.TH "laqhb" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME laqhb \- laqhb: row/col scale matrix .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBclaqhb\fP (uplo, n, kd, ab, ldab, s, scond, amax, equed)" .br .RI "\fBCLAQHB\fP scales a Hermitian band matrix, using scaling factors computed by cpbequ\&. " .ti -1c .RI "subroutine \fBclaqsb\fP (uplo, n, kd, ab, ldab, s, scond, amax, equed)" .br .RI "\fBCLAQSB\fP scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ\&. " .ti -1c .RI "subroutine \fBdlaqsb\fP (uplo, n, kd, ab, ldab, s, scond, amax, equed)" .br .RI "\fBDLAQSB\fP scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ\&. " .ti -1c .RI "subroutine \fBslaqsb\fP (uplo, n, kd, ab, ldab, s, scond, amax, equed)" .br .RI "\fBSLAQSB\fP scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ\&. " .ti -1c .RI "subroutine \fBzlaqhb\fP (uplo, n, kd, ab, ldab, s, scond, amax, equed)" .br .RI "\fBZLAQHB\fP scales a Hermitian band matrix, using scaling factors computed by cpbequ\&. " .ti -1c .RI "subroutine \fBzlaqsb\fP (uplo, n, kd, ab, ldab, s, scond, amax, equed)" .br .RI "\fBZLAQSB\fP scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine claqhb (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real amax, character equed)" .PP \fBCLAQHB\fP scales a Hermitian band matrix, using scaling factors computed by cpbequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLAQHB equilibrates an Hermitian band 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 \fIKD\fP .PP .nf KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'\&. KD >= 0\&. .fi .PP .br \fIAB\fP .PP .nf AB is COMPLEX array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array\&. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)\&. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, in the same storage format as A\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KD+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 claqsb (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real amax, character equed)" .PP \fBCLAQSB\fP scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLAQSB equilibrates a symmetric band 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 \fIKD\fP .PP .nf KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'\&. KD >= 0\&. .fi .PP .br \fIAB\fP .PP .nf AB is COMPLEX array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array\&. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)\&. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, in the same storage format as A\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KD+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 dlaqsb (character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)" .PP \fBDLAQSB\fP scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLAQSB equilibrates a symmetric band 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 \fIKD\fP .PP .nf KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'\&. KD >= 0\&. .fi .PP .br \fIAB\fP .PP .nf AB is DOUBLE PRECISION array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array\&. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)\&. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, in the same storage format as A\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KD+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 slaqsb (character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) s, real scond, real amax, character equed)" .PP \fBSLAQSB\fP scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLAQSB equilibrates a symmetric band 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 \fIKD\fP .PP .nf KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'\&. KD >= 0\&. .fi .PP .br \fIAB\fP .PP .nf AB is REAL array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array\&. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)\&. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, in the same storage format as A\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KD+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 zlaqhb (character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)" .PP \fBZLAQHB\fP scales a Hermitian band matrix, using scaling factors computed by cpbequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLAQHB equilibrates a Hermitian band 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 \fIKD\fP .PP .nf KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'\&. KD >= 0\&. .fi .PP .br \fIAB\fP .PP .nf AB is COMPLEX*16 array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array\&. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)\&. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, in the same storage format as A\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KD+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 zlaqsb (character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) s, double precision scond, double precision amax, character equed)" .PP \fBZLAQSB\fP scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLAQSB equilibrates a symmetric band 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 \fIKD\fP .PP .nf KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'\&. KD >= 0\&. .fi .PP .br \fIAB\fP .PP .nf AB is COMPLEX*16 array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array\&. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)\&. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, in the same storage format as A\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KD+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\&.