00001 /* cgebd2.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 cgebd2_(integer *m, integer *n, complex *a, integer *lda, 00021 real *d__, real *e, complex *tauq, complex *taup, complex *work, 00022 integer *info) 00023 { 00024 /* System generated locals */ 00025 integer a_dim1, a_offset, i__1, i__2, i__3; 00026 complex q__1; 00027 00028 /* Builtin functions */ 00029 void r_cnjg(complex *, complex *); 00030 00031 /* Local variables */ 00032 integer i__; 00033 complex alpha; 00034 extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex * 00035 , integer *, complex *, complex *, integer *, complex *), 00036 clarfg_(integer *, complex *, complex *, integer *, complex *), 00037 clacgv_(integer *, complex *, integer *), xerbla_(char *, integer 00038 *); 00039 00040 00041 /* -- LAPACK routine (version 3.2) -- */ 00042 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00043 /* November 2006 */ 00044 00045 /* .. Scalar Arguments .. */ 00046 /* .. */ 00047 /* .. Array Arguments .. */ 00048 /* .. */ 00049 00050 /* Purpose */ 00051 /* ======= */ 00052 00053 /* CGEBD2 reduces a complex general m by n matrix A to upper or lower */ 00054 /* real bidiagonal form B by a unitary transformation: Q' * A * P = B. */ 00055 00056 /* If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */ 00057 00058 /* Arguments */ 00059 /* ========= */ 00060 00061 /* M (input) INTEGER */ 00062 /* The number of rows in the matrix A. M >= 0. */ 00063 00064 /* N (input) INTEGER */ 00065 /* The number of columns in the matrix A. N >= 0. */ 00066 00067 /* A (input/output) COMPLEX array, dimension (LDA,N) */ 00068 /* On entry, the m by n general matrix to be reduced. */ 00069 /* On exit, */ 00070 /* if m >= n, the diagonal and the first superdiagonal are */ 00071 /* overwritten with the upper bidiagonal matrix B; the */ 00072 /* elements below the diagonal, with the array TAUQ, represent */ 00073 /* the unitary matrix Q as a product of elementary */ 00074 /* reflectors, and the elements above the first superdiagonal, */ 00075 /* with the array TAUP, represent the unitary matrix P as */ 00076 /* a product of elementary reflectors; */ 00077 /* if m < n, the diagonal and the first subdiagonal are */ 00078 /* overwritten with the lower bidiagonal matrix B; the */ 00079 /* elements below the first subdiagonal, with the array TAUQ, */ 00080 /* represent the unitary matrix Q as a product of */ 00081 /* elementary reflectors, and the elements above the diagonal, */ 00082 /* with the array TAUP, represent the unitary matrix P as */ 00083 /* a product of elementary reflectors. */ 00084 /* See Further Details. */ 00085 00086 /* LDA (input) INTEGER */ 00087 /* The leading dimension of the array A. LDA >= max(1,M). */ 00088 00089 /* D (output) REAL array, dimension (min(M,N)) */ 00090 /* The diagonal elements of the bidiagonal matrix B: */ 00091 /* D(i) = A(i,i). */ 00092 00093 /* E (output) REAL array, dimension (min(M,N)-1) */ 00094 /* The off-diagonal elements of the bidiagonal matrix B: */ 00095 /* if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */ 00096 /* if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */ 00097 00098 /* TAUQ (output) COMPLEX array dimension (min(M,N)) */ 00099 /* The scalar factors of the elementary reflectors which */ 00100 /* represent the unitary matrix Q. See Further Details. */ 00101 00102 /* TAUP (output) COMPLEX array, dimension (min(M,N)) */ 00103 /* The scalar factors of the elementary reflectors which */ 00104 /* represent the unitary matrix P. See Further Details. */ 00105 00106 /* WORK (workspace) COMPLEX array, dimension (max(M,N)) */ 00107 00108 /* INFO (output) INTEGER */ 00109 /* = 0: successful exit */ 00110 /* < 0: if INFO = -i, the i-th argument had an illegal value. */ 00111 00112 /* Further Details */ 00113 /* =============== */ 00114 00115 /* The matrices Q and P are represented as products of elementary */ 00116 /* reflectors: */ 00117 00118 /* If m >= n, */ 00119 00120 /* Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) */ 00121 00122 /* Each H(i) and G(i) has the form: */ 00123 00124 /* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */ 00125 00126 /* where tauq and taup are complex scalars, and v and u are complex */ 00127 /* vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in */ 00128 /* A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in */ 00129 /* A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */ 00130 00131 /* If m < n, */ 00132 00133 /* Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) */ 00134 00135 /* Each H(i) and G(i) has the form: */ 00136 00137 /* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */ 00138 00139 /* where tauq and taup are complex scalars, v and u are complex vectors; */ 00140 /* v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */ 00141 /* u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */ 00142 /* tauq is stored in TAUQ(i) and taup in TAUP(i). */ 00143 00144 /* The contents of A on exit are illustrated by the following examples: */ 00145 00146 /* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ 00147 00148 /* ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) */ 00149 /* ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) */ 00150 /* ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) */ 00151 /* ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) */ 00152 /* ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) */ 00153 /* ( v1 v2 v3 v4 v5 ) */ 00154 00155 /* where d and e denote diagonal and off-diagonal elements of B, vi */ 00156 /* denotes an element of the vector defining H(i), and ui an element of */ 00157 /* the vector defining G(i). */ 00158 00159 /* ===================================================================== */ 00160 00161 /* .. Parameters .. */ 00162 /* .. */ 00163 /* .. Local Scalars .. */ 00164 /* .. */ 00165 /* .. External Subroutines .. */ 00166 /* .. */ 00167 /* .. Intrinsic Functions .. */ 00168 /* .. */ 00169 /* .. Executable Statements .. */ 00170 00171 /* Test the input parameters */ 00172 00173 /* Parameter adjustments */ 00174 a_dim1 = *lda; 00175 a_offset = 1 + a_dim1; 00176 a -= a_offset; 00177 --d__; 00178 --e; 00179 --tauq; 00180 --taup; 00181 --work; 00182 00183 /* Function Body */ 00184 *info = 0; 00185 if (*m < 0) { 00186 *info = -1; 00187 } else if (*n < 0) { 00188 *info = -2; 00189 } else if (*lda < max(1,*m)) { 00190 *info = -4; 00191 } 00192 if (*info < 0) { 00193 i__1 = -(*info); 00194 xerbla_("CGEBD2", &i__1); 00195 return 0; 00196 } 00197 00198 if (*m >= *n) { 00199 00200 /* Reduce to upper bidiagonal form */ 00201 00202 i__1 = *n; 00203 for (i__ = 1; i__ <= i__1; ++i__) { 00204 00205 /* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */ 00206 00207 i__2 = i__ + i__ * a_dim1; 00208 alpha.r = a[i__2].r, alpha.i = a[i__2].i; 00209 i__2 = *m - i__ + 1; 00210 /* Computing MIN */ 00211 i__3 = i__ + 1; 00212 clarfg_(&i__2, &alpha, &a[min(i__3, *m)+ i__ * a_dim1], &c__1, & 00213 tauq[i__]); 00214 i__2 = i__; 00215 d__[i__2] = alpha.r; 00216 i__2 = i__ + i__ * a_dim1; 00217 a[i__2].r = 1.f, a[i__2].i = 0.f; 00218 00219 /* Apply H(i)' to A(i:m,i+1:n) from the left */ 00220 00221 if (i__ < *n) { 00222 i__2 = *m - i__ + 1; 00223 i__3 = *n - i__; 00224 r_cnjg(&q__1, &tauq[i__]); 