00001 /* sgebd2.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 00020 /* Subroutine */ int sgebd2_(integer *m, integer *n, real *a, integer *lda, 00021 real *d__, real *e, real *tauq, real *taup, real *work, integer *info) 00022 { 00023 /* System generated locals */ 00024 integer a_dim1, a_offset, i__1, i__2, i__3; 00025 00026 /* Local variables */ 00027 integer i__; 00028 extern /* Subroutine */ int slarf_(char *, integer *, integer *, real *, 00029 integer *, real *, real *, integer *, real *), xerbla_( 00030 char *, integer *), slarfg_(integer *, real *, real *, 00031 integer *, real *); 00032 00033 00034 /* -- LAPACK routine (version 3.2) -- */ 00035 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00036 /* November 2006 */ 00037 00038 /* .. Scalar Arguments .. */ 00039 /* .. */ 00040 /* .. Array Arguments .. */ 00041 /* .. */ 00042 00043 /* Purpose */ 00044 /* ======= */ 00045 00046 /* SGEBD2 reduces a real general m by n matrix A to upper or lower */ 00047 /* bidiagonal form B by an orthogonal transformation: Q' * A * P = B. */ 00048 00049 /* If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */ 00050 00051 /* Arguments */ 00052 /* ========= */ 00053 00054 /* M (input) INTEGER */ 00055 /* The number of rows in the matrix A. M >= 0. */ 00056 00057 /* N (input) INTEGER */ 00058 /* The number of columns in the matrix A. N >= 0. */ 00059 00060 /* A (input/output) REAL array, dimension (LDA,N) */ 00061 /* On entry, the m by n general matrix to be reduced. */ 00062 /* On exit, */ 00063 /* if m >= n, the diagonal and the first superdiagonal are */ 00064 /* overwritten with the upper bidiagonal matrix B; the */ 00065 /* elements below the diagonal, with the array TAUQ, represent */ 00066 /* the orthogonal matrix Q as a product of elementary */ 00067 /* reflectors, and the elements above the first superdiagonal, */ 00068 /* with the array TAUP, represent the orthogonal matrix P as */ 00069 /* a product of elementary reflectors; */ 00070 /* if m < n, the diagonal and the first subdiagonal are */ 00071 /* overwritten with the lower bidiagonal matrix B; the */ 00072 /* elements below the first subdiagonal, with the array TAUQ, */ 00073 /* represent the orthogonal matrix Q as a product of */ 00074 /* elementary reflectors, and the elements above the diagonal, */ 00075 /* with the array TAUP, represent the orthogonal matrix P as */ 00076 /* a product of elementary reflectors. */ 00077 /* See Further Details. */ 00078 00079 /* LDA (input) INTEGER */ 00080 /* The leading dimension of the array A. LDA >= max(1,M). */ 00081 00082 /* D (output) REAL array, dimension (min(M,N)) */ 00083 /* The diagonal elements of the bidiagonal matrix B: */ 00084 /* D(i) = A(i,i). */ 00085 00086 /* E (output) REAL array, dimension (min(M,N)-1) */ 00087 /* The off-diagonal elements of the bidiagonal matrix B: */ 00088 /* if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */ 00089 /* if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */ 00090 00091 /* TAUQ (output) REAL array dimension (min(M,N)) */ 00092 /* The scalar factors of the elementary reflectors which */ 00093 /* represent the orthogonal matrix Q. See Further Details. */ 00094 00095 /* TAUP (output) REAL array, dimension (min(M,N)) */ 00096 /* The scalar factors of the elementary reflectors which */ 00097 /* represent the orthogonal matrix P. See Further Details. */ 00098 00099 /* WORK (workspace) REAL array, dimension (max(M,N)) */ 00100 00101 /* INFO (output) INTEGER */ 00102 /* = 0: successful exit. */ 00103 /* < 0: if INFO = -i, the i-th argument had an illegal value. */ 00104 00105 /* Further Details */ 00106 /* =============== */ 00107 00108 /* The matrices Q and P are represented as products of elementary */ 00109 /* reflectors: */ 00110 00111 /* If m >= n, */ 00112 00113 /* Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) */ 00114 00115 /* Each H(i) and G(i) has the form: */ 00116 00117 /* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */ 00118 00119 /* where tauq and taup are real scalars, and v and u are real vectors; */ 00120 /* v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); */ 00121 /* u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); */ 00122 /* tauq is stored in TAUQ(i) and taup in TAUP(i). */ 00123 00124 /* If m < n, */ 00125 00126 /* Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) */ 00127 00128 /* Each H(i) and G(i) has the form: */ 00129 00130 /* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */ 00131 00132 /* where tauq and taup are real scalars, and v and u are real vectors; */ 00133 /* v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */ 00134 /* u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */ 00135 /* tauq is stored in TAUQ(i) and taup in TAUP(i). */ 00136 00137 /* The