int
f2c_ctbsv(char* uplo, char* trans, char* diag, integer* N, integer* K,
complex* A, integer* lda,
complex* X, integer* incX)
{
ctbsv_(uplo, trans, diag,
N, K, A, lda, X, incX);
return 0;
}
void
ctbsv(char uplo, char trans, char diag, int n, int k, complex *a, int lda, complex *x, int incx )
{
ctbsv_( &uplo, &trans, &diag, &n, &k, a, &lda, x, &incx );
}
int cpbtrs_(char *uplo, int *n, int *kd, int *
nrhs, complex *ab, int *ldab, complex *b, int *ldb, int *
info)
{
/* System generated locals */
int ab_dim1, ab_offset, b_dim1, b_offset, i__1;
/* Local variables */
int j;
extern int lsame_(char *, char *);
extern int ctbsv_(char *, char *, char *, int *,
int *, complex *, int *, complex *, int *);
int upper;
extern int xerbla_(char *, int *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CPBTRS solves a system of linear equations A*X = B with a Hermitian */
/* positive definite band matrix A using the Cholesky factorization */
/* A = U**H*U or A = L*L**H computed by CPBTRF. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangular factor stored in AB; */
/* = 'L': Lower triangular factor stored in AB. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* AB (input) COMPLEX array, dimension (LDAB,N) */
/* The triangular factor U or L from the Cholesky factorization */
/* A = U**H*U or A = L*L**H of the band matrix A, stored in the */
/* first KD+1 rows of the array. The j-th column of U or L is */
/* stored in the j-th column of the array AB as follows: */
/* if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for MAX(1,j-kd)<=i<=j; */
/* if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=MIN(n,j+kd). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the right hand side matrix B. */
/* On exit, the solution matrix X. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= MAX(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. 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;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kd < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldab < *kd + 1) {
*info = -6;
} else if (*ldb < MAX(1,*n)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPBTRS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
return 0;
}
if (upper) {
/* Solve A*X = B where A = U'*U. */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
/* Solve U'*X = B, overwriting B with X. */
ctbsv_("Upper", "Conjugate transpose", "Non-unit", n, kd, &ab[
ab_offset], ldab, &b[j * b_dim1 + 1], &c__1);
/* Solve U*X = B, overwriting B with X. */
ctbsv_("Upper", "No transpose", "Non-unit", n, kd, &ab[ab_offset],
ldab, &b[j * b_dim1 + 1], &c__1);
/* L10: */
}
} else {
/* Solve A*X = B where A = L*L'. */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
/* Solve L*X = B, overwriting B with X. */
ctbsv_("Lower", "No transpose", "Non-unit", n, kd, &ab[ab_offset],
ldab, &b[j * b_dim1 + 1], &c__1);
/* Solve L'*X = B, overwriting B with X. */
ctbsv_("Lower", "Conjugate transpose", "Non-unit", n, kd, &ab[
ab_offset], ldab, &b[j * b_dim1 + 1], &c__1);
/* L20: */
}
}
return 0;
/* End of CPBTRS */
} /* cpbtrs_ */
/* Subroutine */ int ctbtrs_(char *uplo, char *trans, char *diag, integer *n,
integer *kd, integer *nrhs, complex *ab, integer *ldab, complex *b,
integer *ldb, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, b_dim1, b_offset, i__1, i__2;
/* Local variables */
integer j;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ctbsv_(char *, char *, char *, integer *,
integer *, complex *, integer *, complex *, integer *);
logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
logical nounit;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CTBTRS solves a triangular system of the form */
/* A * X = B, A**T * X = B, or A**H * X = B, */
/* where A is a triangular band matrix of order N, and B is an */
/* N-by-NRHS matrix. A check is made to verify that A is nonsingular. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': A is upper triangular; */
/* = 'L': A is lower triangular. */
/* 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) */
/* DIAG (input) CHARACTER*1 */
/* = 'N': A is non-unit triangular; */
/* = 'U': A is unit triangular. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of superdiagonals or subdiagonals of the */
/* triangular band matrix A. KD >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* AB (input) COMPLEX array, dimension (LDAB,N) */
/* The upper or lower triangular band matrix A, stored in the */
/* first kd+1 rows of AB. The j-th column of A is stored */
/* in the j-th column of the array AB as follows: */
/* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). */
/* If DIAG = 'U', the diagonal elements of A are not referenced */
/* and are assumed to be 1. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the right hand side matrix B. */
/* On exit, if INFO = 0, the solution matrix X. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the i-th diagonal element of A is zero, */
/* indicating that the matrix is singular and the */
/* solutions X have not been computed. */
/* ===================================================================== */
/* .. 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;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
nounit = lsame_(diag, "N");
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! lsame_(trans, "N") && ! lsame_(trans,
"T") && ! lsame_(trans, "C")) {
*info = -2;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*kd < 0) {
*info = -5;
} else if (*nrhs < 0) {
*info = -6;
} else if (*ldab < *kd + 1) {
*info = -8;
} else if (*ldb < max(1,*n)) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CTBTRS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Check for singularity. */
if (nounit) {
if (upper) {
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
i__2 = *kd + 1 + *info * ab_dim1;
if (ab[i__2].r == 0.f && ab[i__2].i == 0.f) {
return 0;
}
/* L10: */
}
} else {
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
i__2 = *info * ab_dim1 + 1;
if (ab[i__2].r == 0.f && ab[i__2].i == 0.f) {
return 0;
}
/* L20: */
}
}
}
*info = 0;
/* Solve A * X = B, A**T * X = B, or A**H * X = B. */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ctbsv_(uplo, trans, diag, n, kd, &ab[ab_offset], ldab, &b[j * b_dim1
+ 1], &c__1);
/* L30: */
}
return 0;
/* End of CTBTRS */
} /* ctbtrs_ */
/* Subroutine */ int cgbtrs_(char *trans, integer *n, integer *kl, integer *
ku, integer *nrhs, complex *ab, integer *ldab, integer *ipiv, complex
*b, integer *ldb, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, b_dim1, b_offset, i__1, i__2, i__3;
complex q__1;
/* Local variables */
integer i__, j, l, kd, lm;
logical lnoti;
logical notran;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* CGBTRS solves a system of linear equations */
/* A * X = B, A**T * X = B, or A**H * X = B */
/* with a general band matrix A using the LU factorization computed */
/* by CGBTRF. */
/* 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 matrix B. NRHS >= 0. */
/* AB (input) COMPLEX array, dimension (LDAB,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. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices; for 1 <= i <= N, row i of the matrix was */
/* interchanged with row IPIV(i). */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the right hand side matrix B. */
/* On exit, the solution matrix X. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* 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 << 1) + *ku + 1) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGBTRS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
return 0;
}
kd = *ku + *kl + 1;
lnoti = *kl > 0;
if (notran) {
/* Solve A*X = B. */
/* Solve L*X = B, overwriting B with X. */
/* L is represented as a product of permutations and unit lower */
/* where each transformation L(i) is a rank-one modification of */
/* the identity matrix. */
if (lnoti) {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__2 = *kl, i__3 = *n - j;
lm = min(i__2,i__3);
l = ipiv[j];
if (l != j) {
cswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb);
}
q__1.r = -1.f, q__1.i = -0.f;
cgeru_(&lm, nrhs, &q__1, &ab[kd + 1 + j * ab_dim1], &c__1, &b[
j + b_dim1], ldb, &b[j + 1 + b_dim1], ldb);
}
}
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Solve U*X = B, overwriting B with X. */
i__2 = *kl + *ku;
ctbsv_("Upper", "No transpose", "Non-unit", n, &i__2, &ab[
ab_offset], ldab, &b[i__ * b_dim1 + 1], &c__1);
}
} else if (lsame_(trans, "T")) {
/* Solve A**T * X = B. */
