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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/dsbtrd.c | |
parent | 01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff) | |
download | ydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz |
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/dsbtrd.c')
-rw-r--r-- | contrib/libs/clapack/dsbtrd.c | 713 |
1 files changed, 713 insertions, 0 deletions
diff --git a/contrib/libs/clapack/dsbtrd.c b/contrib/libs/clapack/dsbtrd.c new file mode 100644 index 0000000000..70bddbdf97 --- /dev/null +++ b/contrib/libs/clapack/dsbtrd.c @@ -0,0 +1,713 @@ +/* dsbtrd.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 doublereal c_b9 = 0.; +static doublereal c_b10 = 1.; +static integer c__1 = 1; + +/* Subroutine */ int dsbtrd_(char *vect, char *uplo, integer *n, integer *kd, + doublereal *ab, integer *ldab, doublereal *d__, doublereal *e, + doublereal *q, integer *ldq, doublereal *work, integer *info) +{ + /* System generated locals */ + integer ab_dim1, ab_offset, q_dim1, q_offset, i__1, i__2, i__3, i__4, + i__5; + + /* Local variables */ + integer i__, j, k, l, i2, j1, j2, nq, nr, kd1, ibl, iqb, kdn, jin, nrt, + kdm1, inca, jend, lend, jinc, incx, last; + doublereal temp; + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *); + integer j1end, j1inc, iqend; + extern logical lsame_(char *, char *); + logical initq, wantq, upper; + extern /* Subroutine */ int dlar2v_(integer *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, doublereal *, integer *); + integer iqaend; + extern /* Subroutine */ int dlaset_(char *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *), + dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *), xerbla_(char *, integer *), dlargv_( + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *), dlartv_(integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *); + + +/* -- LAPACK routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* DSBTRD reduces a real symmetric band matrix A to symmetric */ +/* tridiagonal form T by an orthogonal similarity transformation: */ +/* Q**T * A * Q = T. */ + +/* Arguments */ +/* ========= */ + +/* VECT (input) CHARACTER*1 */ +/* = 'N': do not form Q; */ +/* = 'V': form Q; */ +/* = 'U': update a matrix X, by forming X*Q. */ + +/* UPLO (input) CHARACTER*1 */ +/* = 'U': Upper triangle of A is stored; */ +/* = 'L': Lower triangle of A is stored. */ + +/* N (input) INTEGER */ +/* The order of the matrix A. N >= 0. */ + +/* KD (input) INTEGER */ +/* The number of superdiagonals of the matrix A if UPLO = 'U', */ +/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */ + +/* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) */ +/* On entry, the upper or lower triangle of the symmetric band */ +/* matrix A, stored in the first KD+1 rows of the array. The */ +/* j-th column of A is stored in the j-th column of the array AB */ +/* as follows: */ +/* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */ +/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). */ +/* On exit, the diagonal elements of AB are overwritten by the */ +/* diagonal elements of the tridiagonal matrix T; if KD > 0, the */ +/* elements on the