mirror of https://github.com/opencv/opencv.git
Open Source Computer Vision Library
https://opencv.org/
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
515 lines
15 KiB
515 lines
15 KiB
/* dgels.f -- translated by f2c (version 20061008). |
|
You must link the resulting object file with libf2c: |
|
on Microsoft Windows system, link with libf2c.lib; |
|
on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
|
or, if you install libf2c.a in a standard place, with -lf2c -lm |
|
-- in that order, at the end of the command line, as in |
|
cc *.o -lf2c -lm |
|
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
|
|
|
http://www.netlib.org/f2c/libf2c.zip |
|
*/ |
|
|
|
#include "clapack.h" |
|
|
|
|
|
/* Table of constant values */ |
|
|
|
static integer c__1 = 1; |
|
static integer c_n1 = -1; |
|
static doublereal c_b33 = 0.; |
|
static integer c__0 = 0; |
|
|
|
/* Subroutine */ int dgels_(char *trans, integer *m, integer *n, integer * |
|
nrhs, doublereal *a, integer *lda, doublereal *b, integer *ldb, |
|
doublereal *work, integer *lwork, integer *info) |
|
{ |
|
/* System generated locals */ |
|
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; |
|
|
|
/* Local variables */ |
|
integer i__, j, nb, mn; |
|
doublereal anrm, bnrm; |
|
integer brow; |
|
logical tpsd; |
|
integer iascl, ibscl; |
|
extern logical lsame_(char *, char *); |
|
integer wsize; |
|
doublereal rwork[1]; |
|
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *); |
|
extern doublereal dlamch_(char *), dlange_(char *, integer *, |
|
integer *, doublereal *, integer *, doublereal *); |
|
extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, |
|
integer *, doublereal *, doublereal *, integer *, integer *), |
|
dlascl_(char *, integer *, integer *, doublereal *, doublereal *, |
|
integer *, integer *, doublereal *, integer *, integer *), |
|
dgeqrf_(integer *, integer *, doublereal *, integer *, |
|
doublereal *, doublereal *, integer *, integer *), dlaset_(char *, |
|
integer *, integer *, doublereal *, doublereal *, doublereal *, |
|
integer *), xerbla_(char *, integer *); |
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, |
|
integer *, integer *); |
|
integer scllen; |
|
doublereal bignum; |
|
extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, |
|
integer *, doublereal *, integer *, doublereal *, doublereal *, |
|
integer *, doublereal *, integer *, integer *), |
|
dormqr_(char *, char *, integer *, integer *, integer *, |
|
doublereal *, integer *, doublereal *, doublereal *, integer *, |
|
doublereal *, integer *, integer *); |
|
doublereal smlnum; |
|
logical lquery; |
|
extern /* Subroutine */ int dtrtrs_(char *, char *, char *, integer *, |
|
integer *, doublereal *, integer *, doublereal *, integer *, |
|
integer *); |
|
|
|
|
|
/* -- LAPACK driver routine (version 3.2) -- */ |
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
|
/* November 2006 */ |
|
|
|
/* .. Scalar Arguments .. */ |
|
/* .. */ |
|
/* .. Array Arguments .. */ |
|
/* .. */ |
|
|
|
/* Purpose */ |
|
/* ======= */ |
|
|
|
