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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine zlatm4 | ( | integer | itype, |
| integer | n, | ||
| integer | nz1, | ||
| integer | nz2, | ||
| logical | rsign, | ||
| double precision | amagn, | ||
| double precision | rcond, | ||
| double precision | triang, | ||
| integer | idist, | ||
| integer, dimension( 4 ) | iseed, | ||
| complex*16, dimension( lda, * ) | a, | ||
| integer | lda | ||
| ) |
ZLATM4
ZLATM4 generates basic square matrices, which may later be multiplied by others in order to produce test matrices. It is intended mainly to be used to test the generalized eigenvalue routines. It first generates the diagonal and (possibly) subdiagonal, according to the value of ITYPE, NZ1, NZ2, RSIGN, AMAGN, and RCOND. It then fills in the upper triangle with random numbers, if TRIANG is non-zero.
| [in] | ITYPE | ITYPE is INTEGER
The "type" of matrix on the diagonal and sub-diagonal.
If ITYPE < 0, then type abs(ITYPE) is generated and then
swapped end for end (A(I,J) := A'(N-J,N-I).) See also
the description of AMAGN and RSIGN.
Special types:
= 0: the zero matrix.
= 1: the identity.
= 2: a transposed Jordan block.
= 3: If N is odd, then a k+1 x k+1 transposed Jordan block
followed by a k x k identity block, where k=(N-1)/2.
If N is even, then k=(N-2)/2, and a zero diagonal entry
is tacked onto the end.
Diagonal types. The diagonal consists of NZ1 zeros, then
k=N-NZ1-NZ2 nonzeros. The subdiagonal is zero. ITYPE
specifies the nonzero diagonal entries as follows:
= 4: 1, ..., k
= 5: 1, RCOND, ..., RCOND
= 6: 1, ..., 1, RCOND
= 7: 1, a, a^2, ..., a^(k-1)=RCOND
= 8: 1, 1-d, 1-2*d, ..., 1-(k-1)*d=RCOND
= 9: random numbers chosen from (RCOND,1)
= 10: random numbers with distribution IDIST (see ZLARND.) |
| [in] | N | N is INTEGER
The order of the matrix. |
| [in] | NZ1 | NZ1 is INTEGER
If abs(ITYPE) > 3, then the first NZ1 diagonal entries will
be zero. |
| [in] | NZ2 | NZ2 is INTEGER
If abs(ITYPE) > 3, then the last NZ2 diagonal entries will
be zero. |
| [in] | RSIGN | RSIGN is LOGICAL
= .TRUE.: The diagonal and subdiagonal entries will be
multiplied by random numbers of magnitude 1.
= .FALSE.: The diagonal and subdiagonal entries will be
left as they are (usually non-negative real.) |
| [in] | AMAGN | AMAGN is DOUBLE PRECISION
The diagonal and subdiagonal entries will be multiplied by
AMAGN. |
| [in] | RCOND | RCOND is DOUBLE PRECISION
If abs(ITYPE) > 4, then the smallest diagonal entry will be
RCOND. RCOND must be between 0 and 1. |
| [in] | TRIANG | TRIANG is DOUBLE PRECISION
The entries above the diagonal will be random numbers with
magnitude bounded by TRIANG (i.e., random numbers multiplied
by TRIANG.) |
| [in] | IDIST | IDIST is INTEGER
On entry, DIST specifies the type of distribution to be used
to generate a random matrix .
= 1: real and imaginary parts each UNIFORM( 0, 1 )
= 2: real and imaginary parts each UNIFORM( -1, 1 )
= 3: real and imaginary parts each NORMAL( 0, 1 )
= 4: complex number uniform in DISK( 0, 1 ) |
| [in,out] | ISEED | ISEED is INTEGER array, dimension (4)
On entry ISEED specifies the seed of the random number
generator. The values of ISEED are changed on exit, and can
be used in the next call to ZLATM4 to continue the same
random number sequence.
Note: ISEED(4) should be odd, for the random number generator
used at present. |
| [out] | A | A is COMPLEX*16 array, dimension (LDA, N)
Array to be computed. |
| [in] | LDA | LDA is INTEGER
Leading dimension of A. Must be at least 1 and at least N. |
Definition at line 169 of file zlatm4.f.
1.9.7