--- name: "laqhp" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/laqhp" --- # laqhp(3) laqhp: row/col scale matrix ## NAME laqhp - laqhp: row/col scale matrix ## SYNOPSIS ### Functions subroutine **claqhp** (uplo, n, ap, s, scond, amax, equed)\ **CLAQHP** scales a Hermitian matrix stored in packed form. subroutine **claqsp** (uplo, n, ap, s, scond, amax, equed)\ **CLAQSP** scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. subroutine **dlaqsp** (uplo, n, ap, s, scond, amax, equed)\ **DLAQSP** scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. subroutine **slaqsp** (uplo, n, ap, s, scond, amax, equed)\ **SLAQSP** scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. subroutine **zlaqhp** (uplo, n, ap, s, scond, amax, equed)\ **ZLAQHP** scales a Hermitian matrix stored in packed form. subroutine **zlaqsp** (uplo, n, ap, s, scond, amax, equed)\ **ZLAQSP** scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. ## Detailed Description ## Function Documentation ### subroutine claqhp (character uplo, integer n, complex, dimension( \* ) ap, real, dimension( \* ) s, real scond, real amax, character equed) **CLAQHP** scales a Hermitian matrix stored in packed form. **Purpose:** ``` !> !> CLAQHP equilibrates a Hermitian matrix A using the scaling factors !> in the vector S. !> ``` **Parameters** *UPLO* ``` !> 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 !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *AP* ``` !> 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. !> ``` *S* ``` !> S is REAL array, dimension (N) !> The scale factors for A. !> ``` *SCOND* ``` !> SCOND is REAL !> Ratio of the smallest S(i) to the largest S(i). !> ``` *AMAX* ``` !> AMAX is REAL !> Absolute value of largest matrix entry. !> ``` *EQUED* ``` !> 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). !> ``` **Internal Parameters:** ``` !> 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. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **125** of file **claqhp.f**. ### subroutine claqsp (character uplo, integer n, complex, dimension( \* ) ap, real, dimension( \* ) s, real scond, real amax, character equed) **CLAQSP** scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. **Purpose:** ``` !> !> CLAQSP equilibrates a symmetric matrix A using the scaling factors !> in the vector S. !> ``` **Parameters** *UPLO* ``` !> 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 !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *AP* ``` !> 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. !> ``` *S* ``` !> S is REAL array, dimension (N) !> The scale factors for A. !> ``` *SCOND* ``` !> SCOND is REAL !> Ratio of the smallest S(i) to the largest S(i). !> ``` *AMAX* ``` !> AMAX is REAL !> Absolute value of largest matrix entry. !> ``` *EQUED* ``` !> 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). !> ``` **Internal Parameters:** ``` !> 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. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **125** of file **claqsp.f**. ### subroutine dlaqsp (character uplo, integer n, double precision, dimension( \* ) ap, double precision, dimension( \* ) s, double precision scond, double precision amax, character equed) **DLAQSP** scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. **Purpose:** ``` !> !> DLAQSP equilibrates a symmetric matrix A using the scaling factors !> in the vector S. !> ``` **Parameters** *UPLO* ``` !> 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 !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *AP* ``` !> 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. !> ``` *S* ``` !> S is DOUBLE PRECISION array, dimension (N) !> The scale factors for A. !> ``` *SCOND* ``` !> SCOND is DOUBLE PRECISION !> Ratio of the smallest S(i) to the largest S(i). !> ``` *AMAX* ``` !> AMAX is DOUBLE PRECISION !> Absolute value of largest matrix entry. !> ``` *EQUED* ``` !> 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). !> ``` **Internal Parameters:** ``` !> 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. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **124** of file **dlaqsp.f**. ### subroutine slaqsp (character uplo, integer n, real, dimension( \* ) ap, real, dimension( \* ) s, real scond, real amax, character equed) **SLAQSP** scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. **Purpose:** ``` !> !> SLAQSP equilibrates a symmetric matrix A using the scaling factors !> in the vector S. !> ``` **Parameters** *UPLO* ``` !> 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 !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *AP* ``` !> 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. !> ``` *S* ``` !> S is REAL array, dimension (N) !> The scale factors for A. !> ``` *SCOND* ``` !> SCOND is REAL !> Ratio of the smallest S(i) to the largest S(i). !> ``` *AMAX* ``` !> AMAX is REAL !> Absolute value of largest matrix entry. !> ``` *EQUED* ``` !> 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). !> ``` **Internal Parameters:** ``` !> 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. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **124** of file **slaqsp.f**. ### subroutine zlaqhp (character uplo, integer n, complex\*16, dimension( \* ) ap, double precision, dimension( \* ) s, double precision scond, double precision amax, character equed) **ZLAQHP** scales a Hermitian matrix stored in packed form. **Purpose:** ``` !> !> ZLAQHP equilibrates a Hermitian matrix A using the scaling factors !> in the vector S. !> ``` **Parameters** *UPLO* ``` !> 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 !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *AP* ``` !> 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. !> ``` *S* ``` !> S is DOUBLE PRECISION array, dimension (N) !> The scale factors for A. !> ``` *SCOND* ``` !> SCOND is DOUBLE PRECISION !> Ratio of the smallest S(i) to the largest S(i). !> ``` *AMAX* ``` !> AMAX is DOUBLE PRECISION !> Absolute value of largest matrix entry. !> ``` *EQUED* ``` !> 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). !> ``` **Internal Parameters:** ``` !> 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. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **125** of file **zlaqhp.f**. ### subroutine zlaqsp (character uplo, integer n, complex\*16, dimension( \* ) ap, double precision, dimension( \* ) s, double precision scond, double precision amax, character equed) **ZLAQSP** scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. **Purpose:** ``` !> !> ZLAQSP equilibrates a symmetric matrix A using the scaling factors !> in the vector S. !> ``` **Parameters** *UPLO* ``` !> 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 !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *AP* ``` !> 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. !> ``` *S* ``` !> S is DOUBLE PRECISION array, dimension (N) !> The scale factors for A. !> ``` *SCOND* ``` !> SCOND is DOUBLE PRECISION !> Ratio of the smallest S(i) to the largest S(i). !> ``` *AMAX* ``` !> AMAX is DOUBLE PRECISION !> Absolute value of largest matrix entry. !> ``` *EQUED* ``` !> 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). !> ``` **Internal Parameters:** ``` !> 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. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **125** of file **zlaqsp.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.