/* dlantb.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
doublereal dlantb_(char *norm, char *uplo, char *diag, integer *n, integer *k,
doublereal *ab, integer *ldab, doublereal *work)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5;
doublereal ret_val, d__1, d__2, d__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, l;
doublereal sum, scale;
logical udiag;
extern logical lsame_(char *, char *);
doublereal value;
extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *,
doublereal *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLANTB returns the value of the one norm, or the Frobenius norm, or */
/* the infinity norm, or the element of largest absolute value of an */
/* n by n triangular band matrix A, with ( k + 1 ) diagonals. */
/* Description */
/* =========== */
/* DLANTB returns the value */
/* DLANTB = ( max(abs(A(i,j))), NORM = 'M' or 'm' */
/* ( */
/* ( norm1(A), NORM = '1', 'O' or 'o' */
/* ( */
/* ( normI(A), NORM = 'I' or 'i' */
/* ( */
/* ( normF(A), NORM = 'F', 'f', 'E' or 'e' */
/* where norm1 denotes the one norm of a matrix (maximum column sum), */
/* normI denotes the infinity norm of a matrix (maximum row sum) and */
/* normF denotes the Frobenius norm of a matrix (square root of sum of */
/* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */
/* Arguments */
/* ========= */
/* NORM (input) CHARACTER*1 */
/* Specifies the value to be returned in DLANTB as described */
/* above. */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the matrix A is upper or lower triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* DIAG (input) CHARACTER*1 */
/* Specifies whether or not the matrix A is unit triangular. */
/* = 'N': Non-unit triangular */
/* = 'U': Unit triangular */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. When N = 0, DLANTB is */
/* set to zero. */
/* K (input) INTEGER */
/* The number of super-diagonals of the matrix A if UPLO = 'U', */
/* or the number of sub-diagonals of the matrix A if UPLO = 'L'. */
/* K >= 0. */
/* AB (input) DOUBLE PRECISION array, dimension (LDAB,N) */
/* The upper or lower triangular band matrix A, stored in the */
/* first k+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(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). */
/* Note that when DIAG = 'U', the elements of the array AB */
/* corresponding to the diagonal elements of the matrix A are */
/* not referenced, but are assumed to be one. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= K+1. */
/* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */
/* where LWORK >= N when NORM = 'I'; otherwise, WORK is not */
/* referenced. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--work;
/* Function Body */
if (*n == 0) {
value = 0.;
} else if (lsame_(norm, "M")) {
/* Find max(abs(A(i,j))). */
if (lsame_(diag, "U")) {
value = 1.;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = *k + 2 - j;
i__3 = *k;
for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
/* Computing MAX */
d__2 = value, d__3 = (d__1 = ab[i__ + j * ab_dim1],
abs(d__1));
value = max(d__2,d__3);
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__2 = *n + 1 - j, i__4 = *k + 1;
i__3 = min(i__2,i__4);
for (i__ = 2; i__ <= i__3; ++i__) {
/* Computing MAX */
d__2 = value, d__3 = (d__1 = ab[i__ + j * ab_dim1],
abs(d__1));
value = max(d__2,d__3);
/* L30: */
}
/* L40: */
}
}
} else {
value = 0.;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__3 = *k + 2 - j;
i__2 = *k + 1;
for (i__ = max(i__3,1); i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = value, d__3 = (d__1 = ab[i__ + j * ab_dim1],
abs(d__1));
value = max(d__2,d__3);
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *n + 1 - j, i__4 = *k + 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = value, d__3 = (d__1 = ab[i__ + j * ab_dim1],
abs(d__1));
value = max(d__2,d__3);
/* L70: */
