Annotation of rpl/lapack/lapack/zhegst.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZHEGST
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZHEGST + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegst.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhegst.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhegst.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, ITYPE, LDA, LDB, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 A( LDA, * ), B( LDB, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZHEGST reduces a complex Hermitian-definite generalized
! 38: *> eigenproblem to standard form.
! 39: *>
! 40: *> If ITYPE = 1, the problem is A*x = lambda*B*x,
! 41: *> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
! 42: *>
! 43: *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
! 44: *> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
! 45: *>
! 46: *> B must have been previously factorized as U**H*U or L*L**H by ZPOTRF.
! 47: *> \endverbatim
! 48: *
! 49: * Arguments:
! 50: * ==========
! 51: *
! 52: *> \param[in] ITYPE
! 53: *> \verbatim
! 54: *> ITYPE is INTEGER
! 55: *> = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
! 56: *> = 2 or 3: compute U*A*U**H or L**H*A*L.
! 57: *> \endverbatim
! 58: *>
! 59: *> \param[in] UPLO
! 60: *> \verbatim
! 61: *> UPLO is CHARACTER*1
! 62: *> = 'U': Upper triangle of A is stored and B is factored as
! 63: *> U**H*U;
! 64: *> = 'L': Lower triangle of A is stored and B is factored as
! 65: *> L*L**H.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] N
! 69: *> \verbatim
! 70: *> N is INTEGER
! 71: *> The order of the matrices A and B. N >= 0.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in,out] A
! 75: *> \verbatim
! 76: *> A is COMPLEX*16 array, dimension (LDA,N)
! 77: *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
! 78: *> N-by-N upper triangular part of A contains the upper
! 79: *> triangular part of the matrix A, and the strictly lower
! 80: *> triangular part of A is not referenced. If UPLO = 'L', the
! 81: *> leading N-by-N lower triangular part of A contains the lower
! 82: *> triangular part of the matrix A, and the strictly upper
! 83: *> triangular part of A is not referenced.
! 84: *>
! 85: *> On exit, if INFO = 0, the transformed matrix, stored in the
! 86: *> same format as A.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in] LDA
! 90: *> \verbatim
! 91: *> LDA is INTEGER
! 92: *> The leading dimension of the array A. LDA >= max(1,N).
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in] B
! 96: *> \verbatim
! 97: *> B is COMPLEX*16 array, dimension (LDB,N)
! 98: *> The triangular factor from the Cholesky factorization of B,
! 99: *> as returned by ZPOTRF.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in] LDB
! 103: *> \verbatim
! 104: *> LDB is INTEGER
! 105: *> The leading dimension of the array B. LDB >= max(1,N).
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[out] INFO
! 109: *> \verbatim
! 110: *> INFO is INTEGER
! 111: *> = 0: successful exit
! 112: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 113: *> \endverbatim
! 114: *
! 115: * Authors:
! 116: * ========
! 117: *
! 118: *> \author Univ. of Tennessee
! 119: *> \author Univ. of California Berkeley
! 120: *> \author Univ. of Colorado Denver
! 121: *> \author NAG Ltd.
! 122: *
! 123: *> \date November 2011
! 124: *
! 125: *> \ingroup complex16HEcomputational
! 126: *
! 127: * =====================================================================
1.1 bertrand 128: SUBROUTINE ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
129: *
1.9 ! bertrand 130: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 131: * -- LAPACK is a software package provided by Univ. of Tennessee, --
132: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 133: * November 2011
1.1 bertrand 134: *
135: * .. Scalar Arguments ..
136: CHARACTER UPLO
137: INTEGER INFO, ITYPE, LDA, LDB, N
138: * ..
139: * .. Array Arguments ..
140: COMPLEX*16 A( LDA, * ), B( LDB, * )
141: * ..
142: *
143: * =====================================================================
144: *
145: * .. Parameters ..
146: DOUBLE PRECISION ONE
147: PARAMETER ( ONE = 1.0D+0 )
148: COMPLEX*16 CONE, HALF
149: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
150: $ HALF = ( 0.5D+0, 0.0D+0 ) )
151: * ..
152: * .. Local Scalars ..
153: LOGICAL UPPER
154: INTEGER K, KB, NB
155: * ..
156: * .. External Subroutines ..
157: EXTERNAL XERBLA, ZHEGS2, ZHEMM, ZHER2K, ZTRMM, ZTRSM
158: * ..
159: * .. Intrinsic Functions ..
160: INTRINSIC MAX, MIN
161: * ..
162: * .. External Functions ..
163: LOGICAL LSAME
164: INTEGER ILAENV
165: EXTERNAL LSAME, ILAENV
166: * ..
167: * .. Executable Statements ..
168: *
169: * Test the input parameters.
170: *
171: INFO = 0
172: UPPER = LSAME( UPLO, 'U' )
173: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
174: INFO = -1
175: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
176: INFO = -2
177: ELSE IF( N.LT.0 ) THEN
178: INFO = -3
179: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
180: INFO = -5
181: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
182: INFO = -7
183: END IF
184: IF( INFO.NE.0 ) THEN
185: CALL XERBLA( 'ZHEGST', -INFO )
186: RETURN
187: END IF
188: *
189: * Quick return if possible
190: *
191: IF( N.EQ.0 )
192: $ RETURN
193: *
194: * Determine the block size for this environment.
