MB01PD

Matrix scaling (higher level routine)

[Specification] [Arguments] [Method] [References] [Comments] [Example]

Purpose

```  To scale a matrix or undo scaling.  Scaling is performed, if
necessary, so that the matrix norm will be in a safe range of
representable numbers.

```
Specification
```      SUBROUTINE MB01PD( SCUN, TYPE, M, N, KL, KU, ANRM, NBL, NROWS, A,
\$                   LDA, INFO )
C     .. Scalar Arguments ..
CHARACTER          SCUN, TYPE
INTEGER            INFO, KL, KU, LDA, M, MN, N, NBL
DOUBLE PRECISION   ANRM
C     .. Array Arguments ..
INTEGER            NROWS ( * )
DOUBLE PRECISION   A( LDA, * )

```
Arguments

Mode Parameters

```  SCUN    CHARACTER*1
SCUN indicates the operation to be performed.
= 'S':  scale the matrix.
= 'U':  undo scaling of the matrix.

TYPE    CHARACTER*1
TYPE indicates the storage type of the input matrix.
= 'G':  A is a full matrix.
= 'L':  A is a (block) lower triangular matrix.
= 'U':  A is an (block) upper triangular matrix.
= 'H':  A is an (block) upper Hessenberg matrix.
= 'B':  A is a symmetric band matrix with lower bandwidth
KL and upper bandwidth KU and with the only the
lower half stored.
= 'Q':  A is a symmetric band matrix with lower bandwidth
KL and upper bandwidth KU and with the only the
upper half stored.
= 'Z':  A is a band matrix with lower bandwidth KL and
upper bandwidth KU.

```
Input/Output Parameters
```  M       (input) INTEGER
The number of rows of the matrix A. M >= 0.

N       (input) INTEGER
The number of columns of the matrix A. N >= 0.

KL      (input) INTEGER
The lower bandwidth of A.  Referenced only if TYPE = 'B',
'Q' or 'Z'.

KU      (input) INTEGER
The upper bandwidth of A.  Referenced only if TYPE = 'B',
'Q' or 'Z'.

ANRM    (input) DOUBLE PRECISION
The norm of the initial matrix A.  ANRM >= 0.
When  ANRM = 0  then an immediate return is effected.
ANRM should be preserved between the call of the routine
with SCUN = 'S' and the corresponding one with SCUN = 'U'.

NBL     (input) INTEGER
The number of diagonal blocks of the matrix A, if it has a
block structure.  To specify that matrix A has no block
structure, set NBL = 0.  NBL >= 0.

NROWS   (input) INTEGER array, dimension max(1,NBL)
NROWS(i) contains the number of rows and columns of the
i-th diagonal block of matrix A.  The sum of the values
NROWS(i),  for  i = 1: NBL,  should be equal to min(M,N).
The elements of the array  NROWS  are not referenced if
NBL = 0.

A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading M by N part of this array must
contain the matrix to be scaled/unscaled.
On exit, the leading M by N part of A will contain
the modified matrix.
The storage mode of A is specified by TYPE.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA  >= max(1,M).

```
Error Indicator
```  INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value.

```
Method
```  Denote by ANRM the norm of the matrix, and by SMLNUM and BIGNUM,
two positive numbers near the smallest and largest safely
representable numbers, respectively.  The matrix is scaled, if
needed, such that the norm of the result is in the range
[SMLNUM, BIGNUM].  The scaling factor is represented as a ratio
of two numbers, one of them being ANRM, and the other one either
SMLNUM or BIGNUM, depending on ANRM being less than SMLNUM or
larger than BIGNUM, respectively.  For undoing the scaling, the
norm is again compared with SMLNUM or BIGNUM, and the reciprocal
of the previous scaling factor is used.

```
```  None
```
Example

Program Text

```  None
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Program Data
```  None
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Program Results
```  None
```