Annotation of rpl/lapack/lapack/zhetrf.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZHETRF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZHETRF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetrf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetrf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetrf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZHETRF( 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: *> ZHETRF computes the factorization of a complex Hermitian matrix A
! 39: *> using the Bunch-Kaufman diagonal pivoting method. The form of the
! 40: *> factorization is
! 41: *>
! 42: *> A = U*D*U**H or A = L*D*L**H
! 43: *>
! 44: *> where U (or L) is a product of permutation and unit upper (lower)
! 45: *> triangular matrices, and D is Hermitian 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 Hermitian 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: *> \endverbatim
! 113: *>
! 114: *> \param[out] INFO
! 115: *> \verbatim
! 116: *> INFO is INTEGER
! 117: *> = 0: successful exit
! 118: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 119: *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
! 120: *> has been completed, but the block diagonal matrix D is
! 121: *> exactly singular, and division by zero will occur if it
! 122: *> is used to solve a system of equations.
! 123: *> \endverbatim
! 124: *
! 125: * Authors:
! 126: * ========
! 127: *
! 128: *> \author Univ. of Tennessee
! 129: *> \author Univ. of California Berkeley
! 130: *> \author Univ. of Colorado Denver
! 131: *> \author NAG Ltd.
! 132: *
! 133: *> \date November 2011
! 134: *
! 135: *> \ingroup complex16HEcomputational
! 136: *
! 137: *> \par Further Details:
! 138: * =====================
! 139: *>
! 140: *> \verbatim
! 141: *>
! 142: *> If UPLO = 'U', then A = U*D*U**H, where
! 143: *> U = P(n)*U(n)* ... *P(k)U(k)* ...,
! 144: *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
! 145: *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
! 146: *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
! 147: *> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
! 148: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 149: *>
! 150: *> ( I v 0 ) k-s
! 151: *> U(k) = ( 0 I 0 ) s
! 152: *> ( 0 0 I ) n-k
! 153: *> k-s s n-k
! 154: *>
! 155: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
! 156: *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
! 157: *> and A(k,k), and v overwrites A(1:k-2,k-1:k).
! 158: *>
! 159: *> If UPLO = 'L', then A = L*D*L**H, where
! 160: *> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
! 161: *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
! 162: *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
! 163: *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
! 164: *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
! 165: *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
! 166: *>
! 167: *> ( I 0 0 ) k-1
! 168: *> L(k) = ( 0 I 0 ) s
! 169: *> ( 0 v I ) n-k-s+1
! 170: *> k-1 s n-k-s+1
! 171: *>
! 172: *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
! 173: *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
! 174: *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
! 175: *> \endverbatim
! 176: *>
! 177: * =====================================================================
1.1 bertrand 178: SUBROUTINE ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
179: *
1.9 ! bertrand 180: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 181: * -- LAPACK is a software package provided by Univ. of Tennessee, --
182: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 183: * November 2011
1.1 bertrand 184: *
185: * .. Scalar Arguments ..
186: CHARACTER UPLO
187: INTEGER INFO, LDA, LWORK, N
188: * ..
189: * .. Array Arguments ..
190: INTEGER IPIV( * )
191: COMPLEX*16 A( LDA, * ), WORK( * )
192: * ..
193: *
194: * =====================================================================
195: *
196: * .. Local Scalars ..
197: LOGICAL LQUERY, UPPER
198: INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
199: * ..
200: * .. External Functions ..
201: LOGICAL LSAME
202: INTEGER ILAENV
203: EXTERNAL LSAME, ILAENV
204: * ..
205: * .. External Subroutines ..
206: EXTERNAL XERBLA, ZHETF2, ZLAHEF
207: * ..
208: * .. Intrinsic Functions ..
209: INTRINSIC MAX
210: * ..
211: * .. Executable Statements ..
212: *
213: * Test the input parameters.