}
/* L80: */
}
}
}
} else if (lsame_(norm, "O") || *(unsigned char *)
norm == '1') {
/* Find norm1(A). */
value = 0.;
udiag = lsame_(diag, "U");
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (udiag) {
sum = 1.;
/* Computing MAX */
i__2 = *k + 2 - j;
i__3 = *k;
for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
sum += (d__1 = ab[i__ + j * ab_dim1], abs(d__1));
/* L90: */
}
} else {
sum = 0.;
/* Computing MAX */
i__3 = *k + 2 - j;
i__2 = *k + 1;
for (i__ = max(i__3,1); i__ <= i__2; ++i__) {
sum += (d__1 = ab[i__ + j * ab_dim1], abs(d__1));
/* L100: */
}
}
value = max(value,sum);
/* L110: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (udiag) {
sum = 1.;
/* Computing MIN */
i__3 = *n + 1 - j, i__4 = *k + 1;
i__2 = min(i__3,i__4);
for (i__ = 2; i__ <= i__2; ++i__) {
sum += (d__1 = ab[i__ + j * ab_dim1], abs(d__1));
/* L120: */
}
} else {
sum = 0.;
/* Computing MIN */
i__3 = *n + 1 - j, i__4 = *k + 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
sum += (d__1 = ab[i__ + j * ab_dim1], abs(d__1));
/* L130: */
}
}
value = max(value,sum);
/* L140: */
}
}
} else if (lsame_(norm, "I")) {
/* Find normI(A). */
value = 0.;
if (lsame_(uplo, "U")) {
if (lsame_(diag, "U")) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 1.;
/* L150: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = *k + 1 - j;
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__4 = j - 1;
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
work[i__] += (d__1 = ab[l + i__ + j * ab_dim1], abs(
d__1));
/* L160: */
}
/* L170: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L180: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = *k + 1 - j;
/* Computing MAX */
i__4 = 1, i__2 = j - *k;
i__3 = j;
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
work[i__] += (d__1 = ab[l + i__ + j * ab_dim1], abs(
d__1));
/* L190: */
}
/* L200: */
}
}
} else {
if (lsame_(diag, "U")) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 1.;
/* L210: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = 1 - j;
/* Computing MIN */
i__4 = *n, i__2 = j + *k;
i__3 = min(i__4,i__2);
for (i__ = j + 1; i__ <= i__3; ++i__) {
work[i__] += (d__1 = ab[l + i__ + j * ab_dim1], abs(
d__1));
/* L220: */
}
/* L230: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L240: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = 1 - j;
/* Computing MIN */
i__4 = *n, i__2 = j + *k;
i__3 = min(i__4,i__2);
for (i__ = j; i__ <= i__3; ++i__) {
work[i__] += (d__1 = ab[l + i__ + j * ab_dim1], abs(
d__1));
/* L250: */
}
/* L260: */
}
}
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = work[i__];
value = max(d__1,d__2);
/* L270: */
}
} else if (lsame_(norm, "F") || lsame_(norm, "E")) {
/* Find normF(A). */
if (lsame_(uplo, "U")) {
if (lsame_(diag, "U")) {
scale = 1.;
sum = (doublereal) (*n);
if (*k > 0) {
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
/* Computing MIN */
i__4 = j - 1;
i__3 = min(i__4,*k);
/* Computing MAX */
i__2 = *k + 2 - j;
dlassq_(&i__3, &ab[max(i__2, 1)+ j * ab_dim1], &c__1,
&scale, &sum);
/* L280: */
}
}
} else {
scale = 0.;
sum = 1.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__4 = j, i__2 = *k + 1;
i__3 = min(i__4,i__2);
/* Computing MAX */
i__5 = *k + 2 - j;
dlassq_(&i__3, &ab[max(i__5, 1)+ j * ab_dim1], &c__1, &
scale, &sum);
/* L290: */
}
}
} else {
if (lsame_(diag, "U")) {
scale = 1.;
sum = (doublereal) (*n);
if (*k > 0) {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__4 = *n - j;
i__3 = min(i__4,*k);
dlassq_(&i__3, &ab[j * ab_dim1 + 2], &c__1, &scale, &
sum);
/* L300: */
}
}
} else {
scale = 0.;
sum = 1.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__4 = *n - j + 1, i__2 = *k + 1;
i__3 = min(i__4,i__2);
dlassq_(&i__3, &ab[j * ab_dim1 + 1], &c__1, &scale, &sum);
/* L310: */
}
}
}
value = scale * sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of DLANTB */
} /* dlantb_ */