00001 /* spftri.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 real c_b11 = 1.f; 00019 00020 /* Subroutine */ int spftri_(char *transr, char *uplo, integer *n, real *a, 00021 integer *info) 00022 { 00023 /* System generated locals */ 00024 integer i__1, i__2; 00025 00026 /* Local variables */ 00027 integer k, n1, n2; 00028 logical normaltransr; 00029 extern logical lsame_(char *, char *); 00030 logical lower; 00031 extern /* Subroutine */ int strmm_(char *, char *, char *, char *, 00032 integer *, integer *, real *, real *, integer *, real *, integer * 00033 ), ssyrk_(char *, char *, integer 00034 *, integer *, real *, real *, integer *, real *, real *, integer * 00035 ), xerbla_(char *, integer *); 00036 logical nisodd; 00037 extern /* Subroutine */ int slauum_(char *, integer *, real *, integer *, 00038 integer *), stftri_(char *, char *, char *, integer *, 00039 real *, integer *); 00040 00041 00042 /* -- LAPACK routine (version 3.2) -- */ 00043 00044 /* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- */ 00045 /* -- November 2008 -- */ 00046 00047 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00048 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ 00049 00050 /* .. Scalar Arguments .. */ 00051 /* .. Array Arguments .. */ 00052 /* .. */ 00053 00054 /* Purpose */ 00055 /* ======= */ 00056 00057 /* SPFTRI computes the inverse of a real (symmetric) positive definite */ 00058 /* matrix A using the Cholesky factorization A = U**T*U or A = L*L**T */ 00059 /* computed by SPFTRF. */ 00060 00061 /* Arguments */ 00062 /* ========= */ 00063 00064 /* TRANSR (input) CHARACTER */ 00065 /* = 'N': The Normal TRANSR of RFP A is stored; */ 00066 /* = 'T': The Transpose TRANSR of RFP A is stored. */ 00067 00068 /* UPLO (input) CHARACTER */ 00069 /* = 'U': Upper triangle of A is stored; */ 00070 /* = 'L': Lower triangle of A is stored. */ 00071 00072 /* N (input) INTEGER */ 00073 /* The order of the matrix A. N >= 0. */ 00074 00075 /* A (input/output) REAL array, dimension ( N*(N+1)/2 ) */ 00076 /* On entry, the symmetric matrix A in RFP format. RFP format is */ 00077 /* described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' */ 00078 /* then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is */ 00079 /* (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is */ 00080 /* the transpose of RFP A as defined when */ 00081 /* TRANSR = 'N'. The contents of RFP A are defined by UPLO as */ 00082 /* follows: If UPLO = 'U' the RFP A contains the nt elements of */ 00083 /* upper packed A. If UPLO = 'L' the RFP A contains the elements */ 00084 /* of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = */ 00085 /* 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N */ 00086 /* is odd. See the Note below for more details. */ 00087 00088 /* On exit, the symmetric inverse of the original matrix, in the */ 00089 /* same storage format. */ 00090 00091 /* INFO (output) INTEGER */ 00092 /* = 0: successful exit */ 00093 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00094 /* > 0: if INFO = i, the (i,i) element of the factor U or L is */ 00095 /* zero, and the inverse could not be computed. */ 00096 00097 /* Notes */ 00098 /* ===== */ 00099 00100 /* We first consider Rectangular Full Packed (RFP) Format when N is */ 00101 /* even. We give an example where N = 6. */ 00102 00103 /* AP is Upper AP is Lower */ 00104 00105 /* 00 01 02 03 04 05 00 */ 00106 /* 11 12 13 14 15 10 11 */ 00107 /* 22 23 24 25 20 21 22 */ 00108 /* 33 34 35 30 31 32 33 */ 00109 /* 44 45 40 41 42 43 44 */ 00110 /* 55 50 51 52 53 54 55 */ 00111 00112 00113 /* Let TRANSR = 'N'. RFP holds AP as follows: */ 00114 /* For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */ 00115 /* three columns of AP upper. The lower triangle A(4:6,0:2) consists of */ 00116 /* the transpose of the first three columns of AP upper. */ 00117 /* For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */ 00118 /* three columns of AP lower. The upper triangle A(0:2,0:2) consists of */ 00119 /* the transpose of