00001 /* zggqrf.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 integer c_n1 = -1; 00020 00021 /* Subroutine */ int zggqrf_(integer *n, integer *m, integer *p, 00022 doublecomplex *a, integer *lda, doublecomplex *taua, doublecomplex *b, 00023 integer *ldb, doublecomplex *taub, doublecomplex *work, integer * 00024 lwork, integer *info) 00025 { 00026 /* System generated locals */ 00027 integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; 00028 00029 /* Local variables */ 00030 integer nb, nb1, nb2, nb3, lopt; 00031 extern /* Subroutine */ int xerbla_(char *, integer *); 00032 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00033 integer *, integer *); 00034 extern /* Subroutine */ int zgeqrf_(integer *, integer *, doublecomplex *, 00035 integer *, doublecomplex *, doublecomplex *, integer *, integer * 00036 ), zgerqf_(integer *, integer *, doublecomplex *, integer *, 00037 doublecomplex *, doublecomplex *, integer *, integer *); 00038 integer lwkopt; 00039 logical lquery; 00040 extern /* Subroutine */ int zunmqr_(char *, char *, integer *, integer *, 00041 integer *, doublecomplex *, integer *, doublecomplex *, 00042 doublecomplex *, integer *, doublecomplex *, integer *, integer *); 00043 00044 00045 /* -- LAPACK routine (version 3.2) -- */ 00046 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00047 /* November 2006 */ 00048 00049 /* .. Scalar Arguments .. */ 00050 /* .. */ 00051 /* .. Array Arguments .. */ 00052 /* .. */ 00053 00054 /* Purpose */ 00055 /* ======= */ 00056 00057 /* ZGGQRF computes a generalized QR factorization of an N-by-M matrix A */ 00058 /* and an N-by-P matrix B: */ 00059 00060 /* A = Q*R, B = Q*T*Z, */ 00061 00062 /* where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix, */ 00063 /* and R and T assume one of the forms: */ 00064 00065 /* if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N, */ 00066 /* ( 0 ) N-M N M-N */ 00067 /* M */ 00068 00069 /* where R11 is upper triangular, and */ 00070 00071 /* if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P, */ 00072 /* P-N N ( T21 ) P */ 00073 /* P */ 00074 00075 /* where T12 or T21 is upper triangular. */ 00076 00077 /* In particular, if B is square and nonsingular, the GQR factorization */ 00078 /* of A and B implicitly gives the QR factorization of inv(B)*A: */ 00079 00080 /* inv(B)*A = Z'*(inv(T)*R) */ 00081 00082 /* where inv(B) denotes the inverse of the matrix B, and Z' denotes the */ 00083 /* conjugate transpose of matrix Z. */ 00084 00085 /* Arguments */ 00086 /* ========= */ 00087 00088 /* N (input) INTEGER */ 00089 /* The number of rows of the matrices A and B. N >= 0. */ 00090 00091 /* M (input) INTEGER */ 00092 /* The number of columns of the matrix A. M >= 0. */ 00093 00094 /* P (input) INTEGER */ 00095 /* The number of columns of the matrix B. P >= 0. */ 00096 00097 /* A (input/output) COMPLEX*16 array, dimension (LDA,M) */ 00098 /* On entry, the N-by-M matrix A. */ 00099 /* On exit, the elements on and above the diagonal of the array */ 00100 /* contain the min(N,M)-by-M upper trapezoidal matrix R (R is */ 00101 /* upper triangular if N >= M); the elements below the diagonal, */ 00102 /* with the array TAUA, represent the unitary matrix Q as a */ 00103 /* product of min(N,M) elementary reflectors (see Further */ 00104 /* Details). */ 00105 00106 /* LDA (input) INTEGER */ 00107 /* The leading dimension of the array A. LDA >= max(1,N). */ 00108 00109 /* TAUA (output) COMPLEX*16 array, dimension (min(N,M)) */ 00110 /* The scalar factors of the elementary reflectors which */ 00111 /* represent the unitary matrix Q (see Further Details). */ 00112 00113 /* B (input/output) COMPLEX*16 array, dimension (LDB,P) */ 00114 /* On entry, the N-by-P matrix B. */ 00115 /* On exit, if N <= P, the upper triangle of the subarray */ 00116 /* B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T; */ 00117 /* if N > P, the elements on and above the (N-P)-th subdiagonal */ 00118 /* contain the N-by-P upper trapezoidal matrix T; the remaining */ 00119 /* elements, with the array TAUB, represent the unitary */ 00120 /* matrix Z as a product of elementary reflectors (see Further */ 00121 /* Details). */ 00122 00123 /* LDB (input) INTEGER */ 00124 /* The leading dimension of the array B. LDB >= max(1,N). */ 00125 00126 /* TAUB (output) COMPLEX*16 array, dimension (min(N,P)) */ 00127 /* The scalar factors of the elementary reflectors which */ 00128 /* represent the unitary matrix Z (see Further Details). */ 00129 00130 /* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */ 00131 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00132 