00001 /* ssytd2.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 real c_b8 = 0.f; 00020 static real c_b14 = -1.f; 00021 00022 /* Subroutine */ int ssytd2_(char *uplo, integer *n, real *a, integer *lda, 00023 real *d__, real *e, real *tau, integer *info) 00024 { 00025 /* System generated locals */ 00026 integer a_dim1, a_offset, i__1, i__2, i__3; 00027 00028 /* Local variables */ 00029 integer i__; 00030 real taui; 00031 extern doublereal sdot_(integer *, real *, integer *, real *, integer *); 00032 extern /* Subroutine */ int ssyr2_(char *, integer *, real *, real *, 00033 integer *, real *, integer *, real *, integer *); 00034 real alpha; 00035 extern logical lsame_(char *, char *); 00036 logical upper; 00037 extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *, 00038 real *, integer *), ssymv_(char *, integer *, real *, real *, 00039 integer *, real *, integer *, real *, real *, integer *), 00040 xerbla_(char *, integer *), slarfg_(integer *, real *, 00041 real *, integer *, real *); 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 /* SSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal */ 00057 /* form T by an orthogonal similarity transformation: Q' * A * Q = T. */ 00058 00059 /* Arguments */ 00060 /* ========= */ 00061 00062 /* UPLO (input) CHARACTER*1 */ 00063 /* Specifies whether the upper or lower triangular part of the */ 00064 /* symmetric matrix A is stored: */ 00065 /* = 'U': Upper triangular */ 00066 /* = 'L': Lower triangular */ 00067 00068 /* N (input) INTEGER */ 00069 /* The order of the matrix A. N >= 0. */ 00070 00071 /* A (input/output) REAL array, dimension (LDA,N) */ 00072 /* On entry, the symmetric matrix A. If UPLO = 'U', the leading */ 00073 /* n-by-n upper triangular part of A contains the upper */ 00074 /* triangular part of the matrix A, and the strictly lower */ 00075 /* triangular part of A is not referenced. If UPLO = 'L', the */ 00076 /* leading n-by-n lower triangular part of A contains the lower */ 00077 /* triangular part of the matrix A, and the strictly upper */ 00078 /* triangular part of A is not referenced. */ 00079 /* On exit, if UPLO = 'U', the diagonal and first superdiagonal */ 00080 /* of A are overwritten by the corresponding elements of the */ 00081 /* tridiagonal matrix T, and the elements above the first */ 00082 /* superdiagonal, with the array TAU, represent the orthogonal */ 00083 /* matrix Q as a product of elementary reflectors; if UPLO */ 00084 /* = 'L', the diagonal and first subdiagonal of A are over- */ 00085 /* written by the corresponding elements of the tridiagonal */ 00086 /* matrix T, and the elements below the first subdiagonal, with */ 00087 /* the array TAU, represent the orthogonal matrix Q as a product */ 00088 /* of elementary reflectors. See Further Details. */ 00089 00090 /* LDA (input) INTEGER */ 00091 /* The leading dimension of the array A. LDA >= max(1,N). */ 00092 00093 /* D (output) REAL array, dimension (N) */ 00094 /* The diagonal elements of the tridiagonal matrix T: */ 00095 /* D(i) = A(i,i). */ 00096 00097 /* E (output) REAL array, dimension (N-1) */ 00098 /* The off-diagonal elements of the tridiagonal matrix T: */ 00099 /* E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */ 00100 00101 /* TAU (output) REAL array, dimension (N-1) */ 00102 /* The scalar factors of the elementary reflectors (see Further */ 00103 /* Details). */ 00104 00105 /* INFO (output) INTEGER */ 00106 /* = 0: successful exit */ 00107 /* < 0: if INFO = -i, the i-th argument had an illegal value. */ 00108 00109 /* Further Details */ 00110 /* =============== */ 00111 00112 /* If UPLO = 'U', the matrix Q is represented as a product of elementary */ 00113 /* reflectors */ 00114 00115 /* Q = H(n-1) . . . H(2) H(1). */ 00116 00117 /* Each H(i) has the form */ 00118 00119 /* H(i) = I - tau * v * v' */ 00120 00121 /* where tau is a real scalar, and v is a real vector with */ 00122 /* v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */ 00123 /* A(1:i-1,i+1), and tau in TAU(i). */ 00124 00125 /* If UPLO = 'L', the matrix Q is represented as a product of elementary */ 00126 /* reflectors */ 00127 00128 /* Q = H(1) H(2) . . . H(n-1). */ 00129 00130 /* Each H(i) has the form */ 00131 00132 /* H(i) = I - tau * v * v' */ 00133 00134 /* where tau is a real scalar, and v is a real vector with */ 00135 /* v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */ 00136 /* and tau in TAU(i). */ 00137 00138 /* The contents of A on exit are