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Solve U**T * X = B, overwriting B with X. */
i__2 = *kl + *ku;
ctbsv_("Upper", "Transpose", "Non-unit", n, &i__2, &ab[ab_offset],
ldab, &b[i__ * b_dim1 + 1], &c__1);
}
/* Solve L**T * X = B, overwriting B with X. */
if (lnoti) {
for (j = *n - 1; j >= 1; --j) {
/* Computing MIN */
i__1 = *kl, i__2 = *n - j;
lm = min(i__1,i__2);
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("Transpose", &lm, nrhs, &q__1, &b[j + 1 + b_dim1], ldb,
&ab[kd + 1 + j * ab_dim1], &c__1, &c_b1, &b[j +
b_dim1], ldb);
l = ipiv[j];
if (l != j) {
cswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb);
}
}
}
} else {
/* Solve A**H * X = B. */
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Solve U**H * X = B, overwriting B with X. */
i__2 = *kl + *ku;
ctbsv_("Upper", "Conjugate transpose", "Non-unit", n, &i__2, &ab[
ab_offset], ldab, &b[i__ * b_dim1 + 1], &c__1);
}
/* Solve L**H * X = B, overwriting B with X. */
if (lnoti) {
for (j = *n - 1; j >= 1; --j) {
/* Computing MIN */
i__1 = *kl, i__2 = *n - j;
lm = min(i__1,i__2);
clacgv_(nrhs, &b[j + b_dim1], ldb);
q__1.r = -1.f, q__1.i = -0.f;
cgemv_("Conjugate transpose", &lm, nrhs, &q__1, &b[j + 1 +
b_dim1], ldb, &ab[kd + 1 + j * ab_dim1], &c__1, &c_b1,
&b[j + b_dim1], ldb);
clacgv_(nrhs, &b[j + b_dim1], ldb);
l = ipiv[j];
if (l != j) {
cswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb);
}
}
}
}
return 0;
/* End of CGBTRS */
} /* cgbtrs_ */
/* Subroutine */ int clatbs_(char *uplo, char *trans, char *diag, char *
normin, integer *n, integer *kd, complex *ab, integer *ldab, complex *
x, real *scale, real *cnorm, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1, q__2, q__3, q__4;
/* Builtin functions */
double r_imag(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
integer i__, j;
real xj, rec, tjj;
integer jinc, jlen;
real xbnd;
integer imax;
real tmax;
complex tjjs;
real xmax, grow;
integer maind;
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
real tscal;
complex uscal;
integer jlast;
extern /* Complex */ VOID cdotu_(complex *, integer *, complex *, integer
*, complex *, integer *);
complex csumj;
extern /* Subroutine */ int ctbsv_(char *, char *, char *, integer *,
integer *, complex *, integer *, complex *, integer *), caxpy_(integer *, complex *, complex *, integer *
, complex *, integer *);
logical upper;
extern /* Subroutine */ int slabad_(real *, real *);
extern integer icamax_(integer *, complex *, integer *);
extern /* Complex */ VOID cladiv_(complex *, complex *, complex *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
*), xerbla_(char *, integer *);
real bignum;
extern integer isamax_(integer *, real *, integer *);
extern doublereal scasum_(integer *, complex *, integer *);
logical notran;
integer jfirst;
real smlnum;
logical nounit;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLATBS solves one of the triangular systems */
/* A * x = s*b, A**T * x = s*b, or A**H * x = s*b, */
/* with scaling to prevent overflow, where A is an upper or lower */
/* triangular band matrix. Here A' denotes the transpose of A, x and b */
/* are n-element vectors, and s is a scaling factor, usually less than */
/* or equal to 1, chosen so that the components of x will be less than */
/* the overflow threshold. If the unscaled problem will not cause */
/* overflow, the Level 2 BLAS routine CTBSV is called. If the matrix A */
/* is singular (A(j,j) = 0 for some j), then s is set to 0 and a */
/* non-trivial solution to A*x = 0 is returned. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the matrix A is upper or lower triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* TRANS (input) CHARACTER*1 */
/* Specifies the operation applied to A. */
/* = 'N': Solve A * x = s*b (No transpose) */
/* = 'T': Solve A**T * x = s*b (Transpose) */
/* = 'C': Solve A**H * x = s*b (Conjugate transpose) */
/* DIAG (input) CHARACTER*1 */
/* Specifies whether or not the matrix A is unit triangular. */
/* = 'N': Non-unit triangular */
/* = 'U': Unit triangular */
/* NORMIN (input) CHARACTER*1 */
/* Specifies whether CNORM has been set or not. */
/* = 'Y': CNORM contains the column norms on entry */
/* = 'N': CNORM is not set on entry. On exit, the norms will */
/* be computed and stored in CNORM. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of subdiagonals or superdiagonals in the */
/* triangular matrix A. KD >= 0. */
/* AB (input) COMPLEX array, dimension (LDAB,N) */
/* The upper or lower triangular band matrix A, stored in the */
/* first KD+1 rows of the array. The j-th column of A is stored */
/* in the j-th column of the array AB as follows: */
/* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* X (input/output) COMPLEX array, dimension (N) */
/* On entry, the right hand side b of the triangular system. */
/* On exit, X is overwritten by the solution vector x. */
/* SCALE (output) REAL */
/* The scaling factor s for the triangular system */
/* A * x = s*b, A**T * x = s*b, or A**H * x = s*b. */
/* If SCALE = 0, the matrix A is singular or badly scaled, and */
/* the vector x is an exact or approximate solution to A*x = 0. */
/* CNORM (input or output) REAL array, dimension (N) */
/* If NORMIN = 'Y', CNORM is an input argument and CNORM(j) */
/* contains the norm of the off-diagonal part of the j-th column */
/* of A. If TRANS = 'N', CNORM(j) must be greater than or equal */
/* to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) */
/* must be greater than or equal to the 1-norm. */
/* If NORMIN = 'N', CNORM is an output argument and CNORM(j) */
/* returns the 1-norm of the offdiagonal part of the j-th column */
/* of A. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -k, the k-th argument had an illegal value */
/* Further Details */
/* ======= ======= */
/* A rough bound on x is computed; if that is less than overflow, CTBSV */
/* is called, otherwise, specific code is used which checks for possible */
/* overflow or divide-by-zero at every operation. */
/* A columnwise scheme is used for solving A*x = b. The basic algorithm */
/* if A is lower triangular is */
/* x[1:n] := b[1:n] */
/* for j = 1, ..., n */
/* x(j) := x(j) / A(j,j) */
/* x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j] */
/* end */
/* Define bounds on the components of x after j iterations of the loop: */
/* M(j) = bound on x[1:j] */
/* G(j) = bound on x[j+1:n] */
/* Initially, let M(0) = 0 and G(0) = max{x(i), i=1,...,n}. */
/* Then for iteration j+1 we have */
/* M(j+1) <= G(j) / | A(j+1,j+1) | */
/* G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] | */
/* <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | ) */
/* where CNORM(j+1) is greater than or equal to the infinity-norm of */
/* column j+1 of A, not counting the diagonal. Hence */
/* G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | ) */
/* 1<=i<=j */
/* and */
/* |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| ) */
/* 1<=i< j */
/* Since |x(j)| <= M(j), we use the Level 2 BLAS routine CTBSV if the */
/* reciprocal of the largest M(j), j=1,..,n, is larger than */
/* max(underflow, 1/overflow). */
/* The bound on x(j) is also used to determine when a step in the */
/* columnwise method can be performed without fear of overflow. If */
/* the computed bound is greater than a large constant, x is scaled to */
/* prevent overflow, but if the bound overflows, x is set to 0, x(j) to */
/* 1, and scale to 0, and a non-trivial solution to A*x = 0 is found. */
/* Similarly, a row-wise scheme is used to solve A**T *x = b or */
/* A**H *x = b. The basic algorithm for A upper triangular is */
/* for j = 1, ..., n */
/* x(j) := ( b(j) - A[1:j-1,j]' * x[1:j-1] ) / A(j,j) */
/* end */
/* We simultaneously compute two bounds */
/* G(j) = bound on ( b(i) - A[1:i-1,i]' * x[1:i-1] ), 1<=i<=j */
/* M(j) = bound on x(i), 1<=i<=j */
/* The initial values are G(0) = 0, M(0) = max{b(i), i=1,..,n}, and we */
/* add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1. */
/* Then the bound on x(j) is */
/* M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) | */
/* <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| ) */
/* 1<=i<=j */
/* and we can safely call CTBSV if 1/M(n) and 1/G(n) are both greater */
/* than max(underflow, 1/overflow). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--x;
--cnorm;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
notran = lsame_(trans, "N");
nounit = lsame_(diag, "N");
/* Test the input parameters. */
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T") && !