195: *
196: NB = ILAENV( 1, 'ZHEGST', UPLO, N, -1, -1, -1 )
197: *
198: IF( NB.LE.1 .OR. NB.GE.N ) THEN
199: *
200: * Use unblocked code
201: *
202: CALL ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
203: ELSE
204: *
205: * Use blocked code
206: *
207: IF( ITYPE.EQ.1 ) THEN
208: IF( UPPER ) THEN
209: *
1.8 bertrand 210: * Compute inv(U**H)*A*inv(U)
1.1 bertrand 211: *
212: DO 10 K = 1, N, NB
213: KB = MIN( N-K+1, NB )
214: *
215: * Update the upper triangle of A(k:n,k:n)
216: *
217: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
218: $ B( K, K ), LDB, INFO )
219: IF( K+KB.LE.N ) THEN
220: CALL ZTRSM( 'Left', UPLO, 'Conjugate transpose',
221: $ 'Non-unit', KB, N-K-KB+1, CONE,
222: $ B( K, K ), LDB, A( K, K+KB ), LDA )
223: CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
224: $ A( K, K ), LDA, B( K, K+KB ), LDB,
225: $ CONE, A( K, K+KB ), LDA )
226: CALL ZHER2K( UPLO, 'Conjugate transpose', N-K-KB+1,
227: $ KB, -CONE, A( K, K+KB ), LDA,
228: $ B( K, K+KB ), LDB, ONE,
229: $ A( K+KB, K+KB ), LDA )
230: CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
231: $ A( K, K ), LDA, B( K, K+KB ), LDB,
232: $ CONE, A( K, K+KB ), LDA )
233: CALL ZTRSM( 'Right', UPLO, 'No transpose',
234: $ 'Non-unit', KB, N-K-KB+1, CONE,
235: $ B( K+KB, K+KB ), LDB, A( K, K+KB ),
236: $ LDA )
237: END IF
238: 10 CONTINUE
239: ELSE
240: *
1.8 bertrand 241: * Compute inv(L)*A*inv(L**H)
1.1 bertrand 242: *
243: DO 20 K = 1, N, NB
244: KB = MIN( N-K+1, NB )
245: *
246: * Update the lower triangle of A(k:n,k:n)
247: *
248: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
249: $ B( K, K ), LDB, INFO )
250: IF( K+KB.LE.N ) THEN
251: CALL ZTRSM( 'Right', UPLO, 'Conjugate transpose',
252: $ 'Non-unit', N-K-KB+1, KB, CONE,
253: $ B( K, K ), LDB, A( K+KB, K ), LDA )
254: CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
255: $ A( K, K ), LDA, B( K+KB, K ), LDB,
256: $ CONE, A( K+KB, K ), LDA )
257: CALL ZHER2K( UPLO, 'No transpose', N-K-KB+1, KB,
258: $ -CONE, A( K+KB, K ), LDA,
259: $ B( K+KB, K ), LDB, ONE,
260: $ A( K+KB, K+KB ), LDA )
261: CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
262: $ A( K, K ), LDA, B( K+KB, K ), LDB,
263: $ CONE, A( K+KB, K ), LDA )
264: CALL ZTRSM( 'Left', UPLO, 'No transpose',
265: $ 'Non-unit', N-K-KB+1, KB, CONE,
266: $ B( K+KB, K+KB ), LDB, A( K+KB, K ),
267: $ LDA )
268: END IF
269: 20 CONTINUE
270: END IF
271: ELSE
272: IF( UPPER ) THEN
273: *
1.8 bertrand 274: * Compute U*A*U**H
1.1 bertrand 275: *
276: DO 30 K = 1, N, NB
277: KB = MIN( N-K+1, NB )
278: *
279: * Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
280: *
281: CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Non-unit',
282: $ K-1, KB, CONE, B, LDB, A( 1, K ), LDA )
283: CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
284: $ LDA, B( 1, K ), LDB, CONE, A( 1, K ),
285: $ LDA )
286: CALL ZHER2K( UPLO, 'No transpose', K-1, KB, CONE,
287: $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A,
288: $ LDA )
289: CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
290: $ LDA, B( 1, K ), LDB, CONE, A( 1, K ),
291: $ LDA )
292: CALL ZTRMM( 'Right', UPLO, 'Conjugate transpose',
293: $ 'Non-unit', K-1, KB, CONE, B( K, K ), LDB,
294: $ A( 1, K ), LDA )
295: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
296: $ B( K, K ), LDB, INFO )
297: 30 CONTINUE
298: ELSE
299: *
1.8 bertrand 300: * Compute L**H*A*L
1.1 bertrand 301: *
302: DO 40 K = 1, N, NB
303: KB = MIN( N-K+1, NB )
304: *
305: * Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
306: *
307: CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Non-unit',
308: $ KB, K-1, CONE, B, LDB, A( K, 1 ), LDA )
309: CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
310: $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ),
311: $ LDA )
312: CALL ZHER2K( UPLO, 'Conjugate transpose', K-1, KB,
313: $ CONE, A( K, 1 ), LDA, B( K, 1 ), LDB,
314: $ ONE, A, LDA )
315: CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
316: $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ),
317: $ LDA )
318: CALL ZTRMM( 'Left', UPLO, 'Conjugate transpose',
319: $ 'Non-unit', KB, K-1, CONE, B( K, K ), LDB,
320: $ A( K, 1 ), LDA )
321: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
322: $ B( K, K ), LDB, INFO )
323: 40 CONTINUE
324: END IF
325: END IF
326: END IF
327: RETURN
328: *
329: * End of ZHEGST
330: *
331: END
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