# csyequb.f(3) [debian man page]

csyequb.f(3) LAPACK csyequb.f(3)NAME

csyequb.f-SYNOPSIS

Functions/Subroutines subroutine csyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) CSYEQUBFunction/Subroutine Documentation subroutine csyequb (characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, real, dimension( * )S, realSCOND, realAMAX, complex, dimension( * )WORK, integerINFO) CSYEQUB Purpose: CSYEQUB computes row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. Parameters: UPLO UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX array, dimension (LDA,N) The N-by-N symmetric matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). S S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A. SCOND SCOND is REAL If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S. 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. WORK WORK is COMPLEX array, dimension (3*N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 References: Livne, O.E. and Golub, G.H., 'Scaling by Binormalization', Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004. DOI 10.1023/B:NUMA.0000016606.32820.69 Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf Definition at line 137 of file csyequb.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.1Sun May 26 2013 csyequb.f(3)

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ssyequb.f(3) LAPACK ssyequb.f(3)NAME

ssyequb.f-SYNOPSIS

Functions/Subroutines subroutine ssyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) SSYEQUBFunction/Subroutine Documentation subroutine ssyequb (characterUPLO, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )S, realSCOND, realAMAX, real, dimension( * )WORK, integerINFO) SSYEQUB Purpose: SSYEQUB computes row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. Parameters: UPLO UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T. N N is INTEGER The order of the matrix A. N >= 0. A A is REAL array, dimension (LDA,N) The N-by-N symmetric matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). S S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A. SCOND SCOND is REAL If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S. 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. WORK WORK is REAL array, dimension (3*N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 References: Livne, O.E. and Golub, G.H., 'Scaling by Binormalization', Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004. DOI 10.1023/B:NUMA.0000016606.32820.69 Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf Definition at line 136 of file ssyequb.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.1Sun May 26 2013 ssyequb.f(3)