Annotation of rpl/lapack/lapack/zsytrf_rook.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZSYTRF_ROOK
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZSYTRF_ROOK + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytrf_rook.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytrf_rook.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytrf_rook.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, LDA, LWORK, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * INTEGER IPIV( * )
! 29: * COMPLEX*16 A( LDA, * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> ZSYTRF_ROOK computes the factorization of a complex symmetric matrix A
! 39: *> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
! 40: *> The form of the factorization is
! 41: *>
! 42: *> A = U*D*U**T or A = L*D*L**T
! 43: *>
! 44: *> where U (or L) is a product of permutation and unit upper (lower)
! 45: *> triangular matrices, and D is symmetric and block diagonal with
! 46: *> 1-by-1 and 2-by-2 diagonal blocks.
! 47: *>
! 48: *> This is the blocked version of the algorithm, calling Level 3 BLAS.
! 49: *> \endverbatim
! 50: *
! 51: * Arguments:
! 52: * ==========
! 53: *
! 54: *> \param[in] UPLO
! 55: *> \verbatim
! 56: *> UPLO is CHARACTER*1
! 57: *> = 'U': Upper triangle of A is stored;
! 58: *> = 'L': Lower triangle of A is stored.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] N
! 62: *> \verbatim
! 63: *> N is INTEGER
! 64: *> The order of the matrix A. N >= 0.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in,out] A
! 68: *> \verbatim
! 69: *> A is COMPLEX*16 array, dimension (LDA,N)
! 70: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
! 71: *> N-by-N upper triangular part of A contains the upper
! 72: *> triangular part of the matrix A, and the strictly lower
! 73: *> triangular part of A is not referenced. If UPLO = 'L', the
! 74: *> leading N-by-N lower triangular part of A contains the lower
! 75: *> triangular part of the matrix A, and the strictly upper
! 76: *> triangular part of A is not referenced.
! 77: *>
! 78: *> On exit, the block diagonal matrix D and the multipliers used
! 79: *> to obtain the factor U or L (see below for further details).
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] LDA
! 83: *> \verbatim
! 84: *> LDA is INTEGER
! 85: *> The leading dimension of the array A. LDA >= max(1,N).
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[out] IPIV
! 89: *> \verbatim
! 90: *> IPIV is INTEGER array, dimension (N)
! 91: *> Details of the interchanges and the block structure of D.
! 92: *>
! 93: *> If UPLO = 'U':
! 94: *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
! 95: *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
! 96: *>
! 97: *> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
! 98: *> columns k and -IPIV(k) were interchanged and rows and
! 99: *> columns k-1 and -IPIV(k-1) were inerchaged,
! 100: *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
! 101: *>
! 102: *> If UPLO = 'L':
! 103: *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
! 104: *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
! 105: *>
! 106: *> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
! 107: *> columns k and -IPIV(k) were interchanged and rows and
! 108: *> columns k+1 and -IPIV(k+1) were inerchaged,
! 109: *> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
! 110: *> \endverbatim
! 111: *>
! 112: *> \param[out] WORK
! 113: *> \verbatim
! 114: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)).
! 115: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 116: *> \endverbatim
! 117: *>
! 118: *> \param[in] LWORK
! 119: *> \verbatim
! 120: *> LWORK is INTEGER
! 121: *> The length of WORK. LWORK >=1. For best performance
! 122: *> LWORK >= N*NB, where NB is the block size returned by ILAENV.
! 123: *>
! 124: *> If LWORK = -1, then a workspace query is assumed; the routine
! 125: *> only calculates the optimal size of the WORK array, returns
! 126: *> this value as the first entry of the WORK array, and no error
! 127: *> message related to LWORK is issued by XERBLA.
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[out] INFO
! 131: *> \verbatim
! 132: *> INFO is INTEGER
! 133: *> = 0: successful exit
! 134: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 135: *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
! 136: *> has been completed, but the block diagonal matrix D is
! 137: *> exactly singular, and division by zero will occur if it
! 138: *> is used to solve a system of equations.
! 139: *> \endverbatim
! 140: *
! 141: * Authors:
! 142: * ========
! 143: *
! 144: *> \author Univ. of Tennessee
! 145: *> \author Univ. of California Berkeley
! 146: *> \author Univ. of Colorado Denver
! 147: *> \author NAG Ltd.
