Annotation of rpl/lapack/lapack/zsycon_rook.f, revision 1.5

1.1       bertrand    1: *> \brief \b ZSYCON_ROOK
                      2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
1.5     ! bertrand    5: * Online html documentation available at
        !             6: *            http://www.netlib.org/lapack/explore-html/
1.1       bertrand    7: *
                      8: *> \htmlonly
1.5     ! bertrand    9: *> Download ZSYCON_ROOK + dependencies
        !            10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsycon_rook.f">
        !            11: *> [TGZ]</a>
        !            12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsycon_rook.f">
        !            13: *> [ZIP]</a>
        !            14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsycon_rook.f">
1.1       bertrand   15: *> [TXT]</a>
1.5     ! bertrand   16: *> \endhtmlonly
1.1       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE ZSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND,
                     22: *                               WORK, INFO )
1.5     ! bertrand   23: *
1.1       bertrand   24: *       .. Scalar Arguments ..
                     25: *       CHARACTER          UPLO
                     26: *       INTEGER            INFO, LDA, N
                     27: *       DOUBLE PRECISION   ANORM, RCOND
                     28: *       ..
                     29: *       .. Array Arguments ..
                     30: *       INTEGER            IPIV( * )
                     31: *       COMPLEX*16         A( LDA, * ), WORK( * )
                     32: *       ..
1.5     ! bertrand   33: *
1.1       bertrand   34: *
                     35: *> \par Purpose:
                     36: *  =============
                     37: *>
                     38: *> \verbatim
                     39: *>
                     40: *> ZSYCON_ROOK estimates the reciprocal of the condition number (in the
                     41: *> 1-norm) of a complex symmetric matrix A using the factorization
                     42: *> A = U*D*U**T or A = L*D*L**T computed by ZSYTRF_ROOK.
                     43: *>
                     44: *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
                     45: *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
                     46: *> \endverbatim
                     47: *
                     48: *  Arguments:
                     49: *  ==========
                     50: *
                     51: *> \param[in] UPLO
                     52: *> \verbatim
                     53: *>          UPLO is CHARACTER*1
                     54: *>          Specifies whether the details of the factorization are stored
                     55: *>          as an upper or lower triangular matrix.
                     56: *>          = 'U':  Upper triangular, form is A = U*D*U**T;
                     57: *>          = 'L':  Lower triangular, form is A = L*D*L**T.
                     58: *> \endverbatim
                     59: *>
                     60: *> \param[in] N
                     61: *> \verbatim
                     62: *>          N is INTEGER
                     63: *>          The order of the matrix A.  N >= 0.
                     64: *> \endverbatim
                     65: *>
                     66: *> \param[in] A
                     67: *> \verbatim
                     68: *>          A is COMPLEX*16 array, dimension (LDA,N)
                     69: *>          The block diagonal matrix D and the multipliers used to
                     70: *>          obtain the factor U or L as computed by ZSYTRF_ROOK.
                     71: *> \endverbatim
                     72: *>
                     73: *> \param[in] LDA
                     74: *> \verbatim
                     75: *>          LDA is INTEGER
                     76: *>          The leading dimension of the array A.  LDA >= max(1,N).
                     77: *> \endverbatim
                     78: *>
                     79: *> \param[in] IPIV
                     80: *> \verbatim
                     81: *>          IPIV is INTEGER array, dimension (N)
                     82: *>          Details of the interchanges and the block structure of D
                     83: *>          as determined by ZSYTRF_ROOK.
                     84: *> \endverbatim
                     85: *>
                     86: *> \param[in] ANORM
                     87: *> \verbatim
                     88: *>          ANORM is DOUBLE PRECISION
                     89: *>          The 1-norm of the original matrix A.
                     90: *> \endverbatim
                     91: *>
                     92: *> \param[out] RCOND
                     93: *> \verbatim
                     94: *>          RCOND is DOUBLE PRECISION
                     95: *>          The reciprocal of the condition number of the matrix A,
                     96: *>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
                     97: *>          estimate of the 1-norm of inv(A) computed in this routine.
                     98: *> \endverbatim
                     99: *>
                    100: *> \param[out] WORK
                    101: *> \verbatim
                    102: *>          WORK is COMPLEX*16 array, dimension (2*N)
                    103: *> \endverbatim
                    104: *>
                    105: *> \param[out] INFO
                    106: *> \verbatim
                    107: *>          INFO is INTEGER
                    108: *>          = 0:  successful exit
                    109: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
                    110: *> \endverbatim
                    111: *
                    112: *  Authors:
                    113: *  ========
                    114: *
1.5     ! bertrand  115: *> \author Univ. of Tennessee
        !           116: *> \author Univ. of California Berkeley
        !           117: *> \author Univ. of Colorado Denver
        !           118: *> \author NAG Ltd.
