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