/* dsbgst.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_b8 = 0.; static doublereal c_b9 = 1.; static integer c__1 = 1; static doublereal c_b20 = -1.; /* Subroutine */ int dsbgst_(char *vect, char *uplo, integer *n, integer *ka, integer *kb, doublereal *ab, integer *ldab, doublereal *bb, integer * ldbb, doublereal *x, integer *ldx, doublereal *work, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, bb_dim1, bb_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4; doublereal d__1; /* Local variables */ integer i__, j, k, l, m; doublereal t; integer i0, i1, i2, j1, j2; doublereal ra; integer nr, nx, ka1, kb1; doublereal ra1; integer j1t, j2t; doublereal bii; integer kbt, nrt, inca; extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *), drot_(integer *, doublereal *, integer *, doublereal * , integer *, doublereal *, doublereal *), dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *); logical upper, wantx; extern /* Subroutine */ int dlar2v_(integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *), 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 *); logical update; extern /* Subroutine */ int 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 */ /* ======= */ /* DSBGST reduces a real symmetric-definite banded generalized */ /* eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, */ /* such that C has the same bandwidth as A. */ /* B must have been previously factorized as S**T*S by DPBSTF, using a */ /* split Cholesky factorization. A is overwritten by C = X**T*A*X, where */ /* X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the */ /* bandwidth of A. */ /* Arguments */ /* ========= */ /* VECT (input) CHARACTER*1 */ /* = 'N': do not form the transformation matrix X; */ /* = 'V': form X. */ /* 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 matrices A and B. N >= 0. */ /* KA (input) INTEGER */ /* The number of superdiagonals of the matrix A if UPLO = 'U', */ /* or the number of subdiagonals if UPLO = 'L'. KA >= 0. */ /* KB (input) INTEGER */ /* The number of superdiagonals of the matrix B if UPLO = 'U', */ /* or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; */ /* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). */ /* On exit, the transformed matrix X**T*A*X, stored in the same */ /* format as A. */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= KA+1. */ /* BB (input) DOUBLE PRECISION array, dimension (LDBB,N) */ /* The banded factor S from the split Cholesky factorization of */ /* B, as returned by DPBSTF, stored in the first KB+1 rows of */ /* the array. */ /* LDBB (input) INTEGER */ /* The leading dimension of the array BB. LDBB >= KB+1. */ /* X (output) DOUBLE PRECISION array, dimension (LDX,N) */ /* If VECT = 'V', the n-by-n matrix X. */ /* If VECT = 'N', the array X is not referenced. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. */ /* LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. */ /* WORK (workspace) DOUBLE PRECISION array, dimension (2*N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; bb_dim1 = *ldbb; bb_offset = 1 + bb_dim1; bb -= bb_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; --work; /* Function Body */ wantx = lsame_(vect, "V"); upper = lsame_(uplo, "U"); ka1 = *ka + 1; kb1 = *kb + 1; *info = 0; if (! wantx && ! lsame_(vect, "N")) { *info = -1; } else if (! upper && ! lsame_(uplo, "L")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ka < 0) { *info = -4; } else if (*kb < 0 || *kb > *ka) { *info = -5; } else if (*ldab < *ka + 1) { *info = -7; } else if (*ldbb < *kb + 1) { *info = -9; } else if (*ldx < 1 || wantx && *ldx < max(1,*n)) { *info = -11; } if (*info != 0) { i__1 = -(*info); xerbla_("DSBGST", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } inca = *ldab * ka1; /* Initialize X to the unit matrix, if needed */ if (wantx) { dlaset_("Full", n, n, &c_b8, &c_b9, &x[x_offset], ldx); } /* Set M to the splitting point m. It must be the same value as is */ /* used in DPBSTF. The chosen value allows the arrays WORK and RWORK */ /* to be of dimension (N). */ m = (*n + *kb) / 2; /* The routine works in two phases, corresponding to the two halves */ /* of the split Cholesky factorization of B as S**T*S where */ /* S = ( U ) */ /* ( M L ) */ /* with U upper triangular of order m, and L lower triangular of */ /* order n-m. S has the same bandwidth as B. */ /* S is treated as a product of elementary matrices: */ /* S = S(m)*S(m-1)*...*S(2)*S(1)*S(m+1)*S(m+2)*...