# poequb - Man Page

poequb: equilibration, power of 2

## Synopsis

### Functions

subroutine **cpoequb** (n, a, lda, s, scond, amax, info)**CPOEQUB**

subroutine **dpoequb** (n, a, lda, s, scond, amax, info)**DPOEQUB**

subroutine **spoequb** (n, a, lda, s, scond, amax, info)**SPOEQUB**

subroutine **zpoequb** (n, a, lda, s, scond, amax, info)**ZPOEQUB**

## Detailed Description

## Function Documentation

### subroutine cpoequb (integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info)

**CPOEQUB**

**Purpose:**

CPOEQUB computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. This routine differs from CPOEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled diagonal entries are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).

**Parameters***N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is COMPLEX array, dimension (LDA,N) The N-by-N Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*S*S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A.

*SCOND*SCOND is REAL If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.

*AMAX*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.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **118** of file **cpoequb.f**.

### subroutine dpoequb (integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)

**DPOEQUB**

**Purpose:**

DPOEQUB computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. This routine differs from DPOEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled diagonal entries are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).

**Parameters***N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is DOUBLE PRECISION array, dimension (LDA,N) The N-by-N symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*S*S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A.

*SCOND*SCOND is DOUBLE PRECISION If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.

*AMAX*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.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **117** of file **dpoequb.f**.

### subroutine spoequb (integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info)

**SPOEQUB**

**Purpose:**

SPOEQUB computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. This routine differs from SPOEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled diagonal entries are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).

**Parameters***N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is REAL array, dimension (LDA,N) The N-by-N symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*S*S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A.

*SCOND*SCOND is REAL If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.

*AMAX*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.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **117** of file **spoequb.f**.

### subroutine zpoequb (integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision scond, double precision amax, integer info)

**ZPOEQUB**

**Purpose:**

ZPOEQUB computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. This routine differs from ZPOEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled diagonal entries are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).

**Parameters***N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is COMPLEX*16 array, dimension (LDA,N) The N-by-N Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*S*S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A.

*SCOND*SCOND is DOUBLE PRECISION If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.

*AMAX*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.

*INFO***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **118** of file **zpoequb.f**.

## Author

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