Annotation of rpl/lapack/lapack/zsycon_rook.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZSYCON_ROOK
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 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">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZSYCON_ROOK( UPLO, N, A, LDA, IPIV, ANORM, RCOND,
! 22: * WORK, INFO )
! 23: *
! 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: * ..
! 33: *
! 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: *
! 115: *> \author Univ. of Tennessee
! 116: *> \author Univ. of California Berkeley
! 117: *> \author Univ. of Colorado Denver
! 118: *> \author NAG Ltd.
! 119: *
! 120: *> \date November 2011
! 121: *
! 122: *> \ingroup complex16SYcomputational
! 123: *
! 124: *> \par Contributors:
! 125: * ==================
! 126: *> \verbatim
! 127: *>
! 128: *> November 2011, Igor Kozachenko,
! 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: *
! 142: * -- LAPACK computational routine (version 3.4.0) --
! 143: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 144: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 145: * November 2011
! 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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