*S(n-1)*S(n) */ /* where S(i) is determined by the i-th row of S. */ /* In phase 1, the index i takes the values n, n-1, ... , m+1; */ /* in phase 2, it takes the values 1, 2, ... , m. */ /* For each value of i, the current matrix A is updated by forming */ /* inv(S(i))**T*A*inv(S(i)). This creates a triangular bulge outside */ /* the band of A. The bulge is then pushed down toward the bottom of */ /* A in phase 1, and up toward the top of A in phase 2, by applying */ /* plane rotations. */ /* There are kb*(kb+1)/2 elements in the bulge, but at most 2*kb-1 */ /* of them are linearly independent, so annihilating a bulge requires */ /* only 2*kb-1 plane rotations. The rotations are divided into a 1st */ /* set of kb-1 rotations, and a 2nd set of kb rotations. */ /* Wherever possible, rotations are generated and applied in vector */ /* operations of length NR between the indices J1 and J2 (sometimes */ /* replaced by modified values NRT, J1T or J2T). */ /* The cosines and sines of the rotations are stored in the array */ /* WORK. The cosines of the 1st set of rotations are stored in */ /* elements n+2:n+m-kb-1 and the sines of the 1st set in elements */ /* 2:m-kb-1; the cosines of the 2nd set are stored in elements */ /* n+m-kb+1:2*n and the sines of the second set in elements m-kb+1:n. */ /* The bulges are not formed explicitly; nonzero elements outside the */ /* band are created only when they are required for generating new */ /* rotations; they are stored in the array WORK, in positions where */ /* they are later overwritten by the sines of the rotations which */ /* annihilate them. */ /* **************************** Phase 1 ***************************** */ /* The logical structure of this phase is: */ /* UPDATE = .TRUE. */ /* DO I = N, M + 1, -1 */ /* use S(i) to update A and create a new bulge */ /* apply rotations to push all bulges KA positions downward */ /* END DO */ /* UPDATE = .FALSE. */ /* DO I = M + KA + 1, N - 1 */ /* apply rotations to push all bulges KA positions downward */ /* END DO */ /* To avoid duplicating code, the two loops are merged. */ update = TRUE_; i__ = *n + 1; L10: if (update) { --i__; /* Computing MIN */ i__1 = *kb, i__2 = i__ - 1; kbt = min(i__1,i__2); i0 = i__ - 1; /* Computing MIN */ i__1 = *n, i__2 = i__ + *ka; i1 = min(i__1,i__2); i2 = i__ - kbt + ka1; if (i__ < m + 1) { update = FALSE_; ++i__; i0 = m; if (*ka == 0) { goto L480; } goto L10; } } else { i__ += *ka; if (i__ > *n - 1) { goto L480; } } if (upper) { /* Transform A, working with the upper triangle */ if (update) { /* Form inv(S(i))**T * A * inv(S(i)) */ bii = bb[kb1 + i__ * bb_dim1]; i__1 = i1; for (j = i__; j <= i__1; ++j) { ab[i__ - j + ka1 + j * ab_dim1] /= bii; /* L20: */ } /* Computing MAX */ i__1 = 1, i__2 = i__ - *ka; i__3 = i__; for (j = max(i__1,i__2); j <= i__3; ++j) { ab[j - i__ + ka1 + i__ * ab_dim1] /= bii; /* L30: */ } i__3 = i__ - 1; for (k = i__ - kbt; k <= i__3; ++k) { i__1 = k; for (j = i__ - kbt; j <= i__1; ++j) { ab[j - k + ka1 + k * ab_dim1] = ab[j - k + ka1 + k * ab_dim1] - bb[j - i__ + kb1 + i__ * bb_dim1] * ab[ k - i__ + ka1 + i__ * ab_dim1] - bb[k - i__ + kb1 + i__ * bb_dim1] * ab[j - i__ + ka1 + i__ * ab_dim1] + ab[ka1 + i__ * ab_dim1] * bb[j - i__ + kb1 + i__ * bb_dim1] * bb[k - i__ + kb1 + i__ * bb_dim1]; /* L40: */ } /* Computing MAX */ i__1 = 1, i__2 = i__ - *ka; i__4 = i__ - kbt - 1; for (j = max(i__1,i__2); j <= i__4; ++j) { ab[j - k + ka1 + k * ab_dim1] -= bb[k - i__ + kb1 + i__ * bb_dim1] * ab[j - i__ + ka1 + i__ * ab_dim1]; /* L50: */ } /* L60: */ } i__3 = i1; for (j = i__; j <= i__3; ++j) { /* Computing MAX */ i__4 = j - *ka, i__1 = i__ - kbt; i__2 = i__ - 1; for (k = max(i__4,i__1); k <= i__2; ++k) { ab[k - j + ka1 + j * ab_dim1] -= bb[k - i__ + kb1 + i__ * bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1]; /* L70: */ } /* L80: */ } if (wantx) { /* post-multiply X by inv(S(i)) */ i__3 = *n - m; d__1 = 1. / bii; dscal_(&i__3, &d__1, &x[m + 1 + i__ * x_dim1], &c__1); if (kbt > 0) { i__3 = *n - m; dger_(&i__3, &kbt, &c_b20, &x[m + 1 + i__ * x_dim1], & c__1, &bb[kb1 - kbt + i__ * bb_dim1], &c__1, &x[m + 1 + (i__ - kbt) * x_dim1], ldx); } } /* store a(i,i1) in RA1 for use in next loop over K */ ra1 = ab[i__ - i1 + ka1 + i1 * ab_dim1]; } /* Generate and apply vectors of rotations to chase all the */ /* existing bulges KA positions down toward the bottom of the */ /* band */ i__3 = *kb - 1; for (k = 1; k <= i__3; ++k) { if (update) { /* Determine the rotations which would annihilate the bulge */ /* which has in theory just been created */ if (i__ - k + *ka < *n && i__ - k > 1) { /* generate rotation to annihilate a(i,i-k+ka+1) */ dlartg_(&ab[k + 1 + (i__ - k + *ka) * ab_dim1], &ra1, & work[*n + i__ - k + *ka - m], &work[i__ - k + *ka - m], &ra); /* create nonzero element a(i-k,i-k+ka+1) outside the */ /* band and store it in WORK(i-k) */ t = -bb[kb1 - k + i__ * bb_dim1] * ra1; work[i__ - k] = work[*n + i__ - k + *ka - m] * t - work[ i__ - k + *ka - m] * ab[(i__ - k + *ka) * ab_dim1 + 1]; ab[(i__ - k + *ka) * ab_dim1 + 1] = work[i__ - k + *ka - m] * t + work[*n + i__ - k + *ka - m] * ab[(i__ - k + *ka) * ab_dim1 + 1]; ra1 = ra; } } /* Computing MAX */ i__2 = 1, i__4 = k - i0 + 2; j2 = i__ - k - 1 + max(i__2,i__4) * ka1; nr = (*n - j2 + *ka) / ka1; j1 = j2 + (nr - 1) * ka1; if (update) { /* Computing MAX */ i__2 = j2, i__4 = i__ + (*ka << 1) - k + 1; j2t = max(i__2,i__4); } else { j2t = j2; } nrt = (*n - j2t + *ka) / ka1; i__2 = j1; i__4 = ka1; for (j = j2t; i__4 < 0 ? j >= i__2 : j <= i__2; j += i__4) { /* create nonzero element a(j-ka,j+1) outside the band */ /* and store it in WORK(j-m) */ work[j - m] *= ab[(j + 1) * ab_dim1 + 