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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/cgtrfs.c | |
parent | 01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff) | |
download | ydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz |
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/cgtrfs.c')
-rw-r--r-- | contrib/libs/clapack/cgtrfs.c | 553 |
1 files changed, 553 insertions, 0 deletions
diff --git a/contrib/libs/clapack/cgtrfs.c b/contrib/libs/clapack/cgtrfs.c new file mode 100644 index 0000000000..85898224ae --- /dev/null +++ b/contrib/libs/clapack/cgtrfs.c @@ -0,0 +1,553 @@ +/* cgtrfs.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" + +/* Table of constant values */ + +static integer c__1 = 1; +static real c_b18 = -1.f; +static real c_b19 = 1.f; +static complex c_b26 = {1.f,0.f}; + +/* Subroutine */ int cgtrfs_(char *trans, integer *n, integer *nrhs, complex * + dl, complex *d__, complex *du, complex *dlf, complex *df, complex * + duf, complex *du2, integer *ipiv, complex *b, integer *ldb, complex * + x, integer *ldx, real *ferr, real *berr, complex *work, real *rwork, + integer *info) +{ + /* System generated locals */ + integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5, + i__6, i__7, i__8, i__9; + real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8, r__9, r__10, r__11, + r__12, r__13, r__14; + complex q__1; + + /* Builtin functions */ + double r_imag(complex *); + + /* Local variables */ + integer i__, j; + real s; + integer nz; + real eps; + integer kase; + real safe1, safe2; + extern logical lsame_(char *, char *); + integer isave[3]; + extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, + complex *, integer *), caxpy_(integer *, complex *, complex *, + integer *, complex *, integer *); + integer count; + extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real + *, integer *, integer *), clagtm_(char *, integer *, integer *, + real *, complex *, complex *, complex *, complex *, integer *, + real *, complex *, integer *); + extern doublereal slamch_(char *); + real safmin; + extern /* Subroutine */ int xerbla_(char *, integer *); + logical notran; + char transn[1]; + extern /* Subroutine */ int cgttrs_(char *, integer *, integer *, complex + *, complex *, complex *, complex *, integer *, complex *, integer + *, integer *); + char transt[1]; + real lstres; + + +/* -- LAPACK routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* CGTRFS improves the computed solution to a system of linear */ +/* equations when the coefficient matrix is tridiagonal, and provides */ +/* error bounds and backward error estimates for the solution. */ + +/* Arguments */ +/* ========= */ + +/* 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 (Conjugate transpose) */ + +/* N (input) INTEGER */ +/* 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 matrix B. NRHS >= 0. */ + +/* DL (input) COMPLEX array, dimension (N-1) */ +/* The (n-1) subdiagonal elements of A. */ + +/* D (input) COMPLEX array, dimension (N) */ +/* The diagonal elements of A. */ + +/* DU (input) COMPLEX array, dimension (N-1) */ +/* The (n-1) superdiagonal elements of A. */ + +/* DLF (input) COMPLEX array, dimension (N-1) */ +/* The (n-1) multipliers that define the matrix L from the */ +/* LU factorization of A as computed by CGTTRF. */ + +/* DF (input) COMPLEX array, dimension (N) */ +/* The n diagonal elements of the upper triangular matrix U from */ +/* the LU factorization of A. */ + +/* DUF (input) COMPLEX array, dimension (N-1) */ +/* The (n-1) elements of the first superdiagonal of U. */ + +/* DU2 (input) COMPLEX array, dimension (N-2) */ +/* The (n-2) elements of the second superdiagonal of U. */ + +/* IPIV (input) INTEGER array, dimension (N) */ +/* The pivot indices; for 1 <= i <= n, row i of the