/* DGELS solves overdetermined or underdetermined real linear systems */ |
|
/* involving an M-by-N matrix A, or its transpose, using a QR or LQ */ |
|
/* factorization of A. It is assumed that A has full rank. */ |
|
|
|
/* The following options are provided: */ |
|
|
|
/* 1. If TRANS = 'N' and m >= n: find the least squares solution of */ |
|
/* an overdetermined system, i.e., solve the least squares problem */ |
|
/* minimize || B - A*X ||. */ |
|
|
|
/* 2. If TRANS = 'N' and m < n: find the minimum norm solution of */ |
|
/* an underdetermined system A * X = B. */ |
|
|
|
/* 3. If TRANS = 'T' and m >= n: find the minimum norm solution of */ |
|
/* an undetermined system A**T * X = B. */ |
|
|
|
/* 4. If TRANS = 'T' and m < n: find the least squares solution of */ |
|
/* an overdetermined system, i.e., solve the least squares problem */ |
|
/* minimize || B - A**T * X ||. */ |
|
|
|
/* Several right hand side vectors b and solution vectors x can be */ |
|
/* handled in a single call; they are stored as the columns of the */ |
|
/* M-by-NRHS right hand side matrix B and the N-by-NRHS solution */ |
|
/* matrix X. */ |
|
|
|
/* Arguments */ |
|
/* ========= */ |
|
|
|
/* TRANS (input) CHARACTER*1 */ |
|
/* = 'N': the linear system involves A; */ |
|
/* = 'T': the linear system involves A**T. */ |
|
|
|
/* M (input) INTEGER */ |
|
/* The number of rows of the matrix A. M >= 0. */ |
|
|
|
/* N (input) INTEGER */ |
|
/* The number of columns of the matrix A. N >= 0. */ |
|
|
|
/* NRHS (input) INTEGER */ |
|
/* The number of right hand sides, i.e., the number of */ |
|
/* columns of the matrices B and X. NRHS >=0. */ |
|
|
|
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */ |
|
/* On entry, the M-by-N matrix A. */ |
|
/* On exit, */ |
|
/* if M >= N, A is overwritten by details of its QR */ |
|
/* factorization as returned by DGEQRF; */ |
|
/* if M < N, A is overwritten by details of its LQ */ |
|
/* factorization as returned by DGELQF. */ |
|
|
|
/* LDA (input) INTEGER */ |
|
/* The leading dimension of the array A. LDA >= max(1,M). */ |
|
|
|
/* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */ |
|
/* On entry, the matrix B of right hand side vectors, stored */ |
|
/* columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS */ |
|
/* if TRANS = 'T'. */ |
|
/* On exit, if INFO = 0, B is overwritten by the solution */ |
|
/* vectors, stored columnwise: */ |
|
/* if TRANS = 'N' and m >= n, rows 1 to n of B contain the least */ |
|
/* squares solution vectors; the residual sum of squares for the */ |
|
/* solution in each column is given by the sum of squares of */ |
|
/* elements N+1 to M in that column; */ |
|
/* if TRANS = 'N' and m < n, rows 1 to N of B contain the */ |
|
/* minimum norm solution vectors; */ |
|
/* if TRANS = 'T' and m >= n, rows 1 to M of B contain the */ |
|
/* minimum norm solution vectors; */ |
|
/* if TRANS = 'T' and m < n, rows 1 to M of B contain the */ |
|
/* least squares solution vectors; the residual sum of squares */ |
|
/* for the solution in each column is given by the sum of */ |