1]; ab[(j + 1) * ab_dim1 + 1] = work[*n + j - m] * ab[(j + 1) * ab_dim1 + 1]; /* L90: */ } /* generate rotations in 1st set to annihilate elements which */ /* have been created outside the band */ if (nrt > 0) { dlargv_(&nrt, &ab[j2t * ab_dim1 + 1], &inca, &work[j2t - m], & ka1, &work[*n + j2t - m], &ka1); } if (nr > 0) { /* apply rotations in 1st set from the right */ i__4 = *ka - 1; for (l = 1; l <= i__4; ++l) { dlartv_(&nr, &ab[ka1 - l + j2 * ab_dim1], &inca, &ab[*ka - l + (j2 + 1) * ab_dim1], &inca, &work[*n + j2 - m], &work[j2 - m], &ka1); /* L100: */ } /* apply rotations in 1st set from both sides to diagonal */ /* blocks */ dlar2v_(&nr, &ab[ka1 + j2 * ab_dim1], &ab[ka1 + (j2 + 1) * ab_dim1], &ab[*ka + (j2 + 1) * ab_dim1], &inca, &work[ *n + j2 - m], &work[j2 - m], &ka1); } /* start applying rotations in 1st set from the left */ i__4 = *kb - k + 1; for (l = *ka - 1; l >= i__4; --l) { nrt = (*n - j2 + l) / ka1; if (nrt > 0) { dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, & ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, & work[*n + j2 - m], &work[j2 - m], &ka1); } /* L110: */ } if (wantx) { /* post-multiply X by product of rotations in 1st set */ i__4 = j1; i__2 = ka1; for (j = j2; i__2 < 0 ? j >= i__4 : j <= i__4; j += i__2) { i__1 = *n - m; drot_(&i__1, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j + 1) * x_dim1], &c__1, &work[*n + j - m], &work[j - m]); /* L120: */ } } /* L130: */ } if (update) { if (i2 <= *n && kbt > 0) { /* create nonzero element a(i-kbt,i-kbt+ka+1) outside the */ /* band and store it in WORK(i-kbt) */ work[i__ - kbt] = -bb[kb1 - kbt + i__ * bb_dim1] * ra1; } } for (k = *kb; k >= 1; --k) { if (update) { /* Computing MAX */ i__3 = 2, i__2 = k - i0 + 1; j2 = i__ - k - 1 + max(i__3,i__2) * ka1; } else { /* Computing MAX */ i__3 = 1, i__2 = k - i0 + 1; j2 = i__ - k - 1 + max(i__3,i__2) * ka1; } /* finish applying rotations in 2nd set from the left */ for (l = *kb - k; l >= 1; --l) { nrt = (*n - j2 + *ka + l) / ka1; if (nrt > 0) { dlartv_(&nrt, &ab[l + (j2 - l + 1) * ab_dim1], &inca, &ab[ l + 1 + (j2 - l + 1) * ab_dim1], &inca, &work[*n + j2 - *ka], &work[j2 - *ka], &ka1); } /* L140: */ } nr = (*n - j2 + *ka) / ka1; j1 = j2 + (nr - 1) * ka1; i__3 = j2; i__2 = -ka1; for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) { work[j] = work[j - *ka]; work[*n + j] = work[*n + j - *ka]; /* L150: */ } i__2 = j1; i__3 = ka1; for (j = j2; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3) { /* create nonzero element a(j-ka,j+1) outside the band */ /* and store it in WORK(j) */ work[j] *= ab[(j + 1) * ab_dim1 + 1]; ab[(j + 1) * ab_dim1 + 1] = work[*n + j] * ab[(j + 1) * ab_dim1 + 1]; /* L160: */ } if (update) { if (i__ - k < *n - *ka && k <= kbt) { work[i__ - k + *ka] = work[i__ - k]; } } /* L170: */ } for (k = *kb; k >= 1; --k) { /* Computing MAX */ i__3 = 1, i__2 = k - i0 + 1; j2 = i__ - k - 1 + max(i__3,i__2) * ka1; nr = (*n - j2 + *ka) / ka1; j1 = j2 + (nr - 1) * ka1; if (nr > 0) { /* generate rotations in 2nd set to annihilate elements */ /* which have been created outside the band */ dlargv_(&nr, &ab[j2 * ab_dim1 + 1], &inca, &work[j2], &ka1, & work[*n + j2], &ka1); /* apply rotations in 2nd set from the right */ i__3 = *ka - 1; for (l = 1; l <= i__3; ++l) { dlartv_(&nr, &ab[ka1 - l + j2 * ab_dim1], &inca, &ab[*ka - l + (j2 + 1) * ab_dim1], &inca, &work[*n + j2], &work[j2], &ka1); /* L180: */ } /* apply rotations in 2nd set from both sides to diagonal */ /* blocks */ dlar2v_(&nr, &ab[ka1 + j2 * ab_dim1], &ab[ka1 + (j2 + 1) * ab_dim1], &ab[*ka + (j2 + 1) * ab_dim1], &inca, &work[ *n + j2], &work[j2], &ka1); } /* start applying rotations in 2nd set from the left */ i__3 = *kb - k + 1; for (l = *ka - 1; l >= i__3; --l) { nrt = (*n - j2 + l) / ka1; if (nrt > 0) { dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, & ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, & work[*n + j2], &work[j2], &ka1); } /* L190: */ } if (wantx) { /* post-multiply X by product of rotations in 2nd set */ i__3 = j1; i__2 = ka1; for (j = j2; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) { i__4 = *n - m; drot_(&i__4, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j + 1) * x_dim1], &c__1, &work[*n + j], &work[j]); /* L200: */ } } /* L210: */ } i__2 = *kb - 1; for (k = 1; k <= i__2; ++k) { /* Computing MAX */ i__3 = 1, i__4 = k - i0 + 2; j2 = i__ - k - 1 + max(i__3,i__4) * ka1; /* finish applying rotations in 1st set from the left */ for (l = *kb - k; l >= 1; --l) { nrt = (*n - j2 + l) / ka1; if (nrt > 0) { dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, & ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, & work[*n + j2 - m], &work[j2 - m], &ka1); } /* L220: */ } /* L230: */ } if (*kb > 1) { i__2 = i__ - *kb + (*ka << 1) + 1; for (j = *n - 1; j >= i__2; --j) { work[*n + j - m] = work[*n + j - *ka - m]; work[j - m] = work[j - *ka - m]; /* L240: */ } } } else { /* Transform A, working with the lower triangle */ if (update) { /* Form inv(S(i))**T * A * inv(S(i)) */ bii = bb[i__ * bb_dim1 + 1]; i__2 = i1; for (j = i__; j <= i__2; ++j) { ab[j - i__ + 1 + i__ * ab_dim1] /= bii; /* L250: */ } /* Computing MAX */ i__2 = 1, i__3 = i__ - *ka; i__4 = i__; for (j = max(i__2,i__3); j <= i__4; ++j) { ab[i__ - j + 1 + j * ab_dim1] /= bii; /* L260: */ } i__4 = i__ - 1; for (k = i__ - kbt; k <= i__4; ++k) { i__2 = k; for (j = i__ - kbt; j <= i__2; ++j) { ab[k - j + 1 + j * ab_dim1] = ab[k - j + 1 + j * ab_dim1] - bb[i__ - j + 1 + j * bb_dim1] * ab[i__ - k + 1 + k * ab_dim1] - bb[i__ - k + 1 + k * bb_dim1] * ab[i__ - j + 1 + j * ab_dim1] + ab[i__ * ab_dim1 + 1] * bb[i__ - j + 1 + j * bb_dim1] * bb[i__ - k + 1 + k * bb_dim1]; /* L270: */ } /* Computing MAX */ i__2 = 1, i__3 = i__ - *ka; i__1 = i__ - kbt - 1; for (j = max(i__2,i__3); j <= i__1; ++j) { ab[k - j + 1 + j * ab_dim1] -= bb[i__ - k + 1 + k * bb_dim1] * ab[i__ - j + 1 + j * ab_dim1]; /* L280: */ } /* L290: */ } i__4 = i1; for (j = i__; j <= i__4; ++j) { /* Computing MAX */ i__1 = j - *ka, i__2 = i__ - kbt; i__3 = i__ - 1; for (k = max(i__1,i__2); k <= i__3; ++k) { ab[j - k + 1 + k * ab_dim1] -= bb[i__ - k + 1 + k * bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1]; /* L300: */ } /* L310: */ } if (wantx) { /* post-multiply X by inv(S(i)) */ i__4 = *n - m; d__1 = 1. / bii; dscal_(&i__4, &d__1, &x[m + 1 + i__ * x_dim1], &c__1); if (kbt > 0) { i__4 = *n - m; i__3 = *ldbb - 1; dger_(&i__4, &kbt, &c_b20, &x[m + 1 + i__ * x_dim1], & c__1, &bb[kbt + 1 + (i__ - kbt) * bb_dim1], &i__3, &x[m + 1 + (i__ - kbt) * x_dim1], ldx); } } /* store a(i1,i) in RA1 for use in next loop over K */ ra1 = ab[i1 - i__ + 1 + i__ * ab_dim1]; } /* Generate and apply vectors of rotations to chase all the */ /* existing bulges KA positions down toward the bottom of the */ /* band */ i__4 = *kb - 1; for (k = 1; k <= i__4; ++k) { if (update) { /* Determine the rotations which would annihilate the bulge */ /* which has in theory just been created */ if (i__ - k + *ka < *n && i__ - k > 1) { /* generate rotation to annihilate a(i-k+ka+1,i) */ dlartg_(&ab[ka1 - k + i__ * ab_dim1], &ra1, &work[*n + i__ - k + *ka - m], &work[i__ - k + *ka - m], &ra) ; /* create nonzero element a(i-k+ka+1,i-k) outside the */ /* band and store it in WORK(i-k) */ t = -bb[k + 1 + (i__ - k) * bb_dim1] * ra1; work[i__ - k] = work[*n + i__ - k + *ka - m] * t - work[ i__ - k + *ka - m] * ab[ka1 + (i__ - k) * ab_dim1] ; ab[ka1 + (i__ - k) * ab_dim1] = work[i__ - k + *ka - m] * t + work[*n + i__ - k + *ka - m] * ab[ka1 + (i__ - k) * ab_dim1]; ra1 = ra; } } /* Computing MAX */ i__3 = 1, i__1 = k - i0 + 2; j2 = i__ - k - 1 + max(i__3,i__1) * ka1; nr = (*n - j2 + *ka) / ka1; j1 = j2 + (nr - 1) * ka1; if (update) { /* Computing MAX */ i__3 = j2, i__1 = i__ + (*ka << 1) - k + 1; j2t = max(i__3,i__1); } else { j2t = j2; } nrt = (*n - j2t + *ka) / ka1; i__3 = j1; i__1 = ka1; for (j = j2t; i__1 < 0 ? j >= i__3 : j <= i__3; j += i__1) { /* create nonzero element a(j+1,j-ka) outside the band */ /* and store it in WORK(j-m) */ work[j - m] *= ab[ka1 + (j - *ka + 1) * ab_dim1]; ab[ka1 + (j - *ka + 1) * ab_dim1] = work[*n + j - m] * ab[ka1 + (j - *ka + 1) * ab_dim1]; /* L320: */ } /* generate rotations in 1st set to annihilate elements which */ /* have been created outside the band */ if (nrt > 0) { dlargv_(&nrt, &ab[ka1 + (j2t - *ka) * ab_dim1], &inca, &work[ j2t - m], &ka1, &work[*n + j2t - m], &ka1); } if (nr > 0) { /* apply rotations in 1st set from the left */ i__1 = *ka - 1; for (l = 1; l <= i__1; ++l) { dlartv_(&nr, &ab[l + 1 + (j2 - l) * ab_dim1], &inca, &ab[ l + 2 + (j2 - l) * ab_dim1], &inca, &work[*n + j2 - m], &work[j2 - m], &ka1); /* L330: */ } /* apply rotations in 1st set from both sides to diagonal */ /* blocks */ dlar2v_(&nr, &ab[j2 * ab_dim1 + 1], &ab[(j2 + 1) * ab_dim1 + 1], &ab[j2 * ab_dim1 + 2], &inca, &work[*n + j2 - m], &work[j2 - m], &ka1); } /* start applying rotations in 1st set from the right */ i__1 = *kb - k + 1; for (l = *ka - 1; l >= i__1; --l) { nrt = (*n - j2 + l) / ka1; if (nrt > 0) { dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[ ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n + j2 - m], &work[j2 - m], &ka1); } /* L340: */ } if (wantx) { /* post-multiply X by product of rotations in 1st set */ i__1 = j1; i__3 = ka1; for (j = j2; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) { i__2 = *n - m; drot_(&i__2, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j + 1) * x_dim1], &c__1, &work[*n + j - m], &work[j - m]); /* L350: */ } } /* L360: */ } if (update) { if (i2 <= *n && kbt > 0) { /* create nonzero element a(i-kbt+ka+1,i-kbt) outside the */ /* band and store it in WORK(i-kbt) */ work[i__ - kbt] = -bb[kbt + 1 + (i__ - kbt) * bb_dim1] * ra1; } } for (k = *kb; k >= 1; --k) { if (update) { /* Computing MAX */ i__4 = 2, i__3 = k - i0 + 1; j2 = i__ - k - 1 + max(i__4,i__3) * ka1; } else { /* Computing MAX */ i__4 = 1, i__3 = k - i0 + 1; j2 = i__ - k - 1 + max(i__4,i__3) * ka1; } /* finish applying rotations in 2nd set from the right */ for (l = *kb - k; l >= 1; --l) { nrt = (*n - j2 + *ka + l) / ka1; if (nrt > 0) { dlartv_(&nrt, &ab[ka1 - l + 1 + (j2 - *ka) * ab_dim1], & inca, &ab[ka1 - l + (j2 - *ka + 1) * ab_dim1], & inca, &work[*n + j2 - *ka], &work[j2 - *ka], &ka1) ; } /* L370: */ } nr = (*n - j2 + *ka) / ka1; j1 = j2 + (nr - 1) * ka1; i__4 = j2; i__3 = -ka1; for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) { work[j] = work[j - *ka]; work[*n + j] = work[*n + j - *ka]; /* L380: */ } i__3 = j1; i__4 = ka1; for (j = j2; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) { /* create nonzero element a(j+1,j-ka) outside the band */ /* and store it in WORK(j) */ work[j] *= ab[ka1 + (j - *ka + 1) * ab_dim1]; ab[ka1 + (j - *ka + 1) * ab_dim1] = work[*n + j] * ab[ka1 + ( j - *ka + 1) * ab_dim1]; /* L390: */ } if (update) { if (i__ - k < *n - *ka && k <= kbt) { work[i__ - k + *ka] = work[i__ - k]; } } /* L400: */ } for (k = *kb; k >= 1; --k) { /* Computing MAX */ i__4 = 1, i__3 = k - i0 + 1; j2 = i__ - k - 1 + max(i__4,i__3) * ka1; nr = (*n - j2 + *ka) / ka1; j1 = j2 + (nr - 1) * ka1; if (nr > 0) { /* generate rotations in 2nd set to annihilate elements */ /* which have been created outside the band */ dlargv_(&nr, &ab[ka1 + (j2 - *ka) * ab_dim1], &inca, &work[j2] , &ka1, &work[*n + j2], &ka1); /* apply rotations in 2nd set from the left */ i__4 = *ka - 1; for (l = 1; l <= i__4; ++l) { dlartv_(&nr, &ab[l + 1 + (j2 - l) * ab_dim1], &inca, &ab[ l + 2 + (j2 - l) * ab_dim1], &inca, &work[*n + j2] , &work[j2], &ka1); /* L410: */ } /* apply rotations in 2nd set from both sides to diagonal */ /* blocks */ dlar2v_(&nr, &ab[j2 * ab_dim1 + 1], &ab[(j2 + 1) * ab_dim1 + 1], &ab[j2 * ab_dim1 + 2], &inca, &work[*n + j2], & work[j2], &ka1); } /* start applying rotations in 2nd set from the right */ i__4 = *kb - k + 1; for (l = *ka - 1; l >= i__4; --l) { nrt = (*n - j2 + l) / ka1; if (nrt > 0) { dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[ ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n + j2], &work[j2], &ka1); } /* L420: */ } if (wantx) { /* post-multiply X by product of rotations in 2nd set */ i__4 = j1; i__3 = ka1; for (j = j2; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) { i__1 = *n - m; drot_(&i__1, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j + 1) * x_dim1], &c__1, &work[*n + j], &work[j]); /* L430: */ } } /* L440: */ } i__3 = *kb - 1; for (k = 1; k <= i__3; ++k) { /* Computing MAX */ i__4 = 1, i__1 = k - i0 + 2; j2 = i__ - k - 1 + max(i__4,i__1) * ka1; /* finish applying rotations in 1st set from the right */ for (l = *kb - k; l >= 1; --l) { nrt = (*n - j2 + l) / ka1; if (nrt > 0) { dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[ ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n + j2 - m], &work[j2 - m], &ka1); } /* L450: */ } /* L460: */ } if (*kb > 1) { i__3 = i__ - *kb + (*ka << 1) + 1; for (j = *n - 1; j >= i__3; --j) { work[*n + j - m] = work[*n + j - *ka - m]; work[j - m] = work[j - *ka - m]; /* L470: */ } } } goto L10; L480: /* **************************** Phase 2 ***************************** */ /* The logical structure of this phase is: */ /* UPDATE = .TRUE. */ /* DO I = 1, M */ /* use S(i) to update A and create a new bulge */ /* apply rotations to push all bulges KA positions upward */ /* END DO */ /* UPDATE = .FALSE. */ /* DO I = M - KA - 1, 2, -1 */ /* apply rotations to push all bulges KA positions upward */ /* END DO */ /* To avoid duplicating code, the two loops are merged. */ update = TRUE_; i__ = 0; L490: if (update) { ++i__; /* Computing MIN */ i__3 = *kb, i__4 = m - i__; kbt = min(i__3,i__4); i0 = i__ + 1; /* Computing MAX */ i__3 = 1, i__4 = i__ - *ka; i1 = max(i__3,i__4); i2 = i__ + kbt - ka1; if (i__ > m) { update = FALSE_; --i__; i0 = m + 1; if (*ka == 0) { return 0; } goto L490; } } else { i__ -= *ka; if (i__ < 2) { return 0; } } if (i__ < m - kbt) { nx = m; } else { nx = *n; } if (upper) { /* Transform A, working with the upper triangle */ if (update) { /* Form inv(S(i))**T * A * inv(S(i)) */ bii = bb[kb1 + i__ * bb_dim1]; i__3 = i__; for (j = i1; j <= i__3; ++j) { ab[j - i__ + ka1 + i__ * ab_dim1] /= bii; /* L500: */ } /* Computing MIN */ i__4 = *n, i__1 = i__ + *ka; i__3 = min(i__4,i__1); for (j = i__; j <= i__3; ++j) { ab[i__ - j + ka1 + j * ab_dim1] /= bii; /* L510: */ } i__3 = i__ + kbt; for (k = i__ + 1; k <= i__3; ++k) { i__4 = i__ + kbt; for (j = k; j <= i__4; ++j) { ab[k - j + ka1 + j * ab_dim1] = ab[k - j + ka1 + j * ab_dim1] - bb[i__ - j + kb1 + j * bb_dim1] * ab[ i__ - k + ka1 + k * ab_dim1] - bb[i__ - k + kb1 + k * bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1] + ab[ka1 + i__ * ab_dim1] * bb[i__ - j + kb1 + j * bb_dim1] * bb[i__ - k + kb1 + k * bb_dim1]; /* L520: */ } /* Computing MIN */ i__1 = *n, i__2 = i__ + *ka; i__4 = min(i__1,i__2); for (j = i__ + kbt + 1; j <= i__4; ++j) { ab[k - j + ka1 + j * ab_dim1] -= bb[i__ - k + kb1 + k * bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1]; /* L530: */ } /* L540: */ } i__3 = i__; for (j = i1; j <= i__3; ++j) { /* Computing MIN */ i__1 = j + *ka, i__2 = i__ + kbt; i__4 = min(i__1,i__2); for (k = i__ + 1; k <= i__4; ++k) { ab[j - k + ka1 + k * ab_dim1] -= bb[i__ - k + kb1 + k * bb_dim1] * ab[j - i__ + ka1 + i__ * ab_dim1]; /* L550: */ } /* L560: */ } if (wantx) { /* post-multiply X by inv(S(i)) */ d__1 = 1. / bii; dscal_(&nx, &d__1, &x[i__ * x_dim1 + 1], &c__1); if (kbt > 0) { i__3 = *ldbb - 1; dger_(&nx, &kbt, &c_b20, &x[i__ * x_dim1 + 1], &c__1, &bb[ *kb + (i__ + 1) * bb_dim1], &i__3, &x[(i__ + 1) * x_dim1 + 1], ldx); } } /* store a(i1,i) in RA1 for use in next loop over K */ ra1 = ab[i1 - i__ + ka1 + i__ * ab_dim1]; } /* Generate and apply vectors of rotations to chase all the */ /* existing bulges KA positions up toward the top of the band */ i__3 = *kb - 1; for (k = 1; k <= i__3; ++k) { if (update) { /* Determine the rotations which would annihilate the bulge */ /* which has in theory just been created */ if (i__ + k - ka1 > 0 && i__ + k < m) { /* generate rotation to annihilate a(i+k-ka-1,i) */ dlartg_(&ab[k + 1 + i__ * ab_dim1], &ra1, &work[*n + i__ + k - *ka], &work[i__ + k - *ka], &ra); /* create nonzero element a(i+k-ka-1,i+k) outside the */ /* band and store it in WORK(m-kb+i+k) */ t = -bb[kb1 - k + (i__ + k) * bb_dim1] * ra1; work[m - *kb + i__ + k] = work[*n + i__ + k - *ka] * t - work[i__ + k - *ka] * ab[(i__ + k) * ab_dim1 + 1]; ab[(i__ + k) * ab_dim1 + 1] = work[i__ + k - *ka] * t + work[*n + i__ + k - *ka] * ab[(i__ + k) * ab_dim1 + 1]; ra1 = ra; } } /* Computing MAX */ i__4 = 1, i__1 = k + i0 - m + 1; j2 = i__ + k + 1 - max(i__4,i__1) * ka1; nr = (j2 + *ka - 1) / ka1; j1 = j2 - (nr - 1) * ka1; if (update) { /* Computing MIN */ i__4 = j2, i__1 = i__ - (*ka << 1) + k - 1; j2t = min(i__4,i__1); } else { j2t = j2; } nrt = (j2t + *ka - 1) / ka1; i__4 = j2t; i__1 = ka1; for (j = j1; i__1 < 0 ? j >= i__4 : j <= i__4; j += i__1) { /* create nonzero element a(j-1,j+ka) outside the band */ /* and store it in WORK(j) */ work[j] *= ab[(j + *ka - 1) * ab_dim1 + 1]; ab[(j + *ka - 1) * ab_dim1 + 1] = work[*n + j] * ab[(j + *ka - 1) * ab_dim1 + 1]; /* L570: */ } /* generate rotations in 1st set to annihilate elements which */ /* have been created outside the band */ if (nrt > 0) { dlargv_(&nrt, &ab[(j1 + *ka) * ab_dim1 + 1], &inca, &work[j1], &ka1, &work[*n + j1], &ka1); } if (nr > 0) { /* apply rotations in 1st set from the left */ i__1 = *ka - 1; for (l = 1; l <= i__1; ++l) { dlartv_(&nr, &ab[ka1 - l + (j1 + l) * ab_dim1], &inca, & ab[*ka - l + (j1 + l) * ab_dim1], &inca, &work[*n + j1], &work[j1], &ka1); /* L580: */ } /* apply rotations in 1st set from both sides to diagonal */ /* blocks */ dlar2v_(&nr, &ab[ka1 + j1 * ab_dim1], &ab[ka1 + (j1 - 1) * ab_dim1], &ab[*ka + j1 * ab_dim1], &inca, &work[*n + j1], &work[j1], &ka1); } /* start applying rotations in 1st set from the right */ i__1 = *kb - k + 1; for (l = *ka - 1; l >= i__1; --l) { nrt = (j2 + l - 1) / ka1; j1t = j2 - (nrt - 1) * ka1; if (nrt > 0) { dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + ( j1t - 1) * ab_dim1], &inca, &work[*n + j1t], & work[j1t], &ka1); } /* L590: */ } if (wantx) { /* post-multiply X by product of rotations in 1st set */ i__1 = j2; i__4 = ka1; for (j = j1; i__4 < 0 ? j >= i__1 : j <= i__1; j += i__4) { drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1 + 1], &c__1, &work[*n + j], &work[j]); /* L600: */ } } /* L610: */ } if (update) { if (i2 > 0 && kbt > 0) { /* create nonzero element a(i+kbt-ka-1,i+kbt) outside the */ /* band and store it in WORK(m-kb+i+kbt) */ work[m - *kb + i__ + kbt] = -bb[kb1 - kbt + (i__ + kbt) * bb_dim1] * ra1; } } for (k = *kb; k >= 1; --k) { if (update) { /* Computing MAX */ i__3 = 2, i__4 = k + i0 - m; j2 = i__ + k + 1 - max(i__3,i__4) * ka1; } else { /* Computing MAX */ i__3 = 1, i__4 = k + i0 - m; j2 = i__ + k + 1 - max(i__3,i__4) * ka1; } /* finish applying rotations in 2nd set from the right */ for (l = *kb - k; l >= 1; --l) { nrt = (j2 + *ka + l - 1) / ka1; j1t = j2 - (nrt - 1) * ka1; if (nrt > 0) { dlartv_(&nrt, &ab[l + (j1t + *ka) * ab_dim1], &inca, &ab[ l + 1 + (j1t + *ka - 1) * ab_dim1], &inca, &work[* n + m - *kb + j1t + *ka], &work[m - *kb + j1t + * ka], &ka1); } /* L620: */ } nr = (j2 + *ka - 1) / ka1; j1 = j2 - (nr - 1) * ka1; i__3 = j2; i__4 = ka1; for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) { work[m - *kb + j] = work[m - *kb + j + *ka]; work[*n + m - *kb + j] = work[*n + m - *kb + j + *ka]; /* L630: */ } i__4 = j2; i__3 = ka1; for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) { /* create nonzero element a(j-1,j+ka) outside the band */ /* and store it in WORK(m-kb+j) */ work[m - *kb + j] *= ab[(j + *ka - 1) * ab_dim1 + 1]; ab[(j + *ka - 1) * ab_dim1 + 1] = work[*n + m - *kb + j] * ab[ (j + *ka - 1) * ab_dim1 + 1]; /* L640: */ } if (update) { if (i__ + k > ka1 && k <= kbt) { work[m - *kb + i__ + k - *ka] = work[m - *kb + i__ + k]; } } /* L650: */ } for (k = *kb; k >= 1; --k) { /* Computing MAX */ i__3 = 1, i__4 = k + i0 - m; j2 = i__ + k + 1 - max(i__3,i__4) * ka1; nr = (j2 + *ka - 1) / ka1; j1 = j2 - (nr - 1) * ka1; if (nr > 0) { /* generate rotations in 2nd set to annihilate elements */ /* which have been created outside the band */ dlargv_(&nr, &ab[(j1 + *ka) * ab_dim1 + 1], &inca, &work[m - * kb + j1], &ka1, &work[*n + m - *kb + j1], &ka1); /* apply rotations in 2nd set from the left */ i__3 = *ka - 1; for (l = 1; l <= i__3; ++l) { dlartv_(&nr, &ab[ka1 - l + (j1 + l) * ab_dim1], &inca, & ab[*ka - l + (j1 + l) * ab_dim1], &inca, &work[*n + m - *kb + j1], &work[m - *kb + j1], &ka1); /* L660: */ } /* apply rotations in 2nd set from both sides to diagonal */ /* blocks */ dlar2v_(&nr, &ab[ka1 + j1 * ab_dim1], &ab[ka1 + (j1 - 1) * ab_dim1], &ab[*ka + j1 * ab_dim1], &inca, &work[*n + m - *kb + j1], &work[m - *kb + j1], &ka1); } /* start applying rotations in 2nd set from the right */ i__3 = *kb - k + 1; for (l = *ka - 1; l >= i__3; --l) { nrt = (j2 + l - 1) / ka1; j1t = j2 - (nrt - 1) * ka1; if (nrt > 0) { dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + ( j1t - 1) * ab_dim1], &inca, &work[*n + m - *kb + j1t], &work[m - *kb + j1t], &ka1); } /* L670: */ } if (wantx) { /* post-multiply X by product of rotations in 2nd set */ i__3 = j2; i__4 = ka1; for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) { drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1 + 1], &c__1, &work[*n + m - *kb + j], &work[m - * kb + j]); /* L680: */ } } /* L690: */ } i__4 = *kb - 1; for (k = 1; k <= i__4; ++k) { /* Computing MAX */ i__3 = 1, i__1 = k + i0 - m + 1; j2 = i__ + k + 1 - max(i__3,i__1) * ka1; /* finish applying rotations in 1st set from the right */ for (l = *kb - k; l >= 1; --l) { nrt = (j2 + l - 1) / ka1; j1t = j2 - (nrt - 1) * ka1; if (nrt > 0) { dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + ( j1t - 1) * ab_dim1], &inca, &work[*n + j1t], & work[j1t], &ka1); } /* L700: */ } /* L710: */ } if (*kb > 1) { /* Computing MIN */ i__3 = i__ + *kb; i__4 = min(i__3,m) - (*ka << 1) - 1; for (j = 2; j <= i__4; ++j) { work[*n + j] = work[*n + j + *ka]; work[j] = work[j + *ka]; /* L720: */ } } } else { /* Transform A, working with the lower triangle */ if (update) { /* Form inv(S(i))**T * A * inv(S(i)) */ bii = bb[i__ * bb_dim1 + 1]; i__4 = i__; for (j = i1; j <= i__4; ++j) { ab[i__ - j + 1 + j * ab_dim1] /= bii; /* L730: */ } /* Computing MIN */ i__3 = *n, i__1 = i__ + *ka; i__4 = min(i__3,i__1); for (j = i__; j <= i__4; ++j) { ab[j - i__ + 1 + i__ * ab_dim1] /= bii; /* L740: */ } i__4 = i__ + kbt; for (k = i__ + 1; k <= i__4; ++k) { i__3 = i__ + kbt; for (j = k; j <= i__3; ++j) { ab[j - k + 1 + k * ab_dim1] = ab[j - k + 1 + k * ab_dim1] - bb[j - i__ + 1 + i__ * bb_dim1] * ab[k - i__ + 1 + i__ * ab_dim1] - bb[k - i__ + 1 + i__ * bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1] + ab[ i__ * ab_dim1 + 1] * bb[j - i__ + 1 + i__ * bb_dim1] * bb[k - i__ + 1 + i__ * bb_dim1]; /* L750: */ } /* Computing MIN */ i__1 = *n, i__2 = i__ + *ka; i__3 = min(i__1,i__2); for (j = i__ + kbt + 1; j <= i__3; ++j) { ab[j - k + 1 + k * ab_dim1] -= bb[k - i__ + 1 + i__ * bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1]; /* L760: */ } /* L770: */ } i__4 = i__; for (j = i1; j <= i__4; ++j) { /* Computing MIN */ i__1 = j + *ka, i__2 = i__ + kbt; i__3 = min(i__1,i__2); for (k = i__ + 1; k <= i__3; ++k) { ab[k - j + 1 + j * ab_dim1] -= bb[k - i__ + 1 + i__ * bb_dim1] * ab[i__ - j + 1 + j * ab_dim1]; /* L780: */ } /* L790: */ } if (wantx) { /* post-multiply X by inv(S(i)) */ d__1 = 1. / bii; dscal_(&nx, &d__1, &x[i__ * x_dim1 + 1], &c__1); if (kbt > 0) { dger_(&nx, &kbt, &c_b20, &x[i__ * x_dim1 + 1], &c__1, &bb[ i__ * bb_dim1 + 2], &c__1, &x[(i__ + 1) * x_dim1 + 1], ldx); } } /* store a(i,i1) in RA1 for use in next loop over K */ ra1 = ab[i__ - i1 + 1 + i1 * ab_dim1]; } /* Generate and apply vectors of rotations to chase all the */ /* existing bulges KA positions up toward the top of the band */ i__4 = *kb - 1; for (k = 1; k <= i__4; ++k) { if (update) { /* Determine the rotations which would annihilate the bulge */ /* which has in theory just been created */ if (i__ + k - ka1 > 0 && i__ + k < m) { /* generate rotation to annihilate a(i,i+k-ka-1) */ dlartg_(&ab[ka1 - k + (i__ + k - *ka) * ab_dim1], &ra1, & work[*n + i__ + k - *ka], &work[i__ + k - *ka], & ra); /* create nonzero element a(i+k,i+k-ka-1) outside the */ /* band and store it in WORK(m-kb+i+k) */ t = -bb[k + 1 + i__ * bb_dim1] * ra1; work[m - *kb + i__ + k] = work[*n + i__ + k - *ka] * t - work[i__ + k - *ka] * ab[ka1 + (i__ + k - *ka) * ab_dim1]; ab[ka1 + (i__ + k - *ka) * ab_dim1] = work[i__ + k - *ka] * t + work[*n + i__ + k - *ka] * ab[ka1 + (i__ + k - *ka) * ab_dim1]; ra1 = ra; } } /* Computing MAX */ i__3 = 1, i__1 = k + i0 - m + 1; j2 = i__ + k + 1 - max(i__3,i__1) * ka1; nr = (j2 + *ka - 1) / ka1; j1 = j2 - (nr - 1) * ka1; if (update) { /* Computing MIN */ i__3 = j2, i__1 = i__ - (*ka << 1) + k - 1; j2t = min(i__3,i__1); } else { j2t = j2; } nrt = (j2t + *ka - 1) / ka1; i__3 = j2t; i__1 = ka1; for (j = j1; i__1 < 0 ? j >= i__3 : j <= i__3; j += i__1) { /* create nonzero element a(j+ka,j-1) outside the band */ /* and store it in WORK(j) */ work[j] *= ab[ka1 + (j - 1) * ab_dim1]; ab[ka1 + (j - 1) * ab_dim1] = work[*n + j] * ab[ka1 + (j - 1) * ab_dim1]; /* L800: */ } /* generate rotations in 1st set