LAPACK 3.3.0

# csytrf.f

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```00001       SUBROUTINE CSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          UPLO
00010       INTEGER            INFO, LDA, LWORK, N
00011 *     ..
00012 *     .. Array Arguments ..
00013       INTEGER            IPIV( * )
00014       COMPLEX            A( LDA, * ), WORK( * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  CSYTRF computes the factorization of a complex symmetric matrix A
00021 *  using the Bunch-Kaufman diagonal pivoting method.  The form of the
00022 *  factorization is
00023 *
00024 *     A = U*D*U**T  or  A = L*D*L**T
00025 *
00026 *  where U (or L) is a product of permutation and unit upper (lower)
00027 *  triangular matrices, and D is symmetric and block diagonal with
00028 *  with 1-by-1 and 2-by-2 diagonal blocks.
00029 *
00030 *  This is the blocked version of the algorithm, calling Level 3 BLAS.
00031 *
00032 *  Arguments
00033 *  =========
00034 *
00035 *  UPLO    (input) CHARACTER*1
00036 *          = 'U':  Upper triangle of A is stored;
00037 *          = 'L':  Lower triangle of A is stored.
00038 *
00039 *  N       (input) INTEGER
00040 *          The order of the matrix A.  N >= 0.
00041 *
00042 *  A       (input/output) COMPLEX array, dimension (LDA,N)
00043 *          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
00044 *          N-by-N upper triangular part of A contains the upper
00045 *          triangular part of the matrix A, and the strictly lower
00046 *          triangular part of A is not referenced.  If UPLO = 'L', the
00047 *          leading N-by-N lower triangular part of A contains the lower
00048 *          triangular part of the matrix A, and the strictly upper
00049 *          triangular part of A is not referenced.
00050 *
00051 *          On exit, the block diagonal matrix D and the multipliers used
00052 *          to obtain the factor U or L (see below for further details).
00053 *
00054 *  LDA     (input) INTEGER
00055 *          The leading dimension of the array A.  LDA >= max(1,N).
00056 *
00057 *  IPIV    (output) INTEGER array, dimension (N)
00058 *          Details of the interchanges and the block structure of D.
00059 *          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
00060 *          interchanged and D(k,k) is a 1-by-1 diagonal block.
00061 *          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
00062 *          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
00063 *          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
00064 *          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
00065 *          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
00066 *
00067 *  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
00068 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00069 *
00070 *  LWORK   (input) INTEGER
00071 *          The length of WORK.  LWORK >=1.  For best performance
00072 *          LWORK >= N*NB, where NB is the block size returned by ILAENV.
00073 *
00074 *          If LWORK = -1, then a workspace query is assumed; the routine
00075 *          only calculates the optimal size of the WORK array, returns
00076 *          this value as the first entry of the WORK array, and no error
00077 *          message related to LWORK is issued by XERBLA.
00078 *
00079 *  INFO    (output) INTEGER
00080 *          = 0:  successful exit
00081 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00082 *          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
00083 *                has been completed, but the block diagonal matrix D is
00084 *                exactly singular, and division by zero will occur if it
00085 *                is used to solve a system of equations.
00086 *
00087 *  Further Details
00088 *  ===============
00089 *
00090 *  If UPLO = 'U', then A = U*D*U', where
00091 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
00092 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
00093 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
00094 *  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
00095 *  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
00096 *  that if the diagonal block D(k) is of order s (s = 1 or 2), then
00097 *
00098 *             (   I    v    0   )   k-s
00099 *     U(k) =  (   0    I    0   )   s
00100 *             (   0    0    I   )   n-k
00101 *                k-s   s   n-k
00102 *
00103 *  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
00104 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
00105 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
00106 *
00107 *  If UPLO = 'L', then A = L*D*L', where
00108 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
00109 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
00110 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
00111 *  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
00112 *  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
00113 *  that if the diagonal block D(k) is of order s (s = 1 or 2), then
00114 *
00115 *             (   I    0     0   )  k-1
00116 *     L(k) =  (   0    I     0   )  s
00117 *             (   0    v     I   )  n-k-s+1
00118 *                k-1   s  n-k-s+1
00119 *
00120 *  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
00121 *  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
00122 *  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
00123 *
00124 *  =====================================================================
00125 *
00126 *     .. Local Scalars ..
00127       LOGICAL            LQUERY, UPPER
00128       INTEGER            IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
00129 *     ..
00130 *     .. External Functions ..
00131       LOGICAL            LSAME
00132       INTEGER            ILAENV
00133       EXTERNAL           LSAME, ILAENV
00134 *     ..
00135 *     .. External Subroutines ..
00136       EXTERNAL           CLASYF, CSYTF2, XERBLA
00137 *     ..
00138 *     .. Intrinsic Functions ..
00139       INTRINSIC          MAX
00140 *     ..
00141 *     .. Executable Statements ..
00142 *
00143 *     Test the input parameters.
