Annotation of rpl/lapack/lapack/zsysv_aa.f, revision 1.4

1.1       bertrand    1: *> \brief <b> ZSYSV_AA 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 ZSYSV_AA + dependencies
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsysv_aa.f">
                     11: *> [TGZ]</a>
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsysv_aa.f">
                     13: *> [ZIP]</a>
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsysv_aa.f">
                     15: *> [TXT]</a>
                     16: *> \endhtmlonly
                     17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE ZSYSV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
                     22: *                            LWORK, INFO )
                     23: *
                     24: *       .. Scalar Arguments ..
                     25: *       CHARACTER          UPLO
                     26: *       INTEGER            N, NRHS, LDA, LDB, LWORK, INFO
                     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: *> ZSYSV computes the solution to a complex system of linear equations
                     40: *>    A * X = B,
                     41: *> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
                     42: *> matrices.
                     43: *>
                     44: *> Aasen's algorithm is used to factor A as
                     45: *>    A = U * T * U**T,  if UPLO = 'U', or
                     46: *>    A = L * T * L**T,  if UPLO = 'L',
                     47: *> where U (or L) is a product of permutation and unit upper (lower)
                     48: *> triangular matrices, and T is symmetric tridiagonal. The factored
                     49: *> form of A is then used to solve the system of equations A * X = B.
                     50: *> \endverbatim
                     51: *
                     52: *  Arguments:
                     53: *  ==========
                     54: *
                     55: *> \param[in] UPLO
                     56: *> \verbatim
                     57: *>          UPLO is CHARACTER*1
                     58: *>          = 'U':  Upper triangle of A is stored;
                     59: *>          = 'L':  Lower triangle of A is stored.
                     60: *> \endverbatim
                     61: *>
                     62: *> \param[in] N
                     63: *> \verbatim
                     64: *>          N is INTEGER
                     65: *>          The number of linear equations, i.e., the order of the
                     66: *>          matrix A.  N >= 0.
                     67: *> \endverbatim
                     68: *>
                     69: *> \param[in] NRHS
                     70: *> \verbatim
                     71: *>          NRHS is INTEGER
                     72: *>          The number of right hand sides, i.e., the number of columns
                     73: *>          of the matrix B.  NRHS >= 0.
                     74: *> \endverbatim
                     75: *>
                     76: *> \param[in,out] A
                     77: *> \verbatim
                     78: *>          A is COMPLEX*16 array, dimension (LDA,N)
                     79: *>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
                     80: *>          N-by-N upper triangular part of A contains the upper
                     81: *>          triangular part of the matrix A, and the strictly lower
                     82: *>          triangular part of A is not referenced.  If UPLO = 'L', the
                     83: *>          leading N-by-N lower triangular part of A contains the lower
                     84: *>          triangular part of the matrix A, and the strictly upper
                     85: *>          triangular part of A is not referenced.
                     86: *>
                     87: *>          On exit, if INFO = 0, the tridiagonal matrix T and the
                     88: *>          multipliers used to obtain the factor U or L from the
                     89: *>          factorization A = U*T*U**T or A = L*T*L**T as computed by
                     90: *>          ZSYTRF.
                     91: *> \endverbatim
                     92: *>
                     93: *> \param[in] LDA
                     94: *> \verbatim
                     95: *>          LDA is INTEGER
                     96: *>          The leading dimension of the array A.  LDA >= max(1,N).
                     97: *> \endverbatim
                     98: *>
                     99: *> \param[out] IPIV
                    100: *> \verbatim
                    101: *>          IPIV is INTEGER array, dimension (N)
                    102: *>          On exit, it contains the details of the interchanges, i.e.,
                    103: *>          the row and column k of A were interchanged with the
                    104: *>          row and column IPIV(k).
                    105: *> \endverbatim
                    106: *>
                    107: *> \param[in,out] B
                    108: *> \verbatim
                    109: *>          B is COMPLEX*16 array, dimension (LDB,NRHS)
                    110: *>          On entry, the N-by-NRHS right hand side matrix B.
                    111: *>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
                    112: *> \endverbatim
                    113: *>
                    114: *> \param[in] LDB
                    115: *> \verbatim
                    116: *>          LDB is INTEGER
                    117: *>          The leading dimension of the array B.  LDB >= max(1,N).
                    118: *> \endverbatim
                    119: *>
                    120: *> \param[out] WORK
                    121: *> \verbatim
                    122: *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                    123: *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
                    124: *> \endverbatim
                    125: *>
                    126: *> \param[in] LWORK
                    127: *> \verbatim
                    128: *>          LWORK is INTEGER
                    129: *>          The length of WORK.  LWORK >= MAX(1,2*N,3*N-2), and for
                    130: *>          the best performance, LWORK >= MAX(1,N*NB), where NB is
                    131: *>          the optimal blocksize for ZSYTRF_AA.
