00001 /* dsytrf.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 dsytrf_(char *uplo, integer *n, doublereal *a, integer * 00023 lda, integer *ipiv, doublereal *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 dsytf2_(char *, integer *, doublereal *, 00034 integer *, integer *, integer *), xerbla_(char *, integer 00035 *); 00036 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00037 integer *, integer *); 00038 extern /* Subroutine */ int dlasyf_(char *, integer *, integer *, integer 00039 *, doublereal *, integer *, integer *, doublereal *, integer *, 00040 integer *); 00041 integer ldwork, lwkopt; 00042 logical lquery; 00043 00044 00045 /* -- LAPACK routine (version 3.2) -- */ 00046 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00047 /* November 2006 */ 00048 00049 /* .. Scalar Arguments .. */ 00050 /* .. */ 00051 /* .. Array Arguments .. */ 00052 /* .. */ 00053 00054 /* Purpose */ 00055 /* ======= */ 00056 00057 /* DSYTRF computes the factorization of a real symmetric matrix A using */ 00058 /* the Bunch-Kaufman diagonal pivoting method. The form of the */ 00059 /* factorization is */ 00060 00061 /* A = U*D*U**T or A = L*D*L**T */ 00062 00063 /* where U (or L) is a product of permutation and unit upper (lower) */ 00064 /* triangular matrices, and D is symmetric and block diagonal with */ 00065 /* 1-by-1 and 2-by-2 diagonal blocks. */ 00066 00067 /* This is the blocked version of the algorithm, calling Level 3 BLAS. */ 00068 00069 /* Arguments */ 00070 /* ========= */ 00071 00072 /* UPLO (input) CHARACTER*1 */ 00073 /* = 'U': Upper triangle of A is stored; */ 00074 /* = 'L': Lower triangle of A is stored. */ 00075 00076 /* N (input) INTEGER */ 00077 /* The order of the matrix A. N >= 0. */ 00078 00079 /* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ 00080 /* On entry, the symmetric matrix A. If UPLO = 'U', the leading */ 00081 /* N-by-N upper triangular part of A contains the upper */ 00082 /* triangular part of the matrix A, and the strictly lower */ 00083 /* triangular part of A is not referenced. If UPLO = 'L', the */ 00084 /* leading N-by-N lower triangular part of A contains the lower */ 00085 /* triangular part of the matrix A, and the strictly upper */ 00086 /* triangular part of A is not referenced. */ 00087 00088 /* On exit, the block diagonal matrix D and the multipliers used */ 00089 /* to obtain the factor U or L (see below for further details). */ 00090 00091 /* LDA (input) INTEGER */ 00092 /* The leading dimension of the array A. LDA >= max(1,N). */ 00093 00094 /* IPIV (output) INTEGER array, dimension (N) */ 00095 /* Details of the interchanges and the block structure of D. */ 00096 /* If IPIV(k) > 0, then rows and columns k and IPIV(k) were */ 00097 /* interchanged and D(k,k) is a 1-by-1 diagonal block. */ 00098 /* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */ 00099 /* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */ 00100 /* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = */ 00101 /* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */ 00102 /* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */ 00103 00104 /* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ 00105 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00106 00107 /* LWORK (input) INTEGER */ 00108 /* The length of WORK. LWORK >=1. For best performance */ 