! 148: *
! 149: *> \date November 2011
! 150: *
! 151: *> \ingroup complex16SYcomputational
! 152: *
! 153: *> \par Further Details:
! 154: * =====================
! 155: *>
! 156: *> \verbatim
! 157: *>
! 158: *> If UPLO = 'U', then A = U*D*U**T, where
! 159: *> U = P(n)*U(n)* ... *P(k)U(k)* ...,
! 160: *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
! 161: *> 1 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 U(k) is a unit upper triangular matrix, such
! 164: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 165: *>
! 166: *> ( I v 0 ) k-s
! 167: *> U(k) = ( 0 I 0 ) s
! 168: *> ( 0 0 I ) n-k
! 169: *> k-s s n-k
! 170: *>
! 171: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
! 172: *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
! 173: *> and A(k,k), and v overwrites A(1:k-2,k-1:k).
! 174: *>
! 175: *> If UPLO = 'L', then A = L*D*L**T, where
! 176: *> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
! 177: *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
! 178: *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
! 179: *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
! 180: *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
! 181: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 182: *>
! 183: *> ( I 0 0 ) k-1
! 184: *> L(k) = ( 0 I 0 ) s
! 185: *> ( 0 v I ) n-k-s+1
! 186: *> k-1 s n-k-s+1
! 187: *>
! 188: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
! 189: *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
! 190: *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
! 191: *> \endverbatim
! 192: *
! 193: *> \par Contributors:
! 194: * ==================
! 195: *>
! 196: *> \verbatim
! 197: *>
! 198: *> November 2011, Igor Kozachenko,
! 199: *> Computer Science Division,
! 200: *> University of California, Berkeley
! 201: *>
! 202: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
! 203: *> School of Mathematics,
! 204: *> University of Manchester
! 205: *>
! 206: *> \endverbatim
! 207: *
! 208: * =====================================================================
! 209: SUBROUTINE ZSYTRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
! 210: *
! 211: * -- LAPACK computational routine (version 3.4.0) --
! 212: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 213: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 214: * November 2011
! 215: *
! 216: * .. Scalar Arguments ..
! 217: CHARACTER UPLO
! 218: INTEGER INFO, LDA, LWORK, N
! 219: * ..
! 220: * .. Array Arguments ..
! 221: INTEGER IPIV( * )
! 222: COMPLEX*16 A( LDA, * ), WORK( * )
! 223: * ..
! 224: *
! 225: * =====================================================================
! 226: *
! 227: * .. Local Scalars ..
! 228: LOGICAL LQUERY, UPPER
! 229: INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
! 230: * ..
! 231: * .. External Functions ..
! 232: LOGICAL LSAME
! 233: INTEGER ILAENV
! 234: EXTERNAL LSAME, ILAENV
! 235: * ..
! 236: * .. External Subroutines ..
! 237: EXTERNAL ZLASYF_ROOK, ZSYTF2_ROOK, XERBLA
! 238: * ..
! 239: * .. Intrinsic Functions ..
! 240: INTRINSIC MAX
! 241: * ..
! 242: * .. Executable Statements ..
! 243: *
! 244: * Test the input parameters.
