#include "blaswrap.h" #include "f2c.h" doublereal dlangt_(char *norm, integer *n, doublereal *dl, doublereal *d__, doublereal *du) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DLANGT returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A. Description =========== DLANGT returns the value DLANGT = ( 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 DLANGT as described above. N (input) INTEGER The order of the matrix A. N >= 0. When N = 0, DLANGT is set to zero. DL (input) DOUBLE PRECISION array, dimension (N-1) The (n-1) sub-diagonal elements of A. D (input) DOUBLE PRECISION array, dimension (N) The diagonal elements of A. DU (input) DOUBLE PRECISION array, dimension (N-1) The (n-1) super-diagonal elements of A. ===================================================================== Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; /* System generated locals */ integer i__1; doublereal ret_val, d__1, d__2, d__3, d__4, d__5; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer i__; static doublereal sum, scale; extern logical lsame_(char *, char *); static doublereal anorm; extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, doublereal *, doublereal *); --du; --d__; --dl; /* Function Body */ if (*n <= 0) { anorm = 0.; } else if (lsame_(norm, "M")) { /* Find max(abs(A(i,j))). */ anorm = (d__1 = d__[*n], abs(d__1)); i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ d__2 = anorm, d__3 = (d__1 = dl[i__], abs(d__1)); anorm = max(d__2,d__3); /* Computing MAX */ d__2 = anorm, d__3 = (d__1 = d__[i__], abs(d__1)); anorm = max(d__2,d__3); /* Computing MAX */ d__2 = anorm, d__3 = (d__1 = du[i__], abs(d__1)); anorm = max(d__2,d__3); /* L10: */ } } else if (lsame_(norm, "O") || *(unsigned char *) norm == '1') { /* Find norm1(A). */ if (*n == 1) { anorm = abs(d__[1]); } else { /* Computing MAX */ d__3 = abs(d__[1]) + abs(dl[1]), d__4 = (d__1 = d__[*n], abs(d__1) ) + (d__2 = du[*n - 1], abs(d__2)); anorm = max(d__3,d__4); i__1 = *n - 1; for (i__ = 2; i__ <= i__1; ++i__) { /* Computing MAX */ d__4 = anorm, d__5 = (d__1 = d__[i__], abs(d__1)) + (d__2 = dl[i__], abs(d__2)) + (d__3 = du[i__ - 1], abs(d__3)); anorm = max(d__4,d__5); /* L20: */ } } } else if (lsame_(norm, "I")) { /* Find normI(A). */ if (*n == 1) { anorm = abs(d__[1]); } else { /* Computing MAX */ d__3 = abs(d__[1]) + abs(du[1]), d__4 = (d__1 = d__[*n], abs(d__1) ) + (d__2 = dl[*n - 1], abs(d__2)); anorm = max(d__3,d__4); i__1 = *n - 1; for (i__ = 2; i__ <= i__1; ++i__) { /* Computing MAX */ d__4 = anorm, d__5 = (d__1 = d__[i__], abs(d__1)) + (d__2 = du[i__], abs(d__2)) + (d__3 = dl[i__ - 1], abs(d__3)); anorm = max(d__4,d__5); /* L30: */ } } } else if (lsame_(norm, "F") || lsame_(norm, "E")) { /* Find normF(A). */ scale = 0.; sum = 1.; dlassq_(n, &d__[1], &c__1, &scale, &sum); if (*n > 1) { i__1 = *n - 1; dlassq_(&i__1, &dl[1], &c__1, &scale, &sum); i__1 = *n - 1; dlassq_(&i__1, &du[1], &c__1, &scale, &sum); } anorm = scale * sqrt(sum); } ret_val = anorm; return ret_val; /* End of DLANGT */ } /* dlangt_ */