#include "blaswrap.h" #include "f2c.h" doublereal slangb_(char *norm, integer *n, integer *kl, integer *ku, real *ab, integer *ldab, real *work) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SLANGB 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 band matrix A, with kl sub-diagonals and ku super-diagonals. Description =========== SLANGB returns the value SLANGB = ( 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 SLANGB as described above. N (input) INTEGER The order of the matrix A. N >= 0. When N = 0, SLANGB is set to zero. KL (input) INTEGER The number of sub-diagonals of the matrix A. KL >= 0. KU (input) INTEGER The number of super-diagonals of the matrix A. KU >= 0. AB (input) REAL array, dimension (LDAB,N) The band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. WORK (workspace) REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. ===================================================================== Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; /* System generated locals */ integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5, i__6; real ret_val, r__1, r__2, r__3; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer i__, j, k, l; static real sum, scale; extern logical lsame_(char *, char *); static real value; extern /* Subroutine */ int slassq_(integer *, real *, integer *, real *, real *); ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; --work; /* Function Body */ if (*n == 0) { value = 0.f; } else if (lsame_(norm, "M")) { /* Find max(abs(A(i,j))). */ value = 0.f; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = *ku + 2 - j; /* Computing MIN */ i__4 = *n + *ku + 1 - j, i__5 = *kl + *ku + 1; i__3 = min(i__4,i__5); for (i__ = max(i__2,1); i__ <= i__3; ++i__) { /* Computing MAX */ r__2 = value, r__3 = (r__1 = ab[i__ + j * ab_dim1], dabs(r__1) ); value = dmax(r__2,r__3); /* L10: */ } /* L20: */ } } else if (lsame_(norm, "O") || *(unsigned char *) norm == '1') { /* Find norm1(A). */ value = 0.f; i__1 = *n; for (j = 1; j <= i__1; ++j) { sum = 0.f; /* Computing MAX */ i__3 = *ku + 2 - j; /* Computing MIN */ i__4 = *n + *ku + 1 - j, i__5 = *kl + *ku + 1; i__2 = min(i__4,i__5); for (i__ = max(i__3,1); i__ <= i__2; ++i__) { sum += (r__1 = ab[i__ + j * ab_dim1], dabs(r__1)); /* L30: */ } value = dmax(value,sum); /* L40: */ } } else if (lsame_(norm, "I")) { /* Find normI(A). */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { work[i__] = 0.f; /* L50: */ } i__1 = *n; for (j = 1; j <= i__1; ++j) { k = *ku + 1 - j; /* Computing MAX */ i__2 = 1, i__3 = j - *ku; /* Computing MIN */ i__5 = *n, i__6 = j + *kl; i__4 = min(i__5,i__6); for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) { work[i__] += (r__1 = ab[k + i__ + j * ab_dim1], dabs(r__1)); /* L60: */ } /* L70: */ } value = 0.f; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ r__1 = value, r__2 = work[i__]; value = dmax(r__1,r__2); /* L80: */ } } else if (lsame_(norm, "F") || lsame_(norm, "E")) { /* Find normF(A). */ scale = 0.f; sum = 1.f; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__4 = 1, i__2 = j - *ku; l = max(i__4,i__2); k = *ku + 1 - j + l; /* Computing MIN */ i__2 = *n, i__3 = j + *kl; i__4 = min(i__2,i__3) - l + 1; slassq_(&i__4, &ab[k + j * ab_dim1], &c__1, &scale, &sum); /* L90: */ } value = scale * sqrt(sum); } ret_val = value; return ret_val; /* End of SLANGB */ } /* slangb_ */