matrix was */ +/* interchanged with row IPIV(i). IPIV(i) will always be either */ +/* i or i+1; IPIV(i) = i indicates a row interchange was not */ +/* required. */ + +/* B (input) COMPLEX array, dimension (LDB,NRHS) */ +/* The right hand side matrix B. */ + +/* LDB (input) INTEGER */ +/* The leading dimension of the array B. LDB >= max(1,N). */ + +/* X (input/output) COMPLEX array, dimension (LDX,NRHS) */ +/* On entry, the solution matrix X, as computed by CGTTRS. */ +/* On exit, the improved solution matrix X. */ + +/* LDX (input) INTEGER */ +/* The leading dimension of the array X. LDX >= max(1,N). */ + +/* FERR (output) REAL 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) REAL 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) COMPLEX array, dimension (2*N) */ + +/* RWORK (workspace) REAL array, dimension (N) */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -i, the i-th argument had an illegal value */ + +/* Internal Parameters */ +/* =================== */ + +/* ITMAX is the maximum number of steps of iterative refinement. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Statement Functions .. */ +/* .. */ +/* .. Statement Function definitions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --dl; + --d__; + --du; + --dlf; + --df; + --duf; + --du2; + --ipiv; + 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; + --rwork; + + /* Function Body */ + *info = 0; + notran = lsame_(trans, "N"); + if (! notran && ! lsame_(trans, "T") && ! lsame_( + trans, "C")) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*nrhs < 0) { + *info = -3; + } else if (*ldb < max(1,*n)) { + *info = -13; + } else if (*ldx < max(1,*n)) { + *info = -15; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_("CGTRFS", &i__1); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0 || *nrhs == 0) { + i__1 = *nrhs; + for (j = 1; j <= i__1; ++j) { + ferr[j] = 0.f; + berr[j] = 0.f; +/* L10: */ + } + return 0; + } + + if (notran) { + *(unsigned char *)transn = 'N'; + *(unsigned char *)transt = 'C'; + } else { + *(unsigned char *)transn = 'C'; + *(unsigned char *)transt = 'N'; + } + +/* NZ = maximum number of nonzero elements in each row of A, plus 1 */ + + nz = 4; + eps = slamch_("Epsilon"); + safmin = slamch_("Safe minimum"); + safe1 = nz * safmin; + safe2 = safe1 / eps; + +/* Do for each right hand side */ + + i__1 = *nrhs; + for (j = 1; j <= i__1; ++j) { + + count = 1; + lstres = 3.f; +L20: + +/* Loop until stopping criterion is satisfied. */ + +/* Compute residual R = B - op(A) * X, */ +/* where op(A) = A, A**T, or A**H, depending on TRANS. */ + + ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1); + clagtm_(trans, n, &c__1, &c_b18, &dl[1], &d__[1], &du[1], &x[j * + x_dim1 + 1], ldx, &c_b19, &work[1], n); + +/* Compute abs(op(A))*abs(x) + abs(b) for use in the backward */ +/* error bound. */ + + if (notran) { + if (*n == 1) { + i__2 = j * b_dim1 + 1; + i__3 = j * x_dim1 + 1; + rwork[1] = (r__1 = b[i__2].r, dabs(r__1)) + (r__2 = r_imag(&b[ + j * b_dim1 + 1]), dabs(r__2)) + ((r__3 = d__[1].r, + dabs(r__3)) + (r__4 = r_imag(&d__[1]), dabs(r__4))) * + ((r__5 = x[i__3].r, dabs(r__5)) + (r__6 = r_imag(&x[j + * x_dim1 + 1]), dabs(r__6))); + } else { + i__2 = j * b_dim1 + 1; + i__3 = j * x_dim1 + 1; + i__4 = j * x_dim1 + 2; + rwork[1] = (r__1 = b[i__2].r, dabs(r__1)) + (r__2 = r_imag(&b[ + j * b_dim1 + 1]), dabs(r__2)) + ((r__3 = d__[1].r, + dabs(r__3)) + (r__4 = r_imag(&d__[1]), dabs(r__4))) * + ((r__5 = x[i__3].r, dabs(r__5)) + (r__6 = r_imag(&x[j + * x_dim1 + 1]), dabs(r__6))) + ((r__7 = du[1].r, dabs( + r__7)) + (r__8 = r_imag(&du[1]), dabs(r__8))) * (( + r__9 = x[i__4].r, dabs(r__9)) + (r__10 = r_imag(&x[j * + x_dim1 + 2]), dabs(r__10))); + i__2 = *n - 1; + for (i__ = 2; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ - 1; + i__5 = i__ - 1 + j * x_dim1; + i__6 = i__; + i__7 = i__ + j * x_dim1; + i__8 = i__; + i__9 = i__ + 1 + j * x_dim1; + rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = + r_imag(&b[i__ + j * b_dim1]), dabs(r__2)) + (( + r__3 = dl[i__4].r, dabs(r__3)) + (r__4 = r_imag(& + dl[i__ - 1]), dabs(r__4))) * ((r__5 = x[i__5].r, + dabs(r__5)) + (r__6 = r_imag(&x[i__ - 1 + j * + x_dim1]), dabs(r__6))) + ((r__7 = d__[i__6].r, + dabs(r__7)) + (r__8 = r_imag(&d__[i__]), dabs( + r__8))) * ((r__9 = x[i__7].r, dabs(r__9)) + ( + r__10 = r_imag(&x[i__ + j * x_dim1]), dabs(r__10)) + ) + ((r__11 = du[i__8].r, dabs(r__11)) + (r__12 = + r_imag(&du[i__]), dabs(r__12))) * ((r__13 = x[ + i__9].r, dabs(r__13)) + (r__14 = r_imag(&x[i__ + + 1 + j * x_dim1]), dabs(r__14))); +/* L30: */ + } + i__2 = *n + j * b_dim1; + i__3 = *n - 1; + i__4 = *n - 1 + j * x_dim1; + i__5 = *n; + i__6 = *n + j * x_dim1; + rwork[*n] = (r__1 = b[i__2].r, dabs(r__1)) + (r__2 = r_imag(& + b[*n + j * b_dim1]), dabs(r__2)) + ((r__3 = dl[i__3] + .r, dabs(r__3)) + (r__4 = r_imag(&dl[*n - 1]), dabs( + r__4))) * ((r__5 = x[i__4].r, dabs(r__5)) + (r__6 = + r_imag(&x[*n - 1 + j * x_dim1]), dabs(r__6))) + (( + r__7 = d__[i__5].r, dabs(r__7)) + (r__8 = r_imag(&d__[ + *n]), dabs(r__8))) * ((r__9 = x[i__6].r, dabs(r__9)) + + (r__10 = r_imag(&x[*n + j * x_dim1]), dabs(r__10))); + } + } else { + if (*n == 1) { + i__2 = j * b_dim1 + 1; + i__3 = j * x_dim1 + 1; + rwork[1] = (r__1 = b[i__2].r, dabs(r__1)) + (r__2 = r_imag(&b[ + j * b_dim1 + 1]), dabs(r__2)) + ((r__3 = d__[1].r, + dabs(r__3)) + (r__4 = r_imag(&d__[1]), dabs(r__4))) * + ((r__5 = x[i__3].r, dabs(r__5)) + (r__6 = r_imag(&x[j + * x_dim1 + 1]), dabs(r__6))); + } else { + i__2 = j * b_dim1 + 1; + i__3 = j * x_dim1 + 1; + i__4 = j * x_dim1 + 2; + rwork[1] = (r__1 = b[i__2].r, dabs(r__1)) + (r__2 = r_imag(&b[ + j * b_dim1 + 1]), dabs(r__2)) + ((r__3 = d__[1].r, + dabs(r__3)) + (r__4 = r_imag(&d__[1]), dabs(r__4))) * + ((r__5 = x[i__3].r, dabs(r__5)) + (r__6 = r_imag(&x[j + * x_dim1 + 1]), dabs(r__6))) + ((r__7 = dl[1].r, dabs( + r__7)) + (r__8 = r_imag(&dl[1]), dabs(r__8))) * (( + r__9 = x[i__4].r, dabs(r__9)) + (r__10 = r_imag(&x[j * + x_dim1 + 2]), dabs(r__10))); + i__2 = *n - 1; + for (i__ = 2; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ - 1; + i__5 = i__ - 1 + j * x_dim1; + i__6 = i__; + i__7 = i__ + j * x_dim1; + i__8 = i__; + i__9 = i__ + 1 + j * x_dim1; + rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = + r_imag(&b[i__ + j * b_dim1]), dabs(r__2)) + (( + r__3 = du[i__4].r, dabs(r__3)) + (r__4 = r_imag(& + du[i__ - 1]), dabs(r__4))) * ((r__5 = x[i__5].r, + dabs(r__5)) + (r__6 = r_imag(&x[i__ - 1 + j * + x_dim1]), dabs(r__6))) + ((r__7 = d__[i__6].r, + dabs(r__7)) + (r__8 = r_imag(&d__[i__]), dabs( + r__8))) * ((r__9 = x[i__7].r, dabs(r__9)) + ( + r__10 = r_imag(&x[i__ + j * x_dim1]), dabs(r__10)) + ) + ((r__11 = dl[i__8].r, dabs(r__11)) + (r__12 = + r_imag(&dl[i__]), dabs(r__12))) * ((r__13 = x[ + i__9].r, dabs(r__13)) + (r__14 = r_imag(&x[i__ + + 1 + j * x_dim1]), dabs(r__14))); +/* L40: */ + } + i__2 = *n + j * b_dim1; + i__3 = *n - 1; + i__4 = *n - 1 + j * x_dim1; + i__5 = *n; + i__6 = *n + j * x_dim1; + rwork[*n] = (r__1 = b[i__2].r, dabs(r__1)) + (r__2 = r_imag(& + b[*n + j * b_dim1]), dabs(r__2)) + ((r__3 = du[i__3] + .r, dabs(r__3)) + (r__4 = r_imag(&du[*n - 1]), dabs( + r__4))) * ((r__5 = x[i__4].r, dabs(r__5)) + (r__6 = + r_imag(&x[*n - 1 + j * x_dim1]), dabs(r__6))) + (( + r__7 = d__[i__5].r, dabs(r__7)) + (r__8 = r_imag(&d__[ + *n]), dabs(r__8))) * ((r__9 = x[i__6].r, dabs(r__9)) + + (r__10 = r_imag(&x[*n + j * x_dim1]), dabs(r__10))); + } + } + +/* Compute componentwise relative backward error from formula */ + +/* max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) ) */ + +/* where abs(Z) is the