00001 /* csytrf.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 csytrf_(char *uplo, integer *n, complex *a, integer *lda, 00023 integer *ipiv, complex *work, integer *lwork, integer *info) 00024 { 00025 /* System generated locals */ 00026 integer a_dim1, a_offset, i__1, i__2; 00027 00028 /* Local variables */ 00029 integer j, k, kb, nb, iws; 00030 extern logical lsame_(char *, char *); 00031 integer nbmin, iinfo; 00032 logical upper; 00033 extern /* Subroutine */ int csytf2_(char *, integer *, complex *, integer 00034 *, integer *, integer *), xerbla_(char *, integer *); 00035 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00036 integer *, integer *); 00037 extern /* Subroutine */ int clasyf_(char *, integer *, integer *, integer 00038 *, complex *, integer *, integer *, complex *, integer *, integer 00039 *); 00040 integer ldwork, lwkopt; 00041 logical lquery; 00042 00043 00044 /* -- LAPACK routine (version 3.2) -- */ 00045 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00046 /* November 2006 */ 00047 00048 /* .. Scalar Arguments .. */ 00049 /* .. */ 00050 /* .. Array Arguments .. */ 00051 /* .. */ 00052 00053 /* Purpose */ 00054 /* ======= */ 00055 00056 /* CSYTRF computes the factorization of a complex symmetric matrix A */ 00057 /* using the Bunch-Kaufman diagonal pivoting method. The form of the */ 00058 /* factorization is */ 00059 00060 /* A = U*D*U**T or A = L*D*L**T */ 00061 00062 /* where U (or L) is a product of permutation and unit upper (lower) */ 00063 /* triangular matrices, and D is symmetric and block diagonal with */ 00064 /* with 1-by-1 and 2-by-2 diagonal blocks. */ 00065 00066 /* This is the blocked version of the algorithm, calling Level 3 BLAS. */ 00067 00068 /* Arguments */ 00069 /* ========= */ 00070 00071 /* UPLO (input) CHARACTER*1 */ 00072 /* = 'U': Upper triangle of A is stored; */ 00073 /* = 'L': Lower triangle of A is stored. */ 00074 00075 /* N (input) INTEGER */ 00076 /* The order of the matrix A. N >= 0. */ 00077 00078 /* A (input/output) COMPLEX array, dimension (LDA,N) */ 00079 /* On entry, the symmetric matrix A. If UPLO = 'U', the leading */ 00080 /* N-by-N upper triangular part of A contains the upper */ 00081 /* triangular part of the matrix A, and the strictly lower */ 00082 /* triangular part of A is not referenced. If UPLO = 'L', the */ 00083 /* leading N-by-N lower triangular part of A contains the lower */ 00084 /* triangular part of the matrix A, and the strictly upper */ 00085 /* triangular part of A is not referenced. */ 00086 00087 /* On exit, the block diagonal matrix D and the multipliers used */ 00088 /* to obtain the factor U or L (see below for further details). */ 00089 00090 /* LDA (input) INTEGER */ 00091 /* The leading dimension of the array A. LDA >= max(1,N). */ 00092 00093 /* IPIV (output) INTEGER array, dimension (N) */ 00094 /* Details of the interchanges and the block structure of D. */ 00095 /* If IPIV(k) > 0, then rows and columns k and IPIV(k) were */ 00096 /* interchanged and D(k,k) is a 1-by-1 diagonal block. */ 00097 /* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */ 00098 /* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */ 00099 /* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = */ 00100 /* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */ 00101 /* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */ 00102 00103 /* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */ 