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author | shmel1k <shmel1k@ydb.tech> | 2022-09-02 12:44:59 +0300 |
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committer | shmel1k <shmel1k@ydb.tech> | 2022-09-02 12:44:59 +0300 |
commit | 90d450f74722da7859d6f510a869f6c6908fd12f (patch) | |
tree | 538c718dedc76cdfe37ad6d01ff250dd930d9278 /contrib/libs/clapack/dgesvx.c | |
parent | 01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff) | |
download | ydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz |
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/dgesvx.c')
-rw-r--r-- | contrib/libs/clapack/dgesvx.c | 587 |
1 files changed, 587 insertions, 0 deletions
diff --git a/contrib/libs/clapack/dgesvx.c b/contrib/libs/clapack/dgesvx.c new file mode 100644 index 0000000000..ab372d0edf --- /dev/null +++ b/contrib/libs/clapack/dgesvx.c @@ -0,0 +1,587 @@ +/* dgesvx.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 "f2c.h" +#include "blaswrap.h" + +/* Subroutine */ int dgesvx_(char *fact, char *trans, integer *n, integer * + nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, + integer *ipiv, char *equed, doublereal *r__, doublereal *c__, + doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal * + rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer * + iwork, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, + x_offset, i__1, i__2; + doublereal d__1, d__2; + + /* Local variables */ + integer i__, j; + doublereal amax; + char norm[1]; + extern logical lsame_(char *, char *); + doublereal rcmin, rcmax, anorm; + logical equil; + extern doublereal dlamch_(char *), dlange_(char *, integer *, + integer *, doublereal *, integer *, doublereal *); + extern /* Subroutine */ int dlaqge_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, char *), dgecon_(char *, integer *, + doublereal *, integer *, doublereal *, doublereal *, doublereal *, + integer *, integer *); + doublereal colcnd; + logical nofact; + extern /* Subroutine */ int dgeequ_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *), dgerfs_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, integer *, integer *), + dgetrf_(integer *, integer *, doublereal *, integer *, integer *, + integer *), dlacpy_(char *, integer *, integer *, doublereal *, + integer *, doublereal *, integer *), xerbla_(char *, + integer *); + doublereal bignum; + extern doublereal dlantr_(char *, char *, char *, integer *, integer *, + doublereal *, integer *, doublereal *); + integer infequ; + logical colequ; + extern /* Subroutine */ int dgetrs_(char *, integer *, integer *, + doublereal *, integer *, integer *, doublereal *, integer *, + integer *); + doublereal rowcnd; + logical notran; + doublereal smlnum; + logical rowequ; + doublereal rpvgrw; + + +/* -- LAPACK driver routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DGESVX uses the LU factorization to compute the solution to a real */ +/* system of linear equations */ +/* A * X = B, */ +/* where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */ + +/* Error bounds on the solution and a condition estimate are also */ +/* provided. */ + +/* Description */ +/* =========== */ + +/* The following steps are performed: */ + +/* 1. If FACT = 'E', real scaling factors are computed to equilibrate */ +/* the system: */ +/* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */ +/* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */ +/* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */ +/* Whether or not the system will be equilibrated depends on the */ +/* scaling of the matrix A, but if equilibration is used, A is */ +/* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */ +/* or diag(C)*B (if TRANS = 'T' or 'C'). */ + +/* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the */ +/* matrix A (after equilibration if FACT = 'E') as */ +/* A = P * L * U, */ +/* where P is a permutation matrix, L is a unit lower triangular */ +/* matrix, and U is upper triangular. */ + +/* 3. If some U(i,i)=0, so that U is exactly singular, then the routine */ +/* returns with INFO = i. Otherwise, the factored form of A is used */ +/* to estimate the condition number of the matrix A. If the */ +/* reciprocal of the condition number is less than machine precision, */ +/* INFO = N+1 is returned as a warning, but the routine still goes on */ +/* to solve for X and compute error bounds as described below. */ + +/* 4. The system of equations is solved for X using the factored form */ +/* of A. */ + +/* 5. Iterative