sgbequ.f(3) [debian man page]
sgbequ.f(3) LAPACK sgbequ.f(3) NAME
sgbequ.f - SYNOPSIS
Functions/Subroutines subroutine sgbequ (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO) SGBEQU Function/Subroutine Documentation subroutine sgbequ (integerM, integerN, integerKL, integerKU, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )R, real, dimension( * )C, realROWCND, realCOLCND, realAMAX, integerINFO) SGBEQU Purpose: SGBEQU computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1. R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A but works well in practice. Parameters: M M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0. KL KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. KU KU is INTEGER The number of superdiagonals within the band of 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(m,j+kl). LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. R R is REAL array, dimension (M) If INFO = 0, or INFO > M, R contains the row scale factors for A. C C is REAL array, dimension (N) If INFO = 0, C contains the column scale factors for A. ROWCND ROWCND is REAL If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R. COLCND COLCND is REAL If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C. AMAX AMAX is REAL Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, and i is <= M: the i-th row of A is exactly zero > M: the (i-M)-th column of A is exactly zero Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Definition at line 153 of file sgbequ.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 sgbequ.f(3)
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sgbequb.f(3) LAPACK sgbequb.f(3) NAME
sgbequb.f - SYNOPSIS
Functions/Subroutines subroutine sgbequb (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO) SGBEQUB Function/Subroutine Documentation subroutine sgbequb (integerM, integerN, integerKL, integerKU, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )R, real, dimension( * )C, realROWCND, realCOLCND, realAMAX, integerINFO) SGBEQUB Purpose: SGBEQUB computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most the radix. R(i) and C(j) are restricted to be a power of the radix between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A but works well in practice. This routine differs from SGEEQU by restricting the scaling factors to a power of the radix. Baring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries' magnitured are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix). Parameters: M M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0. KL KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. KU KU is INTEGER The number of superdiagonals within the band of A. KU >= 0. AB AB is DOUBLE PRECISION array, dimension (LDAB,N) On entry, the matrix A in band storage, 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 A. LDAB >= max(1,M). R R is REAL array, dimension (M) If INFO = 0 or INFO > M, R contains the row scale factors for A. C C is REAL array, dimension (N) If INFO = 0, C contains the column scale factors for A. ROWCND ROWCND is REAL If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R. COLCND COLCND is REAL If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C. AMAX AMAX is REAL Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, and i is <= M: the i-th row of A is exactly zero > M: the (i-M)-th column of A is exactly zero Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Definition at line 160 of file sgbequb.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 sgbequb.f(3)