Annotation of rpl/lapack/lapack/zhesv.f, revision 1.10
1.10 ! bertrand 1: *> \brief <b> ZHESV computes the solution to system of linear equations A * X = B for HE matrices</b>
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZHESV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhesv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhesv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhesv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
! 22: * LWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER UPLO
! 26: * INTEGER INFO, LDA, LDB, LWORK, N, NRHS
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * INTEGER IPIV( * )
! 30: * COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> ZHESV computes the solution to a complex system of linear equations
! 40: *> A * X = B,
! 41: *> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
! 42: *> matrices.
! 43: *>
! 44: *> The diagonal pivoting method is used to factor A as
! 45: *> A = U * D * U**H, if UPLO = 'U', or
! 46: *> A = L * D * L**H, if UPLO = 'L',
! 47: *> where U (or L) is a product of permutation and unit upper (lower)
! 48: *> triangular matrices, and D is Hermitian and block diagonal with
! 49: *> 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
! 50: *> used to solve the system of equations A * X = B.
! 51: *> \endverbatim
! 52: *
! 53: * Arguments:
! 54: * ==========
! 55: *
! 56: *> \param[in] UPLO
! 57: *> \verbatim
! 58: *> UPLO is CHARACTER*1
! 59: *> = 'U': Upper triangle of A is stored;
! 60: *> = 'L': Lower triangle of A is stored.
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in] N
! 64: *> \verbatim
! 65: *> N is INTEGER
! 66: *> The number of linear equations, i.e., the order of the
! 67: *> matrix A. N >= 0.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] NRHS
! 71: *> \verbatim
! 72: *> NRHS is INTEGER
! 73: *> The number of right hand sides, i.e., the number of columns
! 74: *> of the matrix B. NRHS >= 0.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in,out] A
! 78: *> \verbatim
! 79: *> A is COMPLEX*16 array, dimension (LDA,N)
! 80: *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
! 81: *> N-by-N upper triangular part of A contains the upper
! 82: *> triangular part of the matrix A, and the strictly lower
! 83: *> triangular part of A is not referenced. If UPLO = 'L', the
! 84: *> leading N-by-N lower triangular part of A contains the lower
! 85: *> triangular part of the matrix A, and the strictly upper
! 86: *> triangular part of A is not referenced.
! 87: *>
! 88: *> On exit, if INFO = 0, the block diagonal matrix D and the
! 89: *> multipliers used to obtain the factor U or L from the
! 90: *> factorization A = U*D*U**H or A = L*D*L**H as computed by
! 91: *> ZHETRF.
! 92: *> \endverbatim
! 93: *>
! 94: *> \param[in] LDA
! 95: *> \verbatim
! 96: *> LDA is INTEGER
! 97: *> The leading dimension of the array A. LDA >= max(1,N).
! 98: *> \endverbatim
! 99: *>
! 100: *> \param[out] IPIV
! 101: *> \verbatim
! 102: *> IPIV is INTEGER array, dimension (N)
! 103: *> Details of the interchanges and the block structure of D, as
! 104: *> determined by ZHETRF. If IPIV(k) > 0, then rows and columns
! 105: *> k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
! 106: *> diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
! 107: *> then rows and columns k-1 and -IPIV(k) were interchanged and
! 108: *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
! 109: *> IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
! 110: *> -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
! 111: *> diagonal block.
! 112: *> \endverbatim
! 113: *>
! 114: *> \param[in,out] B
! 115: *> \verbatim
! 116: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
! 117: *> On entry, the N-by-NRHS right hand side matrix B.
! 118: *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
! 119: *> \endverbatim
! 120: *>
! 121: *> \param[in] LDB
! 122: *> \verbatim
! 123: *> LDB is INTEGER
! 124: *> The leading dimension of the array B. LDB >= max(1,N).
! 125: *> \endverbatim
! 126: *>
! 127: *> \param[out] WORK
! 128: *> \verbatim
! 129: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 130: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 131: *> \endverbatim
! 132: *>
! 133: *> \param[in] LWORK
! 134: *> \verbatim
! 135: *> LWORK is INTEGER
! 136: *> The length of WORK. LWORK >= 1, and for best performance
! 137: *> LWORK >= max(1,N*NB), where NB is the optimal blocksize for
! 138: *> ZHETRF.
