00001 /* zsytrf.f -- translated by f2c (version 20061008). 00002 You must link the resulting object file with libf2c: 00003 on Microsoft Windows system, link with libf2c.lib; 00004 on Linux or Unix systems, link with .../path/to/libf2c.a -lm 00005 or, if you install libf2c.a in a standard place, with -lf2c -lm 00006 -- in that order, at the end of the command line, as in 00007 cc *.o -lf2c -lm 00008 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., 00009 00010 http://www.netlib.org/f2c/libf2c.zip 00011 */ 00012 00013 #include "f2c.h" 00014 #include "blaswrap.h" 00015 00016 /* Table of constant values */ 00017 00018 static integer c__1 = 1; 00019 static integer c_n1 = -1; 00020 static integer c__2 = 2; 00021 00022 /* Subroutine */ int zsytrf_(char *uplo, integer *n, doublecomplex *a, 00023 integer *lda, integer *ipiv, doublecomplex *work, integer *lwork, 00024 integer *info) 00025 { 00026 /* System generated locals */ 00027 integer a_dim1, a_offset, i__1, i__2; 00028 00029 /* Local variables */ 00030 integer j, k, kb, nb, iws; 00031 extern logical lsame_(char *, char *); 00032 integer nbmin, iinfo; 00033 logical upper; 00034 extern /* Subroutine */ int zsytf2_(char *, integer *, doublecomplex *, 00035 integer *, integer *, integer *), xerbla_(char *, integer 00036 *); 00037 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00038 integer *, integer *); 00039 integer ldwork; 00040 extern /* Subroutine */ int zlasyf_(char *, integer *, integer *, integer 00041 *, doublecomplex *, integer *, integer *, doublecomplex *, 00042 integer *, integer *); 00043 integer lwkopt; 00044 logical lquery; 00045 00046 00047 /* -- LAPACK routine (version 3.2) -- */ 00048 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00049 /* November 2006 */ 00050 00051 /* .. Scalar Arguments .. */ 00052 /* .. */ 00053 /* .. Array Arguments .. */ 00054 /* .. */ 00055 00056 /* Purpose */ 00057 /* ======= */ 00058 00059 /* ZSYTRF computes the factorization of a complex symmetric matrix A */ 00060 /* using the Bunch-Kaufman diagonal pivoting method. The form of the */ 00061 /* factorization is */ 00062 00063 /* A = U*D*U**T or A = L*D*L**T */ 00064 00065 /* where U (or L) is a product of permutation and unit upper (lower) */ 00066 /* triangular matrices, and D is symmetric and block diagonal with */ 00067 /* with 1-by-1 and 2-by-2 diagonal blocks. */ 00068 00069 /* This is the blocked version of the algorithm, calling Level 3 BLAS. */ 00070 00071 /* Arguments */ 00072 /* ========= */ 00073 00074 /* UPLO (input) CHARACTER*1 */ 00075 /* = 'U': Upper triangle of A is stored; */ 00076 /* = 'L': Lower triangle of A is stored. */ 00077 00078 /* N (input) INTEGER */ 00079 /* The order of the matrix A. N >= 0. */ 00080 00081 /* A (input/output) COMPLEX*16 array, dimension (LDA,N) */ 00082 /* On entry, the symmetric matrix A. If UPLO = 'U', the leading */ 00083 /* N-by-N upper triangular part of A contains the upper */ 00084 /* triangular part of the matrix A, and the strictly lower */ 00085 /* triangular part of A is not referenced. If UPLO = 'L', the */ 00086 /* leading N-by-N lower triangular part of A contains the lower */ 00087 /* triangular part of the matrix A, and the strictly upper */ 00088 /* triangular part of A is not referenced. */ 00089 00090 /* On exit, the block diagonal matrix D and the multipliers used */ 00091 /* to obtain the factor U or L (see below for further details). */ 00092 00093 /* LDA (input) INTEGER */ 00094 /* The leading dimension of the array A. LDA >= max(1,N). */ 00095 00096 /* IPIV (output) INTEGER array, dimension (N) */ 00097 /* Details of the interchanges and the block structure of D. */ 00098 /* If IPIV(k) > 0, then