00001 /* dgebd2.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 dgebd2_(integer *m, integer *n, doublereal *a, integer * 00021 lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * 00022 taup, doublereal *work, integer *info) 00023 { 00024 /* System generated locals */ 00025 integer a_dim1, a_offset, i__1, i__2, i__3; 00026 00027 /* Local variables */ 00028 integer i__; 00029 extern /* Subroutine */ int dlarf_(char *, integer *, integer *, 00030 doublereal *, integer *, doublereal *, doublereal *, integer *, 00031 doublereal *), dlarfg_(integer *, doublereal *, 00032 doublereal *, integer *, doublereal *), xerbla_(char *, integer *); 00033 00034 00035 /* -- LAPACK routine (version 3.2) -- */ 00036 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00037 /* November 2006 */ 00038 00039 /* .. Scalar Arguments .. */ 00040 /* .. */ 00041 /* .. Array Arguments .. */ 00042 /* .. */ 00043 00044 /* Purpose */ 00045 /* ======= */ 00046 00047 /* DGEBD2 reduces a real general m by n matrix A to upper or lower */ 00048 /* bidiagonal form B by an orthogonal transformation: Q' * A * P = B. */ 00049 00050 /* If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */ 00051 00052 /* Arguments */ 00053 /* ========= */ 00054 00055 /* M (input) INTEGER */ 00056 /* The number of rows in the matrix A. M >= 0. */ 00057 00058 /* N (input) INTEGER */ 00059 /* The number of columns in the matrix A. N >= 0. */ 00060 00061 /* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ 00062 /* On entry, the m by n general matrix to be reduced. */ 00063 /* On exit, */ 00064 /* if m >= n, the diagonal and the first superdiagonal are */ 00065 /* overwritten with the upper bidiagonal matrix B; the */ 00066 /* elements below the diagonal, with the array TAUQ, represent */ 00067 /* the orthogonal matrix Q as a product of elementary */ 00068 /* reflectors, and the elements above the first superdiagonal, */ 00069 /* with the array TAUP, represent the orthogonal matrix P as */ 00070 /* a product of elementary reflectors; */ 00071 /* if m < n, the diagonal and the first subdiagonal are */ 00072 /* overwritten with the lower bidiagonal matrix B; the */ 00073 /* elements below the first subdiagonal, with the array TAUQ, */ 00074 /* represent the orthogonal matrix Q as a product of */ 00075 /* elementary reflectors, and the elements above the diagonal, */ 00076 /* with the array TAUP, represent the orthogonal matrix P as */ 00077 /* a product of elementary reflectors. */ 00078 /* See Further Details. */ 00079 00080 /* LDA (input) INTEGER */ 00081 /* The leading dimension of the array A. LDA >= max(1,M). */ 00082 00083 /* D (output) DOUBLE PRECISION array, dimension (min(M,N)) */ 00084 /* The diagonal elements of the bidiagonal matrix B: */ 00085 /* D(i) = A(i,i). */ 00086 00087 /* E (output) DOUBLE PRECISION array, dimension (min(M,N)-1) */ 00088 /* The off-diagonal elements of the bidiagonal matrix B: */ 00089 /* if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */ 00090 /* if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */ 00091 00092 /* TAUQ (output) DOUBLE PRECISION array dimension (min(M,N)) */ 00093 /* The scalar factors of the elementary reflectors which */ 00094 /* represent the orthogonal matrix Q. See Further Details. */ 00095 00096 /* TAUP (output) DOUBLE PRECISION array, dimension (min(M,N)) */ 00097 /* The scalar factors of the elementary reflectors which */ 00098 /* represent the orthogonal matrix P. See Further Details. */ 00099 00100 /* WORK (workspace) DOUBLE PRECISION array, dimension (max(M,N)) */ 00101 00102 /* INFO (output) INTEGER */ 00103 /* = 0: successful exit. */ 00104 /* < 0: if INFO = -i, the i-th argument had an illegal value. */ 00105 00106 /* Further Details */ 00107 /* =============== */ 00108 00109 /* The matrices Q and P are represented as products of elementary */ 00110 /* reflectors: */ 00111 00112 /* If m >= n, */ 00113 00114 /* Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) */ 00115 00116 /* Each H(i) and G(i) has the form: */ 00117 00118 /* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */ 00119 00120 /* where tauq and taup are real scalars, and v and u are real vectors; */ 00121 /* v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); */ 00122 /* u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); */ 00123 /* tauq is stored in TAUQ(i) and taup in TAUP(i). */ 00124 00125 /* If m < n, */ 00126 00127 /* Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) */ 00128 00129 /* Each H(i) and G(i) has the form: */ 00130 00131 /* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */ 00132 00133 /* where tauq and taup are real scalars, and v and u are real vectors; */ 00134 /* v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */ 00135 /* u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */ 00136 /* tauq