! 139: *> for LWORK < N, TRS will be done with Level BLAS 2
! 140: *> for LWORK >= N, TRS will be done with Level BLAS 3
! 141: *>
! 142: *> If LWORK = -1, then a workspace query is assumed; the routine
! 143: *> only calculates the optimal size of the WORK array, returns
! 144: *> this value as the first entry of the WORK array, and no error
! 145: *> message related to LWORK is issued by XERBLA.
! 146: *> \endverbatim
! 147: *>
! 148: *> \param[out] INFO
! 149: *> \verbatim
! 150: *> INFO is INTEGER
! 151: *> = 0: successful exit
! 152: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 153: *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
! 154: *> has been completed, but the block diagonal matrix D is
! 155: *> exactly singular, so the solution could not be computed.
! 156: *> \endverbatim
! 157: *
! 158: * Authors:
! 159: * ========
! 160: *
! 161: *> \author Univ. of Tennessee
! 162: *> \author Univ. of California Berkeley
! 163: *> \author Univ. of Colorado Denver
! 164: *> \author NAG Ltd.
! 165: *
! 166: *> \date November 2011
! 167: *
! 168: *> \ingroup complex16HEsolve
! 169: *
! 170: * =====================================================================
1.1 bertrand 171: SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
172: $ LWORK, INFO )
173: *
1.10 ! bertrand 174: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 175: * -- LAPACK is a software package provided by Univ. of Tennessee, --
176: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.10 ! bertrand 177: * November 2011
1.1 bertrand 178: *
179: * .. Scalar Arguments ..
180: CHARACTER UPLO
181: INTEGER INFO, LDA, LDB, LWORK, N, NRHS
182: * ..
183: * .. Array Arguments ..
184: INTEGER IPIV( * )
185: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
186: * ..
187: *
188: * =====================================================================
189: *
190: * .. Local Scalars ..
191: LOGICAL LQUERY
192: INTEGER LWKOPT, NB
193: * ..
194: * .. External Functions ..
195: LOGICAL LSAME
196: INTEGER ILAENV
197: EXTERNAL LSAME, ILAENV
198: * ..
199: * .. External Subroutines ..
1.9 bertrand 200: EXTERNAL XERBLA, ZHETRF, ZHETRS, ZHETRS2
1.1 bertrand 201: * ..
202: * .. Intrinsic Functions ..
203: INTRINSIC MAX
204: * ..
205: * .. Executable Statements ..
206: *
207: * Test the input parameters.
208: *
209: INFO = 0
210: LQUERY = ( LWORK.EQ.-1 )
211: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
212: INFO = -1
213: ELSE IF( N.LT.0 ) THEN
214: INFO = -2
215: ELSE IF( NRHS.LT.0 ) THEN
216: INFO = -3
217: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
218: INFO = -5
219: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
220: INFO = -8
221: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
222: INFO = -10
223: END IF
224: *
225: IF( INFO.EQ.0 ) THEN
226: IF( N.EQ.0 ) THEN
227: LWKOPT = 1
228: ELSE
229: NB = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 )
230: LWKOPT = N*NB
231: END IF
232: WORK( 1 ) = LWKOPT
233: END IF
234: *
235: IF( INFO.NE.0 ) THEN
236: CALL XERBLA( 'ZHESV ', -INFO )
237: RETURN
238: ELSE IF( LQUERY ) THEN
239: RETURN
240: END IF
241: *
1.9 bertrand 242: * Compute the factorization A = U*D*U**H or A = L*D*L**H.
1.1 bertrand 243: *
244: CALL ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
245: IF( INFO.EQ.0 ) THEN
246: *
247: * Solve the system A*X = B, overwriting B with X.
248: *
1.9 bertrand 249: IF ( LWORK.LT.N ) THEN
250: *
251: * Solve with TRS ( Use Level BLAS 2)
252: *
253: CALL ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
254: *
255: ELSE
256: *
257: * Solve with TRS2 ( Use Level BLAS 3)
258: *
259: CALL ZHETRS2( UPLO,N,NRHS,A,LDA,IPIV,B,LDB,WORK,INFO )
260: *
261: END IF
1.1 bertrand 262: *
263: END IF
264: *
265: WORK( 1 ) = LWKOPT
266: *
267: RETURN
268: *
269: * End of ZHESV
270: *
271: END
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