Annotation of rpl/lapack/lapack/zsytri_3.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZSYTRI_3
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZSYTRI_3 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytri_3.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytri_3.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytri_3.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZSYTRI_3( UPLO, N, A, LDA, E, IPIV, WORK, LWORK,
! 22: * INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER UPLO
! 26: * INTEGER INFO, LDA, LWORK, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * INTEGER IPIV( * )
! 30: * COMPLEX*16 A( LDA, * ), E( * ), WORK( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *> ZSYTRI_3 computes the inverse of a complex symmetric indefinite
! 39: *> matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:
! 40: *>
! 41: *> A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),
! 42: *>
! 43: *> where U (or L) is unit upper (or lower) triangular matrix,
! 44: *> U**T (or L**T) is the transpose of U (or L), P is a permutation
! 45: *> matrix, P**T is the transpose of P, and D is symmetric and block
! 46: *> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
! 47: *>
! 48: *> ZSYTRI_3 sets the leading dimension of the workspace before calling
! 49: *> ZSYTRI_3X that actually computes the inverse. This is the blocked
! 50: *> version of the algorithm, calling Level 3 BLAS.
! 51: *> \endverbatim
! 52: *
! 53: * Arguments:
! 54: * ==========
! 55: *
! 56: *> \param[in] UPLO
! 57: *> \verbatim
! 58: *> UPLO is CHARACTER*1
! 59: *> Specifies whether the details of the factorization are
! 60: *> stored as an upper or lower triangular matrix.
! 61: *> = 'U': Upper triangle of A is stored;
! 62: *> = 'L': Lower triangle of A is stored.
! 63: *> \endverbatim
! 64: *>
! 65: *> \param[in] N
! 66: *> \verbatim
! 67: *> N is INTEGER
! 68: *> The order of the matrix A. N >= 0.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in,out] A
! 72: *> \verbatim
! 73: *> A is COMPLEX*16 array, dimension (LDA,N)
! 74: *> On entry, diagonal of the block diagonal matrix D and
! 75: *> factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK:
! 76: *> a) ONLY diagonal elements of the symmetric block diagonal
! 77: *> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
! 78: *> (superdiagonal (or subdiagonal) elements of D
! 79: *> should be provided on entry in array E), and
! 80: *> b) If UPLO = 'U': factor U in the superdiagonal part of A.
! 81: *> If UPLO = 'L': factor L in the subdiagonal part of A.
! 82: *>
! 83: *> On exit, if INFO = 0, the symmetric inverse of the original
! 84: *> matrix.
! 85: *> If UPLO = 'U': the upper triangular part of the inverse
! 86: *> is formed and the part of A below the diagonal is not
! 87: *> referenced;
! 88: *> If UPLO = 'L': the lower triangular part of the inverse
! 89: *> is formed and the part of A above the diagonal is not
! 90: *> referenced.
! 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[in] E
! 100: *> \verbatim
! 101: *> E is COMPLEX*16 array, dimension (N)
! 102: *> On entry, contains the superdiagonal (or subdiagonal)
! 103: *> elements of the symmetric block diagonal matrix D
! 104: *> with 1-by-1 or 2-by-2 diagonal blocks, where
! 105: *> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not refernced;
! 106: *> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
! 107: *>
! 108: *> NOTE: For 1-by-1 diagonal block D(k), where
! 109: *> 1 <= k <= N, the element E(k) is not referenced in both
! 110: *> UPLO = 'U' or UPLO = 'L' cases.
! 111: *> \endverbatim
! 112: *>
! 113: *> \param[in] IPIV
! 114: *> \verbatim
! 115: *> IPIV is INTEGER array, dimension (N)
! 116: *> Details of the interchanges and the block structure of D
! 117: *> as determined by ZSYTRF_RK or ZSYTRF_BK.
! 118: *> \endverbatim
! 119: *>
! 120: *> \param[out] WORK
! 121: *> \verbatim
! 122: *> WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3).
! 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 >= (N+NB+1)*(NB+3).
