.TH "laqhp" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME laqhp \- laqhp: row/col scale matrix .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBclaqhp\fP (uplo, n, ap, s, scond, amax, equed)" .br .RI "\fBCLAQHP\fP scales a Hermitian matrix stored in packed form\&. " .ti -1c .RI "subroutine \fBclaqsp\fP (uplo, n, ap, s, scond, amax, equed)" .br .RI "\fBCLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. " .ti -1c .RI "subroutine \fBdlaqsp\fP (uplo, n, ap, s, scond, amax, equed)" .br .RI "\fBDLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. " .ti -1c .RI "subroutine \fBslaqsp\fP (uplo, n, ap, s, scond, amax, equed)" .br .RI "\fBSLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. " .ti -1c .RI "subroutine \fBzlaqhp\fP (uplo, n, ap, s, scond, amax, equed)" .br .RI "\fBZLAQHP\fP scales a Hermitian matrix stored in packed form\&. " .ti -1c .RI "subroutine \fBzlaqsp\fP (uplo, n, ap, s, scond, amax, equed)" .br .RI "\fBZLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine claqhp (character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed)" .PP \fBCLAQHP\fP scales a Hermitian matrix stored in packed form\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLAQHP 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 \fIAP\fP .PP .nf AP is COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array\&. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&. On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A\&. .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 claqsp (character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed)" .PP \fBCLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLAQSP 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 \fIAP\fP .PP .nf AP is COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array\&. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&. On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A\&. .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 dlaqsp (character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)" .PP \fBDLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLAQSP 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 \fIAP\fP .PP .nf AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array\&. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&. On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A\&. .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 slaqsp (character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) s, real scond, real amax, character equed)" .PP \fBSLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLAQSP 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 \fIAP\fP .PP .nf AP is REAL array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array\&. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&. On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A\&. .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 zlaqhp (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)" .PP \fBZLAQHP\fP scales a Hermitian matrix stored in packed form\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLAQHP 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 \fIAP\fP .PP .nf AP is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array\&. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&. On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A\&. .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 zlaqsp (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)" .PP \fBZLAQSP\fP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLAQSP 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 \fIAP\fP .PP .nf AP is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array\&. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&. On exit, the equilibrated matrix: diag(S) * A * diag(S), in the same storage format as A\&. .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\&.