lsame_(trans, "C")) {
*info = -2;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -3;
} else if (! lsame_(normin, "Y") && ! lsame_(normin,
"N")) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*kd < 0) {
*info = -6;
} else if (*ldab < *kd + 1) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CLATBS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Determine machine dependent parameters to control overflow. */
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
smlnum /= slamch_("Precision");
bignum = 1.f / smlnum;
*scale = 1.f;
if (lsame_(normin, "N")) {
/* Compute the 1-norm of each column, not including the diagonal. */
if (upper) {
/* A is upper triangular. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__2 = *kd, i__3 = j - 1;
jlen = min(i__2,i__3);
cnorm[j] = scasum_(&jlen, &ab[*kd + 1 - jlen + j * ab_dim1], &
c__1);
/* L10: */
}
} else {
/* A is lower triangular. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__2 = *kd, i__3 = *n - j;
jlen = min(i__2,i__3);
if (jlen > 0) {
cnorm[j] = scasum_(&jlen, &ab[j * ab_dim1 + 2], &c__1);
} else {
cnorm[j] = 0.f;
}
/* L20: */
}
}
}
/* Scale the column norms by TSCAL if the maximum element in CNORM is */
/* greater than BIGNUM/2. */
imax = isamax_(n, &cnorm[1], &c__1);
tmax = cnorm[imax];
if (tmax <= bignum * .5f) {
tscal = 1.f;
} else {
tscal = .5f / (smlnum * tmax);
sscal_(n, &tscal, &cnorm[1], &c__1);
}
/* Compute a bound on the computed solution vector to see if the */
/* Level 2 BLAS routine CTBSV can be used. */
xmax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = j;
r__3 = xmax, r__4 = (r__1 = x[i__2].r / 2.f, dabs(r__1)) + (r__2 =
r_imag(&x[j]) / 2.f, dabs(r__2));
xmax = dmax(r__3,r__4);
/* L30: */
}
xbnd = xmax;
if (notran) {
/* Compute the growth in A * x = b. */
if (upper) {
jfirst = *n;
jlast = 1;
jinc = -1;
maind = *kd + 1;
} else {
jfirst = 1;
jlast = *n;
jinc = 1;
maind = 1;
}
if (tscal != 1.f) {
grow = 0.f;
goto L60;
}
if (nounit) {
/* A is non-unit triangular. */
/* Compute GROW = 1/G(j) and XBND = 1/M(j). */
/* Initially, G(0) = max{x(i), i=1,...,n}. */
grow = .5f / dmax(xbnd,smlnum);
xbnd = grow;
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L60;
}
i__3 = maind + j * ab_dim1;
tjjs.r = ab[i__3].r, tjjs.i = ab[i__3].i;
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj >= smlnum) {
/* M(j) = G(j-1) / abs(A(j,j)) */
/* Computing MIN */
r__1 = xbnd, r__2 = dmin(1.f,tjj) * grow;
xbnd = dmin(r__1,r__2);
} else {
/* M(j) could overflow, set XBND to 0. */
xbnd = 0.f;
}
if (tjj + cnorm[j] >= smlnum) {
/* G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) ) */
grow *= tjj / (tjj + cnorm[j]);
} else {
/* G(j) could overflow, set GROW to 0. */
grow = 0.f;
}
/* L40: */
}
grow = xbnd;
} else {
/* A is unit triangular. */
/* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */
/* Computing MIN */
r__1 = 1.f, r__2 = .5f / dmax(xbnd,smlnum);
grow = dmin(r__1,r__2);
i__2 = jlast;
i__1 = jinc;
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L60;
}
/* G(j) = G(j-1)*( 1 + CNORM(j) ) */
grow *= 1.f / (cnorm[j] + 1.f);
/* L50: */
}
}
L60:
;
} else {
/* Compute the growth in A**T * x = b or A**H * x = b. */
if (upper) {
jfirst = 1;
jlast = *n;
jinc = 1;
maind = *kd + 1;
} else {
jfirst = *n;
jlast = 1;
jinc = -1;
maind = 1;
}
if (tscal != 1.f) {
grow = 0.f;
goto L90;
}
if (nounit) {
/* A is non-unit triangular. */
/* Compute GROW = 1/G(j) and XBND = 1/M(j). */
/* Initially, M(0) = max{x(i), i=1,...,n}. */
grow = .5f / dmax(xbnd,smlnum);
xbnd = grow;
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L90;
}
/* G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) ) */
xj = cnorm[j] + 1.f;
/* Computing MIN */
r__1 = grow, r__2 = xbnd / xj;
grow = dmin(r__1,r__2);
i__3 = maind + j * ab_dim1;
tjjs.r = ab[i__3].r, tjjs.i = ab[i__3].i;
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj >= smlnum) {
/* M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) */
if (xj > tjj) {
xbnd *= tjj / xj;
}
} else {
/* M(j) could overflow, set XBND to 0. */
xbnd = 0.f;
}
/* L70: */
}
grow = dmin(grow,xbnd);
} else {
/* A is unit triangular. */
/* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */
/* Computing MIN */
r__1 = 1.f, r__2 = .5f / dmax(xbnd,smlnum);
grow = dmin(r__1,r__2);
i__2 = jlast;
i__1 = jinc;
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/* Exit the loop if the growth factor is too small. */
if (grow <= smlnum) {
goto L90;
}
/* G(j) = ( 1 + CNORM(j) )*G(j-1) */
xj = cnorm[j] + 1.f;
grow /= xj;
/* L80: */
}
}
L90:
;
}
if (grow * tscal > smlnum) {
/* Use the Level 2 BLAS solve if the reciprocal of the bound on */
/* elements of X is not too small. */
ctbsv_(uplo, trans, diag, n, kd, &ab[ab_offset], ldab, &x[1], &c__1);
} else {
/* Use a Level 1 BLAS solve, scaling intermediate results. */
if (xmax > bignum * .5f) {
/* Scale X so that its components are less than or equal to */
/* BIGNUM in absolute value. */
*scale = bignum * .5f / xmax;
csscal_(n, scale, &x[1], &c__1);
xmax = bignum;
} else {
xmax *= 2.f;
}
if (notran) {
/* Solve A * x = b */
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Compute x(j) = b(j) / A(j,j), scaling x if necessary. */
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]),
dabs(r__2));
if (nounit) {
i__3 = maind + j * ab_dim1;
q__1.r = tscal * ab[i__3].r, q__1.i = tscal * ab[i__3].i;
tjjs.r = q__1.r, tjjs.i = q__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.f;
if (tscal == 1.f) {
goto L105;
}
}
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj > smlnum) {
/* abs(A(j,j)) > SMLNUM: */
if (tjj < 1.f) {
if (xj > tjj * bignum) {
/* Scale x by 1/b(j). */
rec = 1.f / xj;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
), dabs(r__2));
} else if (tjj > 0.f) {
/* 0 < abs(A(j,j)) <= SMLNUM: */
if (xj > tjj * bignum) {
/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM */
/* to avoid overflow when dividing by A(j,j). */
rec = tjj * bignum / xj;
if (cnorm[j] > 1.f) {
/* Scale by 1/CNORM(j) to avoid overflow when */
/* multiplying x(j) times column j. */
rec /= cnorm[j];
}
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
), dabs(r__2));
} else {
/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */
/* scale = 0, and compute a solution to A*x = 0. */
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
x[i__4].r = 0.f, x[i__4].i = 0.f;
/* L100: */
}
i__3 = j;
x[i__3].r = 1.f, x[i__3].i = 0.f;
xj = 1.f;
*scale = 0.f;
xmax = 0.f;
}
L105:
/* Scale x if necessary to avoid overflow when adding a */
/* multiple of column j of A. */
if (xj > 1.f) {
rec = 1.f / xj;
if (cnorm[j] > (bignum - xmax) * rec) {
/* Scale x by 1/(2*abs(x(j))). */
rec *= .5f;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
}
} else if (xj * cnorm[j] > bignum - xmax) {
/* Scale x by 1/2. */
csscal_(n, &c_b36, &x[1], &c__1);
*scale *= .5f;
}
if (upper) {
if (j > 1) {
/* Compute the update */
/* x(max(1,j-kd):j-1) := x(max(1,j-kd):j-1) - */
/* x(j)* A(max(1,j-kd):j-1,j) */
/* Computing MIN */
i__3 = *kd, i__4 = j - 1;
jlen = min(i__3,i__4);
i__3 = j;
q__2.r = -x[i__3].r, q__2.i = -x[i__3].i;
q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
caxpy_(&jlen, &q__1, &ab[*kd + 1 - jlen + j * ab_dim1]
, &c__1, &x[j - jlen], &c__1);
i__3 = j - 1;
i__ = icamax_(&i__3, &x[1], &c__1);
i__3 = i__;
xmax = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__]), dabs(r__2));
}
} else if (j < *n) {
/* Compute the update */
/* x(j+1:min(j+kd,n)) := x(j+1:min(j+kd,n)) - */
/* x(j) * A(j+1:min(j+kd,n),j) */
/* Computing MIN */
i__3 = *kd, i__4 = *n - j;
jlen = min(i__3,i__4);
if (jlen > 0) {
i__3 = j;
q__2.r = -x[i__3].r, q__2.i = -x[i__3].i;
q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
caxpy_(&jlen, &q__1, &ab[j * ab_dim1 + 2], &c__1, &x[
j + 1], &c__1);
}
i__3 = *n - j;
i__ = j + icamax_(&i__3, &x[j + 1], &c__1);
i__3 = i__;
xmax = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[
i__]), dabs(r__2));
}
/* L110: */
}
} else if (lsame_(trans, "T")) {
/* Solve A**T * x = b */
i__2 = jlast;
i__1 = jinc;
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/* Compute x(j) = b(j) - sum A(k,j)*x(k). */
/* k<>j */
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]),
dabs(r__2));
uscal.r = tscal, uscal.i = 0.f;
rec = 1.f / dmax(xmax,1.f);
