langb - langb: general matrix, banded

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realfunctionclangb(characternorm,integern,integerkl,integerku,complex,dimension(ldab,*)ab,integerldab,real,dimension(*)work)CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. Purpose: CLANGB 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. Returns CLANGB CLANGB = ( 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. ParametersNORM NORM is CHARACTER*1 Specifies the value to be returned in CLANGB as described above. N N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANGB is set to zero. KL KL is INTEGER The number of sub-diagonals of the matrix A. KL >= 0. KU KU is INTEGER The number of super-diagonals of the matrix A. KU >= 0. AB AB is COMPLEX 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. WORK WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. doubleprecisionfunctiondlangb(characternorm,integern,integerkl,integerku,doubleprecision,dimension(ldab,*)ab,integerldab,doubleprecision,dimension(*)work)DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. Purpose: DLANGB 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. Returns DLANGB DLANGB = ( 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. ParametersNORM NORM is CHARACTER*1 Specifies the value to be returned in DLANGB as described above. N N is INTEGER The order of the matrix A. N >= 0. When N = 0, DLANGB is set to zero. KL KL is INTEGER The number of sub-diagonals of the matrix A. KL >= 0. KU KU is INTEGER The number of super-diagonals of the matrix A. KU >= 0. AB AB is DOUBLE PRECISION 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. WORK WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. realfunctionslangb(characternorm,integern,integerkl,integerku,real,dimension(ldab,*)ab,integerldab,real,dimension(*)work)SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. 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. Returns SLANGB 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. ParametersNORM NORM is CHARACTER*1 Specifies the value to be returned in SLANGB as described above. N N is INTEGER The order of the matrix A. N >= 0. When N = 0, SLANGB is set to zero. KL KL is INTEGER The number of sub-diagonals of the matrix A. KL >= 0. KU KU is INTEGER The number of super-diagonals of the matrix A. KU >= 0. AB AB is 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. WORK WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. doubleprecisionfunctionzlangb(characternorm,integern,integerkl,integerku,complex*16,dimension(ldab,*)ab,integerldab,doubleprecision,dimension(*)work)ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. Purpose: ZLANGB 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. Returns ZLANGB ZLANGB = ( 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. ParametersNORM NORM is CHARACTER*1 Specifies the value to be returned in ZLANGB as described above. N N is INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANGB is set to zero. KL KL is INTEGER The number of sub-diagonals of the matrix A. KL >= 0. KU KU is INTEGER The number of super-diagonals of the matrix A. KU >= 0. AB AB is COMPLEX*16 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. WORK WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

langb - langb: general matrix, banded

Functions real function clangb (norm, n, kl, ku, ab, ldab, work) CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. double precision function dlangb (norm, n, kl, ku, ab, ldab, work) DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. real function slangb (norm, n, kl, ku, ab, ldab, work) SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. double precision function zlangb (norm, n, kl, ku, ab, ldab, work) ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.