Annotation of rpl/lapack/lapack/zsytrf.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZSYTRF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZSYTRF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytrf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytrf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytrf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZSYTRF( 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 computes the factorization of a complex symmetric matrix A
! 39: *> using the Bunch-Kaufman diagonal pivoting method. The form of the
! 40: *> 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: *> with 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: *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
! 93: *> interchanged and D(k,k) is a 1-by-1 diagonal block.
! 94: *> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
! 95: *> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
! 96: *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
! 97: *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
! 98: *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[out] WORK
! 102: *> \verbatim
! 103: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 104: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 105: *> \endverbatim
! 106: *>
! 107: *> \param[in] LWORK
! 108: *> \verbatim
! 109: *> LWORK is INTEGER
! 110: *> The length of WORK. LWORK >=1. For best performance
! 111: *> LWORK >= N*NB, where NB is the block size returned by ILAENV.
! 112: *>
! 113: *> If LWORK = -1, then a workspace query is assumed; the routine
! 114: *> only calculates the optimal size of the WORK array, returns
! 115: *> this value as the first entry of the WORK array, and no error
! 116: *> message related to LWORK is issued by XERBLA.
! 117: *> \endverbatim
! 118: *>
! 119: *> \param[out] INFO
! 120: *> \verbatim
! 121: *> INFO is INTEGER
! 122: *> = 0: successful exit
! 123: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 124: *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
! 125: *> has been completed, but the block diagonal matrix D is
! 126: *> exactly singular, and division by zero will occur if it
! 127: *> is used to solve a system of equations.
! 128: *> \endverbatim
! 129: *
! 130: * Authors:
! 131: * ========
! 132: *
! 133: *> \author Univ. of Tennessee
! 134: *> \author Univ. of California Berkeley
! 135: *> \author Univ. of Colorado Denver
! 136: *> \author NAG Ltd.
! 137: *
! 138: *> \date November 2011
! 139: *
! 140: *> \ingroup complex16SYcomputational
! 141: *
! 142: *> \par Further Details:
! 143: * =====================
! 144: *>
! 145: *> \verbatim
! 146: *>
! 147: *> If UPLO = 'U', then A = U*D*U**T, where
! 148: *> U = P(n)*U(n)* ... *P(k)U(k)* ...,
! 149: *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
! 150: *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
! 151: *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
! 152: *> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
! 153: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 154: *>
! 155: *> ( I v 0 ) k-s
! 156: *> U(k) = ( 0 I 0 ) s
! 157: *> ( 0 0 I ) n-k
! 158: *> k-s s n-k
! 159: *>
! 160: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
! 161: *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
! 162: *> and A(k,k), and v overwrites A(1:k-2,k-1:k).
! 163: *>
! 164: *> If UPLO = 'L', then A = L*D*L**T, where
! 165: *> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
! 166: *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
! 167: *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
! 168: *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
! 169: *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
! 170: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 171: *>
! 172: *> ( I 0 0 ) k-1
! 173: *> L(k) = ( 0 I 0 ) s
! 174: *> ( 0 v I ) n-k-s+1
! 175: *> k-1 s n-k-s+1
! 176: *>
! 177: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
! 178: *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
! 179: *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
! 180: *> \endverbatim
! 181: *>
! 182: * =====================================================================
1.1 bertrand 183: SUBROUTINE ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
184: *
1.9 ! bertrand 185: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 186: * -- LAPACK is a software package provided by Univ. of Tennessee, --
187: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 188: * November 2011
1.1 bertrand 189: *
190: * .. Scalar Arguments ..
191: CHARACTER UPLO
192: INTEGER INFO, LDA, LWORK, N
193: * ..
194: * .. Array Arguments ..
195: INTEGER IPIV( * )
196: COMPLEX*16 A( LDA, * ), WORK( * )
197: * ..
198: *
199: * =====================================================================
200: *
201: * .. Local Scalars ..
202: LOGICAL LQUERY, UPPER
203: INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
204: * ..
205: * .. External Functions ..
206: LOGICAL LSAME
207: INTEGER ILAENV
208: EXTERNAL LSAME, ILAENV
209: * ..
210: * .. External Subroutines ..
211: EXTERNAL XERBLA, ZLASYF, ZSYTF2
212: * ..
213: * .. Intrinsic Functions ..
214: INTRINSIC MAX
215: * ..
216: * .. Executable Statements ..
217: *
218: * Test the input parameters.