00133 /* LWORK (input) INTEGER */ 00134 /* The dimension of the array WORK. LWORK >= max(1,N,M,P). */ 00135 /* For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3), */ 00136 /* where NB1 is the optimal blocksize for the QR factorization */ 00137 /* of an N-by-M matrix, NB2 is the optimal blocksize for the */ 00138 /* RQ factorization of an N-by-P matrix, and NB3 is the optimal */ 00139 /* blocksize for a call of ZUNMQR. */ 00140 00141 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00142 /* only calculates the optimal size of the WORK array, returns */ 00143 /* this value as the first entry of the WORK array, and no error */ 00144 /* message related to LWORK is issued by XERBLA. */ 00145 00146 /* INFO (output) INTEGER */ 00147 /* = 0: successful exit */ 00148 /* < 0: if INFO = -i, the i-th argument had an illegal value. */ 00149 00150 /* Further Details */ 00151 /* =============== */ 00152 00153 /* The matrix Q is represented as a product of elementary reflectors */ 00154 00155 /* Q = H(1) H(2) . . . H(k), where k = min(n,m). */ 00156 00157 /* Each H(i) has the form */ 00158 00159 /* H(i) = I - taua * v * v' */ 00160 00161 /* where taua is a complex scalar, and v is a complex vector with */ 00162 /* v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */ 00163 /* and taua in TAUA(i). */ 00164 /* To form Q explicitly, use LAPACK subroutine ZUNGQR. */ 00165 /* To use Q to update another matrix, use LAPACK subroutine ZUNMQR. */ 00166 00167 /* The matrix Z is represented as a product of elementary reflectors */ 00168 00169 /* Z = H(1) H(2) . . . H(k), where k = min(n,p). */ 00170 00171 /* Each H(i) has the form */ 00172 00173 /* H(i) = I - taub * v * v' */ 00174 00175 /* where taub is a complex scalar, and v is a complex vector with */ 00176 /* v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in */ 00177 /* B(n-k+i,1:p-k+i-1), and taub in TAUB(i). */ 00178 /* To form Z explicitly, use LAPACK subroutine ZUNGRQ. */ 00179 /* To use Z to update another matrix, use LAPACK subroutine ZUNMRQ. */ 00180 00181 /* ===================================================================== */ 00182 00183 /* .. Local Scalars .. */ 00184 /* .. */ 00185 /* .. External Subroutines .. */ 00186 /* .. */ 00187 /* .. External Functions .. */ 00188 /* .. */ 00189 /* .. Intrinsic Functions .. */ 00190 /* .. */ 00191 /* .. Executable Statements .. */ 00192 00193 /* Test the input parameters */ 00194 00195 /* Parameter adjustments */ 00196 a_dim1 = *lda; 00197 a_offset = 1 + a_dim1; 00198 a -= a_offset; 00199 --taua; 00200 b_dim1 = *ldb; 00201 b_offset = 1 + b_dim1; 00202 b -= b_offset; 00203 --taub; 00204 --work; 00205 00206 /* Function Body */ 00207 *info = 0; 00208 nb1 = ilaenv_(&c__1, "ZGEQRF", " ", n, m, &c_n1, &c_n1); 00209 nb2 = ilaenv_(&c__1, "ZGERQF", " ", n, p, &c_n1, &c_n1); 00210 nb3 = ilaenv_(&c__1, "ZUNMQR", " ", n, m, p, &c_n1); 00211 /* Computing MAX */ 00212 i__1 = max(nb1,nb2); 00213 nb = max(i__1,nb3); 00214 /* Computing MAX */ 00215 i__1 = max(*n,*m); 00216 lwkopt = max(i__1,*p) * nb; 00217 work[1].r = (doublereal) lwkopt, work[1].i = 0.; 00218 lquery = *lwork == -1; 00219 if (*n < 0) { 00220 *info = -1; 00221 } else if (*m < 0) { 00222 *info = -2; 00223 } else if (*p < 0) { 00224 *info = -3; 00225 } else if (*lda < max(1,*n)) { 00226 *info = -5; 00227 } else if (*ldb < max(1,*n)) { 00228 *info = -8; 00229 } else /* if(complicated condition) */ { 00230 /* Computing MAX */ 00231 i__1 = max(1,*n), i__1 = max(i__1,*m); 00232 if (*lwork < max(i__1,*p) && ! lquery) { 00233 *info = -11; 00234 } 00235 } 00236 if (*info != 0) { 00237 i__1 = -(*info); 00238 xerbla_("ZGGQRF", &i__1); 00239 return 0; 00240 } else if (lquery) { 00241 return 0; 00242 } 00243 00244 /* QR factorization of N-by-M matrix A: A = Q*R */ 00245 00246 zgeqrf_(n, m, &a[a_offset], lda, &taua[1], &work[1], lwork, info); 00247 lopt = (integer) work[1].r; 00248 00249 /* Update B := Q'*B. */ 00250 00251 i__1 = min(*n,*m); 00252 zunmqr_("Left", "Conjugate Transpose", n, p, &i__1, &a[a_offset], lda, & 00253 taua[1], &b[b_offset], ldb, &work[1], lwork, info); 00254 /* Computing MAX */ 00255 i__1 = lopt, i__2 = (integer) work[1].r; 00256 lopt = max(i__1,i__2); 00257 00258 /* RQ factorization of N-by-P matrix B: B = T*Z. */ 00259 00260 zgerqf_(n, p, &b[b_offset], ldb, &taub[1], &work[1], lwork, info); 00261 /* Computing MAX */ 00262 i__2 = lopt, i__3 = (integer) work[1].r; 00263 i__1 = max(i__2,i__3); 00264 work[1].r = (doublereal) i__1, work[1].i = 0.; 00265 00266 return 0; 00267 00268 /* End of ZGGQRF */ 00269 00270 } /* zggqrf_ */