rows and columns k and IPIV(k) were */ 00099 /* interchanged and D(k,k) is a 1-by-1 diagonal block. */ 00100 /* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */ 00101 /* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */ 00102 /* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = */ 00103 /* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */ 00104 /* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */ 00105 00106 /* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */ 00107 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00108 00109 /* LWORK (input) INTEGER */ 00110 /* The length of WORK. LWORK >=1. For best performance */ 00111 /* LWORK >= N*NB, where NB is the block size returned by ILAENV. */ 00112 00113 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00114 /* only calculates the optimal size of the WORK array, returns */ 00115 /* this value as the first entry of the WORK array, and no error */ 00116 /* message related to LWORK is issued by XERBLA. */ 00117 00118 /* INFO (output) INTEGER */ 00119 /* = 0: successful exit */ 00120 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00121 /* > 0: if INFO = i, D(i,i) is exactly zero. The factorization */ 00122 /* has been completed, but the block diagonal matrix D is */ 00123 /* exactly singular, and division by zero will occur if it */ 00124 /* is used to solve a system of equations. */ 00125 00126 /* Further Details */ 00127 /* =============== */ 00128 00129 /* If UPLO = 'U', then A = U*D*U', where */ 00130 /* U = P(n)*U(n)* ... *P(k)U(k)* ..., */ 00131 /* i.e., U is a product of terms P(k)*U(k), where k decreases from n to */ 00132 /* 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */ 00133 /* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */ 00134 /* defined by IPIV(k), and U(k) is a unit upper triangular matrix, such */ 00135 /* that if the diagonal block D(k) is of order s (s = 1 or 2), then */ 00136 00137 /* ( I v 0 ) k-s */ 00138 /* U(k) = ( 0 I 0 ) s */ 00139 /* ( 0 0 I ) n-k */ 00140 /* k-s s n-k */ 00141 00142 /* If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). */ 00143 /* If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), */ 00144 /* and A(k,k), and v overwrites A(1:k-2,k-1:k). */ 00145 00146 /* If UPLO = 'L', then A = L*D*L', where */ 00147 /* L = P(1)*L(1)* ... *P(k)*L(k)* ..., */ 00148 /* i.e., L is a product of terms P(k)*L(k), where k increases from 1 to */ 00149 /* n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */ 00150 /* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */ 00151 /* defined by IPIV(k), and L(k) is a unit lower triangular matrix, such */ 00152 /* that if the diagonal block D(k) is of order s (s = 1 or 2), then */ 00153 00154 /* ( I 0 0 ) k-1 */ 00155 /* L(k) = ( 0 I 0 ) s */ 00156 /* ( 0 v I ) n-k-s+1 */ 00157 /* k-1 s n-k-s+1 */ 00158 00159 /* If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). */ 00160 /* If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), */ 00161 /* and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). */ 00162 00163 /* ===================================================================== */ 00164 00165 /* .. Local Scalars .. */ 00166 /* .. */ 00167 /* .. External Functions .. */ 00168 /* .. */ 00169 /* .. External Subroutines .. */ 00170 /* .. */ 00171 /* .. Intrinsic Functions .. */ 00172 /* .. */ 00173 /* .. Executable Statements .. */ 00174 00175 /* Test the input parameters. */ 00176 00177 /* Parameter adjustments */ 00178 a_dim1 = *lda; 00179 a_offset = 1 + a_dim1; 00180 a -= a_offset; 00181 --ipiv; 00182 --work; 00183 00184 /* Function Body */ 00185 *info = 0; 00186 upper = lsame_(uplo, "U"); 00187 lquery = *lwork == -1; 00188 if (! upper && ! lsame_(uplo, "L")) { 00189 *info = -1; 00190 } else if (*n < 0) { 00191 *info = -2; 00192 } else if (*lda < max(1,*n)) { 00193 *info = -4; 00194 } else if (*lwork < 1 && ! lquery) { 00195 *info = -7; 00196 } 00197 00198 if (*info == 0) { 00199 00200 /* Determine the block size */ 00201 00202 nb = ilaenv_(&c__1, "ZSYTRF", uplo, n, &c_n1, &c_n1, &c_n1); 00203 lwkopt = *n * nb; 00204 work[1].r = (doublereal) lwkopt, work[1].i = 0.; 00205 } 00206 00207 if (*info != 0) { 00208 i__1 = -(*info); 00209 xerbla_("ZSYTRF", &i__1); 00210 return 0; 00211 } else if (lquery) { 00212 return 0; 00213 } 00214 00215 nbmin = 2; 00216 ldwork = *n; 00217 if (nb > 1 && nb < *n) { 00218 iws = ldwork * nb; 00219 if (*lwork < iws) { 00220 /* Computing MAX */ 00221 i__1 = *lwork / ldwork; 00222 nb = max(i__1,1); 00223 /* Computing MAX */ 00224 i__1 = 2, i__2 = ilaenv_(&c__2, "ZSYTRF", uplo, n, &c_n1, &c_n1, & 00225 c_n1); 00226 nbmin = max(i__1,i__2); 00227 } 00228 } else { 00229 iws = 1; 00230 } 00231 if (nb < nbmin) { 00232 nb = *n; 00233 } 00234 00235 if (upper) { 00236 00237 /* Factorize A as U*D*U' using the upper triangle of A */ 00238 00239 /* K is the main loop index, decreasing from N to 1 in steps of */ 00240 /* KB, where KB is the number of columns factorized by ZLASYF; */ 00241 /* KB is either NB or NB-1, or K for the last block */ 00242 00243 k = *n; 00244 L10: 00245 00246 /* If K < 1, exit from loop */ 00247 00248 if (k < 1) { 00249 goto L40; 00250 } 00251 00252 if (k > nb) { 00253 00254 /* Factorize columns k-kb+1:k of A and use blocked code to */ 00255 /* update columns 1:k-kb */ 00256 00257 zlasyf_(uplo, &k, &nb, &kb, &a[a_offset], lda, &ipiv[1], &work[1], 00258 n, &iinfo); 00259 } else { 00260 00261 /* Use unblocked code to factorize columns 1:k of A */ 00262 00263 zsytf2_(uplo, &k, &a[a_offset], lda, &ipiv[1], &iinfo); 00264 kb = k; 00265 } 00266 00267 /* Set INFO on the first occurrence of a zero pivot */ 00268 00269 if (*info == 0 && iinfo > 0) { 00270 *info = iinfo; 00271 } 00272 00273 /* Decrease K and return to the start of the main loop */ 00274 00275 k -= kb; 00276 goto L10; 00277 00278 } else { 00279 00280 /* Factorize A as L*D*L' using the lower triangle of A */ 00281 00282 /* K is the main loop index, increasing from 1 to N in steps of */ 00283 /* KB, where KB is the number of columns factorized by ZLASYF; */ 00284 /* KB is either NB or NB-1, or N-K+1 for the last block */ 00285 00286 k = 1; 00287 L20: 00288 00289 /* If K > N, exit from loop */ 00290 00291 if (k > *n) { 00292 goto L40; 00293 } 00294 00295 if (k <= *n - nb) { 00296 00297 /* Factorize columns k:k+kb-1 of A and use blocked code to */ 00298 /* update columns k+kb:n */ 00299 00300 i__1 = *n - k + 1; 00301 zlasyf_(uplo, &i__1, &nb, &kb, &a[k + k * a_dim1], lda, &ipiv[k], 00302 &work[1], n, &iinfo); 00303 } else { 00304 00305 /* Use unblocked code to factorize columns k:n of A */ 00306 00307 i__1 = *n - k + 1; 00308 zsytf2_(uplo, &i__1, &a[k + k * a_dim1], lda, &ipiv[k], &iinfo); 00309 kb = *n - k + 1; 00310 } 00311 00312 /* Set INFO on the first occurrence of a zero pivot */ 00313 00314 if (*info == 0 && iinfo > 0) { 00315 *info = iinfo + k - 1; 00316 } 00317 00318 /* Adjust IPIV */ 00319 00320 i__1 = k + kb - 1; 00321 for (j = k; j <= i__1; ++j) { 00322 if (ipiv[j] > 0) { 00323 ipiv[j] = ipiv[j] + k - 1; 00324 } else { 00325 ipiv[j] = ipiv[j] - k + 1; 00326 } 00327 /* L30: */ 00328 } 00329 00330 /* Increase K and return to the start of the main loop */ 00331 00332 k += kb; 00333 goto L20; 00334 00335 } 00336 00337 L40: 00338 work[1].r = (doublereal) lwkopt, work[1].i = 0.; 00339 return 0; 00340 00341 /* End of ZSYTRF */ 00342 00343 } /* zsytrf_ */