.TH "laqhe" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME laqhe \- laqhe: row/col scale matrix .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBclaqhe\fP (uplo, n, a, lda, s, scond, amax, equed)" .br .RI "\fBCLAQHE\fP scales a Hermitian matrix\&. " .ti -1c .RI "subroutine \fBclaqsy\fP (uplo, n, a, lda, s, scond, amax, equed)" .br .RI "\fBCLAQSY\fP scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ\&. " .ti -1c .RI "subroutine \fBdlaqsy\fP (uplo, n, a, lda, s, scond, amax, equed)" .br .RI "\fBDLAQSY\fP scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ\&. " .ti -1c .RI "subroutine \fBslaqsy\fP (uplo, n, a, lda, s, scond, amax, equed)" .br .RI "\fBSLAQSY\fP scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ\&. " .ti -1c .RI "subroutine \fBzlaqhe\fP (uplo, n, a, lda, s, scond, amax, equed)" .br .RI "\fBZLAQHE\fP scales a Hermitian matrix\&. " .ti -1c .RI "subroutine \fBzlaqsy\fP (uplo, n, a, lda, s, scond, amax, equed)" .br .RI "\fBZLAQSY\fP scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine claqhe (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, character equed)" .PP \fBCLAQHE\fP scales a Hermitian matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLAQHE equilibrates a Hermitian matrix A using the scaling factors in the vector S\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored\&. = 'U': Upper triangular = 'L': Lower triangular .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) On entry, the Hermitian matrix A\&. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced\&. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced\&. On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S)\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(N,1)\&. .fi .PP .br \fIS\fP .PP .nf S is REAL array, dimension (N) The scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf SCOND is REAL Ratio of the smallest S(i) to the largest S(i)\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is REAL Absolute value of largest matrix entry\&. .fi .PP .br \fIEQUED\fP .PP .nf EQUED is CHARACTER*1 Specifies whether or not equilibration was done\&. = 'N': No equilibration\&. = 'Y': Equilibration was done, i\&.e\&., A has been replaced by diag(S) * A * diag(S)\&. .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors\&. If SCOND < THRESH, scaling is done\&. LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element\&. If AMAX > LARGE or AMAX < SMALL, scaling is done\&. .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 claqsy (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, character equed)" .PP \fBCLAQSY\fP scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLAQSY equilibrates a symmetric matrix A using the scaling factors in the vector S\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored\&. = 'U': Upper triangular = 'L': Lower triangular .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) On entry, the symmetric matrix A\&. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced\&. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced\&. On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S)\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(N,1)\&. .fi .PP .br \fIS\fP .PP .nf S is REAL array, dimension (N) The scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf SCOND is REAL Ratio of the smallest S(i) to the largest S(i)\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is REAL Absolute value of largest matrix entry\&. .fi .PP .br \fIEQUED\fP .PP .nf EQUED is CHARACTER*1 Specifies whether or not equilibration was done\&. = 'N': No equilibration\&. = 'Y': Equilibration was done, i\&.e\&., A has been replaced by diag(S) * A * diag(S)\&. .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors\&. If SCOND < THRESH, scaling is done\&. LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element\&. If AMAX > LARGE or AMAX < SMALL, scaling is done\&. .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 dlaqsy (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)" .PP \fBDLAQSY\fP scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLAQSY equilibrates a symmetric matrix A using the scaling factors in the vector S\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored\&. = 'U': Upper triangular = 'L': Lower triangular .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) On entry, the symmetric matrix A\&. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced\&. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced\&. On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S)\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(N,1)\&. .fi .PP .br \fIS\fP .PP .nf S is DOUBLE PRECISION array, dimension (N) The scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i)\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is DOUBLE PRECISION Absolute value of largest matrix entry\&. .fi .PP .br \fIEQUED\fP .PP .nf EQUED is CHARACTER*1 Specifies whether or not equilibration was done\&. = 'N': No equilibration\&. = 'Y': Equilibration was done, i\&.e\&., A has been replaced by diag(S) * A * diag(S)\&. .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors\&. If SCOND < THRESH, scaling is done\&. LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element\&. If AMAX > LARGE or AMAX < SMALL, scaling is done\&. .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 slaqsy (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, character equed)" .PP \fBSLAQSY\fP scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLAQSY equilibrates a symmetric matrix A using the scaling factors in the vector S\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored\&. = 'U': Upper triangular = 'L': Lower triangular .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) On entry, the symmetric matrix A\&. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced\&. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced\&. On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S)\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(N,1)\&. .fi .PP .br \fIS\fP .PP .nf S is REAL array, dimension (N) The scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf SCOND is REAL Ratio of the smallest S(i) to the largest S(i)\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is REAL Absolute value of largest matrix entry\&. .fi .PP .br \fIEQUED\fP .PP .nf EQUED is CHARACTER*1 Specifies whether or not equilibration was done\&. = 'N': No equilibration\&. = 'Y': Equilibration was done, i\&.e\&., A has been replaced by diag(S) * A * diag(S)\&. .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors\&. If SCOND < THRESH, scaling is done\&. LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element\&. If AMAX > LARGE or AMAX < SMALL, scaling is done\&. .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 zlaqhe (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)" .PP \fBZLAQHE\fP scales a Hermitian matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLAQHE equilibrates a Hermitian matrix A using the scaling factors in the vector S\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored\&. = 'U': Upper triangular = 'L': Lower triangular .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) On entry, the Hermitian matrix A\&. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced\&. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced\&. On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S)\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(N,1)\&. .fi .PP .br \fIS\fP .PP .nf S is DOUBLE PRECISION array, dimension (N) The scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i)\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is DOUBLE PRECISION Absolute value of largest matrix entry\&. .fi .PP .br \fIEQUED\fP .PP .nf EQUED is CHARACTER*1 Specifies whether or not equilibration was done\&. = 'N': No equilibration\&. = 'Y': Equilibration was done, i\&.e\&., A has been replaced by diag(S) * A * diag(S)\&. .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors\&. If SCOND < THRESH, scaling is done\&. LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element\&. If AMAX > LARGE or AMAX < SMALL, scaling is done\&. .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 zlaqsy (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)" .PP \fBZLAQSY\fP scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLAQSY equilibrates a symmetric matrix A using the scaling factors in the vector S\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored\&. = 'U': Upper triangular = 'L': Lower triangular .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) On entry, the symmetric matrix A\&. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced\&. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced\&. On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A * diag(S)\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(N,1)\&. .fi .PP .br \fIS\fP .PP .nf S is DOUBLE PRECISION array, dimension (N) The scale factors for A\&. .fi .PP .br \fISCOND\fP .PP .nf SCOND is DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i)\&. .fi .PP .br \fIAMAX\fP .PP .nf AMAX is DOUBLE PRECISION Absolute value of largest matrix entry\&. .fi .PP .br \fIEQUED\fP .PP .nf EQUED is CHARACTER*1 Specifies whether or not equilibration was done\&. = 'N': No equilibration\&. = 'Y': Equilibration was done, i\&.e\&., A has been replaced by diag(S) * A * diag(S)\&. .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors\&. If SCOND < THRESH, scaling is done\&. LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element\&. If AMAX > LARGE or AMAX < SMALL, scaling is done\&. .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\&.