1.1       bertrand  119: *
1.5     ! bertrand  120: *> \date December 2016
1.1       bertrand  121: *
                    122: *> \ingroup complex16SYcomputational
                    123: *
                    124: *> \par Contributors:
                    125: *  ==================
                    126: *> \verbatim
                    127: *>
1.5     ! bertrand  128: *>   December 2016, Igor Kozachenko,
1.1       bertrand  129: *>                  Computer Science Division,
                    130: *>                  University of California, Berkeley
                    131: *>
                    132: *>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                    133: *>                  School of Mathematics,
                    134: *>                  University of Manchester
                    135: *>
                    136: *> \endverbatim
                    137: *
                    138: *  =====================================================================
                    139:       SUBROUTINE ZSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
                    140:      $                        INFO )
                    141: *
1.5     ! bertrand  142: *  -- LAPACK computational routine (version 3.7.0) --
1.1       bertrand  143: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    144: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.5     ! bertrand  145: *     December 2016
1.1       bertrand  146: *
                    147: *     .. Scalar Arguments ..
                    148:       CHARACTER          UPLO
                    149:       INTEGER            INFO, LDA, N
                    150:       DOUBLE PRECISION   ANORM, RCOND
                    151: *     ..
                    152: *     .. Array Arguments ..
                    153:       INTEGER            IPIV( * )
                    154:       COMPLEX*16         A( LDA, * ), WORK( * )
                    155: *     ..
                    156: *
                    157: *  =====================================================================
                    158: *
                    159: *     .. Parameters ..
                    160:       DOUBLE PRECISION   ONE, ZERO
                    161:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
                    162:       COMPLEX*16            CZERO
                    163:       PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ) )
                    164: *     ..
                    165: *     .. Local Scalars ..
                    166:       LOGICAL            UPPER
                    167:       INTEGER            I, KASE
                    168:       DOUBLE PRECISION   AINVNM
                    169: *     ..
                    170: *     .. Local Arrays ..
                    171:       INTEGER            ISAVE( 3 )
                    172: *     ..
                    173: *     .. External Functions ..
                    174:       LOGICAL            LSAME
                    175:       EXTERNAL           LSAME
                    176: *     ..
                    177: *     .. External Subroutines ..
                    178:       EXTERNAL           ZLACN2, ZSYTRS_ROOK, XERBLA
                    179: *     ..
                    180: *     .. Intrinsic Functions ..
                    181:       INTRINSIC          MAX
                    182: *     ..
                    183: *     .. Executable Statements ..
                    184: *
                    185: *     Test the input parameters.
                    186: *
                    187:       INFO = 0
                    188:       UPPER = LSAME( UPLO, 'U' )
                    189:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
                    190:          INFO = -1
                    191:       ELSE IF( N.LT.0 ) THEN
                    192:          INFO = -2
                    193:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
                    194:          INFO = -4
                    195:       ELSE IF( ANORM.LT.ZERO ) THEN
                    196:          INFO = -6
                    197:       END IF
                    198:       IF( INFO.NE.0 ) THEN
                    199:          CALL XERBLA( 'ZSYCON_ROOK', -INFO )
                    200:          RETURN
                    201:       END IF
                    202: *
                    203: *     Quick return if possible
                    204: *
                    205:       RCOND = ZERO
                    206:       IF( N.EQ.0 ) THEN
                    207:          RCOND = ONE
                    208:          RETURN
                    209:       ELSE IF( ANORM.LE.ZERO ) THEN
                    210:          RETURN
                    211:       END IF
                    212: *
                    213: *     Check that the diagonal matrix D is nonsingular.
                    214: *
                    215:       IF( UPPER ) THEN
                    216: *
                    217: *        Upper triangular storage: examine D from bottom to top
                    218: *
                    219:          DO 10 I = N, 1, -1
                    220:             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.CZERO )
                    221:      $         RETURN
                    222:    10    CONTINUE
                    223:       ELSE
                    224: *
                    225: *        Lower triangular storage: examine D from top to bottom.
                    226: *
                    227:          DO 20 I = 1, N
                    228:             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.CZERO )
                    229:      $         RETURN
                    230:    20    CONTINUE
                    231:       END IF
                    232: *
                    233: *     Estimate the 1-norm of the inverse.
                    234: *
                    235:       KASE = 0
                    236:    30 CONTINUE
                    237:       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
                    238:       IF( KASE.NE.0 ) THEN
                    239: *
                    240: *        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
                    241: *
                    242:          CALL ZSYTRS_ROOK( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
                    243:          GO TO 30
                    244:       END IF
                    245: *
                    246: *     Compute the estimate of the reciprocal condition number.
                    247: *
                    248:       IF( AINVNM.NE.ZERO )
                    249:      $   RCOND = ( ONE / AINVNM ) / ANORM
                    250: *
                    251:       RETURN
                    252: *
                    253: *     End of ZSYCON_ROOK
                    254: *
                    255:       END

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