214: *
215: INFO = 0
216: UPPER = LSAME( UPLO, 'U' )
217: LQUERY = ( LWORK.EQ.-1 )
218: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
219: INFO = -1
220: ELSE IF( N.LT.0 ) THEN
221: INFO = -2
222: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
223: INFO = -4
224: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
225: INFO = -7
226: END IF
227: *
228: IF( INFO.EQ.0 ) THEN
229: *
230: * Determine the block size
231: *
232: NB = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 )
233: LWKOPT = N*NB
234: WORK( 1 ) = LWKOPT
235: END IF
236: *
237: IF( INFO.NE.0 ) THEN
238: CALL XERBLA( 'ZHETRF', -INFO )
239: RETURN
240: ELSE IF( LQUERY ) THEN
241: RETURN
242: END IF
243: *
244: NBMIN = 2
245: LDWORK = N
246: IF( NB.GT.1 .AND. NB.LT.N ) THEN
247: IWS = LDWORK*NB
248: IF( LWORK.LT.IWS ) THEN
249: NB = MAX( LWORK / LDWORK, 1 )
250: NBMIN = MAX( 2, ILAENV( 2, 'ZHETRF', UPLO, N, -1, -1, -1 ) )
251: END IF
252: ELSE
253: IWS = 1
254: END IF
255: IF( NB.LT.NBMIN )
256: $ NB = N
257: *
258: IF( UPPER ) THEN
259: *
1.8 bertrand 260: * Factorize A as U*D*U**H using the upper triangle of A
1.1 bertrand 261: *
262: * K is the main loop index, decreasing from N to 1 in steps of
263: * KB, where KB is the number of columns factorized by ZLAHEF;
264: * KB is either NB or NB-1, or K for the last block
265: *
266: K = N
267: 10 CONTINUE
268: *
269: * If K < 1, exit from loop
270: *
271: IF( K.LT.1 )
272: $ GO TO 40
273: *
274: IF( K.GT.NB ) THEN
275: *
276: * Factorize columns k-kb+1:k of A and use blocked code to
277: * update columns 1:k-kb
278: *
279: CALL ZLAHEF( UPLO, K, NB, KB, A, LDA, IPIV, WORK, N, IINFO )
280: ELSE
281: *
282: * Use unblocked code to factorize columns 1:k of A
283: *
284: CALL ZHETF2( UPLO, K, A, LDA, IPIV, IINFO )
285: KB = K
286: END IF
287: *
288: * Set INFO on the first occurrence of a zero pivot
289: *
290: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
291: $ INFO = IINFO
292: *
293: * Decrease K and return to the start of the main loop
294: *
295: K = K - KB
296: GO TO 10
297: *
298: ELSE
299: *
1.8 bertrand 300: * Factorize A as L*D*L**H using the lower triangle of A
1.1 bertrand 301: *
302: * K is the main loop index, increasing from 1 to N in steps of
303: * KB, where KB is the number of columns factorized by ZLAHEF;
304: * KB is either NB or NB-1, or N-K+1 for the last block
305: *
306: K = 1
307: 20 CONTINUE
308: *
309: * If K > N, exit from loop
310: *
311: IF( K.GT.N )
312: $ GO TO 40
313: *
314: IF( K.LE.N-NB ) THEN
315: *
316: * Factorize columns k:k+kb-1 of A and use blocked code to
317: * update columns k+kb:n
318: *
319: CALL ZLAHEF( UPLO, N-K+1, NB, KB, A( K, K ), LDA, IPIV( K ),
320: $ WORK, N, IINFO )
321: ELSE
322: *
323: * Use unblocked code to factorize columns k:n of A
324: *
325: CALL ZHETF2( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ), IINFO )
326: KB = N - K + 1
327: END IF
328: *
329: * Set INFO on the first occurrence of a zero pivot
330: *
331: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
332: $ INFO = IINFO + K - 1
333: *
334: * Adjust IPIV
335: *
336: DO 30 J = K, K + KB - 1
337: IF( IPIV( J ).GT.0 ) THEN
338: IPIV( J ) = IPIV( J ) + K - 1
339: ELSE
340: IPIV( J ) = IPIV( J ) - K + 1
341: END IF
342: 30 CONTINUE
343: *
344: * Increase K and return to the start of the main loop
345: *
346: K = K + KB
347: GO TO 20
348: *
349: END IF
350: *
351: 40 CONTINUE
352: WORK( 1 ) = LWKOPT
353: RETURN
354: *
355: * End of ZHETRF
356: *
357: END
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