! 245: *
! 246: INFO = 0
! 247: UPPER = LSAME( UPLO, 'U' )
! 248: LQUERY = ( LWORK.EQ.-1 )
! 249: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 250: INFO = -1
! 251: ELSE IF( N.LT.0 ) THEN
! 252: INFO = -2
! 253: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 254: INFO = -4
! 255: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
! 256: INFO = -7
! 257: END IF
! 258: *
! 259: IF( INFO.EQ.0 ) THEN
! 260: *
! 261: * Determine the block size
! 262: *
! 263: NB = ILAENV( 1, 'ZSYTRF_ROOK', UPLO, N, -1, -1, -1 )
! 264: LWKOPT = N*NB
! 265: WORK( 1 ) = LWKOPT
! 266: END IF
! 267: *
! 268: IF( INFO.NE.0 ) THEN
! 269: CALL XERBLA( 'ZSYTRF_ROOK', -INFO )
! 270: RETURN
! 271: ELSE IF( LQUERY ) THEN
! 272: RETURN
! 273: END IF
! 274: *
! 275: NBMIN = 2
! 276: LDWORK = N
! 277: IF( NB.GT.1 .AND. NB.LT.N ) THEN
! 278: IWS = LDWORK*NB
! 279: IF( LWORK.LT.IWS ) THEN
! 280: NB = MAX( LWORK / LDWORK, 1 )
! 281: NBMIN = MAX( 2, ILAENV( 2, 'ZSYTRF_ROOK',
! 282: $ UPLO, N, -1, -1, -1 ) )
! 283: END IF
! 284: ELSE
! 285: IWS = 1
! 286: END IF
! 287: IF( NB.LT.NBMIN )
! 288: $ NB = N
! 289: *
! 290: IF( UPPER ) THEN
! 291: *
! 292: * Factorize A as U*D*U**T using the upper triangle of A
! 293: *
! 294: * K is the main loop index, decreasing from N to 1 in steps of
! 295: * KB, where KB is the number of columns factorized by ZLASYF_ROOK;
! 296: * KB is either NB or NB-1, or K for the last block
! 297: *
! 298: K = N
! 299: 10 CONTINUE
! 300: *
! 301: * If K < 1, exit from loop
! 302: *
! 303: IF( K.LT.1 )
! 304: $ GO TO 40
! 305: *
! 306: IF( K.GT.NB ) THEN
! 307: *
! 308: * Factorize columns k-kb+1:k of A and use blocked code to
! 309: * update columns 1:k-kb
! 310: *
! 311: CALL ZLASYF_ROOK( UPLO, K, NB, KB, A, LDA,
! 312: $ IPIV, WORK, LDWORK, IINFO )
! 313: ELSE
! 314: *
! 315: * Use unblocked code to factorize columns 1:k of A
! 316: *
! 317: CALL ZSYTF2_ROOK( UPLO, K, A, LDA, IPIV, IINFO )
! 318: KB = K
! 319: END IF
! 320: *
! 321: * Set INFO on the first occurrence of a zero pivot
! 322: *
! 323: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
! 324: $ INFO = IINFO
! 325: *
! 326: * No need to adjust IPIV
! 327: *
! 328: * Decrease K and return to the start of the main loop
! 329: *
! 330: K = K - KB
! 331: GO TO 10
! 332: *
! 333: ELSE
! 334: *
! 335: * Factorize A as L*D*L**T using the lower triangle of A
! 336: *
! 337: * K is the main loop index, increasing from 1 to N in steps of
! 338: * KB, where KB is the number of columns factorized by ZLASYF_ROOK;
! 339: * KB is either NB or NB-1, or N-K+1 for the last block
! 340: *
! 341: K = 1
! 342: 20 CONTINUE
! 343: *
! 344: * If K > N, exit from loop
! 345: *
! 346: IF( K.GT.N )
! 347: $ GO TO 40
! 348: *
! 349: IF( K.LE.N-NB ) THEN
! 350: *
! 351: * Factorize columns k:k+kb-1 of A and use blocked code to
! 352: * update columns k+kb:n
! 353: *
! 354: CALL ZLASYF_ROOK( UPLO, N-K+1, NB, KB, A( K, K ), LDA,
! 355: $ IPIV( K ), WORK, LDWORK, IINFO )
! 356: ELSE
! 357: *
! 358: * Use unblocked code to factorize columns k:n of A
! 359: *
! 360: CALL ZSYTF2_ROOK( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ),
! 361: $ IINFO )
! 362: KB = N - K + 1
! 363: END IF
! 364: *
! 365: * Set INFO on the first occurrence of a zero pivot
! 366: *
! 367: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
! 368: $ INFO = IINFO + K - 1
! 369: *
! 370: * Adjust IPIV
! 371: *
! 372: DO 30 J = K, K + KB - 1
! 373: IF( IPIV( J ).GT.0 ) THEN
! 374: IPIV( J ) = IPIV( J ) + K - 1
! 375: ELSE
! 376: IPIV( J ) = IPIV( J ) - K + 1
! 377: END IF
! 378: 30 CONTINUE
! 379: *
! 380: * Increase K and return to the start of the main loop
! 381: *
! 382: K = K + KB
! 383: GO TO 20
! 384: *
! 385: END IF
! 386: *
! 387: 40 CONTINUE
! 388: WORK( 1 ) = LWKOPT
! 389: RETURN
! 390: *
! 391: * End of ZSYTRF_ROOK
! 392: *
! 393: END
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