Annotation of rpl/lapack/lapack/zhesv_rk.f, revision 1.1
1.1 ! bertrand 1: *> \brief <b> ZHESV_RK computes the solution to system of linear equations A * X = B for SY 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_RK + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhesv_rk.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhesv_rk.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhesv_rk.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZHESV_RK( UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB,
! 22: * WORK, 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, * ), E( * ), WORK( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *> ZHESV_RK computes the solution to a complex system of linear
! 39: *> equations A * X = B, where A is an N-by-N Hermitian matrix
! 40: *> and X and B are N-by-NRHS matrices.
! 41: *>
! 42: *> The bounded Bunch-Kaufman (rook) diagonal pivoting method is used
! 43: *> to factor A as
! 44: *> A = P*U*D*(U**H)*(P**T), if UPLO = 'U', or
! 45: *> A = P*L*D*(L**H)*(P**T), if UPLO = 'L',
! 46: *> where U (or L) is unit upper (or lower) triangular matrix,
! 47: *> U**H (or L**H) is the conjugate of U (or L), P is a permutation
! 48: *> matrix, P**T is the transpose of P, and D is Hermitian and block
! 49: *> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
! 50: *>
! 51: *> ZHETRF_RK is called to compute the factorization of a complex
! 52: *> Hermitian matrix. The factored form of A is then used to solve
! 53: *> the system of equations A * X = B by calling BLAS3 routine ZHETRS_3.
! 54: *> \endverbatim
! 55: *
! 56: * Arguments:
! 57: * ==========
! 58: *
! 59: *> \param[in] UPLO
! 60: *> \verbatim
! 61: *> UPLO is CHARACTER*1
! 62: *> Specifies whether the upper or lower triangular part of the
! 63: *> Hermitian matrix A is stored:
! 64: *> = 'U': Upper triangle of A is stored;
! 65: *> = 'L': Lower triangle of A is stored.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] N
! 69: *> \verbatim
! 70: *> N is INTEGER
! 71: *> The number of linear equations, i.e., the order of the
! 72: *> matrix A. N >= 0.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] NRHS
! 76: *> \verbatim
! 77: *> NRHS is INTEGER
! 78: *> The number of right hand sides, i.e., the number of columns
! 79: *> of the matrix B. NRHS >= 0.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in,out] A
! 83: *> \verbatim
! 84: *> A is COMPLEX*16 array, dimension (LDA,N)
! 85: *> On entry, the Hermitian matrix A.
! 86: *> If UPLO = 'U': the leading N-by-N upper triangular part
! 87: *> of A contains the upper triangular part of the matrix A,
! 88: *> and the strictly lower triangular part of A is not
! 89: *> referenced.
! 90: *>
! 91: *> If UPLO = 'L': the leading N-by-N lower triangular part
! 92: *> of A contains the lower triangular part of the matrix A,
! 93: *> and the strictly upper triangular part of A is not
! 94: *> referenced.
! 95: *>
! 96: *> On exit, if INFO = 0, diagonal of the block diagonal
! 97: *> matrix D and factors U or L as computed by ZHETRF_RK:
! 98: *> a) ONLY diagonal elements of the Hermitian block diagonal
! 99: *> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
! 100: *> (superdiagonal (or subdiagonal) elements of D
! 101: *> are stored on exit in array E), and
! 102: *> b) If UPLO = 'U': factor U in the superdiagonal part of A.
! 103: *> If UPLO = 'L': factor L in the subdiagonal part of A.
! 104: *>
! 105: *> For more info see the description of ZHETRF_RK routine.
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[in] LDA
! 109: *> \verbatim
! 110: *> LDA is INTEGER
! 111: *> The leading dimension of the array A. LDA >= max(1,N).