componentwise absolute value of the matrix */ +/* or vector Z. If the i-th component of the denominator is less */ +/* than SAFE2, then SAFE1 is added to the i-th components of the */ +/* numerator and denominator before dividing. */ + + s = 0.f; + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + if (rwork[i__] > safe2) { +/* Computing MAX */ + i__3 = i__; + r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 = + r_imag(&work[i__]), dabs(r__2))) / rwork[i__]; + s = dmax(r__3,r__4); + } else { +/* Computing MAX */ + i__3 = i__; + r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 = + r_imag(&work[i__]), dabs(r__2)) + safe1) / (rwork[i__] + + safe1); + s = dmax(r__3,r__4); + } +/* L50: */ + } + berr[j] = s; + +/* Test stopping criterion. Continue iterating if */ +/* 1) The residual BERR(J) is larger than machine epsilon, and */ +/* 2) BERR(J) decreased by at least a factor of 2 during the */ +/* last iteration, and */ +/* 3) At most ITMAX iterations tried. */ + + if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) { + +/* Update solution and try again. */ + + cgttrs_(trans, n, &c__1, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[ + 1], &work[1], n, info); + caxpy_(n, &c_b26, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1); + lstres = berr[j]; + ++count; + goto L20; + } + +/* Bound error from formula */ + +/* norm(X - XTRUE) / norm(X) .le. FERR = */ +/* norm( abs(inv(op(A)))* */ +/* ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X) */ + +/* where */ +/* norm(Z) is the magnitude of the largest component of Z */ +/* inv(op(A)) is the inverse of op(A) */ +/* abs(Z) is the componentwise absolute value of the matrix or */ +/* vector Z */ +/* NZ is the maximum number of nonzeros in any row of A, plus 1 */ +/* EPS is machine epsilon */ + +/* The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B)) */ +/* is incremented by SAFE1 if the i-th component of */ +/* abs(op(A))*abs(X) + abs(B) is less than SAFE2. */ + +/* Use CLACN2 to estimate the infinity-norm of the matrix */ +/* inv(op(A)) * diag(W), */ +/* where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */ + + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + if (rwork[i__] > safe2) { + i__3 = i__; + rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 = + r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[ + i__]; + } else { + i__3 = i__; + rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 = + r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[ + i__] + safe1; + } +/* L60: */ + } + + kase = 0; +L70: + clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave); + if (kase != 0) { + if (kase == 1) { + +/* Multiply by diag(W)*inv(op(A)**H). */ + + cgttrs_(transt, n, &c__1, &dlf[1], &df[1], &duf[1], &du2[1], & + ipiv[1], &work[1], n, info); + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = i__; + q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4] + * work[i__5].i; + work[i__3].r = q__1.r, work[i__3].i = q__1.i; +/* L80: */ + } + } else { + +/* Multiply by inv(op(A))*diag(W). */ + + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = i__; + q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4] + * work[i__5].i; + work[i__3].r = q__1.r, work[i__3].i = q__1.i; +/* L90: */ + } + cgttrs_(transn, n, &c__1, &dlf[1], &df[1], &duf[1], &du2[1], & + ipiv[1], &work[1], n, info); + } + goto L70; + } + +/* Normalize error. */ + + lstres = 0.f; + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { +/* Computing MAX */ + i__3 = i__ + j * x_dim1; + r__3 = lstres, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = + r_imag(&x[i__ + j * x_dim1]), dabs(r__2)); + lstres = dmax(r__3,r__4); +/* L100: */ + } + if (lstres != 0.f) { + ferr[j] /= lstres; + } + +/* L110: */ + } + + return 0; + +/* End of CGTRFS */ + +} /* cgtrfs_ */ |