00001 /* zgebrd.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 doublecomplex c_b1 = {1.,0.}; 00019 static integer c__1 = 1; 00020 static integer c_n1 = -1; 00021 static integer c__3 = 3; 00022 static integer c__2 = 2; 00023 00024 /* Subroutine */ int zgebrd_(integer *m, integer *n, doublecomplex *a, 00025 integer *lda, doublereal *d__, doublereal *e, doublecomplex *tauq, 00026 doublecomplex *taup, doublecomplex *work, integer *lwork, integer * 00027 info) 00028 { 00029 /* System generated locals */ 00030 integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; 00031 doublereal d__1; 00032 doublecomplex z__1; 00033 00034 /* Local variables */ 00035 integer i__, j, nb, nx; 00036 doublereal ws; 00037 integer nbmin, iinfo, minmn; 00038 extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, 00039 integer *, doublecomplex *, doublecomplex *, integer *, 00040 doublecomplex *, integer *, doublecomplex *, doublecomplex *, 00041 integer *), zgebd2_(integer *, integer *, 00042 doublecomplex *, integer *, doublereal *, doublereal *, 00043 doublecomplex *, doublecomplex *, doublecomplex *, integer *), 00044 xerbla_(char *, integer *), zlabrd_(integer *, integer *, 00045 integer *, doublecomplex *, integer *, doublereal *, doublereal *, 00046 doublecomplex *, doublecomplex *, doublecomplex *, integer *, 00047 doublecomplex *, integer *); 00048 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00049 integer *, integer *); 00050 integer ldwrkx, ldwrky, lwkopt; 00051 logical lquery; 00052 00053 00054 /* -- LAPACK routine (version 3.2) -- */ 00055 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00056 /* November 2006 */ 00057 00058 /* .. Scalar Arguments .. */ 00059 /* .. */ 00060 /* .. Array Arguments .. */ 00061 /* .. */ 00062 00063 /* Purpose */ 00064 /* ======= */ 00065 00066 /* ZGEBRD reduces a general complex M-by-N matrix A to upper or lower */ 00067 /* bidiagonal form B by a unitary transformation: Q**H * A * P = B. */ 00068 00069 /* If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */ 00070 00071 /* Arguments */ 00072 /* ========= */ 00073 00074 /* M (input) INTEGER */ 00075 /* The number of rows in the matrix A. M >= 0. */ 00076 00077 /* N (input) INTEGER */ 00078 /* The number of columns in the matrix A. N >= 0. */ 00079 00080 /* A (input/output) COMPLEX*16 array, dimension (LDA,N) */ 00081 /* On entry, the M-by-N general matrix to be reduced. */ 00082 /* On exit, */ 00083 /* if m >= n, the diagonal and the first superdiagonal are */ 00084 /* overwritten with the upper bidiagonal matrix B; the */ 00085 /* elements below the diagonal, with the array TAUQ, represent */ 00086 /* the unitary matrix Q as a product of elementary */ 00087 /* reflectors, and the elements above the first superdiagonal, */ 00088 /* with the array TAUP, represent the unitary matrix P as */ 00089 /* a product of elementary reflectors; */ 00090 /* if m < n, the diagonal and the first subdiagonal are */ 00091 /* overwritten with the lower bidiagonal matrix B; the */ 00092 /* elements below the first subdiagonal, with the array TAUQ, */ 00093 /* represent the unitary matrix Q as a product of */ 00094 /* elementary reflectors, and the elements above the diagonal, */ 00095 /* with the array TAUP, represent the unitary matrix P as */ 00096 /* a product of elementary reflectors. */ 00097 /* See Further Details. */ 00098 00099 /* LDA (input) INTEGER */ 00100 /* The leading dimension of the array A. LDA >= max(1,M). */ 00101 00102 /* D (output) DOUBLE PRECISION array, dimension (min(M,N)) */ 00103 /* The diagonal elements of the bidiagonal matrix B: */ 00104 /* D(i) = A(i,i). */ 00105 00106 /* E (output) DOUBLE PRECISION array, dimension (min(M,N)-1) */ 00107 /* The off-diagonal elements of the bidiagonal matrix B: */ 00108 /* if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */ 00109 /* if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */ 00110 00111 /* TAUQ (output) COMPLEX*16 array dimension (min(M,N)) */ 00112 /* The scalar factors of the elementary reflectors which */ 00113 /* represent the unitary matrix Q. See Further Details. */ 00114 00115 /* TAUP (output) COMPLEX*16 array, dimension (min(M,N)) */ 00116 /* The scalar factors of the elementary reflectors which */ 00117 /* represent the unitary matrix P. See Further Details. */ 00118 00119 /* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */ 00120 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00121 00122 /* LWORK (input) INTEGER */ 00123 /* The length of the array WORK. LWORK >= max(1,M,N). */ 00124 /* For optimum performance LWORK >= (M+N)*NB, where NB */ 00125 /* is the optimal blocksize. */ 00126 00127 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00128 /* only calculates the optimal size of the WORK array, returns */ 00129 /* this value as the first entry of the WORK array, and no error */ 00130 /* message related to LWORK is issued by XERBLA. */ 00131 00132 /* INFO (output) INTEGER */ 00133 /* = 0: successful exit. */ 00134 /* < 0: if INFO = -i, the i-th argument had an illegal value. */ 00135 00136 /* Further Details */ 00137 /* =============== */ 00138 00139 /* The matrices Q and P are represented as products of elementary */ 00140 /* reflectors: */ 00141 00142 /* If m >= n, */ 00143 00144 /* Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) */ 00145 00146 /* Each H(i) and G(i) has the form: */ 00147 00148 /* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */ 00149 00150 /* where tauq and taup are complex scalars, and v and u are complex */ 00151 /* vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in */ 00152 /* A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in */ 00153 /* A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */ 00154 00155 /* If m < n, */ 00156 00157 /* Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) */ 00158 00159 /* Each H(i) and G(i) has the form: */ 00160 00161 /* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */ 00162 00163 /* where tauq and taup are complex scalars, and v and u are complex */ 00164 /* vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in */ 00165 /* A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in */ 00166 /* A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */ 00167 00168 /* The contents of A on exit are illustrated by the following examples: */ 00169 00170 /* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ 00171 00172 /* ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) */ 00173 /* ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) */ 00174 /* ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) */ 00175 /* ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) */ 00176 /* ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) */ 00177 /* ( v1 v2 v3 v4 v5 ) */ 00178 00179 /* where d and e denote diagonal and off-diagonal elements of B, vi */ 00180 /* denotes an element of the vector defining H(i), and ui an element of */ 00181 /* the vector defining G(i). */ 00182 00183 /* ===================================================================== */ 00184 00185 /* .. Parameters .. */ 00186 /* .. */ 00187 /* .. Local Scalars .. */ 00188 /* .. */ 00189 /* .. External Subroutines .. */ 00190 /* .. */ 00191 /* .. Intrinsic Functions .. */ 00192 /* .. */ 00193 /* .. External Functions .. */ 00194 /* .. */ 00195 /* .. Executable Statements .. */ 00196 00197 /* Test the input parameters */ 00198 00199 /* Parameter adjustments */ 00200 a_dim1 = *lda; 00201 a_offset = 1 + a_dim1; 00202 a -= a_offset; 00203 --d__; 00204 --e; 00205 --tauq; 00206 --taup; 00207 --work; 00208 00209 /* Function Body */ 00210 *info = 0; 00211 /* Computing MAX */ 00212 i__1 = 1, i__2 = ilaenv_(&c__1, "ZGEBRD", " ", m, n, &c_n1, &c_n1); 00213 nb = max(i__1,i__2); 00214 lwkopt = (*m + *n) * nb; 00215 d__1 = (doublereal) lwkopt; 00216 work[1].r = d__1, work[1].i = 0.; 00217 lquery = *lwork == -1; 00218 if (*m < 0) { 00219 *info = -1; 00220 } else if (*n < 0) { 00221 *info = -2; 00222 } else if (*lda < max(1,*m)) { 00223 *info = -4; 00224 } else /* if(complicated condition) */ { 00225 /* Computing MAX */ 00226 i__1 = max(1,*m); 00227 if (*lwork < max(i__1,*n) && ! lquery) { 00228 *info = -10; 00229 } 00230 } 00231 if (*info < 0) { 00232 i__1 = -(*info); 00233 xerbla_("ZGEBRD", &i__1); 00234 return 0; 00235 } else if (lquery) { 00236 return 0; 00237 } 00238 00239 /* Quick return if possible */ 00240 00241 minmn = min(*m,*n); 00242 if (minmn == 0) { 00243 work[1].r = 1., work[1].i = 0.; 00244 return 0; 00245 } 00246 00247 ws = (doublereal) max(*m,*n); 00248 ldwrkx = *m; 00249 ldwrky = *n; 00250 00251 if (nb > 1 && nb < minmn) { 00252 00253 /* Set the crossover point NX. */ 00254 00255 /* Computing MAX */ 00256 i__1 = nb, i__2 = ilaenv_(&c__3, "ZGEBRD", " ", m, n, &c_n1, &c_n1); 00257 nx = max(i__1,i__2); 00258 00259 /* Determine when to switch from blocked to unblocked code. */ 00260 00261 if (nx < minmn) { 00262 ws = (doublereal) ((*m + *n) * nb); 00263 if ((doublereal) (*lwork) < ws) { 00264 00265 /* Not enough work space for the optimal NB, consider using */ 00266 /* a smaller block size. */ 00267 00268 nbmin = ilaenv_(&c__2, "ZGEBRD", " ", m, n, &c_n1, &c_n1); 00269 if (*lwork >= (*m + *n) * nbmin) { 00270 nb = *lwork / (*m + *n); 00271 } else { 00272 nb = 1; 00273 nx = minmn; 00274 } 00275 } 00276 } 00277 } else { 00278 nx = minmn; 00279 } 00280 00281 i__1 = minmn - nx; 00282 i__2 = nb; 00283 for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { 00284 00285 /* Reduce rows and columns i:i+ib-1 to bidiagonal form and return */ 00286 /* the matrices X and Y which are needed to update the unreduced */ 00287 /* part of the matrix */ 00288 00289 i__3 = *m - i__ + 1; 00290 i__4 = *n - i__ + 1; 00291 zlabrd_(&i__3, &i__4, &nb, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[ 00292 i__], &tauq[i__], &taup[i__], &work[1], &ldwrkx, &work[ldwrkx 00293 * nb + 1], &ldwrky); 00294 00295 /* Update the trailing submatrix A(i+ib:m,i+ib:n), using */ 00296 /* an update of the form A := A - V*Y' - X*U' */ 00297 00298 i__3 = *m - i__ - nb + 1; 00299 i__4 = *n - i__ - nb + 1; 00300 z__1.r = -1., z__1.i = -0.; 00301 zgemm_("No transpose", "Conjugate transpose", &i__3, &i__4, &nb, & 00302 z__1, &a[i__ + nb + i__ * a_dim1], lda, &work[ldwrkx * nb + 00303 nb + 1], &ldwrky, &c_b1, &a[i__ + nb + (i__ + nb) * a_dim1], 00304 lda); 00305 i__3 = *m - i__ - nb + 1; 00306 i__4 = *n - i__ - nb + 1; 00307 z__1.r = -1., z__1.i = -0.; 00308 zgemm_("No transpose", "No transpose", &i__3, &i__4, &nb, &z__1, & 00309 work[nb + 1], &ldwrkx, &a[i__ + (i__ + nb) * a_dim1], lda, & 00310 c_b1, &a[i__ + nb + (i__ + nb) * a_dim1], lda); 00311 00312 /* Copy diagonal and off-diagonal elements of B back into A */ 00313 00314 if (*m >= *n) { 00315 i__3 = i__ + nb - 1; 00316 for (j = i__; j <= i__3; ++j) { 00317 i__4 = j + j * a_dim1; 00318 i__5 = j; 00319 a[i__4].r = d__[i__5], a[i__4].i = 0.; 00320 i__4 = j + (j + 1) * a_dim1; 00321 i__5 = j; 00322 a[i__4].r = e[i__5], a[i__4].i = 0.; 00323 /* L10: */ 00324 } 00325 } else { 00326 i__3 = i__ + nb - 1; 00327 for (j = i__; j <= i__3; ++j) { 00328 i__4 = j + j * a_dim1; 00329 i__5 = j; 00330 a[i__4].r = d__[i__5], a[i__4].i = 0.; 00331 i__4 = j + 1 + j * a_dim1; 00332 i__5 = j; 00333 a[i__4].r = e[i__5], a[i__4].i = 0.; 00334 /* L20: */ 00335 } 00336 } 00337 /* L30: */ 00338 } 00339 00340 /* Use unblocked code to reduce the remainder of the matrix */ 00341 00342 i__2 = *m - i__ + 1; 00343 i__1 = *n - i__ + 1; 00344 zgebd2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], & 00345 tauq[i__], &taup[i__], &work[1], &iinfo); 00346 work[1].r = ws, work[1].i = 0.; 00347 return 0; 00348 00349 /* End of ZGEBRD */ 00350 00351 } /* zgebrd_ */