stgsja.c

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/* lapack/single/stgsja.f -- translated by f2c (version 20050501).
   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
*/

#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"

/* Table of constant values */

static real c_b13 = (float)0.;
static real c_b14 = (float)1.;
static integer c__1 = 1;
static real c_b43 = (float)-1.;

/*<    >*/
/* 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, ftnlen jobu_len, 
        ftnlen jobv_len, ftnlen jobq_len)
{
    /* 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 *, ftnlen, ftnlen);
    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 *, ftnlen), slapll_(
            integer *, real *, integer *, real *, integer *, real *), slartg_(
            real *, real *, real *, real *, real *), slaset_(char *, integer *
            , integer *, real *, real *, real *, integer *, ftnlen);
    (void)jobu_len;
    (void)jobv_len;
    (void)jobq_len;

/*  -- LAPACK routine (version 3.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     June 30, 1999 */

/*     .. Scalar Arguments .. */
/*<       CHARACTER          JOBQ, JOBU, JOBV >*/
/*<    >*/
/*<       REAL               TOLA, TOLB >*/
/*     .. */
/*     .. 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 .. */
/*<       INTEGER            MAXIT >*/
/*<       PARAMETER          ( MAXIT = 40 ) >*/
/*<       REAL               ZERO, ONE >*/
/*<       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 ) >*/
/*     .. */
/*     .. Local Scalars .. */

/*<       LOGICAL            INITQ, INITU, INITV, UPPER, WANTQ, WANTU, WANTV >*/
/*<       INTEGER            I, J, KCYCLE >*/
/*<    >*/
/*     .. */
/*     .. External Functions .. */
/*<       LOGICAL            LSAME >*/
/*<       EXTERNAL           LSAME >*/
/*     .. */
/*     .. External Subroutines .. */
/*<    >*/
/*     .. */
/*     .. Intrinsic Functions .. */
/*<       INTRINSIC          ABS, MAX, MIN >*/
/*     .. */
/*     .. Executable Statements .. */

/*     Decode and test the input parameters */

/*<       INITU = LSAME( JOBU, 'I' ) >*/
    /* 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", (ftnlen)1, (ftnlen)1);
/*<       WANTU = INITU .OR. LSAME( JOBU, 'U' ) >*/
    wantu = initu || lsame_(jobu, "U", (ftnlen)1, (ftnlen)1);

/*<       INITV = LSAME( JOBV, 'I' ) >*/
    initv = lsame_(jobv, "I", (ftnlen)1, (ftnlen)1);
/*<       WANTV = INITV .OR. LSAME( JOBV, 'V' ) >*/
    wantv = initv || lsame_(jobv, "V", (ftnlen)1, (ftnlen)1);

/*<       INITQ = LSAME( JOBQ, 'I' ) >*/
    initq = lsame_(jobq, "I", (ftnlen)1, (ftnlen)1);
/*<       WANTQ = INITQ .OR. LSAME( JOBQ, 'Q' ) >*/
    wantq = initq || lsame_(jobq, "Q", (ftnlen)1, (ftnlen)1);

/*<       INFO = 0 >*/
    *info = 0;
/*<       IF( .NOT.( INITU .OR. WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN >*/
    if (! (initu || wantu || lsame_(jobu, "N", (ftnlen)1, (ftnlen)1))) {
/*<          INFO = -1 >*/
        *info = -1;
/*<       ELSE IF( .NOT.( INITV .OR. WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN >*/
    } else if (! (initv || wantv || lsame_(jobv, "N", (ftnlen)1, (ftnlen)1))) 
            {
/*<          INFO = -2 >*/
        *info = -2;
/*<       ELSE IF( .NOT.( INITQ .OR. WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN >*/