL ZSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
! 689: IF( ( KK.LT.N ) .AND. ( KP.GT.(KK+1) ) )
! 690: $ CALL ZSWAP( KP-KK-1, A( KK+1, KK ), 1, A( KP, KK+1 ),
! 691: $ LDA )
! 692: T = A( KK, KK )
! 693: A( KK, KK ) = A( KP, KP )
! 694: A( KP, KP ) = T
! 695: IF( KSTEP.EQ.2 ) THEN
! 696: T = A( K+1, K )
! 697: A( K+1, K ) = A( KP, K )
! 698: A( KP, K ) = T
! 699: END IF
! 700: END IF
! 701: *
! 702: * Update the trailing submatrix
! 703: *
! 704: IF( KSTEP.EQ.1 ) THEN
! 705: *
! 706: * 1-by-1 pivot block D(k): column k now holds
! 707: *
! 708: * W(k) = L(k)*D(k)
! 709: *
! 710: * where L(k) is the k-th column of L
! 711: *
! 712: IF( K.LT.N ) THEN
! 713: *
! 714: * Perform a rank-1 update of A(k+1:n,k+1:n) and
! 715: * store L(k) in column k
! 716: *
! 717: IF( CABS1( A( K, K ) ).GE.SFMIN ) THEN
! 718: *
! 719: * Perform a rank-1 update of A(k+1:n,k+1:n) as
! 720: * A := A - L(k)*D(k)*L(k)**T
! 721: * = A - W(k)*(1/D(k))*W(k)**T
! 722: *
! 723: D11 = CONE / A( K, K )
! 724: CALL ZSYR( UPLO, N-K, -D11, A( K+1, K ), 1,
! 725: $ A( K+1, K+1 ), LDA )
! 726: *
! 727: * Store L(k) in column k
! 728: *
! 729: CALL ZSCAL( N-K, D11, A( K+1, K ), 1 )
! 730: ELSE
! 731: *
! 732: * Store L(k) in column k
! 733: *
! 734: D11 = A( K, K )
! 735: DO 46 II = K + 1, N
! 736: A( II, K ) = A( II, K ) / D11
! 737: 46 CONTINUE
! 738: *
! 739: * Perform a rank-1 update of A(k+1:n,k+1:n) as
! 740: * A := A - L(k)*D(k)*L(k)**T
! 741: * = A - W(k)*(1/D(k))*W(k)**T
! 742: * = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
! 743: *
! 744: CALL ZSYR( UPLO, N-K, -D11, A( K+1, K ), 1,
! 745: $ A( K+1, K+1 ), LDA )
! 746: END IF
! 747: END IF
! 748: *
! 749: ELSE
! 750: *
! 751: * 2-by-2 pivot block D(k): columns k and k+1 now hold
! 752: *
! 753: * ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
! 754: *
! 755: * where L(k) and L(k+1) are the k-th and (k+1)-th columns
! 756: * of L
! 757: *
! 758: *
! 759: * Perform a rank-2 update of A(k+2:n,k+2:n) as
! 760: *
! 761: * A := A - ( L(k) L(k+1) ) * D(k) * ( L(k) L(k+1) )**T
! 762: * = A - ( ( A(k)A(k+1) )*inv(D(k) ) * ( A(k)A(k+1) )**T
! 763: *
! 764: * and store L(k) and L(k+1) in columns k and k+1
! 765: *
! 766: IF( K.LT.N-1 ) THEN
! 767: *
! 768: D21 = A( K+1, K )
! 769: D11 = A( K+1, K+1 ) / D21
! 770: D22 = A( K, K ) / D21
! 771: T = CONE / ( D11*D22-CONE )
! 772: *
! 773: DO 60 J = K + 2, N
! 774: *
! 775: * Compute D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J
! 776: *
! 777: WK = T*( D11*A( J, K )-A( J, K+1 ) )
! 778: WKP1 = T*( D22*A( J, K+1 )-A( J, K ) )
! 779: *
! 780: * Perform a rank-2 update of A(k+2:n,k+2:n)
! 781: *
! 782: DO 50 I = J, N
! 783: A( I, J ) = A( I, J ) - ( A( I, K ) / D21 )*WK -
! 784: $ ( A( I, K+1 ) / D21 )*WKP1
! 785: 50 CONTINUE
! 786: *
! 787: * Store L(k) and L(k+1) in cols k and k+1 for row J
! 788: *
! 789: A( J, K ) = WK / D21
! 790: A( J, K+1 ) = WKP1 / D21
! 791: *
! 792: 60 CONTINUE
! 793: *
! 794: END IF
! 795: *
! 796: END IF
! 797: END IF
! 798: *
! 799: * Store details of the interchanges in IPIV
! 800: *
! 801: IF( KSTEP.EQ.1 ) THEN
! 802: IPIV( K ) = KP
! 803: ELSE
! 804: IPIV( K ) = -P
! 805: IPIV( K+1 ) = -KP
! 806: END IF
! 807: *
! 808: * Increase K and return to the start of the main loop
! 809: *
! 810: K = K + KSTEP
! 811: GO TO 40
! 812: *
! 813: END IF
! 814: *
! 815: 70 CONTINUE
! 816: *
! 817: RETURN
! 818: *
! 819: * End of ZSYTF2_ROOK
! 820: *
! 821: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zsytf2_rook.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack