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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/stgsja.c | |
parent | 01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff) | |
download | ydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz |
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/stgsja.c')
-rw-r--r-- | contrib/libs/clapack/stgsja.c | 619 |
1 files changed, 619 insertions, 0 deletions
diff --git a/contrib/libs/clapack/stgsja.c b/contrib/libs/clapack/stgsja.c new file mode 100644 index 0000000000..677fbe3cc1 --- /dev/null +++ b/contrib/libs/clapack/stgsja.c @@ -0,0 +1,619 @@ +/* stgsja.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 real c_b13 = 0.f; +static real c_b14 = 1.f; +static integer c__1 = 1; +static real c_b43 = -1.f; + +/* Subroutine */ int stgsja_(char *jobu, char *jobv, char *jobq, integer *m, + integer *p, integer *n, integer *k, integer *l, real *a, integer *lda, + real *b, integer *ldb, real *tola, real *tolb, real *alpha, real * + beta, real *u, integer *ldu, real *v, integer *ldv, real *q, integer * + ldq, real *work, integer *ncycle, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1, + u_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4; + real r__1; + + /* Local variables */ + integer i__, j; + real a1, a2, a3, b1, b2, b3, csq, csu, csv, snq, rwk, snu, snv; + extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, + integer *, real *, real *); + real gamma; + extern logical lsame_(char *, char *); + extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); + logical initq, initu, initv, wantq, upper; + real error, ssmin; + logical wantu, wantv; + extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, + integer *), slags2_(logical *, real *, real *, real *, real *, + real *, real *, real *, real *, real *, real *, real *, real *); + integer kcycle; + extern /* Subroutine */ int xerbla_(char *, integer *), slapll_( + integer *, real *, integer *, real *, integer *, real *), slartg_( + real *, real *, real *, real *, real *), slaset_(char *, integer * +, integer *, real *, real *, real *, integer *); + + +/* -- LAPACK routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* STGSJA computes the generalized singular value decomposition (GSVD) */ +/* of two real upper triangular (or trapezoidal) matrices A and B. */ + +/* On entry, it is assumed that matrices A and B have the following */ +/* forms, which may be obtained by the preprocessing subroutine SGGSVP */ +/* from a general M-by-N matrix A and P-by-N matrix B: */ + +/* N-K-L K L */ +/* A = K ( 0 A12 A13 ) if M-K-L >= 0; */ +/* L ( 0 0 A23 ) */ +/* M-K-L ( 0 0 0 ) */ + +/* N-K-L K L */ +/* A = K ( 0 A12 A13 ) if M-K-L < 0; */ +/* M-K ( 0 0 A23 ) */ + +/* N-K-L K L */ +/* B = L ( 0 0 B13 ) */ +/* P-L ( 0 0 0 ) */ + +/* where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */ +/* upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */ +/* otherwise A23 is (M-K)-by-L upper trapezoidal. */ + +/* On exit, */ + +/* U'*A*Q = D1*( 0 R ), V'*B*Q = D2*( 0 R ), */ + +/* where U, V and Q are orthogonal matrices, Z' denotes the transpose */ +/* of Z, R is a nonsingular upper triangular matrix, and D1 and D2 are */ +/* ``diagonal'' matrices, which are of the following structures: */ + +/* If M-K-L >= 0, */ + +/* K L */ +/* D1 = K ( I 0 ) */ +/* L ( 0 C ) */ +/* M-K-L ( 0 0 ) */ + +/* K L */ +/* D2 = L ( 0 S ) */ +/* P-L ( 0 0 ) */ + +/* N-K-L K L */ +/* ( 0 R ) = K ( 0 R11 R12 ) K */ +/* L ( 0 0 R22 ) L */ + +/* where */ + +/* C = diag( ALPHA(K+1), ... , ALPHA(K+L) ), */ +/* S = diag( BETA(K+1), ... , BETA(K+L) ), */ +/* C**2 + S**2 = I. */ + +/* R is stored in A(1:K+L,N-K-L+1:N) on exit. */ + +/* If M-K-L < 0, */ + +/* K M-K K+L-M */ +/* D1 = K ( I 0 0 ) */ +/* M-K ( 0 C 0 ) */ + +/* K M-K K+L-M */ +/* D2 = M-K ( 0 S 0 ) */ +/* K+L-M ( 0 0 I ) */ +/* P-L ( 0 0 0 ) */ + +/* N-K-L K M-K K+L-M */ +/* ( 0 R ) = K ( 0 R11 R12 R13 ) */ +/* M-K ( 0 0 R22 R23 ) */ +/* K+L-M ( 0 0 0 R33 ) */ + +/* where */ +/* C = diag( ALPHA(K+1), ... , ALPHA(M) ), */ +/* S = diag( BETA(K+1), ... , BETA(M) ), */ +/* C**2 + S**2 = I. */ + +/* R = ( R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) and R33 is stored */ +/* ( 0 R22 R23 ) */ +/* in B(M-K+1:L,N+M-K-L+1:N) on exit. */ + +/* The computation of the orthogonal transformation matrices U, V or Q */ +/* is optional. These matrices may either be formed explicitly, or they */ +/* may be postmultiplied into input matrices U1, V1, or Q1. */ + +/* Arguments */ +/* ========= */ + +/* JOBU (input) CHARACTER*1 */ +/* = 'U': U must contain an orthogonal matrix U1 on entry, and */ +/* the product U1*U is returned; */ +/* = 'I': U is initialized to the unit matrix, and the */ +/* orthogonal matrix U is returned; */ +/* = 'N': U is not computed. */ + +/* JOBV (input) CHARACTER*1 */ +/* = 'V': V must contain an orthogonal matrix V1 on entry, and */ +/* the product V1*V is returned; */ +/* = 'I': V is initialized to the unit matrix, and the */ +/* orthogonal matrix V is returned; */ +/* = 'N': V is not computed. */ + +/* JOBQ (input) CHARACTER*1 */ +/* = 'Q': Q must contain an orthogonal matrix Q1 on entry, and */ +/* the product Q1*Q is returned; */ +/* = 'I': Q is initialized to the unit matrix, and the */ +/* orthogonal matrix Q is returned; */ +/* = 'N': Q is not computed. */ + +/* M (input) INTEGER */ +/* The number of rows of the matrix A. M >= 0. */ + +/* P (input) INTEGER */ +/* The number of rows of the matrix B. P >= 0. */ + +/* N (input) INTEGER */ +/* The number of columns of the matrices A and B. N >= 0. */ + +/* K (input) INTEGER */ +/* L (input) INTEGER */ +/* K and L specify the subblocks in the input matrices A and B: */ +/* A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,N-L+1:N) */ +/* of A and B, whose GSVD is going to be computed by STGSJA. */ +/* See Further details. */ + +/* A (input/output) REAL array, dimension (LDA,N) */ +/* On entry, the M-by-N matrix A. */ +/* On exit, A(N-K+1:N,1:MIN(K+L,M) ) contains the triangular */ +/* matrix R or part of R. See Purpose for details. */ + +/* LDA (input) INTEGER */ +/* The leading dimension of the array A. LDA >= max(1,M). */ + +/* B (input/output) REAL array, dimension (LDB,N) */ +/* On entry, the P-by-N matrix B. */ +/* On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains */ +/* a part of R. See Purpose for details. */ + +/* LDB (input) INTEGER */ +/* The leading dimension of the array B. LDB >= max(1,P). */ + +/* TOLA (input) REAL */ +/* TOLB (input) REAL */ +/* TOLA and TOLB are the convergence criteria for the Jacobi- */ +/* Kogbetliantz iteration procedure. Generally, they are the */ +/* same as used in the preprocessing step, say */ +/* TOLA = max(M,N)*norm(A)*MACHEPS, */ +/* TOLB = max(P,N)*norm(B)*MACHEPS. */ + +/* ALPHA (output) REAL array, dimension (N) */ +/* BETA (output) REAL array, dimension (N) */ +/* On exit, ALPHA and BETA contain the generalized singular */ +/* value pairs of A and B; */ +/* ALPHA(1:K) = 1, */ +/* BETA(1:K) = 0, */ +/* and if M-K-L >= 0, */ +/* ALPHA(K+1:K+L) = diag(C), */ +/* BETA(K+1:K+L) = diag(S), */ +/* or if M-K-L < 0, */ +/* ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0 */ +/* BETA(K+1:M) = S, BETA(M+1:K+L) = 1. */ +/* Furthermore, if K+L < N, */ +/* ALPHA(K+L+1:N) = 0 and */ +/* BETA(K+L+1:N) = 0. */ + +/* U (input/output) REAL array, dimension (LDU,M) */ +/* On entry, if JOBU = 'U', U must contain a matrix U1 (usually */ +/* the orthogonal matrix returned by SGGSVP). */ +/* On exit, */ +/* if JOBU = 'I', U contains the orthogonal matrix U; */ +/* if JOBU = 'U', U contains the product U1*U. */ +/* If JOBU = 'N', U is not referenced. */ + +/* LDU (input) INTEGER */ +/* The leading dimension of the array U. LDU >= max(1,M) if */ +/* JOBU = 'U'; LDU >= 1 otherwise. */ + +/* V (input/output) REAL array, dimension (LDV,P) */ +/* On entry, if JOBV = 'V', V must contain a matrix V1 (usually */ +/* the orthogonal matrix returned by SGGSVP). */ +/* On exit, */ +/* if JOBV = 'I', V contains the orthogonal matrix V; */ +/* if JOBV = 'V', V contains the product V1*V. */ +/* If JOBV = 'N', V is not referenced. */ + +/* LDV (input) INTEGER */ +/* The leading dimension of the array V. LDV >= max(1,P) if */ +/* JOBV = 'V'; LDV >= 1 otherwise. */ + +/* Q (input/output) REAL array, dimension (LDQ,N) */ +/* On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually */ +/* the orthogonal matrix returned by SGGSVP). */ +/* On exit, */ +/* if JOBQ = 'I', Q contains the orthogonal matrix Q; */ +/* if JOBQ = 'Q', Q contains the product Q1*Q. */ +/* If JOBQ = 'N', Q is not referenced. */ + +/* LDQ (input) INTEGER */ +/* The leading dimension of the array Q. LDQ >= max(1,N) if */ +/* JOBQ = 'Q'; LDQ >= 1 otherwise. */ + +/* WORK (workspace) REAL array, dimension (2*N) */ + +/* NCYCLE (output) INTEGER */ +/* The number of cycles required for convergence. */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* = 1: the procedure does not converge after MAXIT cycles. */ + +/* Internal Parameters */ +/* =================== */ + +/* MAXIT INTEGER */ +/* MAXIT specifies the total loops that the iterative procedure */ +/* may take. If after MAXIT cycles, the routine fails to */ +/* converge, we return INFO = 1. */ + +/* Further Details */ +/* =============== */ + +/* STGSJA essentially uses a variant of Kogbetliantz algorithm to reduce */ +/* min(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L */ +/* matrix B13 to the form: */ + +/* U1'*A13*Q1 = C1*R1; V1'*B13*Q1 = S1*R1, */ + +/* where U1, V1 and Q1 are orthogonal matrix, and Z' is the transpose */ +/* of Z. C1 and S1 are diagonal matrices satisfying */ + +/* C1**2 + S1**2 = I, */ + +/* and R1 is an L-by-L nonsingular upper triangular matrix. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ + +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Decode and test the input parameters */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + --alpha; + --beta; + u_dim1 = *ldu; + u_offset = 1 + u_dim1; + u -= u_offset; + v_dim1 = *ldv; + v_offset = 1 + v_dim1; + v -= v_offset; + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + --work; + + /* Function Body */ + initu = lsame_(jobu, "I"); + wantu = initu || lsame_(jobu, "U"); + + initv = lsame_(jobv, "I"); + wantv = initv || lsame_(jobv, "V"); + + initq = lsame_(jobq, "I"); + wantq = initq || lsame_(jobq, "Q"); + + *info = 0; + if (! (initu || wantu || lsame_(jobu, "N"))) { + *info = -1; + } else if (! (initv || wantv || lsame_(jobv, "N"))) + { + *info = -2; + } else if (! (initq || wantq || lsame_(jobq, "N"))) + { + *info = -3; + } else if (*m < 0) { + *info = -4; + } else if (*p < 0) { + *info = -5; + } else if (*n < 0) { + *info = -6; + } else if (*lda < max(1,*m)) { + *info = -10; + } else if (*ldb < max(1,*p)) { + *info = -12; + } else if (*ldu < 1 || wantu && *ldu < *m) { + *info = -18; + } else if (*ldv < 1 || wantv && *ldv < *p) { + *info = -20; + } else if (*ldq < 1 || wantq && *ldq < *n) { + *info = -22; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_("STGSJA", &i__1); + return 0; + } + +/* Initialize U, V and Q, if necessary */ + + if (initu) { + slaset_("Full", m, m, &c_b13, &c_b14, &u[u_offset], ldu); + } + if (initv) { + slaset_("Full", p, p, &c_b13, &c_b14, &v[v_offset], ldv); + } + if (initq) { + slaset_("Full", n, n, &c_b13, &c_b14, &q[q_offset], ldq); + } + +/* Loop until convergence */ + + upper = FALSE_; + for (kcycle = 1; kcycle <= 40; ++kcycle) { + + upper = ! upper; + + i__1 = *l - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = *l; + for (j = i__ + 1; j <= i__2; ++j) { + + a1 = 0.f; + a2 = 0.f; + a3 = 0.f; + if (*k + i__ <= *m) { + a1 = a[*k + i__ + (*n - *l + i__) * a_dim1]; + } + if (*k + j <= *m) { + a3 = a[*k + j + (*n - *l + j) * a_dim1]; + } + + b1 = b[i__ + (*n - *l + i__) * b_dim1]; + b3 = b[j + (*n - *l + j) * b_dim1]; + + if (upper) { + if (*k + i__ <= *m) { + a2 = a[*k + i__ + (*n - *l + j) * a_dim1]; + } + b2 = b[i__ + (*n - *l + j) * b_dim1]; + } else { + if (*k + j <= *m) { + a2 = a[*k + j + (*n - *l + i__) * a_dim1]; + } + b2 = b[j + (*n - *l + i__) * b_dim1]; + } + + slags2_(&upper, &a1, &a2, &a3, &b1, &b2, &b3, &csu, &snu, & + csv, &snv, &csq, &snq); + +/* Update (K+I)-th and (K+J)-th rows of matrix A: U'*A */ + + if (*k + j <= *m) { + srot_(l, &a[*k + j + (*n - *l + 1) * a_dim1], lda, &a[*k + + i__ + (*n - *l + 1) * a_dim1], lda, &csu, &snu); + } + +/* Update I-th and J-th rows of matrix B: V'*B */ + + srot_(l, &b[j + (*n - *l + 1) * b_dim1], ldb, &b[i__ + (*n - * + l + 1) * b_dim1], ldb, &csv, &snv); + +/* Update (N-L+I)-th and (N-L+J)-th columns of matrices */ +/* A and B: A*Q and B*Q */ + +/* Computing MIN */ + i__4 = *k + *l; + i__3 = min(i__4,*m); + srot_(&i__3, &a[(*n - *l + j) * a_dim1 + 1], &c__1, &a[(*n - * + l + i__) * a_dim1 + 1], &c__1, &csq, &snq); + + srot_(l, &b[(*n - *l + j) * b_dim1 + 1], &c__1, &b[(*n - *l + + i__) * b_dim1 + 1], &c__1, &csq, &snq); + + if (upper) { + if (*k + i__ <= *m) { + a[*k + i__ + (*n - *l + j) * a_dim1] = 0.f; + } + b[i__ + (*n - *l + j) * b_dim1] = 0.f; + } else { + if (*k + j <= *m) { + a[*k + j + (*n - *l + i__) * a_dim1] = 0.f; + } + b[j + (*n - *l + i__) * b_dim1] = 0.f; + } + +/* Update orthogonal matrices U, V, Q, if desired. */ + + if (wantu && *k + j <= *m) { + srot_(m, &u[(*k + j) * u_dim1 + 1], &c__1, &u[(*k + i__) * + u_dim1 + 1], &c__1, &csu, &snu); + } + + if (wantv) { + srot_(p, &v[j * v_dim1 + 1], &c__1, &v[i__ * v_dim1 + 1], + &c__1, &csv, &snv); + } + + if (wantq) { + srot_(n, &q[(*n - *l + j) * q_dim1 + 1], &c__1, &q[(*n - * + l + i__) * q_dim1 + 1], &c__1, &csq, &snq); + } + +/* L10: */ + } +/* L20: */ + } + + if (! upper) { + +/* The matrices A13 and B13 were lower triangular at the start */ +/* of the cycle, and are now upper triangular. */ + +/* Convergence test: test the parallelism of the corresponding */ +/* rows of A and B. */ + + error = 0.f; +/* Computing MIN */ + i__2 = *l, i__3 = *m - *k; + i__1 = min(i__2,i__3); + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = *l - i__ + 1; + scopy_(&i__2, &a[*k + i__ + (*n - *l + i__) * a_dim1], lda, & + work[1], &c__1); + i__2 = *l - i__ + 1; + scopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &work[* + l + 1], &c__1); + i__2 = *l - i__ + 1; + slapll_(&i__2, &work[1], &c__1, &work[*l + 1], &c__1, &ssmin); + error = dmax(error,ssmin); +/* L30: */ + } + + if (dabs(error) <= dmin(*tola,*tolb)) { + goto L50; + } + } + +/* End of cycle loop */ + +/* L40: */ + } + +/* The algorithm has not converged after MAXIT cycles. */ + + *info = 1; + goto L100; + +L50: + +/* If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged. */ +/* Compute the generalized singular value pairs (ALPHA, BETA), and */ +/* set the triangular matrix R to array A. */ + + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + alpha[i__] = 1.f; + beta[i__] = 0.f; +/* L60: */ + } + +/* Computing MIN */ + i__2 = *l, i__3 = *m - *k; + i__1 = min(i__2,i__3); + for (i__ = 1; i__ <= i__1; ++i__) { + + a1 = a[*k + i__ + (*n - *l + i__) * a_dim1]; + b1 = b[i__ + (*n - *l + i__) * b_dim1]; + + if (a1 != 0.f) { + gamma = b1 / a1; + +/* change sign if necessary */ + + if (gamma < 0.f) { + i__2 = *l - i__ + 1; + sscal_(&i__2, &c_b43, &b[i__ + (*n - *l + i__) * b_dim1], ldb) + ; + if (wantv) { + sscal_(p, &c_b43, &v[i__ * v_dim1 + 1], &c__1); + } + } + + r__1 = dabs(gamma); + slartg_(&r__1, &c_b14, &beta[*k + i__], &alpha[*k + i__], &rwk); + + if (alpha[*k + i__] >= beta[*k + i__]) { + i__2 = *l - i__ + 1; + r__1 = 1.f / alpha[*k + i__]; + sscal_(&i__2, &r__1, &a[*k + i__ + (*n - *l + i__) * a_dim1], + lda); + } else { + i__2 = *l - i__ + 1; + r__1 = 1.f / beta[*k + i__]; + sscal_(&i__2, &r__1, &b[i__ + (*n - *l + i__) * b_dim1], ldb); + i__2 = *l - i__ + 1; + scopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k + + i__ + (*n - *l + i__) * a_dim1], lda); + } + + } else { + + alpha[*k + i__] = 0.f; + beta[*k + i__] = 1.f; + i__2 = *l - i__ + 1; + scopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k + + i__ + (*n - *l + i__) * a_dim1], lda); + + } + +/* L70: */ + } + +/* Post-assignment */ + + i__1 = *k + *l; + for (i__ = *m + 1; i__ <= i__1; ++i__) { + alpha[i__] = 0.f; + beta[i__] = 1.f; +/* L80: */ + } + + if (*k + *l < *n) { + i__1 = *n; + for (i__ = *k + *l + 1; i__ <= i__1; ++i__) { + alpha[i__] = 0.f; + beta[i__] = 0.f; +/* L90: */ + } + } + +L100: + *ncycle = kcycle; + return 0; + +/* End of STGSJA */ + +} /* stgsja_ */ |