first superdiagonal (if UPLO = 'U') or the */ +/* first subdiagonal (if UPLO = 'L') are overwritten by the */ +/* off-diagonal elements of T; the rest of AB is overwritten by */ +/* values generated during the reduction. */ + +/* LDAB (input) INTEGER */ +/* The leading dimension of the array AB. LDAB >= KD+1. */ + +/* D (output) DOUBLE PRECISION array, dimension (N) */ +/* The diagonal elements of the tridiagonal matrix T. */ + +/* E (output) DOUBLE PRECISION array, dimension (N-1) */ +/* The off-diagonal elements of the tridiagonal matrix T: */ +/* E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. */ + +/* Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N) */ +/* On entry, if VECT = 'U', then Q must contain an N-by-N */ +/* matrix X; if VECT = 'N' or 'V', then Q need not be set. */ + +/* On exit: */ +/* if VECT = 'V', Q contains the N-by-N orthogonal matrix Q; */ +/* if VECT = 'U', Q contains the product X*Q; */ +/* if VECT = 'N', the array Q is not referenced. */ + +/* LDQ (input) INTEGER */ +/* The leading dimension of the array Q. */ +/* LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. */ + +/* WORK (workspace) DOUBLE PRECISION array, dimension (N) */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -i, the i-th argument had an illegal value */ + +/* Further Details */ +/* =============== */ + +/* Modified by Linda Kaufman, Bell Labs. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters */ + + /* Parameter adjustments */ + ab_dim1 = *ldab; + ab_offset = 1 + ab_dim1; + ab -= ab_offset; + --d__; + --e; + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + --work; + + /* Function Body */ + initq = lsame_(vect, "V"); + wantq = initq || lsame_(vect, "U"); + upper = lsame_(uplo, "U"); + kd1 = *kd + 1; + kdm1 = *kd - 1; + incx = *ldab - 1; + iqend = 1; + + *info = 0; + if (! wantq && ! lsame_(vect, "N")) { + *info = -1; + } else if (! upper && ! lsame_(uplo, "L")) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*kd < 0) { + *info = -4; + } else if (*ldab < kd1) { + *info = -6; + } else if (*ldq < max(1,*n) && wantq) { + *info = -10; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_("DSBTRD", &i__1); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Initialize Q to the unit matrix, if needed */ + + if (initq) { + dlaset_("Full", n, n, &c_b9, &c_b10, &q[q_offset], ldq); + } + +/* Wherever possible, plane rotations are generated and applied in */ +/* vector operations of length NR over the index set J1:J2:KD1. */ + +/* The cosines and sines of the plane rotations are stored in the */ +/* arrays D and WORK. */ + + inca = kd1 * *ldab; +/* Computing MIN */ + i__1 = *n - 1; + kdn = min(i__1,*kd); + if (upper) { + + if (*kd > 1) { + +/* Reduce to tridiagonal form, working with upper triangle */ + + nr = 0; + j1 = kdn + 2; + j2 = 1; + + i__1 = *n - 2; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Reduce i-th row of matrix to tridiagonal form */ + + for (k = kdn + 1; k >= 2; --k) { + j1 += kdn; + j2 += kdn; + + if (nr > 0) { + +/* generate plane rotations to annihilate nonzero */ +/* elements which have been created outside the band */ + + dlargv_(&nr, &ab[(j1 - 1) * ab_dim1 + 1], &inca, & + work[j1], &kd1, &d__[j1], &kd1); + +/* apply