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