if (cnorm[j] > (bignum - xj) * rec) {
/* If x(j) could overflow, scale x by 1/(2*XMAX). */
rec *= .5f;
if (nounit) {
i__3 = maind + j * ab_dim1;
q__1.r = tscal * ab[i__3].r, q__1.i = tscal * ab[i__3]
.i;
tjjs.r = q__1.r, tjjs.i = q__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.f;
}
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj > 1.f) {
/* Divide by A(j,j) when scaling x if A(j,j) > 1. */
/* Computing MIN */
r__1 = 1.f, r__2 = rec * tjj;
rec = dmin(r__1,r__2);
cladiv_(&q__1, &uscal, &tjjs);
uscal.r = q__1.r, uscal.i = q__1.i;
}
if (rec < 1.f) {
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
csumj.r = 0.f, csumj.i = 0.f;
if (uscal.r == 1.f && uscal.i == 0.f) {
/* If the scaling needed for A in the dot product is 1, */
/* call CDOTU to perform the dot product. */
if (upper) {
/* Computing MIN */
i__3 = *kd, i__4 = j - 1;
jlen = min(i__3,i__4);
cdotu_(&q__1, &jlen, &ab[*kd + 1 - jlen + j * ab_dim1]
, &c__1, &x[j - jlen], &c__1);
csumj.r = q__1.r, csumj.i = q__1.i;
} else {
/* Computing MIN */
i__3 = *kd, i__4 = *n - j;
jlen = min(i__3,i__4);
if (jlen > 1) {
cdotu_(&q__1, &jlen, &ab[j * ab_dim1 + 2], &c__1,
&x[j + 1], &c__1);
csumj.r = q__1.r, csumj.i = q__1.i;
}
}
} else {
/* Otherwise, use in-line code for the dot product. */
if (upper) {
/* Computing MIN */
i__3 = *kd, i__4 = j - 1;
jlen = min(i__3,i__4);
i__3 = jlen;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = *kd + i__ - jlen + j * ab_dim1;
q__3.r = ab[i__4].r * uscal.r - ab[i__4].i *
uscal.i, q__3.i = ab[i__4].r * uscal.i +
ab[i__4].i * uscal.r;
i__5 = j - jlen - 1 + i__;
q__2.r = q__3.r * x[i__5].r - q__3.i * x[i__5].i,
q__2.i = q__3.r * x[i__5].i + q__3.i * x[
i__5].r;
q__1.r = csumj.r + q__2.r, q__1.i = csumj.i +
q__2.i;
csumj.r = q__1.r, csumj.i = q__1.i;
/* L120: */
}
} else {
/* Computing MIN */
i__3 = *kd, i__4 = *n - j;
jlen = min(i__3,i__4);
i__3 = jlen;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + 1 + j * ab_dim1;
q__3.r = ab[i__4].r * uscal.r - ab[i__4].i *
uscal.i, q__3.i = ab[i__4].r * uscal.i +
ab[i__4].i * uscal.r;
i__5 = j + i__;
q__2.r = q__3.r * x[i__5].r - q__3.i * x[i__5].i,
q__2.i = q__3.r * x[i__5].i + q__3.i * x[
i__5].r;
q__1.r = csumj.r + q__2.r, q__1.i = csumj.i +
q__2.i;
csumj.r = q__1.r, csumj.i = q__1.i;
/* L130: */
}
}
}
q__1.r = tscal, q__1.i = 0.f;
if (uscal.r == q__1.r && uscal.i == q__1.i) {
/* Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j) */
/* was not used to scale the dotproduct. */
i__3 = j;
i__4 = j;
q__1.r = x[i__4].r - csumj.r, q__1.i = x[i__4].i -
csumj.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
), dabs(r__2));
if (nounit) {
/* Compute x(j) = x(j) / A(j,j), scaling if necessary. */
i__3 = maind + j * ab_dim1;
q__1.r = tscal * ab[i__3].r, q__1.i = tscal * ab[i__3]
.i;
tjjs.r = q__1.r, tjjs.i = q__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.f;
if (tscal == 1.f) {
goto L145;
}
}
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj > smlnum) {
/* abs(A(j,j)) > SMLNUM: */
if (tjj < 1.f) {
if (xj > tjj * bignum) {
/* Scale X by 1/abs(x(j)). */
rec = 1.f / xj;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
} else if (tjj > 0.f) {
/* 0 < abs(A(j,j)) <= SMLNUM: */
if (xj > tjj * bignum) {
/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */
rec = tjj * bignum / xj;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
} else {
/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */
/* scale = 0 and compute a solution to A**T *x = 0. */
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
x[i__4].r = 0.f, x[i__4].i = 0.f;
/* L140: */
}
i__3 = j;
x[i__3].r = 1.f, x[i__3].i = 0.f;
*scale = 0.f;
xmax = 0.f;
}
L145:
;
} else {
/* Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot */
/* product has already been divided by 1/A(j,j). */
i__3 = j;
cladiv_(&q__2, &x[j], &tjjs);
q__1.r = q__2.r - csumj.r, q__1.i = q__2.i - csumj.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
}
/* Computing MAX */
i__3 = j;
r__3 = xmax, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[j]), dabs(r__2));
xmax = dmax(r__3,r__4);
/* L150: */
}
} else {
/* Solve A**H * x = b */
i__1 = jlast;
i__2 = jinc;
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Compute x(j) = b(j) - sum A(k,j)*x(k). */
/* k<>j */
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]),
dabs(r__2));
uscal.r = tscal, uscal.i = 0.f;
rec = 1.f / dmax(xmax,1.f);
if (cnorm[j] > (bignum - xj) * rec) {
/* If x(j) could overflow, scale x by 1/(2*XMAX). */
rec *= .5f;
if (nounit) {
r_cnjg(&q__2, &ab[maind + j * ab_dim1]);
q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
tjjs.r = q__1.r, tjjs.i = q__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.f;
}
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj > 1.f) {
/* Divide by A(j,j) when scaling x if A(j,j) > 1. */
/* Computing MIN */
r__1 = 1.f, r__2 = rec * tjj;
rec = dmin(r__1,r__2);
cladiv_(&q__1, &uscal, &tjjs);
uscal.r = q__1.r, uscal.i = q__1.i;
}
if (rec < 1.f) {
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
csumj.r = 0.f, csumj.i = 0.f;
if (uscal.r == 1.f && uscal.i == 0.f) {
/* If the scaling needed for A in the dot product is 1, */
/* call CDOTC to perform the dot product. */
if (upper) {
/* Computing MIN */
i__3 = *kd, i__4 = j - 1;
jlen = min(i__3,i__4);
cdotc_(&q__1, &jlen, &ab[*kd + 1 - jlen + j * ab_dim1]
, &c__1, &x[j - jlen], &c__1);
csumj.r = q__1.r, csumj.i = q__1.i;
} else {
/* Computing MIN */
i__3 = *kd, i__4 = *n - j;
jlen = min(i__3,i__4);
if (jlen > 1) {
cdotc_(&q__1, &jlen, &ab[j * ab_dim1 + 2], &c__1,
&x[j + 1], &c__1);
csumj.r = q__1.r, csumj.i = q__1.i;
}
}
} else {
/* Otherwise, use in-line code for the dot product. */
if (upper) {
/* Computing MIN */
i__3 = *kd, i__4 = j - 1;
jlen = min(i__3,i__4);
i__3 = jlen;
for (i__ = 1; i__ <= i__3; ++i__) {
r_cnjg(&q__4, &ab[*kd + i__ - jlen + j * ab_dim1])
;
q__3.r = q__4.r * uscal.r - q__4.i * uscal.i,
q__3.i = q__4.r * uscal.i + q__4.i *
uscal.r;
i__4 = j - jlen - 1 + i__;
q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i,
q__2.i = q__3.r * x[i__4].i + q__3.i * x[
i__4].r;
q__1.r = csumj.r + q__2.r, q__1.i = csumj.i +
q__2.i;
csumj.r = q__1.r, csumj.i = q__1.i;
/* L160: */
}
} else {
/* Computing MIN */
i__3 = *kd, i__4 = *n - j;
jlen = min(i__3,i__4);
i__3 = jlen;
for (i__ = 1; i__ <= i__3; ++i__) {
r_cnjg(&q__4, &ab[i__ + 1 + j * ab_dim1]);
q__3.r = q__4.r * uscal.r - q__4.i * uscal.i,
q__3.i = q__4.r * uscal.i + q__4.i *
uscal.r;
i__4 = j + i__;
q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i,
q__2.i = q__3.r * x[i__4].i + q__3.i * x[
i__4].r;
q__1.r = csumj.r + q__2.r, q__1.i = csumj.i +
q__2.i;
csumj.r = q__1.r, csumj.i = q__1.i;
/* L170: */
}
}
}
q__1.r = tscal, q__1.i = 0.f;
if (uscal.r == q__1.r && uscal.i == q__1.i) {
/* Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j) */
/* was not used to scale the dotproduct. */
i__3 = j;
i__4 = j;
q__1.r = x[i__4].r - csumj.r, q__1.i = x[i__4].i -
csumj.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
i__3 = j;
xj = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[j]
), dabs(r__2));
if (nounit) {
/* Compute x(j) = x(j) / A(j,j), scaling if necessary. */
r_cnjg(&q__2, &ab[maind + j * ab_dim1]);
q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i;
tjjs.r = q__1.r, tjjs.i = q__1.i;
} else {
tjjs.r = tscal, tjjs.i = 0.f;
if (tscal == 1.f) {
goto L185;
}
}
tjj = (r__1 = tjjs.r, dabs(r__1)) + (r__2 = r_imag(&tjjs),
dabs(r__2));
if (tjj > smlnum) {
/* abs(A(j,j)) > SMLNUM: */
if (tjj < 1.f) {
if (xj > tjj * bignum) {
/* Scale X by 1/abs(x(j)). */
rec = 1.f / xj;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
} else if (tjj > 0.f) {
/* 0 < abs(A(j,j)) <= SMLNUM: */
if (xj > tjj * bignum) {
/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */
rec = tjj * bignum / xj;
csscal_(n, &rec, &x[1], &c__1);
*scale *= rec;
xmax *= rec;
}
i__3 = j;
cladiv_(&q__1, &x[j], &tjjs);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
} else {
/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */
/* scale = 0 and compute a solution to A**H *x = 0. */
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
x[i__4].r = 0.f, x[i__4].i = 0.f;
/* L180: */
}
i__3 = j;
x[i__3].r = 1.f, x[i__3].i = 0.f;
*scale = 0.f;
xmax = 0.f;
}
L185:
;
} else {
/* Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot */
/* product has already been divided by 1/A(j,j). */
i__3 = j;
cladiv_(&q__2, &x[j], &tjjs);
q__1.r = q__2.r - csumj.r, q__1.i = q__2.i - csumj.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
}
/* Computing MAX */
i__3 = j;
r__3 = xmax, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[j]), dabs(r__2));
xmax = dmax(r__3,r__4);
/* L190: */
}
}
*scale /= tscal;
}
/* Scale the column norms by 1/TSCAL for return. */
if (tscal != 1.f) {
r__1 = 1.f / tscal;
sscal_(n, &r__1, &cnorm[1], &c__1);
}
return 0;
/* End of CLATBS */
} /* clatbs_ */
/* Subroutine */ int cchktb_(logical *dotype, integer *nn, integer *nval,
integer *nns, integer *nsval, real *thresh, logical *tsterr, integer *
nmax, complex *ab, complex *ainv, complex *b, complex *x, complex *
xact, complex *work, real *rwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char uplos[1*2] = "U" "L";
static char transs[1*3] = "N" "T" "C";
/* Format strings */
static char fmt_9999[] = "(\002 UPLO='\002,a1,\002', TRANS='\002,a1,\002"
"', DIAG='\002,a1,\002', N=\002,i5,\002, K"
"D=\002,i5,\002, NRHS=\002,i5,\002, type \002,i2,\002, test(\002,"
"i2,\002)=\002,g12.5)";
static char fmt_9998[] = "(1x,a,\002( '\002,a1,\002', '\002,a1,\002', "
"'\002,a1,\002',\002,i5,\002,\002,i5,\002, ... ), type \002,i2"
",\002, test(\002,i2,\002)=\002,g12.5)";
static char fmt_9997[] = "(1x,a,\002( '\002,a1,\002', '\002,a1,\002', "
"'\002,a1,\002', '\002,a1,\002',\002,i5,\002,\002,i5,\002, ... )"
", type \002,i2,\002, test(\002,i1,\002)=\002,g12.5)";
/* System generated locals */
address a__1[3], a__2[4];
integer i__1, i__2, i__3, i__4, i__5, i__6[3], i__7[4];
char ch__1[3], ch__2[4];
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen), s_cat(char *,
char **, integer *, integer *, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, j, k, n, kd, ik, in, nk, lda, ldab;
char diag[1];
integer imat, info;
char path[3];
integer irhs, nrhs;
char norm[1], uplo[1];
integer nrun;
extern /* Subroutine */ int alahd_(integer *, char *);
integer idiag;
extern /* Subroutine */ int cget04_(integer *, integer *, complex *,
integer *, complex *, integer *, real *, real *);
real scale;
integer nfail, iseed[4];
extern /* Subroutine */ int ctbt02_(char *, char *, char *, integer *,
integer *, integer *, complex *, integer *, complex *, integer *,
complex *, integer *, complex *, real *, real *), ctbt03_(char *, char *, char *, integer *, integer *,
integer *, complex *, integer *, real *, real *, real *, complex *
, integer *, complex *, integer *, complex *, real *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ctbt05_(char *, char *, char *, integer *,
integer *, integer *, complex *, integer *, complex *, integer *,
complex *, integer *, complex *, integer *, real *, real *, real *
), ctbt06_(real *, real *, char *, char *,
integer *, integer *, complex *, integer *, real *, real *);
real rcond;
integer nimat;
real anorm;
integer itran;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), ctbsv_(char *, char *, char *, integer *,
integer *, complex *, integer *, complex *, integer *);
char trans[1];
integer iuplo, nerrs;
char xtype[1];
integer nimat2;
extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *,
char *, integer *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *);
extern doublereal clantb_(char *, char *, char *, integer *, integer *,
complex *, integer *, real *);
real rcondc;
extern /* Subroutine */ int clatbs_(char *, char *, char *, char *,
integer *, integer *, complex *, integer *, complex *, real *,
real *, integer *), clattb_(
integer *, char *, char *, char *, integer *, integer *, integer *
, complex *, integer *, complex *, complex *, real *, integer *), clacpy_(char *, integer *, integer *,
complex *, integer *, complex *, integer *), clarhs_(char
*, char *, char *, char *, integer *, integer *, integer *,
integer *, integer *, complex *, integer *, complex *, integer *,
complex *, integer *, integer *, integer *), claset_(char *, integer *, integer *, complex *,
complex *, complex *, integer *);
real rcondi;
extern /* Subroutine */ int ctbcon_(char *, char *, char *, integer *,
integer *, complex *, integer *, real *, complex *, real *,
integer *);
extern doublereal clantr_(char *, char *, char *, integer *, integer *,
complex *, integer *, real *);
real rcondo;
extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer
*, integer *), ctbrfs_(char *, char *, char *, integer *,
integer *, integer *, complex *, integer *, complex *, integer *,
complex *, integer *, real *, real *, complex *, real *, integer *
);
real ainvnm;
extern /* Subroutine */ int cerrtr_(char *, integer *), ctbtrs_(
char *, char *, char *, integer *, integer *, integer *, complex *
, integer *, complex *, integer *, integer *);
real result[8];
/* Fortran I/O blocks */
static cilist io___39 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9997, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CCHKTB tests CTBTRS, -RFS, and -CON, and CLATBS. */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix column dimension N. */
/* NNS (input) INTEGER */
/* The number of values of NRHS contained in the vector NSVAL. */
/* NSVAL (input) INTEGER array, dimension (NNS) */
/* The values of the number of right hand sides NRHS. */
/* THRESH (input) REAL */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESULT >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. */
/* TSTERR (input) LOGICAL */
/* Flag that indicates whether error exits are to be tested. */
/* NMAX (input) INTEGER */
/* The leading dimension of the work arrays. */
/* NMAX >= the maximum value of N in NVAL. */
/* AB (workspace) COMPLEX array, dimension (NMAX*NMAX) */
/* AINV (workspace) COMPLEX array, dimension (NMAX*NMAX) */
/* B (workspace) COMPLEX array, dimension (NMAX*NSMAX) */
/* where NSMAX is the largest entry in NSVAL. */
/* X (workspace) COMPLEX array, dimension (NMAX*NSMAX) */
/* XACT (workspace) COMPLEX array, dimension (NMAX*NSMAX) */
/* WORK (workspace) COMPLEX array, dimension */
/* (NMAX*max(3,NSMAX)) */
/* RWORK (workspace) REAL array, dimension */
/* (max(NMAX,2*NSMAX)) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--rwork;
--work;
--xact;
--x;
--b;
--ainv;
--ab;
--nsval;
--nval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Complex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "TB", (ftnlen)2, (ftnlen)2);
nrun = 0;
nfail = 0;
nerrs = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
/* Test the error exits */
if (*tsterr) {
cerrtr_(path, nout);
}
infoc_1.infot = 0;
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
/* Do for each value of N in NVAL */
n = nval[in];
lda = max(1,n);
*(unsigned char *)xtype = 'N';
nimat = 9;
nimat2 = 17;
if (n <= 0) {
nimat = 1;
nimat2 = 10;
}
/* Computing MIN */
i__2 = n + 1;
nk = min(i__2,4);
i__2 = nk;
for (ik = 1; ik <= i__2; ++ik) {
/* Do for KD = 0, N, (3N-1)/4, and (N+1)/4. This order makes */
/* it easier to skip redundant values for small values of N. */
if (ik == 1) {
kd = 0;
} else if (ik == 2) {
kd = max(n,0);
} else if (ik == 3) {
kd = (n * 3 - 1) / 4;
} else if (ik == 4) {
kd = (n + 1) / 4;
}
ldab = kd + 1;
i__3 = nimat;
for (imat = 1; imat <= i__3; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L90;
}
for (iuplo = 1; iuplo <= 2; ++iuplo) {
/* Do first for UPLO = 'U', then for UPLO = 'L' */
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo -
1];
/* Call CLATTB to generate a triangular test matrix. */
s_copy(srnamc_1.srnamt, "CLATTB", (ftnlen)32, (ftnlen)6);
clattb_(&imat, uplo, "No transpose", diag, iseed, &n, &kd,
&ab[1], &ldab, &x[1], &work[1], &rwork[1], &info);
/* Set IDIAG = 1 for non-unit matrices, 2 for unit. */
if (lsame_(diag, "N")) {
idiag = 1;
} else {
idiag = 2;
}
/* Form the inverse of A so we can get a good estimate */
/* of RCONDC = 1/(norm(A) * norm(inv(A))). */
claset_("Full", &n, &n, &c_b14, &c_b15, &ainv[1], &lda);
if (lsame_(uplo, "U")) {
i__4 = n;
for (j = 1; j <= i__4; ++j) {
ctbsv_(uplo, "No transpose", diag, &j, &kd, &ab[1]
, &ldab, &ainv[(j - 1) * lda + 1], &c__1);
/* L20: */
}
} else {
i__4 = n;
for (j = 1; j <= i__4; ++j) {
i__5 = n - j + 1;
ctbsv_(uplo, "No transpose", diag, &i__5, &kd, &
ab[(j - 1) * ldab + 1], &ldab, &ainv[(j -
1) * lda + j], &c__1);
/* L30: */
}
}
/* Compute the 1-norm condition number of A. */
anorm = clantb_("1", uplo, diag, &n, &kd, &ab[1], &ldab, &
rwork[1]);
ainvnm = clantr_("1", uplo, diag, &n, &n, &ainv[1], &lda,
&rwork[1]);
if (anorm <= 0.f || ainvnm <= 0.f) {
rcondo = 1.f;
} else {
rcondo = 1.f / anorm / ainvnm;
}
/* Compute the infinity-norm condition number of A. */
anorm = clantb_("I", uplo, diag, &n, &kd, &ab[1], &ldab, &
rwork[1]);
ainvnm = clantr_("I", uplo, diag, &n, &n, &ainv[1], &lda,
&rwork[1]);
if (anorm <= 0.f || ainvnm <= 0.f) {
rcondi = 1.f;
} else {
rcondi = 1.f / anorm / ainvnm;
}
i__4 = *nns;
for (irhs = 1; irhs <= i__4; ++irhs) {
nrhs = nsval[irhs];
*(unsigned char *)xtype = 'N';
for (itran = 1; itran <= 3; ++itran) {
/* Do for op(A) = A, A**T, or A**H. */
*(unsigned char *)trans = *(unsigned char *)&
transs[itran - 1];
if (itran == 1) {
*(unsigned char *)norm = 'O';
rcondc = rcondo;
} else {
*(unsigned char *)norm = 'I';
rcondc = rcondi;
}
/* + TEST 1 */
/* Solve and compute residual for op(A)*x = b. */
s_copy(srnamc_1.srnamt, "CLARHS", (ftnlen)32, (
ftnlen)6);
clarhs_(path, xtype, uplo, trans, &n, &n, &kd, &
idiag, &nrhs, &ab[1], &ldab, &xact[1], &
lda, &b[1], &lda, iseed, &info);
*(unsigned char *)xtype = 'C';
clacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &
lda);
s_copy(srnamc_1.srnamt, "CTBTRS", (ftnlen)32, (
ftnlen)6);
ctbtrs_(uplo, trans, diag, &n, &kd, &nrhs, &ab[1],
&ldab, &x[1], &lda, &info);
/* Check error code from CTBTRS. */
if (info != 0) {
/* Writing concatenation */
i__6[0] = 1, a__1[0] = uplo;
i__6[1] = 1, a__1[1] = trans;
i__6[2] = 1, a__1[2] = diag;
s_cat(ch__1, a__1, i__6, &c__3, (ftnlen)3);
alaerh_(path, "CTBTRS", &info, &c__0, ch__1, &
n, &n, &kd, &kd, &nrhs, &imat, &nfail,
&nerrs, nout);
}
ctbt02_(uplo, trans, diag, &n, &kd, &nrhs, &ab[1],
&ldab, &x[1], &lda, &b[1], &lda, &work[1]
, &rwork[1], result);
/* + TEST 2 */
/* Check solution from generated exact solution. */
cget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[1]);
/* + TESTS 3, 4, and 5 */
/* Use iterative refinement to improve the solution */
/* and compute error bounds. */
s_copy(srnamc_1.srnamt, "CTBRFS", (ftnlen)32, (
ftnlen)6);
ctbrfs_(uplo, trans, diag, &n, &kd, &nrhs, &ab[1],
&ldab, &b[1], &lda, &x[1], &lda, &rwork[
1], &rwork[nrhs + 1], &work[1], &rwork[(
nrhs << 1) + 1], &info);
/* Check error code from CTBRFS. */
if (info != 0) {
/* Writing concatenation */
i__6[0] = 1, a__1[0] = uplo;
i__6[1] = 1, a__1[1] = trans;
i__6[2] = 1, a__1[2] = diag;
s_cat(ch__1, a__1, i__6, &c__3, (ftnlen)3);
alaerh_(path, "CTBRFS", &info, &c__0, ch__1, &
n, &n, &kd, &kd, &nrhs, &imat, &nfail,
&nerrs, nout);
}
cget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[2]);
ctbt05_(uplo, trans, diag, &n, &kd, &nrhs, &ab[1],
&ldab, &b[1], &lda, &x[1], &lda, &xact[1]
, &lda, &rwork[1], &rwork[nrhs + 1], &
result[3]);
/* Print information about the tests that did not */
/* pass the threshold. */
for (k = 1; k <= 5; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___39.ciunit = *nout;
s_wsfe(&io___39);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, diag, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&kd, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&nrhs, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[k - 1], (
ftnlen)sizeof(real));
e_wsfe();
++nfail;
}
/* L40: */
}
nrun += 5;
/* L50: */
}
/* L60: */
}
/* + TEST 6 */
/* Get an estimate of RCOND = 1/CNDNUM. */
for (itran = 1; itran <= 2; ++itran) {
if (itran == 1) {
*(unsigned char *)norm = 'O';
rcondc = rcondo;
} else {
*(unsigned char *)norm = 'I';
rcondc = rcondi;
}
s_copy(srnamc_1.srnamt, "CTBCON", (ftnlen)32, (ftnlen)
6);
ctbcon_(norm, uplo, diag, &n, &kd, &ab[1], &ldab, &
rcond, &work[1], &rwork[1], &info);
/* Check error code from CTBCON. */
if (info != 0) {
/* Writing concatenation */
i__6[0] = 1, a__1[0] = norm;
i__6[1] = 1, a__1[1] = uplo;
i__6[2] = 1, a__1[2] = diag;
s_cat(ch__1, a__1, i__6, &c__3, (ftnlen)3);
alaerh_(path, "CTBCON", &info, &c__0, ch__1, &n, &
n, &kd, &kd, &c_n1, &imat, &nfail, &nerrs,
nout);
}
ctbt06_(&rcond, &rcondc, uplo, diag, &n, &kd, &ab[1],
&ldab, &rwork[1], &result[5]);
/* Print the test ratio if it is .GE. THRESH. */
if (result[5] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___41.ciunit = *nout;
s_wsfe(&io___41);
do_fio(&c__1, "CTBCON", (ftnlen)6);
do_fio(&c__1, norm, (ftnlen)1);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, diag, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&kd, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&c__6, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[5], (ftnlen)sizeof(
real));
e_wsfe();
++nfail;
}
++nrun;
/* L70: */
}
/* L80: */
}
L90:
;
}
/* Use pathological test matrices to test CLATBS. */
i__3 = nimat2;
for (imat = 10; imat <= i__3; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L120;
}
for (iuplo = 1; iuplo <= 2; ++iuplo) {
/* Do first for UPLO = 'U', then for UPLO = 'L' */
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo -
1];
for (itran = 1; itran <= 3; ++itran) {
/* Do for op(A) = A, A**T, and A**H. */
*(unsigned char *)trans = *(unsigned char *)&transs[
itran - 1];
/* Call CLATTB to generate a triangular test matrix. */
s_copy(srnamc_1.srnamt, "CLATTB", (ftnlen)32, (ftnlen)
6);
clattb_(&imat, uplo, trans, diag, iseed, &n, &kd, &ab[
1], &ldab, &x[1], &work[1], &rwork[1], &info);
/* + TEST 7 */
/* Solve the system op(A)*x = b */
s_copy(srnamc_1.srnamt, "CLATBS", (ftnlen)32, (ftnlen)
6);
ccopy_(&n, &x[1], &c__1, &b[1], &c__1);
clatbs_(uplo, trans, diag, "N", &n, &kd, &ab[1], &
ldab, &b[1], &scale, &rwork[1], &info);
/* Check error code from CLATBS. */
if (info != 0) {
/* Writing concatenation */
i__7[0] = 1, a__2[0] = uplo;
i__7[1] = 1, a__2[1] = trans;
i__7[2] = 1, a__2[2] = diag;
i__7[3] = 1, a__2[3] = "N";
s_cat(ch__2, a__2, i__7, &c__4, (ftnlen)4);
alaerh_(path, "CLATBS", &info, &c__0, ch__2, &n, &
n, &kd, &kd, &c_n1, &imat, &nfail, &nerrs,
nout);
}
ctbt03_(uplo, trans, diag, &n, &kd, &c__1, &ab[1], &
ldab, &scale, &rwork[1], &c_b90, &b[1], &lda,
&x[1], &lda, &work[1], &result[6]);
/* + TEST 8 */
/* Solve op(A)*x = b again with NORMIN = 'Y'. */
ccopy_(&n, &x[1], &c__1, &b[1], &c__1);
clatbs_(uplo, trans, diag, "Y", &n, &kd, &ab[1], &
ldab, &b[1], &scale, &rwork[1], &info);
/* Check error code from CLATBS. */
if (info != 0) {
/* Writing concatenation */
i__7[0] = 1, a__2[0] = uplo;
i__7[1] = 1, a__2[1] = trans;
i__7[2] = 1, a__2[2] = diag;
i__7[3] = 1, a__2[3] = "Y";
s_cat(ch__2, a__2, i__7, &c__4, (ftnlen)4);
alaerh_(path, "CLATBS", &info, &c__0, ch__2, &n, &
n, &kd, &kd, &c_n1, &imat, &nfail, &nerrs,
nout);
}
ctbt03_(uplo, trans, diag, &n, &kd, &c__1, &ab[1], &
ldab, &scale, &rwork[1], &c_b90, &b[1], &lda,
&x[1], &lda, &work[1], &result[7]);
/* Print information about the tests that did not pass */
/* the threshold. */
if (result[6] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___43.ciunit = *nout;
s_wsfe(&io___43);
do_fio(&c__1, "CLATBS", (ftnlen)6);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, diag, (ftnlen)1);
do_fio(&c__1, "N", (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&kd, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&c__7, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof(
real));
e_wsfe();
++nfail;
}
if (result[7] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___44.ciunit = *nout;
s_wsfe(&io___44);
do_fio(&c__1, "CLATBS", (ftnlen)6);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, diag, (ftnlen)1);
do_fio(&c__1, "Y", (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&kd, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&c__8, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof(
real));
e_wsfe();
++nfail;
}
nrun += 2;
/* L100: */
}
/* L110: */
}
L120:
;
}
/* L130: */
}
/* L140: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of CCHKTB */
} /* cchktb_ */
/* Subroutine */ int cgbtrs_(char *trans, integer *n, integer *kl, integer *
ku, integer *nrhs, complex *ab, integer *ldab, integer *ipiv, complex
*b, integer *ldb, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CGBTRS solves a system of linear equations
A * X = B, A**T * X = B, or A**H * X = B
with a general band matrix A using the LU factorization computed
by CGBTRF.