                    132: *>
                    133: *>          If LWORK = -1, then a workspace query is assumed; the routine
                    134: *>          only calculates the optimal size of the WORK array, returns
                    135: *>          this value as the first entry of the WORK array, and no error
                    136: *>          message related to LWORK is issued by XERBLA.
                    137: *> \endverbatim
                    138: *>
                    139: *> \param[out] INFO
                    140: *> \verbatim
                    141: *>          INFO is INTEGER
                    142: *>          = 0: successful exit
                    143: *>          < 0: if INFO = -i, the i-th argument had an illegal value
                    144: *>          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                    145: *>               has been completed, but the block diagonal matrix D is
                    146: *>               exactly singular, so the solution could not be computed.
                    147: *> \endverbatim
                    148: *
                    149: *  Authors:
                    150: *  ========
                    151: *
                    152: *> \author Univ. of Tennessee
                    153: *> \author Univ. of California Berkeley
                    154: *> \author Univ. of Colorado Denver
                    155: *> \author NAG Ltd.
                    156: *
1.3       bertrand  157: *> \date November 2017
1.1       bertrand  158: *
                    159: *> \ingroup complex16SYsolve
                    160: *
                    161: *  =====================================================================
                    162:       SUBROUTINE ZSYSV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
                    163:      $                     LWORK, INFO )
                    164: *
1.3       bertrand  165: *  -- LAPACK driver routine (version 3.8.0) --
1.1       bertrand  166: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    167: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.3       bertrand  168: *     November 2017
1.1       bertrand  169: *
                    170: *     .. Scalar Arguments ..
                    171:       CHARACTER          UPLO
                    172:       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
                    173: *     ..
                    174: *     .. Array Arguments ..
                    175:       INTEGER            IPIV( * )
                    176:       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
                    177: *     ..
                    178: *
                    179: *  =====================================================================
                    180: *
                    181: *     .. Local Scalars ..
                    182:       LOGICAL            LQUERY
                    183:       INTEGER            LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
                    184: *     ..
                    185: *     .. External Functions ..
                    186:       LOGICAL            LSAME
                    187:       INTEGER            ILAENV
                    188:       EXTERNAL           ILAENV, LSAME
                    189: *     ..
                    190: *     .. External Subroutines ..
1.3       bertrand  191:       EXTERNAL           XERBLA, ZSYTRF_AA, ZSYTRS_AA
1.1       bertrand  192: *     ..
                    193: *     .. Intrinsic Functions ..
                    194:       INTRINSIC          MAX
                    195: *     ..
                    196: *     .. Executable Statements ..
                    197: *
                    198: *     Test the input parameters.
                    199: *
                    200:       INFO = 0
                    201:       LQUERY = ( LWORK.EQ.-1 )
                    202:       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
                    203:          INFO = -1
                    204:       ELSE IF( N.LT.0 ) THEN
                    205:          INFO = -2
                    206:       ELSE IF( NRHS.LT.0 ) THEN
                    207:          INFO = -3
                    208:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
                    209:          INFO = -5
                    210:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
                    211:          INFO = -8
                    212:       ELSE IF( LWORK.LT.MAX(2*N, 3*N-2) .AND. .NOT.LQUERY ) THEN
                    213:          INFO = -10
                    214:       END IF
                    215: *
                    216:       IF( INFO.EQ.0 ) THEN
                    217:          CALL ZSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
                    218:          LWKOPT_SYTRF = INT( WORK(1) )
                    219:          CALL ZSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
                    220:      $                   -1, INFO )
                    221:          LWKOPT_SYTRS = INT( WORK(1) )
                    222:          LWKOPT = MAX( LWKOPT_SYTRF, LWKOPT_SYTRS )
                    223:          WORK( 1 ) = LWKOPT
                    224:          IF( LWORK.LT.LWKOPT .AND. .NOT.LQUERY ) THEN
                    225:             INFO = -10
                    226:          END IF
                    227:       END IF
                    228: *
                    229:       IF( INFO.NE.0 ) THEN
                    230:          CALL XERBLA( 'ZSYSV_AA ', -INFO )
                    231:          RETURN
                    232:       ELSE IF( LQUERY ) THEN
                    233:          RETURN
                    234:       END IF
                    235: *
                    236: *     Compute the factorization A = U*T*U**T or A = L*T*L**T.
                    237: *
                    238:       CALL ZSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
                    239:       IF( INFO.EQ.0 ) THEN
                    240: *
                    241: *        Solve the system A*X = B, overwriting B with X.
                    242: *
                    243:          CALL ZSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
                    244:      $                      LWORK, INFO )
                    245: *
                    246:       END IF
                    247: *
                    248:       WORK( 1 ) = LWKOPT
                    249: *
                    250:       RETURN
                    251: *
                    252: *     End of ZSYSV_AA
                    253: *
                    254:       END

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