00144 *
00145       INFO = 0
00146       UPPER = LSAME( UPLO, 'U' )
00147       LQUERY = ( LWORK.EQ.-1 )
00148       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00149          INFO = -1
00150       ELSE IF( N.LT.0 ) THEN
00151          INFO = -2
00152       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00153          INFO = -4
00154       ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
00155          INFO = -7
00156       END IF
00157 *
00158       IF( INFO.EQ.0 ) THEN
00159 *
00160 *        Determine the block size
00161 *
00162          NB = ILAENV( 1, 'CSYTRF', UPLO, N, -1, -1, -1 )
00163          LWKOPT = N*NB
00164          WORK( 1 ) = LWKOPT
00165       END IF
00166 *
00167       IF( INFO.NE.0 ) THEN
00168          CALL XERBLA( 'CSYTRF', -INFO )
00169          RETURN
00170       ELSE IF( LQUERY ) THEN
00171          RETURN
00172       END IF
00173 *
00174       NBMIN = 2
00175       LDWORK = N
00176       IF( NB.GT.1 .AND. NB.LT.N ) THEN
00177          IWS = LDWORK*NB
00178          IF( LWORK.LT.IWS ) THEN
00179             NB = MAX( LWORK / LDWORK, 1 )
00180             NBMIN = MAX( 2, ILAENV( 2, 'CSYTRF', UPLO, N, -1, -1, -1 ) )
00181          END IF
00182       ELSE
00183          IWS = 1
00184       END IF
00185       IF( NB.LT.NBMIN )
00186      \$   NB = N
00187 *
00188       IF( UPPER ) THEN
00189 *
00190 *        Factorize A as U*D*U' using the upper triangle of A
00191 *
00192 *        K is the main loop index, decreasing from N to 1 in steps of
00193 *        KB, where KB is the number of columns factorized by CLASYF;
00194 *        KB is either NB or NB-1, or K for the last block
00195 *
00196          K = N
00197    10    CONTINUE
00198 *
00199 *        If K < 1, exit from loop
00200 *
00201          IF( K.LT.1 )
00202      \$      GO TO 40
00203 *
00204          IF( K.GT.NB ) THEN
00205 *
00206 *           Factorize columns k-kb+1:k of A and use blocked code to
00207 *           update columns 1:k-kb
00208 *
00209             CALL CLASYF( UPLO, K, NB, KB, A, LDA, IPIV, WORK, N, IINFO )
00210          ELSE
00211 *
00212 *           Use unblocked code to factorize columns 1:k of A
00213 *
00214             CALL CSYTF2( UPLO, K, A, LDA, IPIV, IINFO )
00215             KB = K
00216          END IF
00217 *
00218 *        Set INFO on the first occurrence of a zero pivot
00219 *
00220          IF( INFO.EQ.0 .AND. IINFO.GT.0 )
00221      \$      INFO = IINFO
00222 *
00223 *        Decrease K and return to the start of the main loop
00224 *
00225          K = K - KB
00226          GO TO 10
00227 *
00228       ELSE
00229 *
00230 *        Factorize A as L*D*L' using the lower triangle of A
00231 *
00232 *        K is the main loop index, increasing from 1 to N in steps of
00233 *        KB, where KB is the number of columns factorized by CLASYF;
00234 *        KB is either NB or NB-1, or N-K+1 for the last block
00235 *
00236          K = 1
00237    20    CONTINUE
00238 *
00239 *        If K > N, exit from loop
00240 *
00241          IF( K.GT.N )
00242      \$      GO TO 40
00243 *
00244          IF( K.LE.N-NB ) THEN
00245 *
00246 *           Factorize columns k:k+kb-1 of A and use blocked code to
00247 *           update columns k+kb:n
00248 *
00249             CALL CLASYF( UPLO, N-K+1, NB, KB, A( K, K ), LDA, IPIV( K ),
00250      \$                   WORK, N, IINFO )
00251          ELSE
00252 *
00253 *           Use unblocked code to factorize columns k:n of A
00254 *
00255             CALL CSYTF2( UPLO, N-K+1, A( K, K ), LDA, IPIV( K ), IINFO )
00256             KB = N - K + 1
00257          END IF
00258 *
00259 *        Set INFO on the first occurrence of a zero pivot
00260 *
00261          IF( INFO.EQ.0 .AND. IINFO.GT.0 )
00262      \$      INFO = IINFO + K - 1
00263 *
00265 *
00266          DO 30 J = K, K + KB - 1
00267             IF( IPIV( J ).GT.0 ) THEN
00268                IPIV( J ) = IPIV( J ) + K - 1
00269             ELSE
00270                IPIV( J ) = IPIV( J ) - K + 1
00271             END IF
00272    30    CONTINUE
00273 *
00274 *        Increase K and return to the start of the main loop
00275 *
00276          K = K + KB
00277          GO TO 20
00278 *
00279       END IF
00280 *
00281    40 CONTINUE
00282       WORK( 1 ) = LWKOPT
00283       RETURN
00284 *
00285 *     End of CSYTRF
00286 *
00287       END
```