|
/* squares of elements M+1 to N in that column. */ |
|
|
|
/* LDB (input) INTEGER */ |
|
/* The leading dimension of the array B. LDB >= MAX(1,M,N). */ |
|
|
|
/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ |
|
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ |
|
|
|
/* LWORK (input) INTEGER */ |
|
/* The dimension of the array WORK. */ |
|
/* LWORK >= max( 1, MN + max( MN, NRHS ) ). */ |
|
/* For optimal performance, */ |
|
/* LWORK >= max( 1, MN + max( MN, NRHS )*NB ). */ |
|
/* where MN = min(M,N) and NB is the optimum block size. */ |
|
|
|
/* If LWORK = -1, then a workspace query is assumed; the routine */ |
|
/* only calculates the optimal size of the WORK array, returns */ |
|
/* this value as the first entry of the WORK array, and no error */ |
|
/* message related to LWORK is issued by XERBLA. */ |
|
|
|
/* INFO (output) INTEGER */ |
|
/* = 0: successful exit */ |
|
/* < 0: if INFO = -i, the i-th argument had an illegal value */ |
|
/* > 0: if INFO = i, the i-th diagonal element of the */ |
|
/* triangular factor of A is zero, so that A does not have */ |
|
/* full rank; the least squares solution could not be */ |
|
/* computed. */ |
|
|
|
/* ===================================================================== */ |
|
|
|
/* .. Parameters .. */ |
|
/* .. */ |
|
/* .. Local Scalars .. */ |
|
/* .. */ |
|
/* .. Local Arrays .. */ |
|
/* .. */ |
|
/* .. External Functions .. */ |
|
/* .. */ |
|
/* .. External Subroutines .. */ |
|
/* .. */ |
|
/* .. Intrinsic Functions .. */ |
|
/* .. */ |
|
/* .. Executable Statements .. */ |
|
|
|
/* Test the input arguments. */ |
|
|
|
/* Parameter adjustments */ |
|
a_dim1 = *lda; |
|
a_offset = 1 + a_dim1; |
|
a -= a_offset; |
|
b_dim1 = *ldb; |
|
b_offset = 1 + b_dim1; |
|
b -= b_offset; |
|
--work; |
|
|
|
/* Function Body */ |
|
*info = 0; |
|
mn = min(*m,*n); |
|
lquery = *lwork == -1; |
|
if (! (lsame_(trans, "N") || lsame_(trans, "T"))) { |
|
*info = -1; |
|
} else if (*m < 0) { |
|
*info = -2; |
|
} else if (*n < 0) { |
|
*info = -3; |
|
} else if (*nrhs < 0) { |
|
*info = -4; |
|
} else if (*lda < max(1,*m)) { |
|
*info = -6; |
|
} else /* if(complicated condition) */ { |
|
/* Computing MAX */ |
|
i__1 = max(1,*m); |
|
if (*ldb < max(i__1,*n)) { |
|
*info = -8; |
|
} else /* if(complicated condition) */ { |
|
/* Computing MAX */ |
|
i__1 = 1, i__2 = mn + max(mn,*nrhs); |
|
if (*lwork < max(i__1,i__2) && ! lquery) { |
|
*info = -10; |
|
} |
|
} |
|
} |
|
|
|
/* Figure out optimal block size */ |
|
|
|
if (*info == 0 || *info == -10) { |
|
|
|
tpsd = TRUE_; |
|
if (lsame_(trans, "N")) { |
|
tpsd = FALSE_; |
|
} |
|
|
|
if (*m >= *n) { |
|
nb = ilaenv_(&c__1, "DGEQRF", " ", m, n, &c_n1, &c_n1); |
|
if (tpsd) { |
|
/* Computing MAX */ |
|
i__1 = nb, i__2 = ilaenv_(&c__1, "DORMQR", "LN", m, nrhs, n, & |
|
c_n1); |
|
nb = max(i__1,i__2); |
|
} else { |
|
/* Computing MAX */ |
|
i__1 = nb, i__2 = ilaenv_(&c__1, "DORMQR", "LT", m, nrhs, n, & |
|
c_n1); |
|
nb = max(i__1,i__2); |
|
} |
|
} else { |
|