the last three columns of AP lower. */ 00120 /* This covers the case N even and TRANSR = 'N'. */ 00121 00122 /* RFP A RFP A */ 00123 00124 /* 03 04 05 33 43 53 */ 00125 /* 13 14 15 00 44 54 */ 00126 /* 23 24 25 10 11 55 */ 00127 /* 33 34 35 20 21 22 */ 00128 /* 00 44 45 30 31 32 */ 00129 /* 01 11 55 40 41 42 */ 00130 /* 02 12 22 50 51 52 */ 00131 00132 /* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */ 00133 /* transpose of RFP A above. One therefore gets: */ 00134 00135 00136 /* RFP A RFP A */ 00137 00138 /* 03 13 23 33 00 01 02 33 00 10 20 30 40 50 */ 00139 /* 04 14 24 34 44 11 12 43 44 11 21 31 41 51 */ 00140 /* 05 15 25 35 45 55 22 53 54 55 22 32 42 52 */ 00141 00142 00143 /* We first consider Rectangular Full Packed (RFP) Format when N is */ 00144 /* odd. We give an example where N = 5. */ 00145 00146 /* AP is Upper AP is Lower */ 00147 00148 /* 00 01 02 03 04 00 */ 00149 /* 11 12 13 14 10 11 */ 00150 /* 22 23 24 20 21 22 */ 00151 /* 33 34 30 31 32 33 */ 00152 /* 44 40 41 42 43 44 */ 00153 00154 00155 /* Let TRANSR = 'N'. RFP holds AP as follows: */ 00156 /* For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */ 00157 /* three columns of AP upper. The lower triangle A(3:4,0:1) consists of */ 00158 /* the transpose of the first two columns of AP upper. */ 00159 /* For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */ 00160 /* three columns of AP lower. The upper triangle A(0:1,1:2) consists of */ 00161 /* the transpose of the last two columns of AP lower. */ 00162 /* This covers the case N odd and TRANSR = 'N'. */ 00163 00164 /* RFP A RFP A */ 00165 00166 /* 02 03 04 00 33 43 */ 00167 /* 12 13 14 10 11 44 */ 00168 /* 22 23 24 20 21 22 */ 00169 /* 00 33 34 30 31 32 */ 00170 /* 01 11 44 40 41 42 */ 00171 00172 /* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */ 00173 /* transpose of RFP A above. One therefore gets: */ 00174 00175 /* RFP A RFP A */ 00176 00177 /* 02 12 22 00 01 00 10 20 30 40 50 */ 00178 /* 03 13 23 33 11 33 11 21 31 41 51 */ 00179 /* 04 14 24 34 44 43 44 22 32 42 52 */ 00180 00181 /* ===================================================================== */ 00182 00183 /* .. Parameters .. */ 00184 /* .. */ 00185 /* .. Local Scalars .. */ 00186 /* .. */ 00187 /* .. External Functions .. */ 00188 /* .. */ 00189 /* .. External Subroutines .. */ 00190 /* .. */ 00191 /* .. Intrinsic Functions .. */ 00192 /* .. */ 00193 /* .. Executable Statements .. */ 00194 00195 /* Test the input parameters. */ 00196 00197 *info = 0; 00198 normaltransr = lsame_(transr, "N"); 00199 lower = lsame_(uplo, "L"); 00200 if (! normaltransr && ! lsame_(transr, "T")) { 00201 *info = -1; 00202 } else if (! lower && ! lsame_(uplo, "U")) { 00203 *info = -2; 00204 } else if (*n < 0) { 00205 *info = -3; 00206 } 00207 if (*info != 0) { 00208 i__1 = -(*info); 00209 xerbla_("SPFTRI", &i__1); 00210 return 0; 00211 } 00212 00213 /* Quick return if possible */ 00214 00215 if (*n == 0) { 00216 return 0; 00217 } 00218 00219 /* Invert the triangular Cholesky factor U or L. */ 00220 00221 stftri_(transr, uplo, "N", n, a, info); 00222 if (*info > 0) { 00223 return 0; 00224 } 00225 00226 /* If N is odd, set NISODD = .TRUE. */ 00227 /* If N is even, set K = N/2 and NISODD = .FALSE. */ 00228 00229 if (*n % 2 == 0) { 00230 k = *n / 2; 00231 nisodd = FALSE_; 00232 } else { 00233 nisodd = TRUE_; 00234 } 00235 00236 /* Set N1 and N2 depending on LOWER */ 00237 00238 if (lower) { 00239 n2 = *n / 2; 00240 n1 = *n - n2; 00241 } else { 00242 n1 = *n / 2; 00243 n2 = *n - n1; 00244 } 00245 00246 /* Start execution of triangular matrix multiply: inv(U)*inv(U)^C or */ 00247 /* inv(L)^C*inv(L). There are eight cases. */ 00248 00249 if (nisodd) { 00250 00251 /* N is odd */ 00252 00253 if (normaltransr) { 00254 00255 /* N is odd and TRANSR = 'N' */ 00256 00257 if (lower) { 00258 00259 /* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:N1-1) ) */ 00260 /* T1 -> a(0,0), T2 -> a(0,1), S -> a(N1,0) */ 00261 /* T1 -> a(0), T2 -> a(n), S -> a(N1) */ 00262 00263 slauum_("L", &n1, a, n, info); 