219: *
220: INFO = 0
221: UPPER = LSAME( UPLO, 'U' )
222: LQUERY = ( LWORK.EQ.-1 )
223: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
224: INFO = -1
225: ELSE IF( N.LT.0 ) THEN
226: INFO = -2
227: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
228: INFO = -4
229: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
230: INFO = -7
231: END IF
232: *
233: IF( INFO.EQ.0 ) THEN
234: *
235: * Determine the block size
236: *
237: NB = ILAENV( 1, 'ZSYTRF', UPLO, N, -1, -1, -1 )
238: LWKOPT = N*NB
239: WORK( 1 ) = LWKOPT
240: END IF
241: *
242: IF( INFO.NE.0 ) THEN
243: CALL XERBLA( 'ZSYTRF', -INFO )
244: RETURN
245: ELSE IF( LQUERY ) THEN
246: RETURN
247: END IF
248: *
249: NBMIN = 2
250: LDWORK = N
251: IF( NB.GT.1 .AND. NB.LT.N ) THEN
252: IWS = LDWORK*NB
253: IF( LWORK.LT.IWS ) THEN
254: NB = MAX( LWORK / LDWORK, 1 )
255: NBMIN = MAX( 2, ILAENV( 2, 'ZSYTRF', UPLO, N, -1, -1, -1 ) )
256: END IF
257: ELSE
258: IWS = 1
259: END IF
260: IF( NB.LT.NBMIN )
261: $ NB = N
262: *
263: IF( UPPER ) THEN
264: *
1.8 bertrand 265: * Factorize A as U*D*U**T using the upper triangle of A
1.1 bertrand 266: *
267: * K is the main loop index, decreasing from N to 1 in steps of
268: * KB, where KB is the number of columns factorized by ZLASYF;
269: * KB is either NB or NB-1, or K for the last block
270: *
271: K = N
272: 10 CONTINUE
273: *
274: * If K < 1, exit from loop
275: *
276: IF( K.LT.1 )
277: $ GO TO 40
278: *
279: IF( K.GT.NB ) THEN
280: *
281: * Factorize columns k-kb+1:k of A and use blocked code to
282: * update columns 1:k-kb
283: *
284: CALL ZLASYF( UPLO, K, NB, KB, A, LDA, IPIV, WORK, N, IINFO )
285: ELSE
286: *
287: * Use unblocked code to factorize columns 1:k of A
288: *
289: CALL ZSYTF2( UPLO, K, A, LDA, IPIV, IINFO )
290: KB = K
291: END IF
292: *
293: * Set INFO on the first occurrence of a zero pivot
294: *
295: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
296: $ INFO = IINFO
297: *
298: * Decrease K and return to the start of the main loop
299: *
300: K = K - KB
301: GO TO 10
302: *
303: ELSE
304: *
1.8 bertrand 305: * Factorize A as L*D*L**T using the lower triangle of A
1.1 bertrand 306: *
307: * K is the main loop index, increasing from 1 to N in steps of
308: * KB, where KB is the number of columns factorized by ZLASYF;
309: * KB is either NB or NB-1, or N-K+1 for the last block
310: *
311: K = 1
312: 20 CONTINUE
313: *
314: * If K > N, exit from loop
315: *
316: IF( K.GT.N )
317: $ GO TO 40
318: *
319: IF( K.LE.N-NB ) THEN
320: *
321: * Factorize columns k:k+kb-1 of A and use blocked code to
322: * update columns k+kb:n
323: *
324: CALL ZLASYF( UPLO, N-K+1, NB, KB, A( K, K ), LDA, IPIV( K ),
325: $ WORK, N, IINFO )
326: ELSE
327: *
328: * Use unblocked code to factorize columns k:n of A
329: *
330: CALL ZSYTF2( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ), IINFO )
331: KB = N - K + 1
332: END IF
333: *
334: * Set INFO on the first occurrence of a zero pivot
335: *
336: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
337: $ INFO = IINFO + K - 1
338: *
339: * Adjust IPIV
340: *
341: DO 30 J = K, K + KB - 1
342: IF( IPIV( J ).GT.0 ) THEN
343: IPIV( J ) = IPIV( J ) + K - 1
344: ELSE
345: IPIV( J ) = IPIV( J ) - K + 1
346: END IF
347: 30 CONTINUE
348: *
349: * Increase K and return to the start of the main loop
350: *
351: K = K + KB
352: GO TO 20
353: *
354: END IF
355: *
356: 40 CONTINUE
357: WORK( 1 ) = LWKOPT
358: RETURN
359: *
360: * End of ZSYTRF
361: *
362: END
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