int f2c_cgbmv(char *trans, integer *M, integer *N, integer *KL, integer *KU, complex *alpha, complex *A, integer *lda, complex *X, integer *incX, complex *beta, complex *Y, integer *incY) { cgbmv_(trans, M, N, KL, KU, alpha, A, lda, X, incX, beta, Y, incY); return 0; }
/* Subroutine */ int cgbrfs_(char *trans, integer *n, integer *kl, integer * ku, integer *nrhs, complex *ab, integer *ldab, complex *afb, integer * ldafb, integer *ipiv, complex *b, integer *ldb, complex *x, integer * ldx, real *ferr, real *berr, complex *work, real *rwork, integer * info) { /* System generated locals */ integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7; real r__1, r__2, r__3, r__4; complex q__1; /* Builtin functions */ double r_imag(complex *); /* Local variables */ integer i__, j, k; real s; integer kk; real xk; integer nz; real eps; integer kase; real safe1, safe2; extern /* Subroutine */ int cgbmv_(char *, integer *, integer *, integer * , integer *, complex *, complex *, integer *, complex *, integer * , complex *, complex *, integer *); 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 *); extern doublereal slamch_(char *); real safmin; extern /* Subroutine */ int xerbla_(char *, integer *), cgbtrs_( char *, integer *, integer *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *); logical notran; char transn[1], 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 */ /* ======= */ /* CGBRFS improves the computed solution to a system of linear */ /* equations when the coefficient matrix is banded, 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. */ /* KL (input) INTEGER */ /* The number of subdiagonals within the band of A. KL >= 0. */ /* KU (input) INTEGER */ /* The number of superdiagonals within the band of A. KU >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrices B and X. NRHS >= 0. */ /* AB (input) COMPLEX array, dimension (LDAB,N) */ /* The original band matrix A, stored in rows 1 to KL+KU+1. */ /* The j-th column of A is stored in the j-th column of the */ /* array AB as follows: */ /* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= KL+KU+1. */ /* AFB (input) COMPLEX array, dimension (LDAFB,N) */ /* Details of the LU factorization of the band matrix A, as */ /* computed by CGBTRF. U is stored as an upper triangular band */ /* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */ /* the multipliers used during the factorization are stored in */ /* rows KL+KU+2 to 2*KL+KU+1. */ /* LDAFB (input) INTEGER */ /* The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1. */ /* IPIV (input) INTEGER array, dimension (N) */ /* The pivot indices from CGBTRF; for 1<=i<=N, row i of the */ /* matrix was interchanged with row IPIV(i). */ /* 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 CGBTRS. */ /* 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 */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; afb_dim1 = *ldafb; afb_offset = 1 + afb_dim1; afb -= afb_offset; --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 (*kl < 0) { *info = -3; } else if (*ku < 0) { *info = -4; } else if (*nrhs < 0) { *info = -5; } else if (*ldab < *kl + *ku + 1) { *info = -7; } else if (*ldafb < (*kl << 1) + *ku + 1) { *info = -9; } else if (*ldb < max(1,*n)) { *info = -12; } else if (*ldx < max(1,*n)) { *info = -14; } if (*info != 0) { i__1 = -(*info); xerbla_("CGBRFS", &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 */ /* Computing MIN */ i__1 = *kl + *ku + 2, i__2 = *n + 1; nz = min(i__1,i__2); 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); q__1.r = -1.f, q__1.i = -0.f; cgbmv_(trans, n, n, kl, ku, &q__1, &ab[ab_offset], ldab, &x[j * x_dim1 + 1], &c__1, &c_b1, &work[1], &c__1); /* 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. */ i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[ i__ + j * b_dim1]), dabs(r__2)); /* L30: */ } /* Compute abs(op(A))*abs(X) + abs(B). */ if (notran) { i__2 = *n; for (k = 1; k <= i__2; ++k) { kk = *ku + 1 - k; i__3 = k + j * x_dim1; xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j * x_dim1]), dabs(r__2)); /* Computing MAX */ i__3 = 1, i__4 = k - *ku; /* Computing MIN */ i__6 = *n, i__7 = k + *kl; i__5 = min(i__6,i__7); for (i__ = max(i__3,i__4); i__ <= i__5; ++i__) { i__3 = kk + i__ + k * ab_dim1; rwork[i__] += ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 = r_imag(&ab[kk + i__ + k * ab_dim1]), dabs(r__2))) * xk; /* L40: */ } /* L50: */ } } else { i__2 = *n; for (k = 1; k <= i__2; ++k) { s = 0.f; kk = *ku + 1 - k; /* Computing MAX */ i__5 = 1, i__3 = k - *ku; /* Computing MIN */ i__6 = *n, i__7 = k + *kl; i__4 = min(i__6,i__7); for (i__ = max(i__5,i__3); i__ <= i__4; ++i__) { i__5 = kk + i__ + k * ab_dim1; i__3 = i__ + j * x_dim1; s += ((r__1 = ab[i__5].r, dabs(r__1)) + (r__2 = r_imag(& ab[kk + i__ + k * ab_dim1]), dabs(r__2))) * (( r__3 = x[i__3].r, dabs(r__3)) + (r__4 = r_imag(&x[ i__ + j * x_dim1]), dabs(r__4))); /* L60: */ } rwork[k] += s; /* L70: */ } } s = 0.f; i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { if (rwork[i__] > safe2) { /* Computing MAX */ i__4 = i__; r__3 = s, r__4 = ((r__1 = work[i__4].