contents of A on exit are illustrated by the following examples: */ 00138 00139 /* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ 00140 00141 /* ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) */ 00142 /* ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) */ 00143 /* ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) */ 00144 /* ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) */ 00145 /* ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) */ 00146 /* ( v1 v2 v3 v4 v5 ) */ 00147 00148 /* where d and e denote diagonal and off-diagonal elements of B, vi */ 00149 /* denotes an element of the vector defining H(i), and ui an element of */ 00150 /* the vector defining G(i). */ 00151 00152 /* ===================================================================== */ 00153 00154 /* .. Parameters .. */ 00155 /* .. */ 00156 /* .. Local Scalars .. */ 00157 /* .. */ 00158 /* .. External Subroutines .. */ 00159 /* .. */ 00160 /* .. Intrinsic Functions .. */ 00161 /* .. */ 00162 /* .. Executable Statements .. */ 00163 00164 /* Test the input parameters */ 00165 00166 /* Parameter adjustments */ 00167 a_dim1 = *lda; 00168 a_offset = 1 + a_dim1; 00169 a -= a_offset; 00170 --d__; 00171 --e; 00172 --tauq; 00173 --taup; 00174 --work; 00175 00176 /* Function Body */ 00177 *info = 0; 00178 if (*m < 0) { 00179 *info = -1; 00180 } else if (*n < 0) { 00181 *info = -2; 00182 } else if (*lda < max(1,*m)) { 00183 *info = -4; 00184 } 00185 if (*info < 0) { 00186 i__1 = -(*info); 00187 xerbla_("SGEBD2", &i__1); 00188 return 0; 00189 } 00190 00191 if (*m >= *n) { 00192 00193 /* Reduce to upper bidiagonal form */ 00194 00195 i__1 = *n; 00196 for (i__ = 1; i__ <= i__1; ++i__) { 00197 00198 /* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */ 00199 00200 i__2 = *m - i__ + 1; 00201 /* Computing MIN */ 00202 i__3 = i__ + 1; 00203 slarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m)+ i__ * 00204 a_dim1], &c__1, &tauq[i__]); 00205 d__[i__] = a[i__ + i__ * a_dim1]; 00206 a[i__ + i__ * a_dim1] = 1.f; 00207 00208 /* Apply H(i) to A(i:m,i+1:n) from the left */ 00209 00210 if (i__ < *n) { 00211 i__2 = *m - i__ + 1; 00212 i__3 = *n - i__; 00213 slarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, & 00214 tauq[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1] 00215 ); 00216 } 00217 a[i__ + i__ * a_dim1] = d__[i__]; 00218 00219 if (i__ < *n) { 00220 00221 /* Generate elementary reflector G(i) to annihilate */ 00222 /* A(i,i+2:n) */ 00223 00224 i__2 = *n - i__; 00225 /* Computing MIN */ 00226 i__3 = i__ + 2; 00227 slarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( 00228 i__3, *n)* a_dim1], lda, &taup[i__]); 00229 e[i__] = a[i__ + (i__ + 1) * a_dim1]; 00230 a[i__ + (i__ + 1) * a_dim1] = 1.f; 00231 00232 /* Apply G(i) to A(i+1:m,i+1:n) from the right */ 00233 00234 i__2 = *m - i__; 00235 i__3 = *n - i__; 00236 slarf_("Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1], 00237 lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], 00238 lda, &work[1]); 00239 a[i__ + (i__ + 1) * a_dim1] = e[i__]; 00240 } else { 00241 taup[i__] = 0.f; 00242 } 00243 /* L10: */ 00244 } 00245 } else { 00246 00247 /* Reduce to lower bidiagonal form */ 00248 00249 i__1 = *m; 00250 for (i__ = 1; i__ <= i__1; ++i__) { 00251 00252 /* Generate elementary reflector G(i) to annihilate A(i,i+1:n) */ 00253 00254 i__2 = *n - i__ + 1; 00255 /* Computing MIN */ 00256 i__3 = i__ + 1; 00257 slarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n)* 00258 a_dim1], lda, &taup[i__]); 00259 d__[i__] = a[i__ + i__ * a_dim1]; 00260 a[i__ + i__ * a_dim1] = 1.f; 00261 00262 /* Apply G(i) to A(i+1:m,i:n) from the right */ 00263 00264 if (i__ < *m) { 00265 i__2 = *m - i__; 00266 i__3 = *n - i__ + 1; 00267 slarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, & 00268 taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]); 00269 } 00270 a[i__ + i__ * a_dim1] = d__[i__]; 00271 00272 if (i__ < *m) { 00273 00274 /* Generate elementary reflector H(i) to annihilate */ 00275 /* A(i+2:m,i) */ 00276 00277 i__2 = *m - i__; 00278 /* Computing MIN */ 00279 i__3 = i__ + 2; 00280 slarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *m)+ 00281 i__ * a_dim1], &c__1, &tauq[i__]); 00282 e[i__] = a[i__ + 1 + i__ * a_dim1]; 00283 a[i__ + 1 + i__ * a_dim1] = 1.f; 00284 00285 /* Apply H(i) to A(i+1:m,i+1:n) from the left */ 00286 00287 i__2 = *m - i__; 00288 i__3 = *n - i__; 00289 slarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], & 00290 c__1, &tauq[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], 00291 lda, &work[1]); 00292 a[i__ + 1 + i__ * a_dim1] = e[i__]; 00293 } else { 00294 tauq[i__] = 0.f; 00295 } 00296 /* L20: */ 00297 } 00298 } 00299 return 0; 00300 00301 /* End of SGEBD2 */ 00302 00303 } /* sgebd2_ */