00104 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00105 00106 /* LWORK (input) INTEGER */ 00107 /* The length of WORK. LWORK >=1. For best performance */ 00108 /* LWORK >= N*NB, where NB is the block size returned by ILAENV. */ 00109 00110 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00111 /* only calculates the optimal size of the WORK array, returns */ 00112 /* this value as the first entry of the WORK array, and no error */ 00113 /* message related to LWORK is issued by XERBLA. */ 00114 00115 /* INFO (output) INTEGER */ 00116 /* = 0: successful exit */ 00117 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00118 /* > 0: if INFO = i, D(i,i) is exactly zero. The factorization */ 00119 /* has been completed, but the block diagonal matrix D is */ 00120 /* exactly singular, and division by zero will occur if it */ 00121 /* is used to solve a system of equations. */ 00122 00123 /* Further Details */ 00124 /* =============== */ 00125 00126 /* If UPLO = 'U', then A = U*D*U', where */ 00127 /* U = P(n)*U(n)* ... *P(k)U(k)* ..., */ 00128 /* i.e., U is a product of terms P(k)*U(k), where k decreases from n to */ 00129 /* 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */ 00130 /* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */ 00131 /* defined by IPIV(k), and U(k) is a unit upper triangular matrix, such */ 00132 /* that if the diagonal block D(k) is of order s (s = 1 or 2), then */ 00133 00134 /* ( I v 0 ) k-s */ 00135 /* U(k) = ( 0 I 0 ) s */ 00136 /* ( 0 0 I ) n-k */ 00137 /* k-s s n-k */ 00138 00139 /* If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). */ 00140 /* If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), */ 00141 /* and A(k,k), and v overwrites A(1:k-2,k-1:k). */ 00142 00143 /* If UPLO = 'L', then A = L*D*L', where */ 00144 /* L = P(1)*L(1)* ... *P(k)*L(k)* ..., */ 00145 /* i.e., L is a product of terms P(k)*L(k), where k increases from 1 to */ 00146 /* n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */ 00147 /* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */ 00148 /* defined by IPIV(k), and L(k) is a unit lower triangular matrix, such */ 00149 /* that if the diagonal block D(k) is of order s (s = 1 or 2), then */ 00150 00151 /* ( I 0 0 ) k-1 */ 00152 /* L(k) = ( 0 I 0 ) s */ 00153 /* ( 0 v I ) n-k-s+1 */ 00154 /* k-1 s n-k-s+1 */ 00155 00156 /* If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). */ 00157 /* If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), */ 00158 /* and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). */ 00159 00160 /* ===================================================================== */ 00161 00162 /* .. Local Scalars .. */ 00163 /* .. */ 00164 /* .. External Functions .. */ 00165 /* .. */ 00166 /* .. External Subroutines .. */ 00167 /* .. */ 00168 /* .. Intrinsic Functions .. */ 00169 /* .. */ 00170 /* .. Executable Statements .. */ 00171 00172 /* Test the input parameters. */ 00173 00174 /* Parameter adjustments */ 00175 a_dim1 = *lda; 00176 a_offset = 1 + a_dim1; 00177 a -= a_offset; 00178 --ipiv; 00179 --work; 00180 00181 /* Function Body */ 00182 *info = 0; 00183 upper = lsame_(uplo, "U"); 00184 lquery = *lwork == -1; 00185 if (! upper && ! lsame_(uplo, "L")) { 00186 *info = -1; 00187 } else if (*n < 0) { 00188 *info = -2; 00189 } else if (*lda < max(1,*n)) { 00190 *info = -4; 00191 } else if (*lwork < 1 && ! lquery) { 00192 *info = -7; 00193 } 00194 00195 if (*info == 0) { 00196 00197 /* Determine the block size */ 00198 00199 nb = ilaenv_(&c__1, "CSYTRF", uplo, n, &c_n1, &c_n1, &c_n1); 00200 lwkopt = *n * nb; 00201 work[1].r = (real) lwkopt, work[1].i = 0.f; 00202 } 00203 00204 if (*info != 0) { 00205 i__1 = -(*info); 00206 xerbla_("CSYTRF", &i__1); 00207 return 0; 00208 } else if (lquery) { 00209 return 0; 00210 } 00211 00212 nbmin = 2; 00213 ldwork = *n; 00214 if (nb > 1 && nb < *n) { 00215 iws = ldwork * nb; 00216 if (*lwork < iws) { 00217 /* Computing MAX */ 00218 i__1 = *lwork / ldwork; 00219 nb = max(i__1,1); 00220 /* Computing MAX */ 00221 i__1 = 2, i__2 = ilaenv_(&c__2, "CSYTRF", uplo, n, &c_n1, &c_n1, & 00222 c_n1); 00223 nbmin = max(i__1,i__2); 00224 } 00225 } else { 00226 iws = 1; 00227 } 00228 if (nb < nbmin) { 00229 nb = *n; 00230 } 00231 00232 if (upper) { 00233 00234 /* Factorize A as U*D*U' using the upper triangle of A */ 00235 00236 /* K is the main loop index, decreasing from N to 1 in steps of */ 00237 /* KB, where KB is the number of columns factorized by CLASYF; */ 00238 /* KB is either NB or NB-1, or K for the last block */ 00239 00240 k = *n; 00241 L10: 00242 00243 /* If K < 1, exit from loop */ 00244 00245 if (k < 1) { 00246 goto L40; 00247 } 00248 00249 if (k > nb) { 00250 00251 /* Factorize columns k-kb+1:k of A and use blocked code to */ 00252 /* update columns 1:k-kb */ 00253 00254 clasyf_(uplo, &k, &nb, &kb, &a[a_offset], lda, &ipiv[1], &work[1], 00255 n, &iinfo); 00256 } else { 00257 00258 /* Use unblocked code to factorize columns 1:k of A */ 00259 00260 csytf2_(uplo, &k, &a[a_offset], lda, &ipiv[1], &iinfo); 00261 kb = k; 00262 } 00263 00264 /* Set INFO on the first occurrence of a zero pivot */ 00265 00266 if (*info == 0 && iinfo > 0) { 00267 *info = iinfo; 00268 } 00269 00270 /* Decrease K and return to the start of the main loop */ 00271 00272 k -= kb; 00273 goto L10; 00274 00275 } else { 00276 00277 /* Factorize A as L*D*L' using the lower triangle of A */ 00278 00279 /* K is the main loop index, increasing from 1 to N in steps of */ 00280 /* KB, where KB is the number of columns factorized by CLASYF; */ 00281 /* KB is either NB or NB-1, or N-K+1 for the last block */ 00282 00283 k = 1; 00284 L20: 00285 00286 /* If K > N, exit from loop */ 00287 00288 if (k > *n) { 00289 goto L40; 00290 } 00291 00292 if (k <= *n - nb) { 00293 00294 /* Factorize columns k:k+kb-1 of A and use blocked code to */ 00295 /* update columns k+kb:n */ 00296 00297 i__1 = *n - k + 1; 00298 clasyf_(uplo, &i__1, &nb, &kb, &a[k + k * a_dim1], lda, &ipiv[k], 00299 &work[1], n, &iinfo); 00300 } else { 00301 00302 /* Use unblocked code to factorize columns k:n of A */ 00303 00304 i__1 = *n - k + 1; 00305 csytf2_(uplo, &i__1, &a[k + k * a_dim1], lda, &ipiv[k], &iinfo); 00306 kb = *n - k + 1; 00307 } 00308 00309 /* Set INFO on the first occurrence of a zero pivot */ 00310 00311 if (*info == 0 && iinfo > 0) { 00312 *info = iinfo + k - 1; 00313 } 00314 00315 /* Adjust IPIV */ 00316 00317 i__1 = k + kb - 1; 00318 for (j = k; j <= i__1; ++j) { 00319 if (ipiv[j] > 0) { 00320 ipiv[j] = ipiv[j] + k - 1; 00321 } else { 00322 ipiv[j] = ipiv[j] - k + 1; 00323 } 00324 /* L30: */ 00325 } 00326 00327 /* Increase K and return to the start of the main loop */ 00328 00329 k += kb; 00330 goto L20; 00331 00332 } 00333 00334 L40: 00335 work[1].r = (real) lwkopt, work[1].i = 0.f; 00336 return 0; 00337 00338 /* End of CSYTRF */ 00339 00340 } /* csytrf_ */