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 matrix B. NRHS >= 0.
AB (input) COMPLEX array, dimension (LDAB,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.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
IPIV (input) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the matrix was
interchanged with row IPIV(i).
B (input/output) COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static complex c_b1 = {1.f,0.f};
static integer c__1 = 1;
/* System generated locals */
integer ab_dim1, ab_offset, b_dim1, b_offset, i__1, i__2, i__3;
complex q__1;
/* Local variables */
static integer i__, j, l;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *), cgeru_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
cswap_(integer *, complex *, integer *, complex *, integer *),
ctbsv_(char *, char *, char *, integer *, integer *, complex *,
integer *, complex *, integer *);
static logical lnoti;
static integer kd, lm;
extern /* Subroutine */ int clacgv_(integer *, complex *, integer *),
xerbla_(char *, integer *);
static logical notran;
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define ab_subscr(a_1,a_2) (a_2)*ab_dim1 + a_1
#define ab_ref(a_1,a_2) ab[ab_subscr(a_1,a_2)]
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1 * 1;
ab -= ab_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* 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 << 1) + *ku + 1) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGBTRS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
return 0;
}
kd = *ku + *kl + 1;
lnoti = *kl > 0;
if (notran) {
/* Solve A*X = B.
Solve L*X = B, overwriting B with X.
L is represented as a product of permutations and unit lower
triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1),
where each transformation L(i) is a rank-one modification of
the identity matrix. */
if (lnoti) {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__2 = *kl, i__3 = *n - j;
lm = min(i__2,i__3);
l = ipiv[j];
if (l != j) {
cswap_(nrhs, &b_ref(l, 1), ldb, &b_ref(j, 1), ldb);
}
q__1.r = -1.f, q__1.i = 0.f;
cgeru_(&lm, nrhs, &q__1, &ab_ref(kd + 1, j), &c__1, &b_ref(j,
1), ldb, &b_ref(j + 1, 1), ldb);
/* L10: */
}
}
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Solve U*X = B, overwriting B with X. */
i__2 = *kl + *ku;
ctbsv_("Upper", "No transpose", "Non-unit", n, &i__2, &ab[
ab_offset], ldab, &b_ref(1, i__), &c__1);
/* L20: */
}
} else if (lsame_(trans, "T")) {
/* Solve A**T * X = B. */
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Solve U**T * X = B, overwriting B with X. */
i__2 = *kl + *ku;
ctbsv_("Upper", "Transpose", "Non-unit", n, &i__2, &ab[ab_offset],
ldab, &b_ref(1, i__), &c__1);
/* L30: */
}
/* Solve L**T * X = B, overwriting B with X. */
if (lnoti) {
for (j = *n - 1; j >= 1; --j) {
/* Computing MIN */
i__1 = *kl, i__2 = *n - j;
lm = min(i__1,i__2);
q__1.r = -1.f, q__1.i = 0.f;
cgemv_("Transpose", &lm, nrhs, &q__1, &b_ref(j + 1, 1), ldb, &
ab_ref(kd + 1, j), &c__1, &c_b1, &b_ref(j, 1), ldb);
l = ipiv[j];
if (l != j) {
cswap_(nrhs, &b_ref(l, 1), ldb, &b_ref(j, 1), ldb);
}
/* L40: */
}
}
} else {
/* Solve A**H * X = B. */
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Solve U**H * X = B, overwriting B with X. */
i__2 = *kl + *ku;
ctbsv_("Upper", "Conjugate transpose", "Non-unit", n, &i__2, &ab[
ab_offset], ldab, &b_ref(1, i__), &c__1);
/* L50: */
}
/* Solve L**H * X = B, overwriting B with X. */
if (lnoti) {
for (j = *n - 1; j >= 1; --j) {
/* Computing MIN */
i__1 = *kl, i__2 = *n - j;
lm = min(i__1,i__2);
clacgv_(nrhs, &b_ref(j, 1), ldb);
q__1.r = -1.f, q__1.i = 0.f;
cgemv_("Conjugate transpose", &lm, nrhs, &q__1, &b_ref(j + 1,
1), ldb, &ab_ref(kd + 1, j), &c__1, &c_b1, &b_ref(j,
1), ldb);
clacgv_(nrhs, &b_ref(j, 1), ldb);
l = ipiv[j];
if (l != j) {
cswap_(nrhs, &b_ref(l, 1), ldb, &b_ref(j, 1), ldb);
}
/* L60: */
}
}
}
return 0;
/* End of CGBTRS */
} /* cgbtrs_ */
int ctbrfs_(char *uplo, char *trans, char *diag, int *n,
int *kd, int *nrhs, complex *ab, int *ldab, complex *b,
int *ldb, complex *x, int *ldx, float *ferr, float *berr,
complex *work, float *rwork, int *info)
{
/* System generated locals */
int ab_dim1, ab_offset, b_dim1, b_offset, x_dim1, x_offset, i__1,
i__2, i__3, i__4, i__5;
float r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
int i__, j, k;
float s, xk;
int nz;
float eps;
int kase;
float safe1, safe2;
extern int lsame_(char *, char *);
int isave[3];
extern int ctbmv_(char *, char *, char *, int *,
int *, complex *, int *, complex *, int *), ccopy_(int *, complex *, int *, complex *
, int *), ctbsv_(char *, char *, char *, int *, int *,
complex *, int *, complex *, int *), caxpy_(int *, complex *, complex *, int *,
complex *, int *);
int upper;
extern int clacn2_(int *, complex *, complex *, float
*, int *, int *);
extern double slamch_(char *);
float safmin;
extern int xerbla_(char *, int *);
int notran;
char transn[1], transt[1];
int nounit;
float 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 */
/* ======= */
/* CTBRFS provides error bounds and backward error estimates for the */
/* solution to a system of linear equations with a triangular band */
/* coefficient matrix. */
/* The solution matrix X must be computed by CTBTRS or some other */
/* means before entering this routine. CTBRFS does not do iterative */
/* refinement because doing so cannot improve the backward error. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': A is upper triangular; */
/* = 'L': A is lower triangular. */
/* 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) */
/* DIAG (input) CHARACTER*1 */
/* = 'N': A is non-unit triangular; */
/* = 'U': A is unit triangular. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of superdiagonals or subdiagonals of the */
/* triangular band matrix A. KD >= 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 upper or lower triangular band matrix A, stored in the */
/* first kd+1 rows of the array. The j-th column of A is stored */
/* in the j-th column of the array AB as follows: */
/* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for MAX(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=MIN(n,j+kd). */
/* If DIAG = 'U', the diagonal elements of A are not referenced */
/* and are assumed to be 1. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* 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) COMPLEX array, dimension (LDX,NRHS) */
/* The 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 */
/* ===================================================================== */
/* .. 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;
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;
upper = lsame_(uplo, "U");
notran = lsame_(trans, "N");
nounit = lsame_(diag, "N");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T") && !