rotations from the right */ + + +/* Dependent on the the number of diagonals either */ +/* DLARTV or DROT is used */ + + if (nr >= (*kd << 1) - 1) { + i__2 = *kd - 1; + for (l = 1; l <= i__2; ++l) { + dlartv_(&nr, &ab[l + 1 + (j1 - 1) * ab_dim1], + &inca, &ab[l + j1 * ab_dim1], &inca, & + d__[j1], &work[j1], &kd1); +/* L10: */ + } + + } else { + jend = j1 + (nr - 1) * kd1; + i__2 = jend; + i__3 = kd1; + for (jinc = j1; i__3 < 0 ? jinc >= i__2 : jinc <= + i__2; jinc += i__3) { + drot_(&kdm1, &ab[(jinc - 1) * ab_dim1 + 2], & + c__1, &ab[jinc * ab_dim1 + 1], &c__1, + &d__[jinc], &work[jinc]); +/* L20: */ + } + } + } + + + if (k > 2) { + if (k <= *n - i__ + 1) { + +/* generate plane rotation to annihilate a(i,i+k-1) */ +/* within the band */ + + dlartg_(&ab[*kd - k + 3 + (i__ + k - 2) * ab_dim1] +, &ab[*kd - k + 2 + (i__ + k - 1) * + ab_dim1], &d__[i__ + k - 1], &work[i__ + + k - 1], &temp); + ab[*kd - k + 3 + (i__ + k - 2) * ab_dim1] = temp; + +/* apply rotation from the right */ + + i__3 = k - 3; + drot_(&i__3, &ab[*kd - k + 4 + (i__ + k - 2) * + ab_dim1], &c__1, &ab[*kd - k + 3 + (i__ + + k - 1) * ab_dim1], &c__1, &d__[i__ + k - + 1], &work[i__ + k - 1]); + } + ++nr; + j1 = j1 - kdn - 1; + } + +/* apply plane rotations from both sides to diagonal */ +/* blocks */ + + if (nr > 0) { + dlar2v_(&nr, &ab[kd1 + (j1 - 1) * ab_dim1], &ab[kd1 + + j1 * ab_dim1], &ab[*kd + j1 * ab_dim1], &inca, + &d__[j1], &work[j1], &kd1); + } + +/* apply plane rotations from the left */ + + if (nr > 0) { + if ((*kd << 1) - 1 < nr) { + +/* Dependent on the the number of diagonals either */ +/* DLARTV or DROT is used */ + + i__3 = *kd - 1; + for (l = 1; l <= i__3; ++l) { + if (j2 + l > *n) { + nrt = nr - 1; + } else { + nrt = nr; + } + if (nrt > 0) { + dlartv_(&nrt, &ab[*kd - l + (j1 + l) * + ab_dim1], &inca, &ab[*kd - l + 1 + + (j1 + l) * ab_dim1], &inca, & + d__[j1], &work[j1], &kd1); + } +/* L30: */ + } + } else { + j1end = j1 + kd1 * (nr - 2); + if (j1end >= j1) { + i__3 = j1end; + i__2 = kd1; + for (jin = j1; i__2 < 0 ? jin >= i__3 : jin <= + i__3; jin += i__2) { + i__4 = *kd - 1; + drot_(&i__4, &ab[*kd - 1 + (jin + 1) * + ab_dim1], &incx, &ab[*kd + (jin + + 1) * ab_dim1], &incx, &d__[jin], & + work[jin]); +/* L40: */ + } + } +/* Computing MIN */ + i__2 = kdm1, i__3 = *n - j2; + lend = min(i__2,i__3); + last = j1end + kd1; + if (lend > 0) { + drot_(&lend, &ab[*kd - 1 + (last + 1) * + ab_dim1], &incx, &ab[*kd + (last + 1) + * ab_dim1], &incx, &d__[last], &work[ + last]); + } + } + } + + if (wantq) { + +/* accumulate product of plane rotations in Q */ + + if (initq) { + +/* take advantage of the fact that Q was */ +/* initially the Identity matrix */ + + iqend = max(iqend,j2); +/* Computing MAX */ + i__2 = 0, i__3 = k - 3; + i2 = max(i__2,i__3); + iqaend = i__ * *kd + 1; + if (k == 2) { + iqaend += *kd; + } + iqaend = min(iqaend,iqend); + i__2 = j2; + i__3 = kd1; + for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j + += i__3) { + ibl = i__ - i2 / kdm1; + ++i2; +/* Computing MAX */ + i__4 = 1, i__5 = j - ibl; + iqb = max(i__4,i__5); + nq = iqaend + 1 - iqb; +/* Computing MIN */ + i__4 = iqaend + *kd; + iqaend = min(i__4,iqend); + drot_(&nq, &q[iqb + (j - 1) * q_dim1], &c__1, + &q[iqb + j * q_dim1], &c__1, &d__[j], + &work[j]); +/* L50: */ + } + } else { + + i__3 = j2; + i__2 = kd1; + for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j + += i__2) { + drot_(n, &q[(j - 1) * q_dim1 + 1], &c__1, &q[ + j * q_dim1 + 1], &c__1, &d__[j], & + work[j]); +/* L60: */ + } + } + + } + + if (j2 + kdn > *n) { + +/* adjust J2 to keep within the bounds of the matrix */ + + --nr; + j2 = j2 - kdn - 1; + } + + i__2 = j2; + i__3 = kd1; + for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3) + { + +/* create nonzero element a(j-1,j+kd) outside the band */ +/* and store it in WORK */ + + work[j + *kd] = work[j] * ab[(j + *kd) * ab_dim1 + 1]; + ab[(j + *kd) * ab_dim1 + 1] = d__[j] * ab[(j + *kd) * + ab_dim1 + 1]; +/* L70: */ + } +/* L80: */ + } +/* L90: */ + } + } + + if (*kd > 0) { + +/* copy off-diagonal elements to E */ + + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + e[i__] = ab[*kd + (i__ + 1) * ab_dim1]; +/* L100: */ + } + } else { + +/* set E to zero if original matrix was diagonal */ + + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + e[i__] = 0.; +/* L110: */ + } + } + +/* copy diagonal elements to D */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d__[i__] = ab[kd1 + i__ * ab_dim1]; +/* L120: */ + } + + } else { + + if (*kd > 1) { + +/* Reduce to tridiagonal form, working with lower triangle */ + + nr = 0; + j1 = kdn + 2; + j2 = 1; + + i__1 = *n - 2; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Reduce i-th column of matrix to tridiagonal form */ + + for (k = kdn + 1; k >= 2; --k) { + j1 += kdn; + j2 += kdn; + + if (nr > 0) { + +/* generate plane rotations to annihilate nonzero */ +/* elements which have been created outside the band */ + + dlargv_(&nr, &ab[kd1 + (j1 - kd1) * ab_dim1], &inca, & + work[j1], &kd1, &d__[j1], &kd1); + +/* apply plane rotations from one side */ + + +/* Dependent on the the number of diagonals either */ +/* DLARTV or DROT is used */ + + if (nr > (*kd << 1) - 1) { + i__3 = *kd - 1; + for (l = 1; l <= i__3; ++l) { + dlartv_(&nr, &ab[kd1 - l + (j1 - kd1 + l) * + ab_dim1], &inca, &ab[kd1 - l + 1 + ( + j1 - kd1 + l) * ab_dim1], &inca, &d__[ + j1], &work[j1], &kd1); +/* L130: */ + } + } else { + jend = j1 + kd1 * (nr - 1); + i__3 = jend; + i__2 = kd1; + for (jinc = j1; i__2 < 0 ? jinc >= i__3 : jinc <= + i__3; jinc += i__2) { + drot_(&kdm1, &ab[*kd + (jinc - *kd) * ab_dim1] +, &incx, &ab[kd1 + (jinc - *kd) * + ab_dim1], &incx, &d__[jinc], &work[ + jinc]); +/* L140: */ + } + } + + } + + if (k > 2) { + if (k <= *n - i__ + 1) { + +/* generate plane rotation to annihilate a(i+k-1,i) */ +/* within the band */ + + dlartg_(&ab[k - 1 + i__ * ab_dim1], &ab[k + i__ * + ab_dim1], &d__[i__ + k - 1], &work[i__ + + k - 1], &temp); + ab[k - 1 + i__ * ab_dim1] = temp; + +/* apply rotation from the left */ + + i__2 = k - 3; + i__3 = *ldab - 1; + i__4 = *ldab - 1; + drot_(&i__2, &ab[k - 2 + (i__ + 1) * ab_dim1], & + i__3, &ab[k - 1 + (i__ + 1) * ab_dim1], & + i__4, &d__[i__ + k - 1], &work[i__ + k - + 1]); + } + ++nr; + j1 = j1 - kdn - 1; + } + +/* apply plane rotations from both sides to diagonal */ +/* blocks */ + + if (nr > 