.TH "geequ" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME geequ \- geequ: equilibration .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcgeequ\fP (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)" .br .RI "\fBCGEEQU\fP " .ti -1c .RI "subroutine \fBdgeequ\fP (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)" .br .RI "\fBDGEEQU\fP " .ti -1c .RI "subroutine \fBsgeequ\fP (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)" .br .RI "\fBSGEEQU\fP " .ti -1c .RI "subroutine \fBzgeequ\fP (m, n, a, lda, r, c, rowcnd, colcnd, amax, info)" .br .RI "\fBZGEEQU\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cgeequ (integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)" .PP \fBCGEEQU\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CGEEQU 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 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension (LDA,N) The M-by-N matrix whose equilibration 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,M)\&. .fi .PP .br \fIR\fP .PP .nf R is REAL array, dimension (M) If INFO = 0 or INFO > M, R contains the row scale factors for A\&. .fi .PP .br \fIC\fP .PP .nf C is REAL array, dimension (N) If INFO = 0, C contains the column scale factors for A\&. .fi .PP .br \fIROWCND\fP .PP .nf 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\&. .fi .PP .br \fICOLCND\fP .PP .nf 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\&. .fi .PP .br \fIAMAX\fP .PP .nf 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\&. .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, and i is <= M: the i-th row of A is exactly zero > M: the (i-M)-th column of A is exactly zero .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 .SS "subroutine dgeequ (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)" .PP \fBDGEEQU\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DGEEQU 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 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension (LDA,N) The M-by-N matrix whose equilibration 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,M)\&. .fi .PP .br \fIR\fP .PP .nf R is DOUBLE PRECISION array, dimension (M) If INFO = 0 or INFO > M, R contains the row scale factors for A\&. .fi .PP .br \fIC\fP .PP .nf C is DOUBLE PRECISION array, dimension (N) If INFO = 0, C contains the column scale factors for A\&. .fi .PP .br \fIROWCND\fP .PP .nf ROWCND is DOUBLE PRECISION 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\&. .fi .PP .br \fICOLCND\fP .PP .nf COLCND is DOUBLE PRECISION 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\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is DOUBLE PRECISION Absolute value of largest matrix element\&. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled\&. .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, and i is <= M: the i-th row of A is exactly zero > M: the (i-M)-th column of A is exactly zero .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 .SS "subroutine sgeequ (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) r, real, dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)" .PP \fBSGEEQU\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SGEEQU 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 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, dimension (LDA,N) The M-by-N matrix whose equilibration 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,M)\&. .fi .PP .br \fIR\fP .PP .nf R is REAL array, dimension (M) If INFO = 0 or INFO > M, R contains the row scale factors for A\&. .fi .PP .br \fIC\fP .PP .nf C is REAL array, dimension (N) If INFO = 0, C contains the column scale factors for A\&. .fi .PP .br \fIROWCND\fP .PP .nf 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\&. .fi .PP .br \fICOLCND\fP .PP .nf 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\&. .fi .PP .br \fIAMAX\fP .PP .nf 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\&. .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, and i is <= M: the i-th row of A is exactly zero > M: the (i-M)-th column of A is exactly zero .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 .SS "subroutine zgeequ (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, integer info)" .PP \fBZGEEQU\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZGEEQU 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 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M >= 0\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension (LDA,N) The M-by-N matrix whose equilibration 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,M)\&. .fi .PP .br \fIR\fP .PP .nf R is DOUBLE PRECISION array, dimension (M) If INFO = 0 or INFO > M, R contains the row scale factors for A\&. .fi .PP .br \fIC\fP .PP .nf C is DOUBLE PRECISION array, dimension (N) If INFO = 0, C contains the column scale factors for A\&. .fi .PP .br \fIROWCND\fP .PP .nf ROWCND is DOUBLE PRECISION 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\&. .fi .PP .br \fICOLCND\fP .PP .nf COLCND is DOUBLE PRECISION 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\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is DOUBLE PRECISION Absolute value of largest matrix element\&. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled\&. .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, and i is <= M: the i-th row of A is exactly zero > M: the (i-M)-th column of A is exactly zero .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 .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.