nb = ilaenv_(&c__1, "DGELQF", " ", m, n, &c_n1, &c_n1); |
|
if (tpsd) { |
|
/* Computing MAX */ |
|
i__1 = nb, i__2 = ilaenv_(&c__1, "DORMLQ", "LT", n, nrhs, m, & |
|
c_n1); |
|
nb = max(i__1,i__2); |
|
} else { |
|
/* Computing MAX */ |
|
i__1 = nb, i__2 = ilaenv_(&c__1, "DORMLQ", "LN", n, nrhs, m, & |
|
c_n1); |
|
nb = max(i__1,i__2); |
|
} |
|
} |
|
|
|
/* Computing MAX */ |
|
i__1 = 1, i__2 = mn + max(mn,*nrhs) * nb; |
|
wsize = max(i__1,i__2); |
|
work[1] = (doublereal) wsize; |
|
|
|
} |
|
|
|
if (*info != 0) { |
|
i__1 = -(*info); |
|
xerbla_("DGELS ", &i__1); |
|
return 0; |
|
} else if (lquery) { |
|
return 0; |
|
} |
|
|
|
/* Quick return if possible */ |
|
|
|
/* Computing MIN */ |
|
i__1 = min(*m,*n); |
|
if (min(i__1,*nrhs) == 0) { |
|
i__1 = max(*m,*n); |
|
dlaset_("Full", &i__1, nrhs, &c_b33, &c_b33, &b[b_offset], ldb); |
|
return 0; |
|
} |
|
|
|
/* Get machine parameters */ |
|
|
|
smlnum = dlamch_("S") / dlamch_("P"); |
|
bignum = 1. / smlnum; |
|
dlabad_(&smlnum, &bignum); |
|
|
|
/* Scale A, B if max element outside range [SMLNUM,BIGNUM] */ |
|
|
|
anrm = dlange_("M", m, n, &a[a_offset], lda, rwork); |
|
iascl = 0; |
|
if (anrm > 0. && anrm < smlnum) { |
|
|
|
/* Scale matrix norm up to SMLNUM */ |
|
|
|
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, |
|
info); |
|
iascl = 1; |
|
} else if (anrm > bignum) { |
|
|
|
/* Scale matrix norm down to BIGNUM */ |
|
|
|
dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, |
|
info); |
|
iascl = 2; |
|
} else if (anrm == 0.) { |
|
|
|
/* Matrix all zero. Return zero solution. */ |
|
|
|
i__1 = max(*m,*n); |
|
dlaset_("F", &i__1, nrhs, &c_b33, &c_b33, &b[b_offset], ldb); |
|
goto L50; |
|
} |
|
|
|
brow = *m; |
|
if (tpsd) { |
|
brow = *n; |
|
} |
|
bnrm = dlange_("M", &brow, nrhs, &b[b_offset], ldb, rwork); |
|
ibscl = 0; |
|
if (bnrm > 0. && bnrm < smlnum) { |
|
|
|
/* Scale matrix norm up to SMLNUM */ |
|
|
|
dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, &brow, nrhs, &b[b_offset], |
|
ldb, info); |
|
ibscl = 1; |
|
} else if (bnrm > bignum) { |
|
|
|
/* Scale matrix norm down to BIGNUM */ |
|
|
|
dlascl_("G", &c__0, &c__0, &bnrm, &bignum, &brow, nrhs, &b[b_offset], |
|
ldb, info); |
|
ibscl = 2; |
|
} |
|
|
|
if (*m >= *n) { |
|
|
|
/* compute QR factorization of A */ |
|
|
|
i__1 = *lwork - mn; |
|
dgeqrf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info) |
|
; |
|
|
|
/* workspace at least N, optimally N*NB */ |
|
|
|
if (! tpsd) { |
|
|
|
/* Least-Squares Problem min || A * X - B || */ |
|
|
|
/* B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */ |
|
|
|
i__1 = *lwork - mn; |
|
dormqr_("Left", "Transpose", m, nrhs, n, &a[a_offset], lda, &work[ |
|
1], &b[b_offset], ldb, &work[mn + 1], &i__1, info); |
|
|
|
/* workspace at least NRHS, optimally NRHS*NB */ |
|
|
|
/* B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */ |
|
|
|
dtrtrs_("Upper", "No transpose", "Non-unit", n, nrhs, &a[a_offset] |
|
, lda, &b[b_offset], ldb, info); |
|
|
|
if (*info > 0) { |
|
return 0; |
|
} |
|
|
|
scllen = *n; |
|
|
|
} else { |
|
|
|