lsame_(trans, "C")) {
*info = -2;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*kd < 0) {
*info = -5;
} else if (*nrhs < 0) {
*info = -6;
} else if (*ldab < *kd + 1) {
*info = -8;
} else if (*ldb < MAX(1,*n)) {
*info = -10;
} else if (*ldx < MAX(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CTBRFS", &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 */
nz = *kd + 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) {
/* Compute residual R = B - op(A) * X, */
/* where op(A) = A, A**T, or A**H, depending on TRANS. */
ccopy_(n, &x[j * x_dim1 + 1], &c__1, &work[1], &c__1);
ctbmv_(uplo, trans, diag, n, kd, &ab[ab_offset], ldab, &work[1], &
c__1);
q__1.r = -1.f, q__1.i = -0.f;
caxpy_(n, &q__1, &b[j * b_dim1 + 1], &c__1, &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, ABS(r__1)) + (r__2 = r_imag(&b[
i__ + j * b_dim1]), ABS(r__2));
/* L20: */
}
if (notran) {
/* Compute ABS(A)*ABS(X) + ABS(B). */
if (upper) {
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, ABS(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), ABS(r__2));
/* Computing MAX */
i__3 = 1, i__4 = k - *kd;
i__5 = k;
for (i__ = MAX(i__3,i__4); i__ <= i__5; ++i__) {
i__3 = *kd + 1 + i__ - k + k * ab_dim1;
rwork[i__] += ((r__1 = ab[i__3].r, ABS(r__1)) + (
r__2 = r_imag(&ab[*kd + 1 + i__ - k + k *
ab_dim1]), ABS(r__2))) * xk;
/* L30: */
}
/* L40: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__5 = k + j * x_dim1;
xk = (r__1 = x[i__5].r, ABS(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), ABS(r__2));
/* Computing MAX */
i__5 = 1, i__3 = k - *kd;
i__4 = k - 1;
for (i__ = MAX(i__5,i__3); i__ <= i__4; ++i__) {
i__5 = *kd + 1 + i__ - k + k * ab_dim1;
rwork[i__] += ((r__1 = ab[i__5].r, ABS(r__1)) + (
r__2 = r_imag(&ab[*kd + 1 + i__ - k + k *
ab_dim1]), ABS(r__2))) * xk;
/* L50: */
}
rwork[k] += xk;
/* L60: */
}
}
} else {
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__4 = k + j * x_dim1;
xk = (r__1 = x[i__4].r, ABS(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), ABS(r__2));
/* Computing MIN */
i__5 = *n, i__3 = k + *kd;
i__4 = MIN(i__5,i__3);
for (i__ = k; i__ <= i__4; ++i__) {
i__5 = i__ + 1 - k + k * ab_dim1;
rwork[i__] += ((r__1 = ab[i__5].r, ABS(r__1)) + (
r__2 = r_imag(&ab[i__ + 1 - k + k *
ab_dim1]), ABS(r__2))) * xk;
/* L70: */
}
/* L80: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__4 = k + j * x_dim1;
xk = (r__1 = x[i__4].r, ABS(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), ABS(r__2));
/* Computing MIN */
i__5 = *n, i__3 = k + *kd;
i__4 = MIN(i__5,i__3);
for (i__ = k + 1; i__ <= i__4; ++i__) {
i__5 = i__ + 1 - k + k * ab_dim1;
rwork[i__] += ((r__1 = ab[i__5].r, ABS(r__1)) + (
r__2 = r_imag(&ab[i__ + 1 - k + k *
ab_dim1]), ABS(r__2))) * xk;
/* L90: */
}
rwork[k] += xk;
/* L100: */
}
}
}
} else {
/* Compute ABS(A**H)*ABS(X) + ABS(B). */
if (upper) {
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
/* Computing MAX */
i__4 = 1, i__5 = k - *kd;
i__3 = k;
for (i__ = MAX(i__4,i__5); i__ <= i__3; ++i__) {
i__4 = *kd + 1 + i__ - k + k * ab_dim1;
i__5 = i__ + j * x_dim1;
s += ((r__1 = ab[i__4].r, ABS(r__1)) + (r__2 =
r_imag(&ab[*kd + 1 + i__ - k + k *
ab_dim1]), ABS(r__2))) * ((r__3 = x[i__5]
.r, ABS(r__3)) + (r__4 = r_imag(&x[i__ +
j * x_dim1]), ABS(r__4)));
/* L110: */
}
rwork[k] += s;
/* L120: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
s = (r__1 = x[i__3].r, ABS(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), ABS(r__2));
/* Computing MAX */
i__3 = 1, i__4 = k - *kd;
i__5 = k - 1;
for (i__ = MAX(i__3,i__4); i__ <= i__5; ++i__) {
i__3 = *kd + 1 + i__ - k + k * ab_dim1;
i__4 = i__ + j * x_dim1;
s += ((r__1 = ab[i__3].r, ABS(r__1)) + (r__2 =
r_imag(&ab[*kd + 1 + i__ - k + k *
ab_dim1]), ABS(r__2))) * ((r__3 = x[i__4]
.r, ABS(r__3)) + (r__4 = r_imag(&x[i__ +
j * x_dim1]), ABS(r__4)));
/* L130: */
}
rwork[k] += s;
/* L140: */
}
}
} else {
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
/* Computing MIN */
i__3 = *n, i__4 = k + *kd;
i__5 = MIN(i__3,i__4);
for (i__ = k; i__ <= i__5; ++i__) {
i__3 = i__ + 1 - k + k * ab_dim1;
i__4 = i__ + j * x_dim1;
s += ((r__1 = ab[i__3].r, ABS(r__1)) + (r__2 =
r_imag(&ab[i__ + 1 - k + k * ab_dim1]),
ABS(r__2))) * ((r__3 = x[i__4].r, ABS(
r__3)) + (r__4 = r_imag(&x[i__ + j *
x_dim1]), ABS(r__4)));
/* L150: */
}
rwork[k] += s;
/* L160: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__5 = k + j * x_dim1;
s = (r__1 = x[i__5].r, ABS(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), ABS(r__2));
/* Computing MIN */
i__3 = *n, i__4 = k + *kd;
i__5 = MIN(i__3,i__4);
for (i__ = k + 1; i__ <= i__5; ++i__) {
i__3 = i__ + 1 - k + k * ab_dim1;
i__4 = i__ + j * x_dim1;
s += ((r__1 = ab[i__3].r, ABS(r__1)) + (r__2 =
r_imag(&ab[i__ + 1 - k + k * ab_dim1]),
ABS(r__2))) * ((r__3 = x[i__4].r, ABS(
r__3)) + (r__4 = r_imag(&x[i__ + j *
x_dim1]), ABS(r__4)));
/* L170: */
}
rwork[k] += s;
/* L180: */
}
}
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__5 = i__;
r__3 = s, r__4 = ((r__1 = work[i__5].r, ABS(r__1)) + (r__2 =
r_imag(&work[i__]), ABS(r__2))) / rwork[i__];
s = MAX(r__3,r__4);
} else {
/* Computing MAX */
i__5 = i__;
r__3 = s, r__4 = ((r__1 = work[i__5].r, ABS(r__1)) + (r__2 =
r_imag(&work[i__]), ABS(r__2)) + safe1) / (rwork[i__]
+ safe1);
s = MAX(r__3,r__4);
}
/* L190: */
}
berr[j] = s;
/* 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__5 = i__;
rwork[i__] = (r__1 = work[i__5].r, ABS(r__1)) + (r__2 =
r_imag(&work[i__]), ABS(r__2)) + nz * eps * rwork[
i__];
} else {
i__5 = i__;
rwork[i__] = (r__1 = work[i__5].r, ABS(r__1)) + (r__2 =
r_imag(&work[i__]), ABS(r__2)) + nz * eps * rwork[
i__] + safe1;
}
/* L200: */
}
kase = 0;
L210:
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). */
ctbsv_(uplo, transt, diag, n, kd, &ab[ab_offset], ldab, &work[
1], &c__1);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__5 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = rwork[i__3] * work[i__4].r, q__1.i = rwork[i__3]
* work[i__4].i;
work[i__5].r = q__1.r, work[i__5].i = q__1.i;
/* L220: */
}
} else {
/* Multiply by inv(op(A))*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__5 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = rwork[i__3] * work[i__4].r, q__1.i = rwork[i__3]
* work[i__4].i;
work[i__5].r = q__1.r, work[i__5].i = q__1.i;
/* L230: */
}
ctbsv_(uplo, transn, diag, n, kd, &ab[ab_offset], ldab, &work[
1], &c__1);
}
goto L210;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__5 = i__ + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = x[i__5].r, ABS(r__1)) + (r__2 =
r_imag(&x[i__ + j * x_dim1]), ABS(r__2));
lstres = MAX(r__3,r__4);
/* L240: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L250: */
}
return 0;
/* End of CTBRFS */
} /* ctbrfs_ */