0) { + dlar2v_(&nr, &ab[(j1 - 1) * ab_dim1 + 1], &ab[j1 * + ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 + 2], & + inca, &d__[j1], &work[j1], &kd1); + } + +/* apply plane rotations from the right */ + + +/* Dependent on the the number of diagonals either */ +/* DLARTV or DROT is used */ + + if (nr > 0) { + if (nr > (*kd << 1) - 1) { + i__2 = *kd - 1; + for (l = 1; l <= i__2; ++l) { + if (j2 + l > *n) { + nrt = nr - 1; + } else { + nrt = nr; + } + if (nrt > 0) { + dlartv_(&nrt, &ab[l + 2 + (j1 - 1) * + ab_dim1], &inca, &ab[l + 1 + j1 * + ab_dim1], &inca, &d__[j1], &work[ + j1], &kd1); + } +/* L150: */ + } + } else { + j1end = j1 + kd1 * (nr - 2); + if (j1end >= j1) { + i__2 = j1end; + i__3 = kd1; + for (j1inc = j1; i__3 < 0 ? j1inc >= i__2 : + j1inc <= i__2; j1inc += i__3) { + drot_(&kdm1, &ab[(j1inc - 1) * ab_dim1 + + 3], &c__1, &ab[j1inc * ab_dim1 + + 2], &c__1, &d__[j1inc], &work[ + j1inc]); +/* L160: */ + } + } +/* Computing MIN */ + i__3 = kdm1, i__2 = *n - j2; + lend = min(i__3,i__2); + last = j1end + kd1; + if (lend > 0) { + drot_(&lend, &ab[(last - 1) * ab_dim1 + 3], & + c__1, &ab[last * ab_dim1 + 2], &c__1, + &d__[last], &work[last]); + } + } + } + + + + if (wantq) { + +/* accumulate product of plane rotations in Q */ + + if (initq) { + +/* take advantage of the fact that Q was */ +/* initially the Identity matrix */ + + iqend = max(iqend,j2); +/* Computing MAX */ + i__3 = 0, i__2 = k - 3; + i2 = max(i__3,i__2); + iqaend = i__ * *kd + 1; + if (k == 2) { + iqaend += *kd; + } + iqaend = min(iqaend,iqend); + i__3 = j2; + i__2 = kd1; + for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j + += i__2) { + ibl = i__ - i2 / kdm1; + ++i2; +/* Computing MAX */ + i__4 = 1, i__5 = j - ibl; + iqb = max(i__4,i__5); + nq = iqaend + 1 - iqb; +/* Computing MIN */ + i__4 = iqaend + *kd; + iqaend = min(i__4,iqend); + drot_(&nq, &q[iqb + (j - 1) * q_dim1], &c__1, + &q[iqb + j * q_dim1], &c__1, &d__[j], + &work[j]); +/* L170: */ + } + } else { + + i__2 = j2; + i__3 = kd1; + for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j + += i__3) { + drot_(n, &q[(j - 1) * q_dim1 + 1], &c__1, &q[ + j * q_dim1 + 1], &c__1, &d__[j], & + work[j]); +/* L180: */ + } + } + } + + if (j2 + kdn > *n) { + +/* adjust J2 to keep within the bounds of the matrix */ + + --nr; + j2 = j2 - kdn - 1; + } + + i__3 = j2; + i__2 = kd1; + for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) + { + +/* create nonzero element a(j+kd,j-1) outside the */ +/* band and store it in WORK */ + + work[j + *kd] = work[j] * ab[kd1 + j * ab_dim1]; + ab[kd1 + j * ab_dim1] = d__[j] * ab[kd1 + j * ab_dim1] + ; +/* L190: */ + } +/* L200: */ + } +/* L210: */ + } + } + + if (*kd > 0) { + +/* copy off-diagonal elements to E */ + + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + e[i__] = ab[i__ * ab_dim1 + 2]; +/* L220: */ + } + } else { + +/* set E to zero if original matrix was diagonal */ + + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + e[i__] = 0.; +/* L230: */ + } + } + +/* copy diagonal elements to D */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d__[i__] = ab[i__ * ab_dim1 + 1]; +/* L240: */ + } + } + + return 0; + +/* End of DSBTRD */ + +} /* dsbtrd_ */ |