to annihilate elements which */ /* have been created outside the band */ if (nrt > 0) { dlargv_(&nrt, &ab[ka1 + j1 * ab_dim1], &inca, &work[j1], &ka1, &work[*n + j1], &ka1); } if (nr > 0) { /* apply rotations in 1st set from the right */ i__1 = *ka - 1; for (l = 1; l <= i__1; ++l) { dlartv_(&nr, &ab[l + 1 + j1 * ab_dim1], &inca, &ab[l + 2 + (j1 - 1) * ab_dim1], &inca, &work[*n + j1], & work[j1], &ka1); /* L810: */ } /* apply rotations in 1st set from both sides to diagonal */ /* blocks */ dlar2v_(&nr, &ab[j1 * ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 + 2], &inca, &work[*n + j1] , &work[j1], &ka1); } /* start applying rotations in 1st set from the left */ i__1 = *kb - k + 1; for (l = *ka - 1; l >= i__1; --l) { nrt = (j2 + l - 1) / ka1; j1t = j2 - (nrt - 1) * ka1; if (nrt > 0) { dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1] , &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1], &inca, &work[*n + j1t], &work[j1t], &ka1); } /* L820: */ } if (wantx) { /* post-multiply X by product of rotations in 1st set */ i__1 = j2; i__3 = ka1; for (j = j1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) { drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1 + 1], &c__1, &work[*n + j], &work[j]); /* L830: */ } } /* L840: */ } if (update) { if (i2 > 0 && kbt > 0) { /* create nonzero element a(i+kbt,i+kbt-ka-1) outside the */ /* band and store it in WORK(m-kb+i+kbt) */ work[m - *kb + i__ + kbt] = -bb[kbt + 1 + i__ * bb_dim1] * ra1; } } for (k = *kb; k >= 1; --k) { if (update) { /* Computing MAX */ i__4 = 2, i__3 = k + i0 - m; j2 = i__ + k + 1 - max(i__4,i__3) * ka1; } else { /* Computing MAX */ i__4 = 1, i__3 = k + i0 - m; j2 = i__ + k + 1 - max(i__4,i__3) * ka1; } /* finish applying rotations in 2nd set from the left */ for (l = *kb - k; l >= 1; --l) { nrt = (j2 + *ka + l - 1) / ka1; j1t = j2 - (nrt - 1) * ka1; if (nrt > 0) { dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t + l - 1) * ab_dim1], &inca, &ab[ka1 - l + (j1t + l - 1) * ab_dim1], & inca, &work[*n + m - *kb + j1t + *ka], &work[m - * kb + j1t + *ka], &ka1); } /* L850: */ } nr = (j2 + *ka - 1) / ka1; j1 = j2 - (nr - 1) * ka1; i__4 = j2; i__3 = ka1; for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) { work[m - *kb + j] = work[m - *kb + j + *ka]; work[*n + m - *kb + j] = work[*n + m - *kb + j + *ka]; /* L860: */ } i__3 = j2; i__4 = ka1; for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) { /* create nonzero element a(j+ka,j-1) outside the band */ /* and store it in WORK(m-kb+j) */ work[m - *kb + j] *= ab[ka1 + (j - 1) * ab_dim1]; ab[ka1 + (j - 1) * ab_dim1] = work[*n + m - *kb + j] * ab[ka1 + (j - 1) * ab_dim1]; /* L870: */ } if (update) { if (i__ + k > ka1 && k <= kbt) { work[m - *kb + i__ + k - *ka] = work[m - *kb + i__ + k]; } } /* L880: */ } for (k = *kb; k >= 1; --k) { /* Computing MAX */ i__4 = 1, i__3 = k + i0 - m; j2 = i__ + k + 1 - max(i__4,i__3) * ka1; nr = (j2 + *ka - 1) / ka1; j1 = j2 - (nr - 1) * ka1; if (nr > 0) { /* generate rotations in 2nd set to annihilate elements */ /* which have been created outside the band */ dlargv_(&nr, &ab[ka1 + j1 * ab_dim1], &inca, &work[m - *kb + j1], &ka1, &work[*n + m - *kb + j1], &ka1); /* apply rotations in 2nd set from the right */ i__4 = *ka - 1; for (l = 1; l <= i__4; ++l) { dlartv_(&nr, &ab[l + 1 + j1 * ab_dim1], &inca, &ab[l + 2 + (j1 - 1) * ab_dim1], &inca, &work[*n + m - *kb + j1], &work[m - *kb + j1], &ka1); /* L890: */ } /* apply rotations in 2nd set from both sides to diagonal */ /* blocks */ dlar2v_(&nr, &ab[j1 * ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 + 2], &inca, &work[*n + m - *kb + j1], &work[m - *kb + j1], &ka1); } /* start applying rotations in 2nd set from the left */ i__4 = *kb - k + 1; for (l = *ka - 1; l >= i__4; --l) { nrt = (j2 + l - 1) / ka1; j1t = j2 - (nrt - 1) * ka1; if (nrt > 0) { dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1] , &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1], &inca, &work[*n + m - *kb + j1t], &work[m - *kb + j1t], &ka1); } /* L900: */ } if (wantx) { /* post-multiply X by product of rotations in 2nd set */ i__4 = j2; i__3 = ka1; for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) { drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1 + 1], &c__1, &work[*n + m - *kb + j], &work[m - * kb + j]); /* L910: */ } } /* L920: */ } i__3 = *kb - 1; for (k = 1; k <= i__3; ++k) { /* Computing MAX */ i__4 = 1, i__1 = k + i0 - m + 1; j2 = i__ + k + 1 - max(i__4,i__1) * ka1; /* finish applying rotations in 1st set from the left */ for (l = *kb - k; l >= 1; --l) { nrt = (j2 + l - 1) / ka1; j1t = j2 - (nrt - 1) * ka1; if (nrt > 0) { dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1] , &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1], &inca, &work[*n + j1t], &work[j1t], &ka1); } /* L930: */ } /* L940: */ } if (*kb > 1) { /* Computing MIN */ i__4 = i__ + *kb; i__3 = min(i__4,m) - (*ka << 1) - 1; for (j = 2; j <= i__3; ++j) { work[*n + j] = work[*n + j + *ka]; work[j] = work[j + *ka]; /* L950: */ } } } goto L490; /* End of DSBGST */ } /* dsbgst_ */