! 130: *>
! 131: *> If LDWORK = -1, then a workspace query is assumed;
! 132: *> the routine only calculates the optimal size of the optimal
! 133: *> size of the WORK array, returns this value as the first
! 134: *> entry of the WORK array, and no error message related to
! 135: *> LWORK is issued by XERBLA.
! 136: *> \endverbatim
! 137: *>
! 138: *> \param[out] INFO
! 139: *> \verbatim
! 140: *> INFO is INTEGER
! 141: *> = 0: successful exit
! 142: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 143: *> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
! 144: *> inverse could not be computed.
! 145: *> \endverbatim
! 146: *
! 147: * Authors:
! 148: * ========
! 149: *
! 150: *> \author Univ. of Tennessee
! 151: *> \author Univ. of California Berkeley
! 152: *> \author Univ. of Colorado Denver
! 153: *> \author NAG Ltd.
! 154: *
! 155: *> \date December 2016
! 156: *
! 157: *> \ingroup complex16SYcomputational
! 158: *
! 159: *> \par Contributors:
! 160: * ==================
! 161: *> \verbatim
! 162: *>
! 163: *> December 2016, Igor Kozachenko,
! 164: *> Computer Science Division,
! 165: *> University of California, Berkeley
! 166: *>
! 167: *> \endverbatim
! 168: *
! 169: * =====================================================================
! 170: SUBROUTINE ZSYTRI_3( UPLO, N, A, LDA, E, IPIV, WORK, LWORK,
! 171: $ INFO )
! 172: *
! 173: * -- LAPACK computational routine (version 3.7.0) --
! 174: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 175: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 176: * December 2016
! 177: *
! 178: * .. Scalar Arguments ..
! 179: CHARACTER UPLO
! 180: INTEGER INFO, LDA, LWORK, N
! 181: * ..
! 182: * .. Array Arguments ..
! 183: INTEGER IPIV( * )
! 184: COMPLEX*16 A( LDA, * ), E( * ), WORK( * )
! 185: * ..
! 186: *
! 187: * =====================================================================
! 188: *
! 189: * .. Local Scalars ..
! 190: LOGICAL UPPER, LQUERY
! 191: INTEGER LWKOPT, NB
! 192: * ..
! 193: * .. External Functions ..
! 194: LOGICAL LSAME
! 195: INTEGER ILAENV
! 196: EXTERNAL LSAME, ILAENV
! 197: * ..
! 198: * .. External Subroutines ..
! 199: EXTERNAL ZSYTRI_3X
! 200: * ..
! 201: * .. Intrinsic Functions ..
! 202: INTRINSIC MAX
! 203: * ..
! 204: * .. Executable Statements ..
! 205: *
! 206: * Test the input parameters.
! 207: *
! 208: INFO = 0
! 209: UPPER = LSAME( UPLO, 'U' )
! 210: LQUERY = ( LWORK.EQ.-1 )
! 211: *
! 212: * Determine the block size
! 213: *
! 214: NB = MAX( 1, ILAENV( 1, 'ZSYTRI_3', UPLO, N, -1, -1, -1 ) )
! 215: LWKOPT = ( N+NB+1 ) * ( NB+3 )
! 216: *
! 217: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 218: INFO = -1
! 219: ELSE IF( N.LT.0 ) THEN
! 220: INFO = -2
! 221: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 222: INFO = -4
! 223: ELSE IF ( LWORK .LT. LWKOPT .AND. .NOT.LQUERY ) THEN
! 224: INFO = -8
! 225: END IF
! 226: *
! 227: IF( INFO.NE.0 ) THEN
! 228: CALL XERBLA( 'ZSYTRI_3', -INFO )
! 229: RETURN
! 230: ELSE IF( LQUERY ) THEN
! 231: WORK( 1 ) = LWKOPT
! 232: RETURN
! 233: END IF
! 234: *
! 235: * Quick return if possible
! 236: *
! 237: IF( N.EQ.0 )
! 238: $ RETURN
! 239: *
! 240: CALL ZSYTRI_3X( UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO )
! 241: *
! 242: WORK( 1 ) = LWKOPT
! 243: *
! 244: RETURN
! 245: *
! 246: * End of ZSYTRI_3
! 247: *
! 248: END
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