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__4 = i__; r__3 = s, r__4 = ((r__1 = work[i__4].r, dabs(r__1)) + (r__2 = r_imag(&work[i__]), dabs(r__2)) + safe1) / (rwork[i__] + safe1); s = dmax(r__3,r__4); } /* L80: */ } 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. */ cgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &ipiv[1] , &work[1], n, info); caxpy_(n, &c_b1, &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__4 = i__; rwork[i__] = (r__1 = work[i__4].r, dabs(r__1)) + (r__2 = r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[ i__]; } else { i__4 = i__; rwork[i__] = (r__1 = work[i__4].r, dabs(r__1)) + (r__2 = r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[ i__] + safe1; } /* L90: */ } kase = 0; L100: 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). */ cgbtrs_(transt, n, kl, ku, &c__1, &afb[afb_offset], ldafb, & ipiv[1], &work[1], n, info); i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__4 = i__; i__5 = i__; i__3 = i__; q__1.r = rwork[i__5] * work[i__3].r, q__1.i = rwork[i__5] * work[i__3].i; work[i__4].r = q__1.r, work[i__4].i = q__1.i; /* L110: */ } } else { /* Multiply by inv(op(A))*diag(W). */ i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__4 = i__; i__5 = i__; i__3 = i__; q__1.r = rwork[i__5] * work[i__3].r, q__1.i = rwork[i__5] * work[i__3].i; work[i__4].r = q__1.r, work[i__4].i = q__1.i; /* L120: */ } cgbtrs_(transn, n, kl, ku, &c__1, &afb[afb_offset], ldafb, & ipiv[1], &work[1], n, info); } goto L100; } /* Normalize error. */ lstres = 0.f; i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { /* Computing MAX */ i__4 = i__ + j * x_dim1; r__3 = lstres, r__4 = (r__1 = x[i__4].r, dabs(r__1)) + (r__2 = r_imag(&x[i__ + j * x_dim1]), dabs(r__2)); lstres = dmax(r__3,r__4); /* L130: */ } if (lstres != 0.f) { ferr[j] /= lstres; } /* L140: */ } return 0; /* End of CGBRFS */ } /* cgbrfs_ */
void cgbmv(char trans, int m, int n, int kl, int ku, complex *alpha, complex *a, int inca, complex *x, int incx, complex *beta, complex *y, int incy ) { cgbmv_( &trans, &m, &n, &kl, &ku, alpha, a, &inca, x, &incx, beta, y, &incy ); }
void cblas_cgbmv(const enum CBLAS_ORDER order, const enum CBLAS_TRANSPOSE TransA, const integer M, const integer N, const integer KL, const integer KU, const void *alpha, const void *A, const integer lda, const void *X, const integer incX, const void *beta, void *Y, const integer incY) { char TA; #ifdef F77_CHAR F77_CHAR F77_TA; #else #define F77_TA &TA #endif #define F77_M M #define F77_N N #define F77_lda lda #define F77_KL KL #define F77_KU KU #define F77_incX incx #define F77_incY incY integer n=0, i=0, incx=incX; const float *xx= (float *)X, *alp= (float *)alpha, *bet = (float *)beta; float ALPHA[2],BETA[2]; integer tincY, tincx; float *x=(float *)X, *y=(float *)Y, *st=0, *tx=0; extern integer CBLAS_CallFromC; extern integer RowMajorStrg; RowMajorStrg = 0; CBLAS_CallFromC = 1; if (order == CblasColMajor) { if (TransA == CblasNoTrans) TA = 'N'; else if (TransA == CblasTrans) TA = 'T'; else if (TransA == CblasConjTrans) TA = 'C'; else { cblas_xerbla(2, "cblas_cgbmv","Illegal TransA setting, %d\n", TransA); CBLAS_CallFromC = 0; RowMajorStrg = 0; return; } #ifdef F77_CHAR F77_TA = C2F_CHAR(&TA); #endif cgbmv_(F77_TA, &F77_M, &F77_N, &F77_KL, &F77_KU, alpha, A, &F77_lda, X, &F77_incX, beta, Y, &F77_incY); } else if (order == CblasRowMajor) { RowMajorStrg = 1; if (TransA == CblasNoTrans) TA = 'T'; else if (TransA == CblasTrans) TA = 'N'; else if (TransA == CblasConjTrans) { ALPHA[0]= *alp; ALPHA[1]= -alp[1]; BETA[0]= *bet; BETA[1]= -bet[1]; TA = 'N'; if (M > 0) { n = M << 1; x = malloc(n*sizeof(float)); tx = x; if( incX > 0 ) { i = incX << 1 ; tincx = 2; st= x+n; } else { i = incX *(-2); tincx = -2; st = x-2; x +=(n-2); } do { *x = *xx; x[1] = -xx[1]; x += tincx ; xx += i; } while (x != st); x=tx; incx = 1; if( incY > 0 ) tincY = incY; else tincY = -incY; y++; if (N > 0) { i = tincY << 1; n = i * N ; st = y + n; do { *y = -(*y); y += i; } while(y != st); y -= n; } } else x = (float *) X; } else { cblas_xerbla(2, "cblas_cgbmv","Illegal TransA setting, %d\n", TransA); CBLAS_CallFromC = 0; RowMajorStrg = 0; return; } #ifdef F77_CHAR F77_TA = C2F_CHAR(&TA); #endif if (TransA == CblasConjTrans) cgbmv_(F77_TA, &F77_N, &F77_M, &F77_KU, &F77_KL, ALPHA, A ,&F77_lda, x,&F77_incX, BETA, Y, &F77_incY); else cgbmv_(F77_TA, &F77_N, &F77_M, &F77_KU, &F77_KL, alpha, A ,&F77_lda, x,&F77_incX, beta, Y, &F77_incY); if (TransA == CblasConjTrans) { if (x != X) free(x); if (N > 0) { do { *y = -(*y); y += i; } while (y != st); } } } else cblas_xerbla(1, "cblas_cgbmv", "Illegal Order setting, %d\n", order); CBLAS_CallFromC = 0; RowMajorStrg = 0; }
/* Subroutine */ int cla_gbrfsx_extended__(integer *prec_type__, integer * trans_type__, integer *n, integer *kl, integer *ku, integer *nrhs, complex *ab, integer *ldab, complex *afb, integer *ldafb, integer * ipiv, logical *colequ, real *c__, complex *b, integer *ldb, complex * y, integer *ldy, real *berr_out__, integer *n_norms__, real * err_bnds_norm__, real *err_bnds_comp__, complex *res, real *ayb, complex *dy, complex *y_tail__, real *rcond, integer *ithresh, real * rthresh, real *dz_ub__, logical *ignore_cwise__, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, y_dim1, y_offset, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3, i__4; real r__1, r__2; char ch__1[1]; /* Builtin functions */ double r_imag(complex *); /* Local variables */ real dxratmax, dzratmax; integer i__, j, m; extern /* Subroutine */ int cla_gbamv__(integer *, integer *, integer *, integer *, integer *, real *, complex *, integer *, complex *, integer *, real *, real *, integer *); logical incr_prec__; real prev_dz_z__, yk, final_dx_x__; extern /* Subroutine */ int cla_wwaddw__(integer *, complex *, complex *, complex *); real final_dz_z__, prevnormdx; integer cnt; real dyk, eps, incr_thresh__, dx_x__, dz_z__; extern /* Subroutine */ int cla_lin_berr__(integer *, integer *, integer * , complex *, real *, real *); real ymin; extern /* Subroutine */ int blas_cgbmv_x__(integer *, integer *, integer * , integer *, integer *, complex *, complex *, integer *, complex * , integer *, complex *, complex *, integer *, integer *); integer y_prec_state__; extern /* Subroutine */ int blas_cgbmv2_x__(integer *, integer *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, complex *, integer *, complex *, complex *, integer *, integer *), cgbmv_(char *, integer *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *), ccopy_(integer *, complex *, integer *, complex *, integer *); real dxrat, dzrat; extern /* Subroutine */ int caxpy_(integer *, complex *, complex *, integer *, complex *, integer *); char trans[1]; real normx, normy; extern doublereal slamch_(char *); extern /* Subroutine */ int cgbtrs_(char *, integer *, integer *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *); real normdx; extern /* Character */ VOID chla_transtype__(char *, ftnlen, integer *); real hugeval; integer x_state__, z_state__; /* -- LAPACK routine (version 3.2.1) -- */ /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ /* -- Jason Riedy of Univ. of California Berkeley. -- */ /* -- April 2009 -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley and NAG Ltd. -- */ /* .. */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CLA_GBRFSX_EXTENDED improves the computed solution to a system of */ /* linear equations by performing extra-precise iterative refinement */ /* and provides error bounds and backward error estimates for the solution. */ /* This subroutine is called by CGBRFSX to perform iterative refinement. */ /* In addition to normwise error bound, the code provides maximum */ /* componentwise error bound if possible. See comments for ERR_BNDS_NORM */ /* and ERR_BNDS_COMP for details of the error bounds. Note that this */ /* subroutine is only resonsible for setting the second fields of */ /* ERR_BNDS_NORM and ERR_BNDS_COMP. */ /* Arguments */ /* ========= */ /* PREC_TYPE (input) INTEGER */ /* Specifies the intermediate precision to be used in refinement. */ /* The value is defined by ILAPREC(P) where P is a CHARACTER and */ /* P = 'S': Single */ /* = 'D': Double */ /* = 'I': Indigenous */ /* = 'X', 'E': Extra */ /* TRANS_TYPE (input) INTEGER */ /* Specifies the transposition operation on A. */ /* The value is defined by ILATRANS(T) where T is a CHARACTER and */ /* T = 'N': No transpose */ /* = 'T': Transpose */ /* = 'C': Conjugate transpose */ /* N (input) INTEGER */ /* The number of linear equations, i.e., the order of the */ /* matrix A. N >= 0. */ /* KL (input) INTEGER */ /* The number of subdiagonals within the band of A. KL >= 0. */ /* KU (input) INTEGER */ /* The number of superdiagonals within the band of A. KU >= 0 */ /* NRHS (input) INTEGER */ /* The number of right-hand-sides, i.e., the number of columns of the */ /* matrix B. */ /* AB (input) COMPLEX array, dimension (LDA,N) */ /* On entry, the N-by-N matrix A. */ /* LDAB (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* AFB (input) COMPLEX array, dimension (LDAF,N) */ /* The factors L and U from the factorization */ /* A = P*L*U as computed by CGBTRF. */ /* LDAFB (input) INTEGER */ /* The leading dimension of the array AF. LDAF >= max(1,N). */ /* IPIV (input) INTEGER array, dimension (N) */ /* The pivot indices from the factorization A = P*L*U */ /* as computed by CGBTRF; row i of the matrix was interchanged */ /* with row IPIV(i). */ /* COLEQU (input) LOGICAL */ /* If .TRUE. then column equilibration was done to A before calling */ /* this routine. This is needed to compute the solution and error */ /* bounds correctly. */ /* C (input) REAL array, dimension (N) */ /* The column scale factors for A. If COLEQU = .FALSE., C */ /* is not accessed. If C is input, each element of C should be a power */ /* of the radix to ensure a reliable solution and error estimates. */ /* Scaling by powers of the radix does not cause rounding errors unless */ /* the result underflows or overflows. Rounding errors during scaling */ /* lead to refining with a matrix that is not equivalent to the */ /* input matrix, producing error estimates that may not be */ /* reliable. */ /* 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). */ /* Y (input/output) COMPLEX array, dimension (LDY,NRHS) */ /* On entry, the solution matrix X, as computed by CGBTRS. */ /* On exit, the improved solution matrix Y. */ /* LDY (input) INTEGER */ /* The leading dimension of the array Y. LDY >= max(1,N). */ /* BERR_OUT (output) REAL array, dimension (NRHS) */ /* On exit, BERR_OUT(j) contains the componentwise relative backward */ /* error for right-hand-side j from the formula */ /* max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ /* where abs(Z) is the componentwise absolute value of the matrix */ /* or vector Z. This is computed by CLA_LIN_BERR. */ /* N_NORMS (input) INTEGER */ /* Determines which error bounds to return (see ERR_BNDS_NORM */ /* and ERR_BNDS_COMP). */ /* If N_NORMS >= 1 return normwise error bounds. */ /* If N_NORMS >= 2 return componentwise error bounds. */ /* ERR_BNDS_NORM (input/output) REAL array, dimension */ /* (NRHS, N_ERR_BNDS) */ /* For each right-hand side, this array contains information about */ /* various error bounds and condition numbers corresponding to the */ /* normwise relative error, which is defined as follows: */ /* Normwise relative error in the ith solution vector: */ /* max_j (abs(XTRUE(j,i) - X(j,i))) */ /* ------------------------------ */ /* max_j abs(X(j,i)) */ /* The array is indexed by the type of error information as described */ /* below. There currently are up to three pieces of information */ /* returned. */ /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ /* right-hand side. */ /* The second index in ERR_BNDS_NORM(:,err) contains the following */ /* three fields: */ /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ /* reciprocal condition number is less than the threshold */ /* sqrt(n) * slamch('Epsilon'). */ /* err = 2 "Guaranteed" error bound: The estimated forward error, */ /* almost certainly within a factor of 10 of the true error */ /* so long as the next entry is greater than the threshold */ /* sqrt(n) * slamch('Epsilon'). This error bound should only */ /* be trusted if the previous boolean is true. */ /* err = 3 Reciprocal condition number: Estimated normwise */ /* reciprocal condition number. Compared with the threshold */ /* sqrt(n) * slamch('Epsilon') to determine if the error */ /* estimate is "guaranteed". These reciprocal condition */ /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ /* appropriately scaled matrix Z. */ /* Let Z = S*A, where S scales each row by a power of the */ /* radix so all absolute row sums of Z are approximately 1. */ /* This subroutine is only responsible for setting the second field */ /* above. */ /* See Lapack Working Note 165 for further details and extra */ /* cautions. */ /* ERR_BNDS_COMP (input/output) REAL array, dimension */ /* (NRHS, N_ERR_BNDS) */ /* For each right-hand side, this array contains information about */ /* various error bounds and condition numbers corresponding to the */ /* componentwise relative error, which is defined as follows: */ /* Componentwise relative error in the ith solution vector: */ /* abs(XTRUE(j,i) - X(j,i)) */ /* max_j ---------------------- */ /* abs(X(j,i)) */ /* The array is indexed by the right-hand side i (on which the */ /* componentwise relative error depends), and the type of error */ /* information as described below. There currently are up to three */ /* pieces of information returned for each right-hand side. If */ /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ /* the first (:,N_ERR_BNDS) entries are returned. */ /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ /* right-hand side. */ /* The second index in ERR_BNDS_COMP(:,err) contains the following */ /* three fields: */ /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ /* reciprocal condition number is less than the threshold */ /* sqrt(n) * slamch('Epsilon'). */ /* err = 2 "Guaranteed" error bound: The estimated forward error, */ /* almost certainly within a factor of 10 of the true error */ /* so long as the next entry is greater than the threshold */ /* sqrt(n) * slamch('Epsilon'). This error bound should only */ /* be trusted if the previous boolean is true. */ /* err = 3 Reciprocal condition number: Estimated componentwise */ /* reciprocal condition number. Compared with the threshold */ /* sqrt(n) * slamch('Epsilon') to determine if the error */ /* estimate is "guaranteed". These reciprocal condition */ /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ /* appropriately scaled matrix Z. */ /* Let Z = S*(A*diag(x)), where x is the solution for the */ /* current right-hand side and S scales each row of */ /* A*diag(x) by a power of the radix so all absolute row */ /* sums of Z are approximately 1. */ /* This subroutine is only responsible for setting the second field */ /* above. */ /* See Lapack Working Note 165 for further details and extra */ /* cautions. */ /* RES (input) COMPLEX array, dimension (N) */ /* Workspace to hold the intermediate residual. */ /* AYB (input) REAL array, dimension (N) */ /* Workspace. */ /* DY (input) COMPLEX array, dimension (N) */ /* Workspace to hold the intermediate solution. */ /* Y_TAIL (input) COMPLEX array, dimension (N) */ /* Workspace to hold the trailing bits of the intermediate solution. */ /* RCOND (input) REAL */ /* Reciprocal scaled condition number. This is an estimate of the */ /* reciprocal Skeel condition number of the matrix A after */ /* equilibration (if done). If this is less than the machine */ /* precision (in particular, if it is zero), the matrix is singular */ /* to working precision. Note that the error may still be small even */ /* if this number is very small and the matrix appears ill- */ /* conditioned. */ /* ITHRESH (input) INTEGER */ /* The maximum number of residual computations allowed for */ /* refinement. The default is 10. For 'aggressive' set to 100 to */ /* permit convergence using approximate factorizations or */ /* factorizations other than LU. If the factorization uses a */ /* technique other than Gaussian elimination, the guarantees in */ /* ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. */ /* RTHRESH (input) REAL */ /* Determines when to stop refinement if the error estimate stops */ /* decreasing. Refinement will stop when the next solution no longer */ /* satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */ /* the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */ /* default value is 0.5. For 'aggressive' set to 0.9 to permit */ /* convergence on extremely ill-conditioned matrices. See LAWN 165 */ /* for more details. */ /* DZ_UB (input) REAL */ /* Determines when to start considering componentwise convergence. */ /* Componentwise convergence is only considered after each component */ /* of the solution Y is stable, which we definte as the relative */ /* change in each component being less than DZ_UB. The default value */ /* is 0.25, requiring the first bit to be stable. See LAWN 165 for */ /* more details. */ /* IGNORE_CWISE (input) LOGICAL */ /* If .TRUE. then ignore componentwise convergence. Default value */ /* is .FALSE.. */ /* INFO (output) INTEGER */ /* = 0: Successful exit. */ /* < 0: if INFO = -i, the ith argument to CGBTRS had an illegal */ /* value */ /* ===================================================================== */ /* .. Local Scalars .. */ /* .. */ /* .. Parameters .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions.. */ /* .. */ /* .. Statement Functions .. */ /* .. */ /* .. Statement Function Definitions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ err_bnds_comp_dim1 = *nrhs; err_bnds_comp_offset = 1 + err_bnds_comp_dim1; err_bnds_comp__ -= err_bnds_comp_offset; err_bnds_norm_dim1 = *nrhs; err_bnds_norm_offset = 1 + err_bnds_norm_dim1; err_bnds_norm__ -= err_bnds_norm_offset; ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; afb_dim1 = *ldafb; afb_offset = 1 + afb_dim1; afb -= afb_offset; --ipiv; --c__; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; y_dim1 = *ldy; y_offset = 1 + y_dim1; y -= y_offset; --berr_out__; --res; --ayb; --dy; --y_tail__; /* Function Body */ if (*info != 0) { return 0; } chla_transtype__(ch__1, (ftnlen)1, trans_type__); *(unsigned char *)trans = *(unsigned char *)&ch__1[0]; eps = slamch_("Epsilon"); hugeval = slamch_("Overflow"); /* Force HUGEVAL to Inf */ hugeval *= hugeval; /* Using HUGEVAL may lead to spurious underflows. */ incr_thresh__ = (real) (*n) * eps; m = *kl + *ku + 1; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { y_prec_state__ = 1; if (y_prec_state__ == 2) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; y_tail__[i__3].r = 0.f, y_tail__[i__3].i = 0.f; } } dxrat = 0.f; dxratmax = 0.f; dzrat = 0.f; dzratmax = 0.f; final_dx_x__ = hugeval; final_dz_z__ = hugeval; prevnormdx = hugeval; prev_dz_z__ = hugeval; dz_z__ = hugeval; dx_x__ = hugeval; x_state__ = 1; z_state__ = 0; incr_prec__ = FALSE_; i__2 = *ithresh; for (cnt = 1; cnt <= i__2; ++cnt) { /* Compute residual RES = B_s - op(A_s) * Y, */ /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); if (y_prec_state__ == 0) { cgbmv_(trans, &m, n, kl, ku, &c_b6, &ab[ab_offset], ldab, &y[ j * y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1); } else if (y_prec_state__ == 1) { blas_cgbmv_x__(trans_type__, n, n, kl, ku, &c_b6, &ab[ ab_offset], ldab, &y[j * y_dim1 + 1], &c__1, &c_b8, & res[1], &c__1, prec_type__); } else { blas_cgbmv2_x__(trans_type__, n, n, kl, ku, &c_b6, &ab[ ab_offset], ldab, &y[j * y_dim1 + 1], &y_tail__[1], & c__1, &c_b8, &res[1], &c__1, prec_type__); } /* XXX: RES is no longer needed. */ ccopy_(n, &res[1], &c__1, &dy[1], &c__1); cgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &ipiv[1] , &dy[1], n, info); /* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */ normx = 0.f; normy = 0.f; normdx = 0.f; dz_z__ = 0.f; ymin = hugeval; i__3 = *n; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__ + j * y_dim1; yk = (r__1 = y[i__4].r, dabs(r__1)) + (r__2 = r_imag(&y[i__ + j * y_dim1]), dabs(r__2)); i__4 = i__; dyk = (r__1 = dy[i__4].r, dabs(r__1)) + (r__2 = r_imag(&dy[ i__]), dabs(r__2)); if (yk != 0.f) { /* Computing MAX */ r__1 = dz_z__, r__2 = dyk / yk; dz_z__ = dmax(r__1,r__2); } else if (dyk != 0.f) { dz_z__ = hugeval; } ymin = dmin(ymin,yk); normy = dmax(normy,yk); if (*colequ) { /* Computing MAX */ r__1 = normx, r__2 = yk * c__[i__]; normx = dmax(r__1,r__2); /* Computing MAX */ r__1 = normdx, r__2 = dyk * c__[i__]; normdx = dmax(r__1,r__2); } else { normx = normy; normdx = dmax(normdx,dyk); } } if (normx != 0.f) { dx_x__ = normdx / normx; } else if (normdx == 0.f) { dx_x__ = 0.f; } else { dx_x__ = hugeval; } dxrat = normdx / prevnormdx; dzrat = dz_z__ / prev_dz_z__; /* Check termination criteria. */ if (! (*ignore_cwise__) && ymin * *rcond < incr_thresh__ * normy && y_prec_state__ < 2) { incr_prec__ = TRUE_; } if (x_state__ == 3 && dxrat <= *rthresh) { x_state__ = 1; } if (x_state__ == 1) { if (dx_x__ <= eps) { x_state__ = 2; } else if (dxrat > *rthresh) { if (y_prec_state__ != 2) { incr_prec__ = TRUE_; } else { x_state__ = 3; } } else { if (dxrat > dxratmax) { dxratmax = dxrat; } } if (x_state__ > 1) { final_dx_x__ = dx_x__; } } if (z_state__ == 0 && dz_z__ <= *dz_ub__) { z_state__ = 1; } if (z_state__ == 3 && dzrat <= *rthresh) { z_state__ = 1; } if (z_state__ == 1) { if (dz_z__ <= eps) { z_state__ = 2; } else if (dz_z__ > *dz_ub__) { z_state__ = 0; dzratmax = 0.f; final_dz_z__ = hugeval; } else if (dzrat > *rthresh) { if (y_prec_state__ != 2) { incr_prec__ = TRUE_; } else { z_state__ = 3; } } else { if (dzrat > dzratmax) { dzratmax = dzrat; } } if (z_state__ > 1) { final_dz_z__ = dz_z__; } } /* Exit if both normwise and componentwise stopped working, */ /* but if componentwise is unstable, let it go at least two */ /* iterations. */ if (x_state__ != 1) { if (*ignore_cwise__) { goto L666; } if (z_state__ == 3 || z_state__ == 2) { goto L666; } if (z_state__ == 0 && cnt > 1) { goto L666; } } if (incr_prec__) { incr_prec__ = FALSE_; ++y_prec_state__; i__3 = *n; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__; y_tail__[i__4].r = 0.f, y_tail__[i__4].i = 0.f; } } prevnormdx = normdx; prev_dz_z__ = dz_z__; /* Update soluton. */ if (y_prec_state__ < 2) { caxpy_(n, &c_b8, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1); } else { cla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]); } } /* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */ L666: /* Set final_* when cnt hits ithresh. */ if (x_state__ == 1) { final_dx_x__ = dx_x__; } if (z_state__ == 1) { final_dz_z__ = dz_z__; } /* Compute error bounds. */ if (*n_norms__ >= 1) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / ( 1 - dxratmax); } if (*n_norms__ >= 2) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / ( 1 - dzratmax); } /* Compute componentwise relative backward error from formula */ /* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */ /* where abs(Z) is the componentwise absolute value of the matrix */ /* or vector Z. */ /* Compute residual RES = B_s - op(A_s) * Y, */ /* op(A) = A, A**T, or A**H depending on TRANS (and type). */ ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1); cgbmv_(trans, n, n, kl, ku, &c_b6, &ab[ab_offset], ldab, &y[j * y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1); i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; ayb[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[i__ + j * b_dim1]), dabs(r__2)); } /* Compute abs(op(A_s))*abs(Y) + abs(B_s). */ cla_gbamv__(trans_type__, n, n, kl, ku, &c_b31, &ab[ab_offset], ldab, &y[j * y_dim1 + 1], &c__1, &c_b31, &ayb[1], &c__1); cla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]); /* End of loop for each RHS. */ } return 0; } /* cla_gbrfsx_extended__ */
/* Subroutine */ int clarhs_(char *path, char *xtype, char *uplo, char *trans, integer *m, integer *n, integer *kl, integer *ku, integer *nrhs, complex *a, integer *lda, complex *x, integer *ldx, complex *b, integer *ldb, integer *iseed, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, i__1; /* Local variables */ integer j; char c1[1], c2[2]; integer mb, nx; logical gen, tri, qrs, sym, band; char diag[1]; logical tran; extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *), chemm_(char *, char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *), cgbmv_(char *, integer *, integer *, integer *, integer * , complex *, complex *, integer *, complex *, integer *, complex * , complex *, integer *), chbmv_(char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *); extern /* Subroutine */ int csbmv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *), ctbmv_(char *, char *, char *, integer *, integer *, complex *, integer *, complex *, integer *), chpmv_(char *, integer *, complex *, complex *, complex *, integer *, complex *, complex *, integer *), ctrmm_(char *, char *, char *, char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *), cspmv_(char *, integer *, complex *, complex *, complex *, integer *, complex *, complex *, integer *), csymm_(char *, char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *), ctpmv_(char *, char *, char *, integer *, complex *, complex *, integer *), clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *); extern logical lsamen_(integer *, char *, char *); extern /* Subroutine */ int clarnv_(integer *, integer *, integer *, complex *); logical notran; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CLARHS chooses a set of NRHS random solution vectors and sets */ /* up the right hand sides for the linear system */ /* op( A ) * X = B, */ /* where op( A ) may be A, A**T (transpose of A), or A**H (conjugate */ /* transpose of A). */ /* Arguments */ /* ========= */ /* PATH (input) CHARACTER*3 */ /* The type of the complex matrix A. PATH may be given in any */ /* combination of upper and lower case. Valid paths include */ /* xGE: General m x n matrix */ /* xGB: General banded matrix */ /* xPO: Hermitian positive definite, 2-D storage */ /* xPP: Hermitian positive definite packed */ /* xPB: Hermitian positive definite banded */ /* xHE: Hermitian indefinite, 2-D storage */ /* xHP: Hermitian indefinite packed */ /* xHB: Hermitian indefinite banded */ /* xSY: Symmetric indefinite, 2-D storage */ /* xSP: Symmetric indefinite packed */ /* xSB: Symmetric indefinite banded */ /* xTR: Triangular */ /* xTP: Triangular packed */ /* xTB: Triangular banded */ /* xQR: General m x n matrix */ /* xLQ: General m x n matrix */ /* xQL: General m x n matrix */ /* xRQ: General m x n matrix */ /* where the leading character indicates the precision. */ /* XTYPE (input) CHARACTER*1 */ /* Specifies how the exact solution X will be determined: */ /* = 'N': New solution; generate a random X. */ /* = 'C': Computed; use value of X on entry. */ /* UPLO (input) CHARACTER*1 */ /* Used only if A is symmetric or triangular; specifies whether */ /* the upper or lower triangular part of the matrix A is stored. */ /* = 'U': Upper triangular */ /* = 'L': Lower triangular */ /* TRANS (input) CHARACTER*1 */ /* Used only if A is nonsymmetric; specifies the operation */ /* applied to the matrix A. */ /* = 'N': B := A * X */ /* = 'T': B := A**T * X */ /* = 'C': B := A**H * X */ /* M (input) INTEGER */ /* The number of rows of the matrix A. M >= 0. */ /* N (input) INTEGER */ /* The number of columns of the matrix A. N >= 0. */ /* KL (input) INTEGER */ /* Used only if A is a band matrix; specifies the number of */ /* subdiagonals of A if A is a general band matrix or if A is */ /* symmetric or triangular and UPLO = 'L'; specifies the number */ /* of superdiagonals of A if A is symmetric or triangular and */ /* UPLO = 'U'. 