! 112: *> \endverbatim
! 113: *>
! 114: *> \param[out] E
! 115: *> \verbatim
! 116: *> E is COMPLEX*16 array, dimension (N)
! 117: *> On exit, contains the output computed by the factorization
! 118: *> routine ZHETRF_RK, i.e. the superdiagonal (or subdiagonal)
! 119: *> elements of the Hermitian block diagonal matrix D
! 120: *> with 1-by-1 or 2-by-2 diagonal blocks, where
! 121: *> If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
! 122: *> If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.
! 123: *>
! 124: *> NOTE: For 1-by-1 diagonal block D(k), where
! 125: *> 1 <= k <= N, the element E(k) is set to 0 in both
! 126: *> UPLO = 'U' or UPLO = 'L' cases.
! 127: *>
! 128: *> For more info see the description of ZHETRF_RK routine.
! 129: *> \endverbatim
! 130: *>
! 131: *> \param[out] IPIV
! 132: *> \verbatim
! 133: *> IPIV is INTEGER array, dimension (N)
! 134: *> Details of the interchanges and the block structure of D,
! 135: *> as determined by ZHETRF_RK.
! 136: *>
! 137: *> For more info see the description of ZHETRF_RK routine.
! 138: *> \endverbatim
! 139: *>
! 140: *> \param[in,out] B
! 141: *> \verbatim
! 142: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
! 143: *> On entry, the N-by-NRHS right hand side matrix B.
! 144: *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
! 145: *> \endverbatim
! 146: *>
! 147: *> \param[in] LDB
! 148: *> \verbatim
! 149: *> LDB is INTEGER
! 150: *> The leading dimension of the array B. LDB >= max(1,N).
! 151: *> \endverbatim
! 152: *>
! 153: *> \param[out] WORK
! 154: *> \verbatim
! 155: *> WORK is COMPLEX*16 array, dimension ( MAX(1,LWORK) ).
! 156: *> Work array used in the factorization stage.
! 157: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 158: *> \endverbatim
! 159: *>
! 160: *> \param[in] LWORK
! 161: *> \verbatim
! 162: *> LWORK is INTEGER
! 163: *> The length of WORK. LWORK >= 1. For best performance
! 164: *> of factorization stage LWORK >= max(1,N*NB), where NB is
! 165: *> the optimal blocksize for ZHETRF_RK.
! 166: *>
! 167: *> If LWORK = -1, then a workspace query is assumed;
! 168: *> the routine only calculates the optimal size of the WORK
! 169: *> array for factorization stage, returns this value as
! 170: *> the first entry of the WORK array, and no error message
! 171: *> related to LWORK is issued by XERBLA.
! 172: *> \endverbatim
! 173: *>
! 174: *> \param[out] INFO
! 175: *> \verbatim
! 176: *> INFO is INTEGER
! 177: *> = 0: successful exit
! 178: *>
! 179: *> < 0: If INFO = -k, the k-th argument had an illegal value
! 180: *>
! 181: *> > 0: If INFO = k, the matrix A is singular, because:
! 182: *> If UPLO = 'U': column k in the upper
! 183: *> triangular part of A contains all zeros.
! 184: *> If UPLO = 'L': column k in the lower
! 185: *> triangular part of A contains all zeros.
! 186: *>
! 187: *> Therefore D(k,k) is exactly zero, and superdiagonal
! 188: *> elements of column k of U (or subdiagonal elements of
! 189: *> column k of L ) are all zeros. The factorization has
! 190: *> been completed, but the block diagonal matrix D is
! 191: *> exactly singular, and division by zero will occur if
! 192: *> it is used to solve a system of equations.
! 193: *>
! 194: *> NOTE: INFO only stores the first occurrence of
! 195: *> a singularity, any subsequent occurrence of singularity
! 196: *> is not stored in INFO even though the factorization
! 197: *> always completes.
! 198: *> \endverbatim
! 199: *
! 200: * Authors:
! 201: * ========
! 202: *
! 203: *> \author Univ. of Tennessee
! 204: *> \author Univ. of California Berkeley
! 205: *> \author Univ. of Colorado Denver
! 206: *> \author NAG Ltd.
