Annotation of rpl/lapack/lapack/zhesv_rook.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZHESV_ROOK + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhesv_rook.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhesv_rook.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhesv_rook.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZHESV_ROOK( 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_ROOK 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 bounded Bunch-Kaufman ("rook") diagonal pivoting method is used
! 45: *> to factor A as
! 46: *> A = U * D * U**T, if UPLO = 'U', or
! 47: *> A = L * D * L**T, if UPLO = 'L',
! 48: *> where U (or L) is a product of permutation and unit upper (lower)
! 49: *> triangular matrices, and D is Hermitian and block diagonal with
! 50: *> 1-by-1 and 2-by-2 diagonal blocks.
! 51: *>
! 52: *> ZHETRF_ROOK is called to compute the factorization of a complex
! 53: *> Hermition matrix A using the bounded Bunch-Kaufman ("rook") diagonal
! 54: *> pivoting method.
! 55: *>
! 56: *> The factored form of A is then used to solve the system
! 57: *> of equations A * X = B by calling ZHETRS_ROOK (uses BLAS 2).
! 58: *> \endverbatim
! 59: *
! 60: * Arguments:
! 61: * ==========
! 62: *
! 63: *> \param[in] UPLO
! 64: *> \verbatim
! 65: *> UPLO is CHARACTER*1
! 66: *> = 'U': Upper triangle of A is stored;
! 67: *> = 'L': Lower triangle of A is stored.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] N
! 71: *> \verbatim
! 72: *> N is INTEGER
! 73: *> The number of linear equations, i.e., the order of the
! 74: *> matrix A. N >= 0.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] NRHS
! 78: *> \verbatim
! 79: *> NRHS is INTEGER
! 80: *> The number of right hand sides, i.e., the number of columns
! 81: *> of the matrix B. NRHS >= 0.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[in,out] A
! 85: *> \verbatim
! 86: *> A is COMPLEX*16 array, dimension (LDA,N)
! 87: *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
! 88: *> N-by-N upper triangular part of A contains the upper
! 89: *> triangular part of the matrix A, and the strictly lower
! 90: *> triangular part of A is not referenced. If UPLO = 'L', the
! 91: *> leading N-by-N lower triangular part of A contains the lower
! 92: *> triangular part of the matrix A, and the strictly upper
! 93: *> triangular part of A is not referenced.
! 94: *>
! 95: *> On exit, if INFO = 0, the block diagonal matrix D and the
! 96: *> multipliers used to obtain the factor U or L from the
! 97: *> factorization A = U*D*U**H or A = L*D*L**H as computed by
! 98: *> ZHETRF_ROOK.
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[in] LDA
! 102: *> \verbatim
! 103: *> LDA is INTEGER
! 104: *> The leading dimension of the array A. LDA >= max(1,N).
! 105: *> \endverbatim
! 106: *>
! 107: *> \param[out] IPIV
! 108: *> \verbatim
! 109: *> IPIV is INTEGER array, dimension (N)
! 110: *> Details of the interchanges and the block structure of D.
! 111: *>
! 112: *> If UPLO = 'U':
! 113: *> Only the last KB elements of IPIV are set.
! 114: *>
! 115: *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
! 116: *> interchanged and D(k,k) is a 1-by-1 diagonal block.
! 117: *>
! 118: *> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
! 119: *> columns k and -IPIV(k) were interchanged and rows and
! 120: *> columns k-1 and -IPIV(k-1) were inerchaged,
! 121: *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
! 122: *>
! 123: *> If UPLO = 'L':
! 124: *> Only the first KB elements of IPIV are set.
! 125: *>
! 126: *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
! 127: *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
! 128: *>
! 129: *> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
! 130: *> columns k and -IPIV(k) were interchanged and rows and
! 131: *> columns k+1 and -IPIV(k+1) were inerchaged,
! 132: *> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
! 133: *> \endverbatim
! 134: *>
! 135: *> \param[in,out] B
! 136: *> \verbatim
! 137: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
! 138: *> On entry, the N-by-NRHS right hand side matrix B.
! 139: *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
! 140: *> \endverbatim
! 141: *>
! 142: *> \param[in] LDB
! 143: *> \verbatim
! 144: *> LDB is INTEGER
! 145: *> The leading dimension of the array B. LDB >= max(1,N).
! 146: *> \endverbatim
! 147: *>
! 148: *> \param[out] WORK
! 149: *> \verbatim
! 150: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 151: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 152: *> \endverbatim
! 153: *>
! 154: *> \param[in] LWORK
! 155: *> \verbatim
! 156: *> LWORK is INTEGER
! 157: *> The length of WORK. LWORK >= 1, and for best performance
! 158: *> LWORK >= max(1,N*NB), where NB is the optimal blocksize for
! 159: *> ZHETRF_ROOK.