0 <= KL <= M-1. */ /* KU (input) INTEGER */ /* Used only if A is a general band matrix or if A is */ /* triangular. */ /* If PATH = xGB, specifies the number of superdiagonals of A, */ /* and 0 <= KU <= N-1. */ /* If PATH = xTR, xTP, or xTB, specifies whether or not the */ /* matrix has unit diagonal: */ /* = 1: matrix has non-unit diagonal (default) */ /* = 2: matrix has unit diagonal */ /* NRHS (input) INTEGER */ /* The number of right hand side vectors in the system A*X = B. */ /* A (input) COMPLEX array, dimension (LDA,N) */ /* The test matrix whose type is given by PATH. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. */ /* If PATH = xGB, LDA >= KL+KU+1. */ /* If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1. */ /* Otherwise, LDA >= max(1,M). */ /* X (input or output) COMPLEX array, dimension (LDX,NRHS) */ /* On entry, if XTYPE = 'C' (for 'Computed'), then X contains */ /* the exact solution to the system of linear equations. */ /* On exit, if XTYPE = 'N' (for 'New'), then X is initialized */ /* with random values. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. If TRANS = 'N', */ /* LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M). */ /* B (output) COMPLEX array, dimension (LDB,NRHS) */ /* The right hand side vector(s) for the system of equations, */ /* computed from B = op(A) * X, where op(A) is determined by */ /* TRANS. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. If TRANS = 'N', */ /* LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N). */ /* ISEED (input/output) INTEGER array, dimension (4) */ /* The seed vector for the random number generator (used in */ /* CLATMS). Modified on exit. */ /* 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 */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; --iseed; /* Function Body */ *info = 0; *(unsigned char *)c1 = *(unsigned char *)path; s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2); tran = lsame_(trans, "T") || lsame_(trans, "C"); notran = ! tran; gen = lsame_(path + 1, "G"); qrs = lsame_(path + 1, "Q") || lsame_(path + 2, "Q"); sym = lsame_(path + 1, "P") || lsame_(path + 1, "S") || lsame_(path + 1, "H"); tri = lsame_(path + 1, "T"); band = lsame_(path + 2, "B"); if (! lsame_(c1, "Complex precision")) { *info = -1; } else if (! (lsame_(xtype, "N") || lsame_(xtype, "C"))) { *info = -2; } else if ((sym || tri) && ! (lsame_(uplo, "U") || lsame_(uplo, "L"))) { *info = -3; } else if ((gen || qrs) && ! (tran || lsame_(trans, "N"))) { *info = -4; } else if (*m < 0) { *info = -5; } else if (*n < 0) { *info = -6; } else if (band && *kl < 0) { *info = -7; } else if (band && *ku < 0) { *info = -8; } else if (*nrhs < 0) { *info = -9; } else if (! band && *lda < max(1,*m) || band && (sym || tri) && *lda < * kl + 1 || band && gen && *lda < *kl + *ku + 1) { *info = -11; } else if (notran && *ldx < max(1,*n) || tran && *ldx < max(1,*m)) { *info = -13; } else if (notran && *ldb < max(1,*m) || tran && *ldb < max(1,*n)) { *info = -15; } if (*info != 0) { i__1 = -(*info); xerbla_("CLARHS", &i__1); return 0; } /* Initialize X to NRHS random vectors unless XTYPE = 'C'. */ if (tran) { nx = *m; mb = *n; } else { nx = *n; mb = *m; } if (! lsame_(xtype, "C")) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { clarnv_(&c__2, &iseed[1], n, &x[j * x_dim1 + 1]); /* L10: */ } } /* Multiply X by op( A ) using an appropriate */ /* matrix multiply routine. */ if (lsamen_(&c__2, c2, "GE") || lsamen_(&c__2, c2, "QR") || lsamen_(&c__2, c2, "LQ") || lsamen_(&c__2, c2, "QL") || lsamen_(&c__2, c2, "RQ")) { /* General matrix */ cgemm_(trans, "N", &mb, nrhs, &nx, &c_b1, &a[a_offset], lda, &x[ x_offset], ldx, &c_b2, &b[b_offset], ldb); } else if (lsamen_(&c__2, c2, "PO") || lsamen_(& c__2, c2, "HE")) { /* Hermitian matrix, 2-D storage */ chemm_("Left", uplo, n, nrhs, &c_b1, &a[a_offset], lda, &x[x_offset], ldx, &c_b2, &b[b_offset], ldb); } else if (lsamen_(&c__2, c2, "SY")) { /* Symmetric matrix, 2-D storage */ csymm_("Left", uplo, n, nrhs, &c_b1, &a[a_offset], lda, &x[x_offset], ldx, &c_b2, &b[b_offset], ldb); } else if (lsamen_(&c__2, c2, "GB")) { /* General matrix, band storage */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { cgbmv_(trans, m, n, kl, ku, &c_b1, &a[a_offset], lda, &x[j * x_dim1 + 1], &c__1, &c_b2, &b[j * b_dim1 + 1], &c__1); /* L20: */ } } else if (lsamen_(&c__2, c2, "PB") || lsamen_(& c__2, c2, "HB")) { /* Hermitian matrix, band storage */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { chbmv_(uplo, n, kl, &c_b1, &a[a_offset], lda, &x[j * x_dim1 + 1], &c__1, &c_b2, &b[j * b_dim1 + 1], &c__1); /* L30: */ } } else if (lsamen_(&c__2, c2, "SB")) { /* Symmetric matrix, band storage */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { csbmv_(uplo, n, kl, &c_b1, &a[a_offset], lda, &x[j * x_dim1 + 1], &c__1, &c_b2, &b[j * b_dim1 + 1], &c__1); /* L40: */ } } else if (lsamen_(&c__2, c2, "PP") || lsamen_(& c__2, c2, "HP")) { /* Hermitian matrix, packed storage */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { chpmv_(uplo, n, &c_b1, &a[a_offset], &x[j * x_dim1 + 1], &c__1, & c_b2, &b[j * b_dim1 + 1], &c__1); /* L50: */ } } else if (lsamen_(&c__2, c2, "SP")) { /* Symmetric matrix, packed storage */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { cspmv_(uplo, n, &c_b1, &a[a_offset], &x[j * x_dim1 + 1], &c__1, & c_b2, &b[j * b_dim1 + 1], &c__1); /* L60: */ } } else if (lsamen_(&c__2, c2, "TR")) { /* Triangular matrix. Note that for triangular matrices, */ /* KU = 1 => non-unit triangular */ /* KU = 2 => unit triangular */ clacpy_("Full", n, nrhs, &x[x_offset], ldx, &b[b_offset], ldb); if (*ku == 2) { *(unsigned char *)diag = 'U'; } else { *(unsigned char *)diag = 'N'; } ctrmm_("Left", uplo, trans, diag, n, nrhs, &c_b1, &a[a_offset], lda, & b[b_offset], ldb); } else if (lsamen_(&c__2, c2, "TP")) { /* Triangular matrix, packed storage */ clacpy_("Full", n, nrhs, &x[x_offset], ldx, &b[b_offset], ldb); if (*ku == 2) { *(unsigned char *)diag = 'U'; } else { *(unsigned char *)diag = 'N'; } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ctpmv_(uplo, trans, diag, n, &a[a_offset], &b[j * b_dim1 + 1], & c__1); /* L70: */ } } else if (lsamen_(&c__2, c2, "TB")) { /* Triangular matrix, banded storage */ clacpy_("Full", n, nrhs, &x[x_offset], ldx, &b[b_offset], ldb); if (*ku == 2) { *(unsigned char *)diag = 'U'; } else { *(unsigned char *)diag = 'N'; } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ctbmv_(uplo, trans, diag, n, kl, &a[a_offset], lda, &b[j * b_dim1 + 1], &c__1); /* L80: */ } } else { /* If none of the above, set INFO = -1 and return */ *info = -1; i__1 = -(*info); xerbla_("CLARHS", &i__1); } return 0; /* End of CLARHS */ } /* clarhs_ */
/* Subroutine */ int cgbt02_(char *trans, integer *m, integer *n, integer *kl, integer *ku, integer *nrhs, complex *a, integer *lda, complex *x, integer *ldx, complex *b, integer *ldb, real *resid) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3; real r__1, r__2; complex q__1; /* Local variables */ integer j, i1, i2, n1, kd; real eps; real anorm, bnorm, xnorm; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CGBT02 computes the residual for a solution of a banded system of */ /* equations A*x = b or A'*x = b: */ /* RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS). */ /* where EPS is the machine precision. */ /* Arguments */ /* ========= */ /* TRANS (input) CHARACTER*1 */ /* Specifies the form of the system of equations: */ /* = 'N': A *x = b */ /* = 'T': A'*x = b, where A' is the transpose of A */ /* = 'C': A'*x = b, where A' is the transpose of A */ /* M (input) INTEGER */ /* The number of rows of the matrix A. M >= 0. */ /* N (input) INTEGER */ /* The number of columns of the matrix A. N >= 0. */ /* KL (input) INTEGER */ /* The number of subdiagonals within the band of A. KL >= 0. */ /* KU (input) INTEGER */ /* The number of superdiagonals within the band of A. KU >= 0. */ /* NRHS (input) INTEGER */ /* The number of columns of B. NRHS >= 0. */ /* A (input) COMPLEX array, dimension (LDA,N) */ /* The original matrix A in band storage, stored in rows 1 to */ /* KL+KU+1. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,KL+KU+1). */ /* X (input) COMPLEX array, dimension (LDX,NRHS) */ /* The computed solution vectors for the system of linear */ /* equations. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. If TRANS = 'N', */ /* LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M). */ /* B (input/output) COMPLEX array, dimension (LDB,NRHS) */ /* On entry, the right hand side vectors for the system of */ /* linear equations. */ /* On exit, B is overwritten with the difference B - A*X. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. IF TRANS = 'N', */ /* LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N). */ /* RESID (output) REAL */ /* The maximum over the number of right hand sides of */ /* norm(B - A*X) / ( norm(A) * norm(X) * EPS ). */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Quick return if N = 0 pr NRHS = 0 */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; /* Function Body */ if (*m <= 0 || *n <= 0 || *nrhs <= 0) { *resid = 0.f; return 0; } /* Exit with RESID = 1/EPS if ANORM = 0. */ eps = slamch_("Epsilon"); kd = *ku + 1; anorm = 0.f; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = kd + 1 - j; i1 = max(i__2,1); /* Computing MIN */ i__2 = kd + *m - j, i__3 = *kl + kd; i2 = min(i__2,i__3); /* Computing MAX */ i__2 = i2 - i1 + 1; r__1 = anorm, r__2 = scasum_(&i__2, &a[i1 + j * a_dim1], &c__1); anorm = dmax(r__1,r__2); /* L10: */ } if (anorm <= 0.f) { *resid = 1.f / eps; return 0; } if (lsame_(trans, "T") || lsame_(trans, "C")) { n1 = *n; } else { n1 = *m; } /* Compute B - A*X (or B - A'*X ) */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { q__1.r = -1.f, q__1.i = -0.f; cgbmv_(trans, m, n, kl, ku, &q__1, &a[a_offset], lda, &x[j * x_dim1 + 1], &c__1, &c_b1, &b[j * b_dim1 + 1], &c__1); /* L20: */ } /* Compute the maximum over the number of right hand sides of */ /* norm(B - A*X) / ( norm(A) * norm(X) * EPS ). */ *resid = 0.f; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { bnorm = scasum_(&n1, &b[j * b_dim1 + 1], &c__1); xnorm = scasum_(&n1, &x[j * x_dim1 + 1], &c__1); if (xnorm <= 0.f) { *resid = 1.f / eps; } else { /* Computing MAX */ r__1 = *resid, r__2 = bnorm / anorm / xnorm / eps; *resid = dmax(r__1,r__2); } /* L30: */ } return 0; /* End of CGBT02 */ } /* cgbt02_ */