00225 clarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, & 00226 q__1, &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]); 00227 } 00228 i__2 = i__ + i__ * a_dim1; 00229 i__3 = i__; 00230 a[i__2].r = d__[i__3], a[i__2].i = 0.f; 00231 00232 if (i__ < *n) { 00233 00234 /* Generate elementary reflector G(i) to annihilate */ 00235 /* A(i,i+2:n) */ 00236 00237 i__2 = *n - i__; 00238 clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda); 00239 i__2 = i__ + (i__ + 1) * a_dim1; 00240 alpha.r = a[i__2].r, alpha.i = a[i__2].i; 00241 i__2 = *n - i__; 00242 /* Computing MIN */ 00243 i__3 = i__ + 2; 00244 clarfg_(&i__2, &alpha, &a[i__ + min(i__3, *n)* a_dim1], lda, & 00245 taup[i__]); 00246 i__2 = i__; 00247 e[i__2] = alpha.r; 00248 i__2 = i__ + (i__ + 1) * a_dim1; 00249 a[i__2].r = 1.f, a[i__2].i = 0.f; 00250 00251 /* Apply G(i) to A(i+1:m,i+1:n) from the right */ 00252 00253 i__2 = *m - i__; 00254 i__3 = *n - i__; 00255 clarf_("Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1], 00256 lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], 00257 lda, &work[1]); 00258 i__2 = *n - i__; 00259 clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda); 00260 i__2 = i__ + (i__ + 1) * a_dim1; 00261 i__3 = i__; 00262 a[i__2].r = e[i__3], a[i__2].i = 0.f; 00263 } else { 00264 i__2 = i__; 00265 taup[i__2].r = 0.f, taup[i__2].i = 0.f; 00266 } 00267 /* L10: */ 00268 } 00269 } else { 00270 00271 /* Reduce to lower bidiagonal form */ 00272 00273 i__1 = *m; 00274 for (i__ = 1; i__ <= i__1; ++i__) { 00275 00276 /* Generate elementary reflector G(i) to annihilate A(i,i+1:n) */ 00277 00278 i__2 = *n - i__ + 1; 00279 clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda); 00280 i__2 = i__ + i__ * a_dim1; 00281 alpha.r = a[i__2].r, alpha.i = a[i__2].i; 00282 i__2 = *n - i__ + 1; 00283 /* Computing MIN */ 00284 i__3 = i__ + 1; 00285 clarfg_(&i__2, &alpha, &a[i__ + min(i__3, *n)* a_dim1], lda, & 00286 taup[i__]); 00287 i__2 = i__; 00288 d__[i__2] = alpha.r; 00289 i__2 = i__ + i__ * a_dim1; 00290 a[i__2].r = 1.f, a[i__2].i = 0.f; 00291 00292 /* Apply G(i) to A(i+1:m,i:n) from the right */ 00293 00294 if (i__ < *m) { 00295 i__2 = *m - i__; 00296 i__3 = *n - i__ + 1; 00297 clarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, & 00298 taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]); 00299 } 00300 i__2 = *n - i__ + 1; 00301 clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda); 00302 i__2 = i__ + i__ * a_dim1; 00303 i__3 = i__; 00304 a[i__2].r = d__[i__3], a[i__2].i = 0.f; 00305 00306 if (i__ < *m) { 00307 00308 /* Generate elementary reflector H(i) to annihilate */ 00309 /* A(i+2:m,i) */ 00310 00311 i__2 = i__ + 1 + i__ * a_dim1; 00312 alpha.r = a[i__2].r, alpha.i = a[i__2].i; 00313 i__2 = *m - i__; 00314 /* Computing MIN */ 00315 i__3 = i__ + 2; 00316 clarfg_(&i__2, &alpha, &a[min(i__3, *m)+ i__ * a_dim1], &c__1, 00317 &tauq[i__]); 00318 i__2 = i__; 00319 e[i__2] = alpha.r; 00320 i__2 = i__ + 1 + i__ * a_dim1; 00321 a[i__2].r = 1.f, a[i__2].i = 0.f; 00322 00323 /* Apply H(i)' to A(i+1:m,i+1:n) from the left */ 00324 00325 i__2 = *m - i__; 00326 i__3 = *n - i__; 00327 r_cnjg(&q__1, &tauq[i__]); 00328 clarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], & 00329 c__1, &q__1, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, & 00330 work[1]); 00331 i__2 = i__ + 1 + i__ * a_dim1; 00332 i__3 = i__; 00333 a[i__2].r = e[i__3], a[i__2].i = 0.f; 00334 } else { 00335 i__2 = i__; 00336 tauq[i__2].r = 0.f, tauq[i__2].i = 0.f; 00337 } 00338 /* L20: */ 00339 } 00340 } 00341 return 0; 00342 00343 /* End of CGEBD2 */ 00344 00345 } /* cgebd2_ */