00109 /* LWORK >= N*NB, where NB is the block size returned by ILAENV. */ 00110 00111 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00112 /* only calculates the optimal size of the WORK array, returns */ 00113 /* this value as the first entry of the WORK array, and no error */ 00114 /* message related to LWORK is issued by XERBLA. */ 00115 00116 /* INFO (output) INTEGER */ 00117 /* = 0: successful exit */ 00118 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00119 /* > 0: if INFO = i, D(i,i) is exactly zero. The factorization */ 00120 /* has been completed, but the block diagonal matrix D is */ 00121 /* exactly singular, and division by zero will occur if it */ 00122 /* is used to solve a system of equations. */ 00123 00124 /* Further Details */ 00125 /* =============== */ 00126 00127 /* If UPLO = 'U', then A = U*D*U', where */ 00128 /* U = P(n)*U(n)* ... *P(k)U(k)* ..., */ 00129 /* i.e., U is a product of terms P(k)*U(k), where k decreases from n to */ 00130 /* 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */ 00131 /* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */ 00132 /* defined by IPIV(k), and U(k) is a unit upper triangular matrix, such */ 00133 /* that if the diagonal block D(k) is of order s (s = 1 or 2), then */ 00134 00135 /* ( I v 0 ) k-s */ 00136 /* U(k) = ( 0 I 0 ) s */ 00137 /* ( 0 0 I ) n-k */ 00138 /* k-s s n-k */ 00139 00140 /* If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). */ 00141 /* If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), */ 00142 /* and A(k,k), and v overwrites A(1:k-2,k-1:k). */ 00143 00144 /* If UPLO = 'L', then A = L*D*L', where */ 00145 /* L = P(1)*L(1)* ... *P(k)*L(k)* ..., */ 00146 /* i.e., L is a product of terms P(k)*L(k), where k increases from 1 to */ 00147 /* n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */ 00148 /* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as */ 00149 /* defined by IPIV(k), and L(k) is a unit lower triangular matrix, such */ 00150 /* that if the diagonal block D(k) is of order s (s = 1 or 2), then */ 00151 00152 /* ( I 0 0 ) k-1 */ 00153 /* L(k) = ( 0 I 0 ) s */ 00154 /* ( 0 v I ) n-k-s+1 */ 00155 /* k-1 s n-k-s+1 */ 00156 00157 /* If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). */ 00158 /* If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), */ 00159 /* and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). */ 00160 00161 /* ===================================================================== */ 00162 00163 /* .. Local Scalars .. */ 00164 /* .. */ 00165 /* .. External Functions .. */ 00166 /* .. */ 00167 /* .. External Subroutines .. */ 00168 /* .. */ 00169 /* .. Intrinsic Functions .. */ 00170 /* .. */ 00171 /* .. Executable Statements .. */ 00172 00173 /* Test the input parameters. */ 00174 00175 /* Parameter adjustments */ 00176 a_dim1 = *lda; 00177 a_offset = 1 + a_dim1; 00178 a -= a_offset; 00179 --ipiv; 00180 --work; 00181 00182 /* Function Body */ 00183 *info = 0; 00184 upper = lsame_(uplo, "U"); 00185 lquery = *lwork == -1; 00186 if (! upper && ! lsame_(uplo, "L")) { 00187 *info = -1; 00188 } else if (*n < 0) { 00189 *info = -2; 00190 } else if (*lda < max(1,*n)) { 00191 *info = -4; 00192 } else if (*lwork < 1 && ! lquery) { 00193 *info = -7; 00194 } 00195 00196 if (*info == 0) { 00197 00198 /* Determine the block size */ 00199 00200 nb = ilaenv_(&c__1, "DSYTRF", uplo, n, &c_n1, &c_n1, &c_n1); 00201 lwkopt = *n * nb; 00202 work[1] = (doublereal) lwkopt; 00203 } 00204 00205 if (*info != 0) { 00206 i__1 = -(*info); 00207 xerbla_("DSYTRF", &i__1); 00208 return 0; 00209 } else if (lquery) { 00210 return 0; 00211 } 00212 00213 nbmin = 2; 00214 ldwork = *n; 00215 if (nb > 1 && nb < *n) { 00216 iws = ldwork * nb; 00217 if (*lwork < iws) { 00218 /* Computing MAX */ 00219 i__1 = *lwork / ldwork; 00220 nb = max(i__1,1); 00221 /* Computing MAX */ 00222 i__1 = 2, i__2 = ilaenv_(&c__2, "DSYTRF", uplo, n, &c_n1, &c_n1, & 00223 c_n1); 00224 nbmin = max(i__1,i__2); 00225 } 00226 } else { 00227 iws = 1; 00228 } 00229 if (nb < nbmin) { 00230 nb = *n; 00231 } 00232 00233 if (upper) { 00234 00235 /* Factorize A as U*D*U' using the upper triangle of A */ 00236 00237 /* K is the main loop index, decreasing from N to 1 in steps of */ 00238 /* KB, where KB is the number of columns factorized by DLASYF; */ 00239 /* KB is either NB or NB-1, or K for the last block */ 00240 00241 k = *n; 00242 L10: 00243 00244 /* If K < 1, exit from loop */ 00245 00246 if (k < 1) { 00247 goto L40; 00248 } 00249 00250 if (k > nb) { 00251 00252 /* Factorize columns k-kb+1:k of A and use blocked code to */ 00253 /* update columns 1:k-kb */ 00254 00255 dlasyf_(uplo, &k, &nb, &kb, &a[a_offset], lda, &ipiv[1], &work[1], 00256 &ldwork, &iinfo); 00257 } else { 00258 00259 /* Use unblocked code to factorize columns 1:k of A */ 00260 00261 dsytf2_(uplo, &k, &a[a_offset], lda, &ipiv[1], &iinfo); 00262 kb = k; 00263 } 00264 00265 /* Set INFO on the first occurrence of a zero pivot */ 00266 00267 if (*info == 0 && iinfo > 0) { 00268 *info = iinfo; 00269 } 00270 00271 /* Decrease K and return to the start of the main loop */ 00272 00273 k -= kb; 00274 goto L10; 00275 00276 } else { 00277 00278 /* Factorize A as L*D*L' using the lower triangle of A */ 00279 00280 /* K is the main loop index, increasing from 1 to N in steps of */ 00281 /* KB, where KB is the number of columns factorized by DLASYF; */ 00282 /* KB is either NB or NB-1, or N-K+1 for the last block */ 00283 00284 k = 1; 00285 L20: 00286 00287 /* If K > N, exit from loop */ 00288 00289 if (k > *n) { 00290 goto L40; 00291 } 00292 00293 if (k <= *n - nb) { 00294 00295 /* Factorize columns k:k+kb-1 of A and use blocked code to */ 00296 /* update columns k+kb:n */ 00297 00298 i__1 = *n - k + 1; 00299 dlasyf_(uplo, &i__1, &nb, &kb, &a[k + k * a_dim1], lda, &ipiv[k], 00300 &work[1], &ldwork, &iinfo); 00301 } else { 00302 00303 /* Use unblocked code to factorize columns k:n of A */ 00304 00305 i__1 = *n - k + 1; 00306 dsytf2_(uplo, &i__1, &a[k + k * a_dim1], lda, &ipiv[k], &iinfo); 00307 kb = *n - k + 1; 00308 } 00309 00310 /* Set INFO on the first occurrence of a zero pivot */ 00311 00312 if (*info == 0 && iinfo > 0) { 00313 *info = iinfo + k - 1; 00314 } 00315 00316 /* Adjust IPIV */ 00317 00318 i__1 = k + kb - 1; 00319 for (j = k; j <= i__1; ++j) { 00320 if (ipiv[j] > 0) { 00321 ipiv[j] = ipiv[j] + k - 1; 00322 } else { 00323 ipiv[j] = ipiv[j] - k + 1; 00324 } 00325 /* L30: */ 00326 } 00327 00328 /* Increase K and return to the start of the main loop */ 00329 00330 k += kb; 00331 goto L20; 00332 00333 } 00334 00335 L40: 00336 work[1] = (doublereal) lwkopt; 00337 return 0; 00338 00339 /* End of DSYTRF */ 00340 00341 } /* dsytrf_ */