! 207: *
! 208: *> \date December 2016
! 209: *
! 210: *> \ingroup complex16HEsolve
! 211: *
! 212: *> \par Contributors:
! 213: * ==================
! 214: *>
! 215: *> \verbatim
! 216: *>
! 217: *> December 2016, Igor Kozachenko,
! 218: *> Computer Science Division,
! 219: *> University of California, Berkeley
! 220: *>
! 221: *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
! 222: *> School of Mathematics,
! 223: *> University of Manchester
! 224: *>
! 225: *> \endverbatim
! 226: *
! 227: * =====================================================================
! 228: SUBROUTINE ZHESV_RK( UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, WORK,
! 229: $ LWORK, INFO )
! 230: *
! 231: * -- LAPACK driver routine (version 3.7.0) --
! 232: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 233: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 234: * December 2016
! 235: *
! 236: * .. Scalar Arguments ..
! 237: CHARACTER UPLO
! 238: INTEGER INFO, LDA, LDB, LWORK, N, NRHS
! 239: * ..
! 240: * .. Array Arguments ..
! 241: INTEGER IPIV( * )
! 242: COMPLEX*16 A( LDA, * ), B( LDB, * ), E( * ), WORK( * )
! 243: * ..
! 244: *
! 245: * =====================================================================
! 246: *
! 247: * .. Local Scalars ..
! 248: LOGICAL LQUERY
! 249: INTEGER LWKOPT
! 250: * ..
! 251: * .. External Functions ..
! 252: LOGICAL LSAME
! 253: EXTERNAL LSAME
! 254: * ..
! 255: * .. External Subroutines ..
! 256: EXTERNAL XERBLA, ZHETRF_RK, ZHETRS_3
! 257: * ..
! 258: * .. Intrinsic Functions ..
! 259: INTRINSIC MAX
! 260: * ..
! 261: * .. Executable Statements ..
! 262: *
! 263: * Test the input parameters.
! 264: *
! 265: INFO = 0
! 266: LQUERY = ( LWORK.EQ.-1 )
! 267: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 268: INFO = -1
! 269: ELSE IF( N.LT.0 ) THEN
! 270: INFO = -2
! 271: ELSE IF( NRHS.LT.0 ) THEN
! 272: INFO = -3
! 273: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 274: INFO = -5
! 275: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 276: INFO = -9
! 277: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
! 278: INFO = -11
! 279: END IF
! 280: *
! 281: IF( INFO.EQ.0 ) THEN
! 282: IF( N.EQ.0 ) THEN
! 283: LWKOPT = 1
! 284: ELSE
! 285: CALL ZHETRF_RK( UPLO, N, A, LDA, E, IPIV, WORK, -1, INFO )
! 286: LWKOPT = WORK(1)
! 287: END IF
! 288: WORK( 1 ) = LWKOPT
! 289: END IF
! 290: *
! 291: IF( INFO.NE.0 ) THEN
! 292: CALL XERBLA( 'ZHESV_RK ', -INFO )
! 293: RETURN
! 294: ELSE IF( LQUERY ) THEN
! 295: RETURN
! 296: END IF
! 297: *
! 298: * Compute the factorization A = P*U*D*(U**H)*(P**T) or
! 299: * A = P*U*D*(U**H)*(P**T).
! 300: *
! 301: CALL ZHETRF_RK( UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO )
! 302: *
! 303: IF( INFO.EQ.0 ) THEN
! 304: *
! 305: * Solve the system A*X = B with BLAS3 solver, overwriting B with X.
! 306: *
! 307: CALL ZHETRS_3( UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, INFO )
! 308: *
! 309: END IF
! 310: *
! 311: WORK( 1 ) = LWKOPT
! 312: *
! 313: RETURN
! 314: *
! 315: * End of ZHESV_RK
! 316: *
! 317: END
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