/* Overdetermined system of equations A' * X = B */ |
|
|
|
/* B(1:N,1:NRHS) := inv(R') * B(1:N,1:NRHS) */ |
|
|
|
dtrtrs_("Upper", "Transpose", "Non-unit", n, nrhs, &a[a_offset], |
|
lda, &b[b_offset], ldb, info); |
|
|
|
if (*info > 0) { |
|
return 0; |
|
} |
|
|
|
/* B(N+1:M,1:NRHS) = ZERO */ |
|
|
|
i__1 = *nrhs; |
|
for (j = 1; j <= i__1; ++j) { |
|
i__2 = *m; |
|
for (i__ = *n + 1; i__ <= i__2; ++i__) { |
|
b[i__ + j * b_dim1] = 0.; |
|
/* L10: */ |
|
} |
|
/* L20: */ |
|
} |
|
|
|
/* B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) */ |
|
|
|
i__1 = *lwork - mn; |
|
dormqr_("Left", "No transpose", m, nrhs, n, &a[a_offset], lda, & |
|
work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info); |
|
|
|
/* workspace at least NRHS, optimally NRHS*NB */ |
|
|
|
scllen = *m; |
|
|
|
} |
|
|
|
} else { |
|
|
|
/* Compute LQ factorization of A */ |
|
|
|
i__1 = *lwork - mn; |
|
dgelqf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info) |
|
; |
|
|
|
/* workspace at least M, optimally M*NB. */ |
|
|
|
if (! tpsd) { |
|
|
|
/* underdetermined system of equations A * X = B */ |
|
|
|
/* B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */ |
|
|
|
dtrtrs_("Lower", "No transpose", "Non-unit", m, nrhs, &a[a_offset] |
|
, lda, &b[b_offset], ldb, info); |
|
|
|
if (*info > 0) { |
|
return 0; |
|
} |
|
|
|
/* B(M+1:N,1:NRHS) = 0 */ |
|
|
|
i__1 = *nrhs; |
|
for (j = 1; j <= i__1; ++j) { |
|
i__2 = *n; |
|
for (i__ = *m + 1; i__ <= i__2; ++i__) { |
|
b[i__ + j * b_dim1] = 0.; |
|
/* L30: */ |
|
} |
|
/* L40: */ |
|
} |
|
|
|
/* B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS) */ |
|
|
|
i__1 = *lwork - mn; |
|
dormlq_("Left", "Transpose", n, nrhs, m, &a[a_offset], lda, &work[ |
|
1], &b[b_offset], ldb, &work[mn + 1], &i__1, info); |
|
|
|
/* workspace at least NRHS, optimally NRHS*NB */ |
|
|
|
scllen = *n; |
|
|
|
} else { |
|
|
|
/* overdetermined system min || A' * X - B || */ |
|
|
|
/* B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) */ |
|
|
|
i__1 = *lwork - mn; |
|
dormlq_("Left", "No transpose", n, nrhs, m, &a[a_offset], lda, & |
|
work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info); |
|
|
|
/* workspace at least NRHS, optimally NRHS*NB */ |
|
|
|
/* B(1:M,1:NRHS) := inv(L') * B(1:M,1:NRHS) */ |
|
|
|
dtrtrs_("Lower", "Transpose", "Non-unit", m, nrhs, &a[a_offset], |
|
lda, &b[b_offset], ldb, info); |
|
|
|
if (*info > 0) { |
|
return 0; |
|
} |
|
|
|
scllen = *m; |
|
|
|
} |
|
|
|
} |
|
|
|
/* Undo scaling */ |
|
|
|
if (iascl == 1) { |
|
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset] |
|
, ldb, info); |
|
} else if (iascl == 2) { |
|
dlascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset] |
|
, ldb, info); |
|
} |
|
if (ibscl == 1) { |
|
dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset] |
|
, ldb, info); |
|
} else if (ibscl == 2) { |
|
dlascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset] |
|
, ldb, info); |
|
} |
|
|
|
L50: |
|
work[1] = (doublereal) wsize; |
|
|
|
return 0; |
|
|
|
/* End of DGELS */ |
|
|
|
} /* dgels_ */
|
|
|