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- /* dlansb.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 _starpu_dlansb_(char *norm, char *uplo, 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;
- doublereal ret_val, d__1, d__2, d__3;
- /* Builtin functions */
- double sqrt(doublereal);
- /* Local variables */
- integer i__, j, l;
- doublereal sum, absa, scale;
- extern logical _starpu_lsame_(char *, char *);
- doublereal value;
- extern /* Subroutine */ int _starpu_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 */
- /* ======= */
- /* DLANSB 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 symmetric band matrix A, with k super-diagonals. */
- /* Description */
- /* =========== */
- /* DLANSB returns the value */
- /* DLANSB = ( 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 DLANSB as described */
- /* above. */
- /* UPLO (input) CHARACTER*1 */
- /* Specifies whether the upper or lower triangular part of the */
- /* band matrix A is supplied. */
- /* = 'U': Upper triangular part is supplied */
- /* = 'L': Lower triangular part is supplied */
- /* N (input) INTEGER */
- /* The order of the matrix A. N >= 0. When N = 0, DLANSB is */
- /* set to zero. */
- /* K (input) INTEGER */
- /* The number of super-diagonals or sub-diagonals of the */
- /* band matrix A. K >= 0. */
- /* AB (input) DOUBLE PRECISION array, dimension (LDAB,N) */
- /* The upper or lower triangle of the symmetric 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). */
- /* 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' or '1' or 'O'; 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 (_starpu_lsame_(norm, "M")) {
- /* Find max(abs(A(i,j))). */
- value = 0.;
- if (_starpu_lsame_(uplo, "U")) {
- i__1 = *n;
- for (j = 1; j <= i__1; ++j) {
- /* Computing MAX */
- i__2 = *k + 2 - j;
- i__3 = *k + 1;
- 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__ = 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);
- /* L30: */
- }
- /* L40: */
- }
- }
- } else if (_starpu_lsame_(norm, "I") || _starpu_lsame_(norm, "O") || *(unsigned char *)norm == '1') {
- /* Find normI(A) ( = norm1(A), since A is symmetric). */
- value = 0.;
- if (_starpu_lsame_(uplo, "U")) {
- i__1 = *n;
- for (j = 1; j <= i__1; ++j) {
- sum = 0.;
- l = *k + 1 - j;
- /* Computing MAX */
- i__3 = 1, i__2 = j - *k;
- i__4 = j - 1;
- for (i__ = max(i__3,i__2); i__ <= i__4; ++i__) {
- absa = (d__1 = ab[l + i__ + j * ab_dim1], abs(d__1));
- sum += absa;
- work[i__] += absa;
- /* L50: */
- }
- work[j] = sum + (d__1 = ab[*k + 1 + j * ab_dim1], abs(d__1));
- /* L60: */
- }
- 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);
- /* L70: */
- }
- } else {
- i__1 = *n;
- for (i__ = 1; i__ <= i__1; ++i__) {
- work[i__] = 0.;
- /* L80: */
- }
- i__1 = *n;
- for (j = 1; j <= i__1; ++j) {
- sum = work[j] + (d__1 = ab[j * ab_dim1 + 1], abs(d__1));
- l = 1 - j;
- /* Computing MIN */
- i__3 = *n, i__2 = j + *k;
- i__4 = min(i__3,i__2);
- for (i__ = j + 1; i__ <= i__4; ++i__) {
- absa = (d__1 = ab[l + i__ + j * ab_dim1], abs(d__1));
- sum += absa;
- work[i__] += absa;
- /* L90: */
- }
- value = max(value,sum);
- /* L100: */
- }
- }
- } else if (_starpu_lsame_(norm, "F") || _starpu_lsame_(norm, "E")) {
- /* Find normF(A). */
- scale = 0.;
- sum = 1.;
- if (*k > 0) {
- if (_starpu_lsame_(uplo, "U")) {
- i__1 = *n;
- for (j = 2; j <= i__1; ++j) {
- /* Computing MIN */
- i__3 = j - 1;
- i__4 = min(i__3,*k);
- /* Computing MAX */
- i__2 = *k + 2 - j;
- _starpu_dlassq_(&i__4, &ab[max(i__2, 1)+ j * ab_dim1], &c__1, &
- scale, &sum);
- /* L110: */
- }
- l = *k + 1;
- } else {
- i__1 = *n - 1;
- for (j = 1; j <= i__1; ++j) {
- /* Computing MIN */
- i__3 = *n - j;
- i__4 = min(i__3,*k);
- _starpu_dlassq_(&i__4, &ab[j * ab_dim1 + 2], &c__1, &scale, &sum);
- /* L120: */
- }
- l = 1;
- }
- sum *= 2;
- } else {
- l = 1;
- }
- _starpu_dlassq_(n, &ab[l + ab_dim1], ldab, &scale, &sum);
- value = scale * sqrt(sum);
- }
- ret_val = value;
- return ret_val;
- /* End of DLANSB */
- } /* _starpu_dlansb_ */
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