is stored in TAUQ(i) and taup in TAUP(i). */ 00137 00138 /* The contents of A on exit are illustrated by the following examples: */ 00139 00140 /* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ 00141 00142 /* ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) */ 00143 /* ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) */ 00144 /* ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) */ 00145 /* ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) */ 00146 /* ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) */ 00147 /* ( v1 v2 v3 v4 v5 ) */ 00148 00149 /* where d and e denote diagonal and off-diagonal elements of B, vi */ 00150 /* denotes an element of the vector defining H(i), and ui an element of */ 00151 /* the vector defining G(i). */ 00152 00153 /* ===================================================================== */ 00154 00155 /* .. Parameters .. */ 00156 /* .. */ 00157 /* .. Local Scalars .. */ 00158 /* .. */ 00159 /* .. External Subroutines .. */ 00160 /* .. */ 00161 /* .. Intrinsic Functions .. */ 00162 /* .. */ 00163 /* .. Executable Statements .. */ 00164 00165 /* Test the input parameters */ 00166 00167 /* Parameter adjustments */ 00168 a_dim1 = *lda; 00169 a_offset = 1 + a_dim1; 00170 a -= a_offset; 00171 --d__; 00172 --e; 00173 --tauq; 00174 --taup; 00175 --work; 00176 00177 /* Function Body */ 00178 *info = 0; 00179 if (*m < 0) { 00180 *info = -1; 00181 } else if (*n < 0) { 00182 *info = -2; 00183 } else if (*lda < max(1,*m)) { 00184 *info = -4; 00185 } 00186 if (*info < 0) { 00187 i__1 = -(*info); 00188 xerbla_("DGEBD2", &i__1); 00189 return 0; 00190 } 00191 00192 if (*m >= *n) { 00193 00194 /* Reduce to upper bidiagonal form */ 00195 00196 i__1 = *n; 00197 for (i__ = 1; i__ <= i__1; ++i__) { 00198 00199 /* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */ 00200 00201 i__2 = *m - i__ + 1; 00202 /* Computing MIN */ 00203 i__3 = i__ + 1; 00204 dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m)+ i__ * 00205 a_dim1], &c__1, &tauq[i__]); 00206 d__[i__] = a[i__ + i__ * a_dim1]; 00207 a[i__ + i__ * a_dim1] = 1.; 00208 00209 /* Apply H(i) to A(i:m,i+1:n) from the left */ 00210 00211 if (i__ < *n) { 00212 i__2 = *m - i__ + 1; 00213 i__3 = *n - i__; 00214 dlarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, & 00215 tauq[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1] 00216 ); 00217 } 00218 a[i__ + i__ * a_dim1] = d__[i__]; 00219 00220 if (i__ < *n) { 00221 00222 /* Generate elementary reflector G(i) to annihilate */ 00223 /* A(i,i+2:n) */ 00224 00225 i__2 = *n - i__; 00226 /* Computing MIN */ 00227 i__3 = i__ + 2; 00228 dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( 00229 i__3, *n)* a_dim1], lda, &taup[i__]); 00230 e[i__] = a[i__ + (i__ + 1) * a_dim1]; 00231 a[i__ + (i__ + 1) * a_dim1] = 1.; 00232 00233 /* Apply G(i) to A(i+1:m,i+1:n) from the right */ 00234 00235 i__2 = *m - i__; 00236 i__3 = *n - i__; 00237 dlarf_("Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1], 00238 lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], 00239 lda, &work[1]); 00240 a[i__ + (i__ + 1) * a_dim1] = e[i__]; 00241 } else { 00242 taup[i__] = 0.; 00243 } 00244 /* L10: */ 00245 } 00246 } else { 00247 00248 /* Reduce to lower bidiagonal form */ 00249 00250 i__1 = *m; 00251 for (i__ = 1; i__ <= i__1; ++i__) { 00252 00253 /* Generate elementary reflector G(i) to annihilate A(i,i+1:n) */ 00254 00255 i__2 = *n - i__ + 1; 00256 /* Computing MIN */ 00257 i__3 = i__ + 1; 00258 dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n)* 00259 a_dim1], lda, &taup[i__]); 00260 d__[i__] = a[i__ + i__ * a_dim1]; 00261 a[i__ + i__ * a_dim1] = 1.; 00262 00263 /* Apply G(i) to A(i+1:m,i:n) from the right */ 00264 00265 if (i__ < *m) { 00266 i__2 = *m - i__; 00267 i__3 = *n - i__ + 1; 00268 dlarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, & 00269 taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]); 00270 } 00271 a[i__ + i__ * a_dim1] = d__[i__]; 00272 00273 if (i__ < *m) { 00274 00275 /* Generate elementary reflector H(i) to annihilate */ 00276 /* A(i+2:m,i) */ 00277 00278 i__2 = *m - i__; 00279 /* Computing MIN */ 00280 i__3 = i__ + 2; 00281 dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *m)+ 00282 i__ * a_dim1], &c__1, &tauq[i__]); 00283 e[i__] = a[i__ + 1 + i__ * a_dim1]; 00284 a[i__ + 1 + i__ * a_dim1] = 1.; 00285 00286 /* Apply H(i) to A(i+1:m,i+1:n) from the left */ 00287 00288 i__2 = *m - i__; 00289 i__3 = *n - i__; 00290 dlarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], & 00291 c__1, &tauq[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], 00292 lda, &work[1]); 00293 a[i__ + 1 + i__ * a_dim1] = e[i__]; 00294 } else { 00295 tauq[i__] = 0.; 00296 } 00297 /* L20: */ 00298 } 00299 } 00300 return 0; 00301 00302 /* End of DGEBD2 */ 00303 00304 } /* dgebd2_ */