illustrated by the following examples */ 00139 /* with n = 5: */ 00140 00141 /* if UPLO = 'U': if UPLO = 'L': */ 00142 00143 /* ( d e v2 v3 v4 ) ( d ) */ 00144 /* ( d e v3 v4 ) ( e d ) */ 00145 /* ( d e v4 ) ( v1 e d ) */ 00146 /* ( d e ) ( v1 v2 e d ) */ 00147 /* ( d ) ( v1 v2 v3 e d ) */ 00148 00149 /* where d and e denote diagonal and off-diagonal elements of T, and vi */ 00150 /* denotes an element of the vector defining H(i). */ 00151 00152 /* ===================================================================== */ 00153 00154 /* .. Parameters .. */ 00155 /* .. */ 00156 /* .. Local Scalars .. */ 00157 /* .. */ 00158 /* .. External Subroutines .. */ 00159 /* .. */ 00160 /* .. External Functions .. */ 00161 /* .. */ 00162 /* .. Intrinsic Functions .. */ 00163 /* .. */ 00164 /* .. Executable Statements .. */ 00165 00166 /* Test the input parameters */ 00167 00168 /* Parameter adjustments */ 00169 a_dim1 = *lda; 00170 a_offset = 1 + a_dim1; 00171 a -= a_offset; 00172 --d__; 00173 --e; 00174 --tau; 00175 00176 /* Function Body */ 00177 *info = 0; 00178 upper = lsame_(uplo, "U"); 00179 if (! upper && ! lsame_(uplo, "L")) { 00180 *info = -1; 00181 } else if (*n < 0) { 00182 *info = -2; 00183 } else if (*lda < max(1,*n)) { 00184 *info = -4; 00185 } 00186 if (*info != 0) { 00187 i__1 = -(*info); 00188 xerbla_("SSYTD2", &i__1); 00189 return 0; 00190 } 00191 00192 /* Quick return if possible */ 00193 00194 if (*n <= 0) { 00195 return 0; 00196 } 00197 00198 if (upper) { 00199 00200 /* Reduce the upper triangle of A */ 00201 00202 for (i__ = *n - 1; i__ >= 1; --i__) { 00203 00204 /* Generate elementary reflector H(i) = I - tau * v * v' */ 00205 /* to annihilate A(1:i-1,i+1) */ 00206 00207 slarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1 00208 + 1], &c__1, &taui); 00209 e[i__] = a[i__ + (i__ + 1) * a_dim1]; 00210 00211 if (taui != 0.f) { 00212 00213 /* Apply H(i) from both sides to A(1:i,1:i) */ 00214 00215 a[i__ + (i__ + 1) * a_dim1] = 1.f; 00216 00217 /* Compute x := tau * A * v storing x in TAU(1:i) */ 00218 00219 ssymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * 00220 a_dim1 + 1], &c__1, &c_b8, &tau[1], &c__1); 00221 00222 /* Compute w := x - 1/2 * tau * (x'*v) * v */ 00223 00224 alpha = taui * -.5f * sdot_(&i__, &tau[1], &c__1, &a[(i__ + 1) 00225 * a_dim1 + 1], &c__1); 00226 saxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[ 00227 1], &c__1); 00228 00229 /* Apply the transformation as a rank-2 update: */ 00230 /* A := A - v * w' - w * v' */ 00231 00232 ssyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1, 00233 &tau[1], &c__1, &a[a_offset], lda); 00234 00235 a[i__ + (i__ + 1) * a_dim1] = e[i__]; 00236 } 00237 d__[i__ + 1] = a[i__ + 1 + (i__ + 1) * a_dim1]; 00238 tau[i__] = taui; 00239 /* L10: */ 00240 } 00241 d__[1] = a[a_dim1 + 1]; 00242 } else { 00243 00244 /* Reduce the lower triangle of A */ 00245 00246 i__1 = *n - 1; 00247 for (i__ = 1; i__ <= i__1; ++i__) { 00248 00249 /* Generate elementary reflector H(i) = I - tau * v * v' */ 00250 /* to annihilate A(i+2:n,i) */ 00251 00252 i__2 = *n - i__; 00253 /* Computing MIN */ 00254 i__3 = i__ + 2; 00255 slarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *n)+ i__ * 00256 a_dim1], &c__1, &taui); 00257 e[i__] = a[i__ + 1 + i__ * a_dim1]; 00258 00259 if (taui != 0.f) { 00260 00261 /* Apply H(i) from both sides to A(i+1:n,i+1:n) */ 00262 00263 a[i__ + 1 + i__ * a_dim1] = 1.f; 00264 00265 /* Compute x := tau * A * v storing y in TAU(i:n-1) */ 00266 00267 i__2 = *n - i__; 00268 ssymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], 00269 lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[ 00270 i__], &c__1); 00271 00272 /* Compute w := x - 1/2 * tau * (x'*v) * v */ 00273 00274 i__2 = *n - i__; 00275 alpha = taui * -.5f * sdot_(&i__2, &tau[i__], &c__1, &a[i__ + 00276 1 + i__ * a_dim1], &c__1); 00277 i__2 = *n - i__; 00278 saxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[ 00279 i__], &c__1); 00280 00281 /* Apply the transformation as a rank-2 update: */ 00282 /* A := A - v * w' - w * v' */ 00283 00284 i__2 = *n - i__; 00285 ssyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1, 00286 &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], 00287 lda); 00288 00289 a[i__ + 1 + i__ * a_dim1] = e[i__]; 00290 } 00291 d__[i__] = a[i__ + i__ * a_dim1]; 00292 tau[i__] = taui; 00293 /* L20: */ 00294 } 00295 d__[*n] = a[*n + *n * a_dim1]; 00296 } 00297 00298 return 0; 00299 00300 /* End of SSYTD2 */ 00301 00302 } /* ssytd2_ */