00264 ssyrk_("L", "T", &n1, &n2, &c_b11, &a[n1], n, &c_b11, a, n); 00265 strmm_("L", "U", "N", "N", &n2, &n1, &c_b11, &a[*n], n, &a[n1] 00266 , n); 00267 slauum_("U", &n2, &a[*n], n, info); 00268 00269 } else { 00270 00271 /* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:N2-1) */ 00272 /* T1 -> a(N1+1,0), T2 -> a(N1,0), S -> a(0,0) */ 00273 /* T1 -> a(N2), T2 -> a(N1), S -> a(0) */ 00274 00275 slauum_("L", &n1, &a[n2], n, info); 00276 ssyrk_("L", "N", &n1, &n2, &c_b11, a, n, &c_b11, &a[n2], n); 00277 strmm_("R", "U", "T", "N", &n1, &n2, &c_b11, &a[n1], n, a, n); 00278 slauum_("U", &n2, &a[n1], n, info); 00279 00280 } 00281 00282 } else { 00283 00284 /* N is odd and TRANSR = 'T' */ 00285 00286 if (lower) { 00287 00288 /* SRPA for LOWER, TRANSPOSE, and N is odd */ 00289 /* T1 -> a(0), T2 -> a(1), S -> a(0+N1*N1) */ 00290 00291 slauum_("U", &n1, a, &n1, info); 00292 ssyrk_("U", "N", &n1, &n2, &c_b11, &a[n1 * n1], &n1, &c_b11, 00293 a, &n1); 00294 strmm_("R", "L", "N", "N", &n1, &n2, &c_b11, &a[1], &n1, &a[ 00295 n1 * n1], &n1); 00296 slauum_("L", &n2, &a[1], &n1, info); 00297 00298 } else { 00299 00300 /* SRPA for UPPER, TRANSPOSE, and N is odd */ 00301 /* T1 -> a(0+N2*N2), T2 -> a(0+N1*N2), S -> a(0) */ 00302 00303 slauum_("U", &n1, &a[n2 * n2], &n2, info); 00304 ssyrk_("U", "T", &n1, &n2, &c_b11, a, &n2, &c_b11, &a[n2 * n2] 00305 , &n2); 00306 strmm_("L", "L", "T", "N", &n2, &n1, &c_b11, &a[n1 * n2], &n2, 00307 a, &n2); 00308 slauum_("L", &n2, &a[n1 * n2], &n2, info); 00309 00310 } 00311 00312 } 00313 00314 } else { 00315 00316 /* N is even */ 00317 00318 if (normaltransr) { 00319 00320 /* N is even and TRANSR = 'N' */ 00321 00322 if (lower) { 00323 00324 /* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) */ 00325 /* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) */ 00326 /* T1 -> a(1), T2 -> a(0), S -> a(k+1) */ 00327 00328 i__1 = *n + 1; 00329 slauum_("L", &k, &a[1], &i__1, info); 00330 i__1 = *n + 1; 00331 i__2 = *n + 1; 00332 ssyrk_("L", "T", &k, &k, &c_b11, &a[k + 1], &i__1, &c_b11, &a[ 00333 1], &i__2); 00334 i__1 = *n + 1; 00335 i__2 = *n + 1; 00336 strmm_("L", "U", "N", "N", &k, &k, &c_b11, a, &i__1, &a[k + 1] 00337 , &i__2); 00338 i__1 = *n + 1; 00339 slauum_("U", &k, a, &i__1, info); 00340 00341 } else { 00342 00343 /* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) */ 00344 /* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0) */ 00345 /* T1 -> a(k+1), T2 -> a(k), S -> a(0) */ 00346 00347 i__1 = *n + 1; 00348 slauum_("L", &k, &a[k + 1], &i__1, info); 00349 i__1 = *n + 1; 00350 i__2 = *n + 1; 00351 ssyrk_("L", "N", &k, &k, &c_b11, a, &i__1, &c_b11, &a[k + 1], 00352 &i__2); 00353 i__1 = *n + 1; 00354 i__2 = *n + 1; 00355 strmm_("R", "U", "T", "N", &k, &k, &c_b11, &a[k], &i__1, a, & 00356 i__2); 00357 i__1 = *n + 1; 00358 slauum_("U", &k, &a[k], &i__1, info); 00359 00360 } 00361 00362 } else { 00363 00364 /* N is even and TRANSR = 'T' */ 00365 00366 if (lower) { 00367 00368 /* SRPA for LOWER, TRANSPOSE, and N is even (see paper) */ 00369 /* T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1), */ 00370 /* T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k */ 00371 00372 slauum_("U", &k, &a[k], &k, info); 00373 ssyrk_("U", "N", &k, &k, &c_b11, &a[k * (k + 1)], &k, &c_b11, 00374 &a[k], &k); 00375 strmm_("R", "L", "N", "N", &k, &k, &c_b11, a, &k, &a[k * (k + 00376 1)], &k); 00377 slauum_("L", &k, a, &k, info); 00378 00379 } else { 00380 00381 /* SRPA for UPPER, TRANSPOSE, and N is even (see paper) */ 00382 /* T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0), */ 00383 /* T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k */ 00384 00385 slauum_("U", &k, &a[k * (k + 1)], &k, info); 00386 ssyrk_("U", "T", &k, &k, &c_b11, a, &k, &c_b11, &a[k * (k + 1) 00387 ], &k); 00388 strmm_("L", "L", "T", "N", &k, &k, &c_b11, &a[k * k], &k, a, & 00389 k); 00390 slauum_("L", &k, &a[k * k], &k, info); 00391 00392 } 00393 00394 } 00395 00396 } 00397 00398 return 0; 00399 00400 /* End of SPFTRI */ 00401 00402 } /* spftri_ */