.TH "heequb" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME heequb \- {he,sy}equb: equilibration, power of 2 .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcheequb\fP (uplo, n, a, lda, s, scond, amax, work, info)" .br .RI "\fBCHEEQUB\fP " .ti -1c .RI "subroutine \fBcsyequb\fP (uplo, n, a, lda, s, scond, amax, work, info)" .br .RI "\fBCSYEQUB\fP " .ti -1c .RI "subroutine \fBdsyequb\fP (uplo, n, a, lda, s, scond, amax, work, info)" .br .RI "\fBDSYEQUB\fP " .ti -1c .RI "subroutine \fBssyequb\fP (uplo, n, a, lda, s, scond, amax, work, info)" .br .RI "\fBSSYEQUB\fP " .ti -1c .RI "subroutine \fBzheequb\fP (uplo, n, a, lda, s, scond, amax, work, info)" .br .RI "\fBZHEEQUB\fP " .ti -1c .RI "subroutine \fBzsyequb\fP (uplo, n, a, lda, s, scond, amax, work, info)" .br .RI "\fBZSYEQUB\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cheequb (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, complex, dimension( * ) work, integer info)" .PP \fBCHEEQUB\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CHEEQUB computes row and column scalings intended to equilibrate a Hermitian matrix A (with respect to the Euclidean norm) and reduce its condition number\&. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension (LDA,N) The N-by-N Hermitian matrix whose scaling factors are to be computed\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,N)\&. .fi .PP .br \fIS\fP .PP .nf S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf 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\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is REAL Largest absolute value of any matrix element\&. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (2*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBReferences:\fP .RS 4 Livne, O\&.E\&. and Golub, G\&.H\&., 'Scaling by Binormalization', .br Numerical Algorithms, vol\&. 35, no\&. 1, pp\&. 97-120, January 2004\&. .br DOI 10\&.1023/B:NUMA\&.0000016606\&.32820\&.69 .br Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 .RE .PP .SS "subroutine csyequb (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, complex, dimension( * ) work, integer info)" .PP \fBCSYEQUB\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CSYEQUB computes row and column scalings intended to equilibrate a symmetric matrix A (with respect to the Euclidean norm) and reduce its condition number\&. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension (LDA,N) The N-by-N symmetric matrix whose scaling factors are to be computed\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,N)\&. .fi .PP .br \fIS\fP .PP .nf S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf 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\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is REAL Largest absolute value of any matrix element\&. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (2*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBReferences:\fP .RS 4 Livne, O\&.E\&. and Golub, G\&.H\&., 'Scaling by Binormalization', .br Numerical Algorithms, vol\&. 35, no\&. 1, pp\&. 97-120, January 2004\&. .br DOI 10\&.1023/B:NUMA\&.0000016606\&.32820\&.69 .br Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 .RE .PP .SS "subroutine dsyequb (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, double precision, dimension( * ) work, integer info)" .PP \fBDSYEQUB\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DSYEQUB computes row and column scalings intended to equilibrate a symmetric matrix A (with respect to the Euclidean norm) and reduce its condition number\&. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension (LDA,N) The N-by-N symmetric matrix whose scaling factors are to be computed\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,N)\&. .fi .PP .br \fIS\fP .PP .nf S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf SCOND is DOUBLE PRECISION 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\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is DOUBLE PRECISION Largest absolute value of any matrix element\&. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (2*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBReferences:\fP .RS 4 Livne, O\&.E\&. and Golub, G\&.H\&., 'Scaling by Binormalization', .br Numerical Algorithms, vol\&. 35, no\&. 1, pp\&. 97-120, January 2004\&. .br DOI 10\&.1023/B:NUMA\&.0000016606\&.32820\&.69 .br Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 .RE .PP .SS "subroutine ssyequb (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, real, dimension( * ) work, integer info)" .PP \fBSSYEQUB\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSYEQUB computes row and column scalings intended to equilibrate a symmetric matrix A (with respect to the Euclidean norm) and reduce its condition number\&. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, dimension (LDA,N) The N-by-N symmetric matrix whose scaling factors are to be computed\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,N)\&. .fi .PP .br \fIS\fP .PP .nf S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf 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\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is REAL Largest absolute value of any matrix element\&. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (2*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBReferences:\fP .RS 4 Livne, O\&.E\&. and Golub, G\&.H\&., 'Scaling by Binormalization', .br Numerical Algorithms, vol\&. 35, no\&. 1, pp\&. 97-120, January 2004\&. .br DOI 10\&.1023/B:NUMA\&.0000016606\&.32820\&.69 .br Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 .RE .PP .SS "subroutine zheequb (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, complex*16, dimension( * ) work, integer info)" .PP \fBZHEEQUB\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZHEEQUB computes row and column scalings intended to equilibrate a Hermitian matrix A (with respect to the Euclidean norm) and reduce its condition number\&. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension (LDA,N) The N-by-N Hermitian matrix whose scaling factors are to be computed\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,N)\&. .fi .PP .br \fIS\fP .PP .nf S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf SCOND is DOUBLE PRECISION 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\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is DOUBLE PRECISION Largest absolute value of any matrix element\&. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (2*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBReferences:\fP .RS 4 Livne, O\&.E\&. and Golub, G\&.H\&., 'Scaling by Binormalization', .br Numerical Algorithms, vol\&. 35, no\&. 1, pp\&. 97-120, January 2004\&. .br DOI 10\&.1023/B:NUMA\&.0000016606\&.32820\&.69 .br Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 .RE .PP .SS "subroutine zsyequb (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, complex*16, dimension( * ) work, integer info)" .PP \fBZSYEQUB\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZSYEQUB computes row and column scalings intended to equilibrate a symmetric matrix A (with respect to the Euclidean norm) and reduce its condition number\&. The scale factors S are computed by the BIN algorithm (see references) so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of the smallest possible condition number over all possible diagonal scalings\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension (LDA,N) The N-by-N symmetric matrix whose scaling factors are to be computed\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,N)\&. .fi .PP .br \fIS\fP .PP .nf S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf SCOND is DOUBLE PRECISION 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\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is DOUBLE PRECISION Largest absolute value of any matrix element\&. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (2*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBReferences:\fP .RS 4 Livne, O\&.E\&. and Golub, G\&.H\&., 'Scaling by Binormalization', .br Numerical Algorithms, vol\&. 35, no\&. 1, pp\&. 97-120, January 2004\&. .br DOI 10\&.1023/B:NUMA\&.0000016606\&.32820\&.69 .br Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.