refinement is applied to improve the computed solution */ +/* matrix and calculate error bounds and backward error estimates */ +/* for it. */ + +/* 6. If equilibration was used, the matrix X is premultiplied by */ +/* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */ +/* that it solves the original system before equilibration. */ + +/* Arguments */ +/* ========= */ + +/* FACT (input) CHARACTER*1 */ +/* Specifies whether or not the factored form of the matrix A is */ +/* supplied on entry, and if not, whether the matrix A should be */ +/* equilibrated before it is factored. */ +/* = 'F': On entry, AF and IPIV contain the factored form of A. */ +/* If EQUED is not 'N', the matrix A has been */ +/* equilibrated with scaling factors given by R and C. */ +/* A, AF, and IPIV are not modified. */ +/* = 'N': The matrix A will be copied to AF and factored. */ +/* = 'E': The matrix A will be equilibrated if necessary, then */ +/* copied to AF and factored. */ + +/* TRANS (input) CHARACTER*1 */ +/* Specifies the form of the system of equations: */ +/* = 'N': A * X = B (No transpose) */ +/* = 'T': A**T * X = B (Transpose) */ +/* = 'C': A**H * X = B (Transpose) */ + +/* N (input) INTEGER */ +/* The number of linear equations, i.e., the order 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 N-by-N matrix A. If FACT = 'F' and EQUED is */ +/* not 'N', then A must have been equilibrated by the scaling */ +/* factors in R and/or C. A is not modified if FACT = 'F' or */ +/* 'N', or if FACT = 'E' and EQUED = 'N' on exit. */ + +/* On exit, if EQUED .ne. 'N', A is scaled as follows: */ +/* EQUED = 'R': A := diag(R) * A */ +/* EQUED = 'C': A := A * diag(C) */ +/* EQUED = 'B': A := diag(R) * A * diag(C). */ + +/* LDA (input) INTEGER */ +/* The leading dimension of the array A. LDA >= max(1,N). */ + +/* AF (input or output) DOUBLE PRECISION array, dimension (LDAF,N) */ +/* If FACT = 'F', then AF is an input argument and on entry */ +/* contains the factors L and U from the factorization */ +/* A = P*L*U as computed by DGETRF. If EQUED .ne. 'N', then */ +/* AF is the factored form of the equilibrated matrix A. */ + +/* If FACT = 'N', then AF is an output argument and on exit */ +/* returns the factors L and U from the factorization A = P*L*U */ +/* of the original matrix A. */ + +/* If FACT = 'E', then AF is an output argument and on exit */ +/* returns the factors L and U from the factorization A = P*L*U */ +/* of the equilibrated matrix A (see the description of A for */ +/* the form of the equilibrated matrix). */ + +/* LDAF (input) INTEGER */ +/* The leading dimension of the array AF. LDAF >= max(1,N). */ + +/* IPIV (input or output) INTEGER array, dimension (N) */ +/* If FACT = 'F', then IPIV is an input argument and on entry */ +/* contains the pivot indices from the factorization A = P*L*U */ +/* as computed by DGETRF; row i of the matrix was interchanged */ +/* with row IPIV(i). */ + +/* If FACT = 'N', then IPIV is an output argument and on exit */ +/* contains the pivot indices from the factorization A = P*L*U */ +/* of the original matrix A. */ + +/* If FACT = 'E', then IPIV is an output argument and on exit */ +/* contains the pivot indices from the factorization A = P*L*U */ +/* of the equilibrated matrix A. */ + +/* EQUED (input or output) CHARACTER*1 */ +/* Specifies the form of equilibration that was done. */ +/* = 'N': No equilibration (always true if FACT = 'N'). */ +/* = 'R': Row equilibration, i.e., A has been premultiplied by */ +/* diag(R). */ +/* = 'C': Column equilibration, i.e., A has been postmultiplied */ +/* by diag(C). */ +/* = 'B': Both row and column equilibration, i.e., A has been */ +/* replaced by diag(R) * A * diag(C). */ +/* EQUED is an input argument if FACT = 'F'; otherwise, it is an */ +/* output argument. */ + +/* R (input or output) DOUBLE PRECISION array, dimension (N) */ +/* The row scale factors for A. If EQUED = 'R' or 'B', A is */ +/* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */ +/* is not accessed. R is an input argument if FACT = 'F'; */ +/* otherwise, R is an output argument. If FACT = 'F' and */ +/* EQUED = 'R' or 'B', each element of R must be positive. */ + +/* C (input or output) DOUBLE PRECISION array, dimension (N) */ +/* The column scale factors for A. If EQUED = 'C' or 'B', A is */ +/* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */ +/* is not accessed. C is an input argument if FACT = 'F'; */ +/* otherwise, C is an output argument. If FACT = 'F' and */ +/* EQUED = 'C' or 'B', each element of C must be positive. */ + +/* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */ +/* On entry, the N-by-NRHS right hand side matrix B. */ +/* On exit, */ +/* if EQUED = 'N', B is not modified; */ +/* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */ +/* diag(R)*B; */ +/* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */ +/* overwritten by diag(C)*B. */ + +/* LDB (input) INTEGER */ +/* The leading dimension of the array B. LDB >= max(1,N). */ + +/* X (output) DOUBLE PRECISION array, dimension (LDX,NRHS) */ +/* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X */ +/* to the original system of equations. Note that A and B are */ +/* modified on exit if EQUED .ne. 'N', and the solution to the */ +/* equilibrated system is inv(diag(C))*X if TRANS = 'N' and */ +/* EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C' */ +/* and EQUED = 'R' or 'B'. */ + +/* LDX (input) INTEGER */ +/* The leading dimension of the array X. LDX >= max(1,N). */ + +/* RCOND (output) DOUBLE PRECISION */ +/* The estimate of the reciprocal condition number of the matrix */ +/* A after equilibration (if done). If RCOND is less than the */ +/* machine precision (in particular, if RCOND = 0), the matrix */ +/* is singular to working precision. This condition is */ +/* indicated by a return code of INFO > 0. */ + +/* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */ +/* The estimated forward error bound for each solution vector */ +/* X(j) (the j-th column of the solution matrix X). */ +/* If XTRUE is the true solution corresponding to X(j), FERR(j) */ +/* is an estimated upper bound for the magnitude of the largest */ +/* element in (X(j) - XTRUE) divided by the magnitude of the */ +/* largest element in X(j). The estimate is as reliable as */ +/* the estimate for RCOND, and is almost always a slight */ +/* overestimate of the true error. */ + +/* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */ +/* The componentwise relative backward error of each solution */ +/* vector X(j) (i.e., the smallest relative change in */ +/* any element of A or B that makes X(j) an exact solution). */ + +/* WORK (workspace/output) DOUBLE PRECISION array, dimension (4*N) */ +/* On exit, WORK(1) contains the reciprocal pivot growth */ +/* factor norm(A)/norm(U). The "max absolute element" norm is */ +/* used. If WORK(1) is much less than 1, then the stability */ +/* of the LU factorization of the (equilibrated) matrix A */ +/* could be poor. This also means that the solution X, condition */ +/* estimator RCOND, and forward error bound FERR could be */ +/* unreliable. If factorization fails with 0<INFO<=N, then */ +/* WORK(1) contains the reciprocal pivot growth factor for the */ +/* leading INFO columns of A. */ + +/* IWORK (workspace) INTEGER array, dimension (N) */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > 0: if INFO = i, and i is */ +/* <= N: U(i,i) is exactly zero. The factorization has */ +/* been completed, but the factor U is exactly */ +/* singular, so the solution and error bounds */ +/* could not be computed. RCOND = 0 is returned. */ +/* = N+1: U is nonsingular, but RCOND is less than machine */ +/* precision, meaning that the matrix is singular */ +/* to working precision. Nevertheless, the */ +/* solution and error bounds are computed because */ +/* there are a number of situations where the */ +/* computed solution can be more accurate than the */ +/* value of RCOND would suggest. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + af_dim1 = *ldaf; + af_offset = 1 + af_dim1; + af -= af_offset; + --ipiv; + --r__; + --c__; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + x_dim1 = *ldx; + x_offset = 1 + x_dim1; + x -= x_offset; + --ferr; + --berr; + --work; + --iwork; + + /* Function Body */ + *info = 0; + nofact = lsame_(fact, "N"); + equil = lsame_(fact, "E"); + notran = lsame_(trans, "N"); + if (nofact || equil) { + *(unsigned char *)equed = 'N'; + rowequ = FALSE_; + colequ = FALSE_; + } else { + rowequ = lsame_(equed, "R") || lsame_(equed, + "B"); + colequ = lsame_(equed, "C") || lsame_(equed, + "B"); + smlnum = dlamch_("Safe minimum"); + bignum = 1. / smlnum; + } + +/* Test the input parameters. */ + + if (! nofact && ! equil && ! lsame_(fact, "F")) { + *info = -1; + } else if (! notran && ! lsame_(trans, "T") && ! + lsame_(trans, "C")) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*nrhs < 0) { + *info = -4; + } else if (*lda < max(1,*n)) { + *info = -6; + } else if (*ldaf < max(1,*n)) { + *info = -8; + } else if (lsame_(fact, "F") && ! (rowequ || colequ + || lsame_(equed, "N"))) { + *info = -10; + } else { + if (rowequ) { + rcmin = bignum; + rcmax = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { +/* Computing MIN */ + d__1 = rcmin, d__2 = r__[j]; + rcmin = min(d__1,d__2); +/* Computing MAX */ + d__1 = rcmax, d__2 = r__[j]; + rcmax = max(d__1,d__2); +/* L10: */ + } + if (rcmin <= 0.) { + *info = -11; + } else if (*n > 0) { + rowcnd = max(rcmin,smlnum) / min(rcmax,bignum); + } else { + rowcnd = 1.; + } + } + if (colequ && *info == 0) { + rcmin = bignum; + rcmax = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { +/* Computing MIN */ + d__1 = rcmin, d__2 = c__[j]; + rcmin = min(d__1,d__2); +/* Computing MAX */ + d__1 = rcmax, d__2 = c__[j]; + rcmax = max(d__1,d__2); +/* L20: */ + } + if (rcmin <= 0.) { + *info = -12; + } else if (*n > 0) { + colcnd = max(rcmin,smlnum) / min(rcmax,bignum); + } else { + colcnd = 1.; + } + } + if (*info == 0) { + if (*ldb < max(1,*n)) { + *info = -14; + } else if (*ldx < max(1,*n)) { + *info = -16; + } + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_("DGESVX", &i__1); + return 0; + } + + if (equil) { + +/* Compute row and column scalings to equilibrate the matrix A. */ + + dgeequ_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, & + amax, &infequ); + if (infequ == 0) { + +/* Equilibrate the matrix. */ + + dlaqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, & + colcnd, &amax, equed); + rowequ = lsame_(equed, "R") || lsame_(equed, + "B"); + colequ = lsame_(equed, "C") || lsame_(equed, + "B"); + } + } + +/* Scale the right hand side. */ + + if (notran) { + if (rowequ) { + i__1 = *nrhs; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = r__[i__] * b[i__ + j * b_dim1]; +/* L30: */ + } +/* L40: */ + } + } + } else if (colequ) { + i__1 = *nrhs; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = c__[i__] * b[i__ + j * b_dim1]; +/* L50: */ + } +/* L60: */ + } + } + + if (nofact || equil) { + +/* Compute the LU factorization of A. */ + + dlacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf); + dgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info); + +/* Return if INFO is non-zero. */ + + if (*info > 0) { + +/* Compute the reciprocal pivot growth factor of the */ +/* leading rank-deficient INFO columns of A. */ + + rpvgrw = dlantr_("M", "U", "N", info, info, &af[af_offset], ldaf, + &work[1]); + if (rpvgrw == 0.) { + rpvgrw = 1.; + } else { + rpvgrw = dlange_("M", n, info, &a[a_offset], lda, &work[1]) / rpvgrw; + } + work[1] = rpvgrw; + *rcond = 0.; + return 0; + } + } + +/* Compute the norm of the matrix A and the */ +/* reciprocal pivot growth factor RPVGRW. */ + + if (notran) { + *(unsigned char *)norm = '1'; + } else { + *(unsigned char *)norm = 'I'; + } + anorm = dlange_(norm, n, n, &a[a_offset], lda, &work[1]); + rpvgrw = dlantr_("M", "U", "N", n, n, &af[af_offset], ldaf, &work[1]); + if (rpvgrw == 0.) { + rpvgrw = 1.; + } else { + rpvgrw = dlange_("M", n, n, &a[a_offset], lda, &work[1]) / + rpvgrw; + } + +/* Compute the reciprocal of the condition number of A. */ + + dgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1], + info); + +/* Compute the solution matrix X. */ + + dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); + dgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, + info); + +/* Use iterative refinement to improve the computed solution and */ +/* compute error bounds and backward error estimates for it. */ + + dgerfs_(trans, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1], + &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[ + 1], &iwork[1], info); + +/* Transform the solution matrix X to a solution of the original */ +/* system. */ + + if (notran) { + if (colequ) { + i__1 = *nrhs; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + x[i__ + j * x_dim1] = c__[i__] * x[i__ + j * x_dim1]; +/* L70: */ + } +/* L80: */ + } + i__1 = *nrhs; + for (j = 1; j <= i__1; ++j) { + ferr[j] /= colcnd; +/* L90: */ + } + } + } else if (rowequ) { + i__1 = *nrhs; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + x[i__ + j * x_dim1] = r__[i__] * x[i__ + j * x_dim1]; +/* L100: */ + } +/* L110: */ + } + i__1 = *nrhs; + for (j = 1; j <= i__1; ++j) { + ferr[j] /= rowcnd; +/* L120: */ + } + } + + work[1] = rpvgrw; + +/* Set INFO = N+1 if the matrix is singular to working precision. */ + + if (*rcond < dlamch_("Epsilon")) { + *info = *n + 1; + } + return 0; + +/* End of DGESVX */ + +} /* dgesvx_ */ |