! 160: *> for LWORK < N, TRS will be done with Level BLAS 2
! 161: *> for LWORK >= N, TRS will be done with Level BLAS 3
! 162: *>
! 163: *> If LWORK = -1, then a workspace query is assumed; the routine
! 164: *> only calculates the optimal size of the WORK array, returns
! 165: *> this value as the first entry of the WORK array, and no error
! 166: *> message related to LWORK is issued by XERBLA.
! 167: *> \endverbatim
! 168: *>
! 169: *> \param[out] INFO
! 170: *> \verbatim
! 171: *> INFO is INTEGER
! 172: *> = 0: successful exit
! 173: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 174: *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
! 175: *> has been completed, but the block diagonal matrix D is
! 176: *> exactly singular, so the solution could not be computed.
! 177: *> \endverbatim
! 178: *
! 179: * Authors:
! 180: * ========
! 181: *
! 182: *> \author Univ. of Tennessee
! 183: *> \author Univ. of California Berkeley
! 184: *> \author Univ. of Colorado Denver
! 185: *> \author NAG Ltd.
! 186: *
! 187: *> \date November 2013
! 188: *
! 189: *> \ingroup complex16HEsolve
! 190: *>
! 191: *> \verbatim
! 192: *>
! 193: *> November 2013, Igor Kozachenko,
! 194: *> Computer Science Division,
! 195: *> University of California, Berkeley
! 196: *>
! 197: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
! 198: *> School of Mathematics,
! 199: *> University of Manchester
! 200: *>
! 201: *> \endverbatim
! 202: *
! 203: *
! 204: * =====================================================================
! 205: SUBROUTINE ZHESV_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
! 206: $ LWORK, INFO )
! 207: *
! 208: * -- LAPACK driver routine (version 3.5.0) --
! 209: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 210: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 211: * November 2013
! 212: *
! 213: * .. Scalar Arguments ..
! 214: CHARACTER UPLO
! 215: INTEGER INFO, LDA, LDB, LWORK, N, NRHS
! 216: * ..
! 217: * .. Array Arguments ..
! 218: INTEGER IPIV( * )
! 219: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
! 220: * ..
! 221: *
! 222: * =====================================================================
! 223: *
! 224: * .. Local Scalars ..
! 225: LOGICAL LQUERY
! 226: INTEGER LWKOPT, NB
! 227: * ..
! 228: * .. External Functions ..
! 229: LOGICAL LSAME
! 230: INTEGER ILAENV
! 231: EXTERNAL LSAME, ILAENV
! 232: * ..
! 233: * .. External Subroutines ..
! 234: EXTERNAL XERBLA, ZHETRF_ROOK, ZHETRS_ROOK
! 235: * ..
! 236: * .. Intrinsic Functions ..
! 237: INTRINSIC MAX
! 238: * ..
! 239: * .. Executable Statements ..
! 240: *
! 241: * Test the input parameters.
! 242: *
! 243: INFO = 0
! 244: LQUERY = ( LWORK.EQ.-1 )
! 245: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 246: INFO = -1
! 247: ELSE IF( N.LT.0 ) THEN
! 248: INFO = -2
! 249: ELSE IF( NRHS.LT.0 ) THEN
! 250: INFO = -3
! 251: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 252: INFO = -5
! 253: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 254: INFO = -8
! 255: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
! 256: INFO = -10
! 257: END IF
! 258: *
! 259: IF( INFO.EQ.0 ) THEN
! 260: IF( N.EQ.0 ) THEN
! 261: LWKOPT = 1
! 262: ELSE
! 263: NB = ILAENV( 1, 'ZHETRF_ROOK', UPLO, N, -1, -1, -1 )
! 264: LWKOPT = N*NB
! 265: END IF
! 266: WORK( 1 ) = LWKOPT
! 267: END IF
! 268: *
! 269: IF( INFO.NE.0 ) THEN
! 270: CALL XERBLA( 'ZHESV_ROOK ', -INFO )
! 271: RETURN
! 272: ELSE IF( LQUERY ) THEN
! 273: RETURN
! 274: END IF
! 275: *
! 276: * Compute the factorization A = U*D*U**H or A = L*D*L**H.
! 277: *
! 278: CALL ZHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
! 279: IF( INFO.EQ.0 ) THEN
! 280: *
! 281: * Solve the system A*X = B, overwriting B with X.
! 282: *
! 283: * Solve with TRS ( Use Level BLAS 2)
! 284: *
! 285: CALL ZHETRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
! 286: *
! 287: END IF
! 288: *
! 289: WORK( 1 ) = LWKOPT
! 290: *
! 291: RETURN
! 292: *
! 293: * End of ZHESV_ROOK
! 294: *
! 295: END
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