00001 /* cggrqf.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 cggrqf_(integer *m, integer *p, integer *n, complex *a, 00022 integer *lda, complex *taua, complex *b, integer *ldb, complex *taub, 00023 complex *work, integer *lwork, integer *info) 00024 { 00025 /* System generated locals */ 00026 integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; 00027 00028 /* Local variables */ 00029 integer nb, nb1, nb2, nb3, lopt; 00030 extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *, 00031 integer *, complex *, complex *, integer *, integer *), cgerqf_( 00032 integer *, integer *, complex *, integer *, complex *, complex *, 00033 integer *, integer *), xerbla_(char *, integer *); 00034 extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 00035 integer *, integer *); 00036 extern /* Subroutine */ int cunmrq_(char *, char *, integer *, integer *, 00037 integer *, complex *, integer *, complex *, complex *, integer *, 00038 complex *, integer *, integer *); 00039 integer lwkopt; 00040 logical lquery; 00041 00042 00043 /* -- LAPACK routine (version 3.2) -- */ 00044 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00045 /* November 2006 */ 00046 00047 /* .. Scalar Arguments .. */ 00048 /* .. */ 00049 /* .. Array Arguments .. */ 00050 /* .. */ 00051 00052 /* Purpose */ 00053 /* ======= */ 00054 00055 /* CGGRQF computes a generalized RQ factorization of an M-by-N matrix A */ 00056 /* and a P-by-N matrix B: */ 00057 00058 /* A = R*Q, B = Z*T*Q, */ 00059 00060 /* where Q is an N-by-N unitary matrix, Z is a P-by-P unitary */ 00061 /* matrix, and R and T assume one of the forms: */ 00062 00063 /* if M <= N, R = ( 0 R12 ) M, or if M > N, R = ( R11 ) M-N, */ 00064 /* N-M M ( R21 ) N */ 00065 /* N */ 00066 00067 /* where R12 or R21 is upper triangular, and */ 00068 00069 /* if P >= N, T = ( T11 ) N , or if P < N, T = ( T11 T12 ) P, */ 00070 /* ( 0 ) P-N P N-P */ 00071 /* N */ 00072 00073 /* where T11 is upper triangular. */ 00074 00075 /* In particular, if B is square and nonsingular, the GRQ factorization */ 00076 /* of A and B implicitly gives the RQ factorization of A*inv(B): */ 00077 00078 /* A*inv(B) = (R*inv(T))*Z' */ 00079 00080 /* where inv(B) denotes the inverse of the matrix B, and Z' denotes the */ 00081 /* conjugate transpose of the matrix Z. */ 00082 00083 /* Arguments */ 00084 /* ========= */ 00085 00086 /* M (input) INTEGER */ 00087 /* The number of rows of the matrix A. M >= 0. */ 00088 00089 /* P (input) INTEGER */ 00090 /* The number of rows of the matrix B. P >= 0. */ 00091 00092 /* N (input) INTEGER */ 00093 /* The number of columns of the matrices A and B. N >= 0. */ 00094 00095 /* A (input/output) COMPLEX array, dimension (LDA,N) */ 00096 /* On entry, the M-by-N matrix A. */ 00097 /* On exit, if M <= N, the upper triangle of the subarray */ 00098 /* A(1:M,N-M+1:N) contains the M-by-M upper triangular matrix R; */ 00099 /* if M > N, the elements on and above the (M-N)-th subdiagonal */ 00100 /* contain the M-by-N upper trapezoidal matrix R; the remaining */ 00101 /* elements, with the array TAUA, represent the unitary */ 00102 /* matrix Q as a product of elementary reflectors (see Further */ 00103 /* Details). */ 00104 00105 /* LDA (input) INTEGER */ 00106 /* The leading dimension of the array A. LDA >= max(1,M). */ 00107 00108 /* TAUA (output) COMPLEX array, dimension (min(M,N)) */ 00109 /* The scalar factors of the elementary reflectors which */ 00110 /* represent the unitary matrix Q (see Further Details). */ 00111 00112 /* B (input/output) COMPLEX array, dimension (LDB,N) */ 00113 /* On entry, the P-by-N matrix B. */ 00114 /* On exit, the elements on and above the diagonal of the array */ 00115 /* contain the min(P,N)-by-N upper trapezoidal matrix T (T is */ 00116 /* upper triangular if P >= N); the elements below the diagonal, */ 00117 /* with the array TAUB, represent the unitary matrix Z as a */ 00118 /* product of elementary reflectors (see Further Details). */ 00119 00120 /* LDB (input) INTEGER */ 00121 /* The leading dimension of the array B. LDB >= max(1,P). */ 00122 00123 /* TAUB (output) COMPLEX array, dimension (min(P,N)) */ 00124 /* The scalar factors of the elementary reflectors which */ 00125 /* represent the unitary matrix Z (see Further Details). */ 00126 00127 /* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */ 00128 /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ 00129 00130 /* LWORK (input) INTEGER */ 00131 /* The dimension of the array WORK. LWORK >= max(1,N,M,P). */ 00132 /* For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3), */ 00133 /* where NB1 is the optimal blocksize for the RQ factorization */ 00134 /* of an M-by-N matrix, NB2 is the optimal blocksize for the */ 00135 /* QR factorization of a P-by-N matrix, and NB3 is the optimal */ 00136 /* blocksize for a call of CUNMRQ. */ 00137 00138 /* If LWORK = -1, then a workspace query is assumed; the routine */ 00139 /* only calculates the optimal size of the WORK array, returns */ 00140 /* this value as the first entry of the WORK array, and no error */ 00141 /* message related to LWORK is issued by XERBLA. */ 00142 00143 /* INFO (output) INTEGER */ 00144 /* = 0: successful exit */ 00145 /* < 0: if INFO=-i, the i-th argument had an illegal value. */ 00146 00147 /* Further Details */ 00148 /* =============== */ 00149 00150 /* The matrix Q is represented as a product of elementary reflectors */ 00151 00152 /* Q = H(1) H(2) . . . H(k), where k = min(m,n). */ 00153 00154 /* Each H(i) has the form */ 00155 00156 /* H(i) = I - taua * v * v' */ 00157 00158 /* where taua is a complex scalar, and v is a complex vector with */ 00159 /* v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in */ 00160 /* A(m-k+i,1:n-k+i-1), and taua in TAUA(i). */ 00161 /* To form Q explicitly, use LAPACK subroutine CUNGRQ. */ 00162 /* To use Q to update another matrix, use LAPACK subroutine CUNMRQ. */ 00163 00164 /* The matrix Z is represented as a product of elementary reflectors */ 00165 00166 /* Z = H(1) H(2) . . . H(k), where k = min(p,n). */ 00167 00168 /* Each H(i) has the form */ 00169 00170 /* H(i) = I - taub * v * v' */ 00171 00172 /* where taub is a complex scalar, and v is a complex vector with */ 00173 /* v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i), */ 00174 /* and taub in TAUB(i). */ 00175 /* To form Z explicitly, use LAPACK subroutine CUNGQR. */ 00176 /* To use Z to update another matrix, use LAPACK subroutine CUNMQR. */ 00177 00178 /* ===================================================================== */ 00179 00180 /* .. Local Scalars .. */ 00181 /* .. */ 00182 /* .. External Subroutines .. */ 00183 /* .. */ 00184 /* .. External Functions .. */ 00185 /* .. */ 00186 /* .. Intrinsic Functions .. */ 00187 /* .. */ 00188 /* .. Executable Statements .. */ 00189 00190 /* Test the input parameters */ 00191 00192 /* Parameter adjustments */ 00193 a_dim1 = *lda; 00194 a_offset = 1 + a_dim1; 00195 a -= a_offset; 00196 --taua; 00197 b_dim1 = *ldb; 00198 b_offset = 1 + b_dim1; 00199 b -= b_offset; 00200 --taub; 00201 --work; 00202 00203 /* Function Body */ 00204 *info = 0; 00205 nb1 = ilaenv_(&c__1, "CGERQF", " ", m, n, &c_n1, &c_n1); 00206 nb2 = ilaenv_(&c__1, "CGEQRF", " ", p, n, &c_n1, &c_n1); 00207 nb3 = ilaenv_(&c__1, "CUNMRQ", " ", m, n, p, &c_n1); 00208 /* Computing MAX */ 00209 i__1 = max(nb1,nb2); 00210 nb = max(i__1,nb3); 00211 /* Computing MAX */ 00212 i__1 = max(*n,*m); 00213 lwkopt = max(i__1,*p) * nb; 00214 work[1].r = (real) lwkopt, work[1].i = 0.f; 00215 lquery = *lwork == -1; 00216 if (*m < 0) { 00217 *info = -1; 00218 } else if (*p < 0) { 00219 *info = -2; 00220 } else if (*n < 0) { 00221 *info = -3; 00222 } else if (*lda < max(1,*m)) { 00223 *info = -5; 00224 } else if (*ldb < max(1,*p)) { 00225 *info = -8; 00226 } else /* if(complicated condition) */ { 00227 /* Computing MAX */ 00228 i__1 = max(1,*m), i__1 = max(i__1,*p); 00229 if (*lwork < max(i__1,*n) && ! lquery) { 00230 *info = -11; 00231 } 00232 } 00233 if (*info != 0) { 00234 i__1 = -(*info); 00235 xerbla_("CGGRQF", &i__1); 00236 return 0; 00237 } else if (lquery) { 00238 return 0; 00239 } 00240 00241 /* RQ factorization of M-by-N matrix A: A = R*Q */ 00242 00243 cgerqf_(m, n, &a[a_offset], lda, &taua[1], &work[1], lwork, info); 00244 lopt = work[1].r; 00245 00246 /* Update B := B*Q' */ 00247 00248 i__1 = min(*m,*n); 00249 /* Computing MAX */ 00250 i__2 = 1, i__3 = *m - *n + 1; 00251 cunmrq_("Right", "Conjugate Transpose", p, n, &i__1, &a[max(i__2, i__3)+ 00252 a_dim1], lda, &taua[1], &b[b_offset], ldb, &work[1], lwork, info); 00253 /* Computing MAX */ 00254 i__1 = lopt, i__2 = (integer) work[1].r; 00255 lopt = max(i__1,i__2); 00256 00257 /* QR factorization of P-by-N matrix B: B = Z*T */ 00258 00259 cgeqrf_(p, n, &b[b_offset], ldb, &taub[1], &work[1], lwork, info); 00260 /* Computing MAX */ 00261 i__2 = lopt, i__3 = (integer) work[1].r; 00262 i__1 = max(i__2,i__3); 00263 work[1].r = (real) i__1, work[1].i = 0.f; 00264 00265 return 0; 00266 00267 /* End of CGGRQF */ 00268 00269 } /* cggrqf_ */